Mechanics of Mine Backfill

Transcription

1 By This thesis is presented for the Degree of Doctor of Philosophy School of Civil and Resource Engineering December 2007

2 DECLARATION FOR THESES CONTAINING PUBLISHED WORK AND/OR WORK PREPARED FOR PUBLICATION The examination of the thesis is an examination of the work of the student. The work must have been substantially conducted by the student during enrolment in the degree. Where the thesis includes work to which others have contributed, the thesis must include a statement that makes the student s contribution clear to the examiners. This may be in the form of a description of the precise contribution of the student to the work presented for examination and/or a statement of the percentage of the work that was done by the student. In addition, in the case of co-authored publications included in the thesis, each author must give their signed permission for the work to be included. If signatures from all the authors cannot be obtained, the statement detailing the student s contribution to the work must be signed by the coordinating supervisor. Please sign one of the statements below. 1. This thesis does not contain work that I have published, nor work under review for publication. (Note: A number of journal and conference papers have been published on various aspects of the work, as listed Page v at the start of the Thesis. However, these are not part of the thesis per se.) Signature: Thought the publications listed are not part of the thesis, the work included in them forms a central part of the thesis. The candidate, Mr Helinski, is first author on all of the publications, and can claim a contribution of > 70% to each of them. Signature: (Martin Fahey, coordinating supervisor) 2. This thesis contains only sole-authored work, some of which has been published and/or prepared for publication under sole authorship. The bibliographical details of the work and where it appears in the thesis are outlined below. Signature This thesis contains published work and/or work prepared for publication, some of which has been coauthored. The bibliographical details of the work and where it appears in the thesis are outlined below. The student must attach to this declaration a statement for each publication that clarifies the contribution of the student to the work. This may be in the form of a description of the precise contributions of the student to the published work and/or a statement of percent contribution by the student. This statement must be signed by all authors. If signatures from all the authors cannot be obtained, the statement detailing the student s contribution to the published work must be signed by the coordinating supervisor. Signatures... Signatures...

3 ABSTRACT Mine backfilling is the process of filling large underground mining voids ( stopes ) with a combination of tailings, water and small amounts of cement, to promote regional stability. Stopes are often in excess of 20 m 20 m in plan dimensions and m tall, and can be filled within a week. Barricades are constructed in all tunnels ( drives ) that access the stope to contain the backfill material. In recent years, a significant number of failures of mine backfill barricades have occurred, resulting in the inrush of slurry backfill into the mine workings. In addition, sampling has shown material strengths in situ to be far greater than equivalent mixes cured in the laboratory (indicating the potential for reducing the cement content). The purpose of this thesis is to apply soil mechanics principles to the mine backfill deposition process with the intent of providing some insight into these issues. In many cases, filling, consolidation and cement hydration all take place at a similar timescale, and therefore, to understand the cemented mine backfill deposition process it was necessary to appropriately couple these activities. Developing appropriate models for these mechanisms, and coupling them into a finite element code, forms the core of this thesis. Firstly, the fundamental processes involved in the cementing mine backfill deposition process are investigated and represented using theory founded on basic physical observations. Using this theory, one- and two-dimensional finite element models (called CeMinTaCo and Minefill-2D, respectively) are developed to fully couple each of the individual mechanisms. A centrifuge experiment was undertaken to investigate the interaction between consolidation and total stress distribution in a cementing soil. The results of this experiment were also used to verify the performance of Minefill 2D. Due to scale effects, the centrifuge experiment was unable to fully couple the interaction of the cement hydration and consolidation timescales. To achieve this, a full scale field experiment was undertaken. The simulated behaviour achieved using Minefill-2D (with independently derived material properties) provided a good representation of the consolidation behaviour. i

4 Finally, a sensitivity study carried out using Minefill-2D is presented. This study enables some useful suggestions to be provided for managing the risk of excessive barricade stress, and for preparing laboratory samples to more appropriately represent in situ curing conditions. ii

5 ACKNOWLEDGEMENTS Firstly I would like to acknowledge the support of my wonderful family throughout the period of my studies. My wife Libby, who after initially being somewhat apprehensive about my decision to return to university, has provided me with undivided support throughout this period. Jessica who was undesirably juggled during my early years of study always had a wonder smile to greet me with and Lucy, our recent addition, who I am equally proud of. To my parents, grandparents and sister who have provided me with the wonderful gift of education and support throughout my life, I am forever grateful of this. To my supervisor Professor Martin Fahey, a true professor in the way he can make the most complicated aspect of soil mechanics appear so clear and simple through the application of his fundamental knowledge. This is something I aspire to. My supervisor Professor Andy Fourie, whose guidance and friendship during my research was essential in developing this project. Andy, I feel very fortunate that you arrived in Australia and supported me when you did. Also, thanks to Dr Mostafa Ismail who assisted me in the laboratory component of this work and Professor Jack Barrett who helped shape this project during the early stages. Thanks to all of my university colleagues, in particular James Schneider and James Doherty and Shambu Sharma, I am extremely appreciative of your supervision and guidance throughout this thesis. Also my industry colleagues Cameron Tucker, Mat Revell and Tony Grice, I appreciate all of your support and encouragement with this work. Thanks to all of the academic and support staff in the Civil Engineering department in particular Binaya, Clair and Natalia (who sadly passed away during this thesis) for their ongoing patience with my chaotic style in the laboratory as well as Tuarn, John, Shane, Phil, Bart, Don and Neil for their assistance with centrifuge testing. Finally, this work would not have been possible without the wonderful post graduate scholarship foundation at. The late Robert John Gledden for establishing the Gledden trust that provided the majority of financial support throughout this work. Merriwa for their wonderful top-up scholarship that iii

6 provided both financial and equipment support. Mrs N. Shaw who established the F.S.Shaw scholarship in memory of her late husband, which provided much needed funding towards the latter stages of this research. And the UWA travel scholarship which allowed me to attend the Minefill 07 conference in Canada. iv

7 DECLARATION I hereby declare that, except where specific reference is made in the text to work of others, the contents of this thesis are original and have not been submitted to any other university. During the compilation of this thesis some of the work has been published in various journals and conference proceedings. I acknowledge the contribution of my co-authors in preparing these publications. Details of these publications are as follows: Journal publications Helinski, M. Fahey, M. and Fourie, A.B. (2007) Numerical modelling of cemented mine backfill deposition, ASCE Journal of Geotechnical and Geoenvironmental Engineering, Vol. 133, Issue 10, Helinski, M., Fourie, A.B. Fahey, M. and Ismail, M. (2007). The self desiccation process in cemented mine backfill. Canadian Geotechnical Journal. Vol. 44, No. 10, Helinski, M. Fahey, M. Fourie, A.B. (2007) An effective stress approach to modelling mine backfilling, CIM technical paper, Issue No. 5, August, Vol.2. Fourie, A.B. Helinski, M. Fahey, M. (2007) Using effective stress theory to characterise the behaviour of backfill. CIM technical paper, Issue No.5, August, Vol. 2 Conference publications Helinski, M., Fourie, A.B. and Fahey, M. (2006) Mechanics of early age cemented paste backfill. Paste 06, Limerick April 3-7, Australian Centre for Geomechanics, ISBN Helinski, M. Coltrona, A.B. Fourie, A.B. and Fahey, M. (2007) Influence of tailings type on barricade loads in backfilled stopes. Paste 07, Perth, March 13-15, Australian Centre for Geomechanics, ISBN Helinski, M. Fahey, M. Fourie, A.B. (2007) An effective stress approach to modelling mine backfilling, Minefill 07, 9 th International Symposium on Mining with Backfill, Montreal, Paper # v

8 Fourie, A.B. Helinski, M. Fahey, M. (2007). Using effective stress theory to characterise the behaviour of backfill. Minefill 07, 9 th International Symposium on Mining with Backfill, Montreal, Paper # Helinski, M. Tucker, C. Grice, A.G. (2007) Water management in hydraulic fill operations. Minefill 07, 9 th International Symposium on Mining with Backfill, Montreal, Paper # December 2007 vi

9 TABLE OF CONTENTS Abstract...i Acknowledgements... iii Declaration...v Table of Contents... vii List of Figures...x List of Tables... xvii Chapter 1 Introduction Significance of consolidation to mine backfill Project methodology Chapter 2 Background & literature review Introduction Mine backfill literature Influence of consolidation on barricade stresses Influence of consolidation on in situ strengths Influence of consolidation on exposure stability Summary Consolidation Consolidation behaviour of cementing soil Structured soil Modelling structured soil behaviour Cementation Cementation behaviour Summary Chapter 3 Behaviour of cementing slurries Introduction Strength and stiffness Uncemented material response Stress-strain behaviour of cemented fill Hardening Damage due to yielding during hydration (dd) Unconfined compression strength (q u ) Stiffness Stress-strain behaviour: summary Permeability Uncemented permeability Cemented permeability Self desiccation Cementation reactions Impact on pore pressure Analytical model Experimental demonstration of effect of self desiccation Material properties influencing self desiccation Experimental derivation of parameters vii

10 3.5 Temperature Material characterisation technique Conclusion Chapter 4 One-dimensional consolidation modelling Introduction Model development Modelling the behaviour of uncemented tailings: the MinTaCo Program Modelling the behaviour of cemented tailings: the CeMinTaCo Program CeMinTaCo governing equations Numerical implementation Model verification Compressibility Self desiccation Sensitivity study Influence of cementation Influence of permeability Typical damage scenario Strain requirements Comparison with data from in situ monitoring of filled stopes Conclusion Chapter 5 Two-dimensional consolidation analysis (Minefill-2D) Introduction Programming requirements Programming Methodology Introduction The finite element method Boundary conditions Solution to the global equations Material Behaviour Influence of cementation on governing equations Constitutive model, [ K G ([ D ( t, e, C c )]) ] Permeability model, [ Φ G ( t, e, Cc )], [ ng ( t, e, Cc )] Self desiccation, Q(t,e,C) Model Verification Comparison with analytical/numerical solutions Comparison with CeMinTaCo Stope mesh details Comparison with in situ measurements Investigation of the arching mechanism Conclusion Chapter 6 Centrifuge modelling Introduction Experimental Apparatus Calibration Experiment Material viii

11 6.4.2 Experimental procedure Experimental results Numerical back analysis Material characterisation Numerical back analysis Conclusion Chapter 7 Sensitivity study Introduction Comparision of hydraulic fill and paste fill Experimental results Modelling Comparison of hydraulic fill and paste fill Consolidating fill Influence of stope geometry Influence of permeability Influence of cementation Influence of filling rate Consolidating fill: discussion Consolidating fill: conclusion Non-consolidating fill Influence of stope geometry Influence of permeability Influence of cementation Filling rate Non-consolidating fill: discussion Non-consolidating fill: conclusion Development of effective stress during curing Comparision between consolidating and non-consolidating fill Development of effective stress in consolidating fill Development of effective stress in non-consolidating fill Curing of fill: discussion and conclusion Conclusion Chapter 8 Concluding remarks and recommendations for future work Concluding remarks Main outcomes Recommendations for future work Chapter 9 References ix

12 LIST OF FIGURES Figure 1.1 Figure 1.2 Figure 1.3 Schematic of a typical mine tailings based backfill system (contributed by Cobar Management Pty Ltd). Schematic showing a typical stope filling situation. Photograph showing a failed barricade (from Revell and Sainsbury, 2007). Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7 Figure 2.8 Stress distribution down the centreline of a stope assuming drained and undrained filling. The impact of drained and undrained filling on barricade stress. Conversion from vertical total stress to horizontal stress. Gibson's(1958) consolidation chart with typical minefills. Comparison between structured and unstructured compression behaviour. Comparison between structured and unstructured yield surfaces. Powers illustration of the Cement hydration process (from Illstron et al. 1979). Relationship between void ratio and binder content to achieve critical porosity and typical mine backfill range. Figure 3.1 Figure 3.2 Figure 3.2 (b) Figure 3.3 Figure 3.4 (a) Figure 3.4 Incremental yield stress as it is defined in this thesis. Relationship between void ratio and q u for CSA hydraulic fill. Relationship between void ratio and q u for Cannington paste fill from Rankin (2004). Normalised q u against time for CSA hydraulic fill and Cannington paste fill. Incremental small strain shear stiffness against q u for CSA hydraulic fill. Young's modulus (at large strains) against q u for Cannington paste fill. x

13 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14 Figure 3.15 Figure 3.16 Figure 3.17 Comparison between one-dimensional compression experiments and the model results. Comparison between e ff and permeability. Particle size distribution curves. Pore water pressure (u) and effective stress changes in triaxial samples hydrating under constant total stress and undrained boundary conditions. Typical result from bender element test. Typical pore water pressure (u) and effective stress changes in a triaxial sample (CSA hydraulic fill material with 5% cement) hydrating under constant total stress and undrained boundary conditions (with periodic re-establishment of back pressure, to minimise effective stress change). The development of bulk stiffness Ks with time for CSA hydraulic fill: experimental data (symbols) and Equation 3.31 (lines). Rate of pore water pressure (u) reduction with time after initial set for various cement contents for CSA hydraulic fill. Normalised apparent water loss rate plotted against time for different cement contents for CSA hydraulic fill: experimental data compared with Equation Comparison of experimental reduction of pore water pressure (u) against time and adjusted theoretical solution for CSA hydraulic fill. Predicted and measured reduction in pore water pressure (u) for KB paste backfill. Temperature variation across stope half-space after 20 hours. Hydration test setup. Figure 4.1 Figure 4.2 Schematic representation showing the relationship between a, ξ and x in the convective coordinate system. Schematic representing pore water continuity across an element a. xi

14 Figure 4.3 Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Figure 4.11 Figure 4.12 Figure 4.13 Figure 4.14 Figure 4.15 Figure 4.16 Schematic showing mesh used in CeMinTaCo finite difference approximation. Comparison between the self desiccation pore pressure reduction in a hydration test and CeMinTaCo output. Idealisation of the base boundary conditions used to represent a stope in CeMinTaCo. CeMinTaCo output illustrating the influence of the cement induced mechanisms on the pore pressure response. Variation in permeability against time Pore pressure against time for the different cases analysed. Pore pressure isochrones for the different permeability cases analysed. e against σ v for different damage parameters. CeMinTaCo output for different damage parameters. Development of material strength against time for different damage parameters. CeMinTaCo output for different damage parameters in free draining Development of material strength for different damage parameters with free draining fill. Axial strain levels for different filling scenarios. Comparison between CeMinTaCo and in situ pore pressure Figure 5.1 Figure 5.2 Figure 5.3 Figure 5.4 Element geometry adopted for plane-strain displacement and pore pressure finite element calculations in this thesis. 8 noded isoparametric element (taken from Potts and Zdravković, 1999) showing (a) the parent element and (b) the global element. Element geometry adopted for axi-symmetric displacement and pore pressure finite element calculations in this thesis. (a) shear stress against axial strain and (b) shear stress against mean stress for a triaxial test. xii

15 Figure 5.5 Figure 5.6 Figure 5.7 Figure 5.8 Figure 5.9 Figure 5.10 Figure 5.11 Figure 5.12 Figure 5.13 Tangent shear stiffness normalised by small strain shear stiffness against shear stress normalised by the peak shear strength. Illustration of one-dimensional consolidation problem. Comparison between Minefill-2D and the analytical solution for onedimensional consolidation analysis. Illustration showing the one-dimensional self weight consolidation problem used in the Minefill-2D verification. Comparison between Minefill-2D and Plaxis for a self weight consolidation problem. Numerical simulation undertaken to verify the performance of the self desiccation mechanism. Comparison between Minefill-2D and the analytical solution for self desiccation. Numerical geometry for comparison between Minefill 2D and Darcy's law for a falling head permeability test. Comparison with Minefill-2D and Darcy's law for the flow through the surface layer of the fill. Figure 5.14 Comparison between Cemintaco and Minefill 2D. Figure 5.15 Figure 5.16 Figure 5.17 Figure 5.18 Figure 5.19 Figure 5.20 Comparison between Cemintaco and Minefill 2D with a modified "initial set" point. Finite element mesh used to represent (a) coarse mesh, (b) medium mesh and (c) a fine mesh. Calculated pore pressure in the centre of the stope floor for different mesh shapes. Calculated barricade stress in the centre of the stope floor for different mesh shapes. Vertical total stress contours at the completion of filling for the (a) coarse mesh, (b) medium mesh and (c) the fine mesh. Comparison between Minefill-2D and in situ measurements. xiii

16 Figure 5.21 Figure 5.22 Figure 5.23 Figure 5.24 Illustration showing the boundary conditions adopted for the (a) fixed- BC and (b) free-bc case in the "arching" analysis. Comparison between u and σ v in a stope with fixed and free vertical displacement boundary conditions. σ v contours for a stope with (a) fixed vertical displacement boundary conditions and (b) with free vertical displacement boundary conditions Total vertical stress along the stope centreline for the fixed and free Figure 6.1 Figure 6.2 Figure 6.3 Figure 6.4 Figure 6.5 Figure 6.6 Figure 6.7 Figure 6.8 Schematic showing a section through the sample container. (a) Photograph of strain gauged cylinder that was used to represent the stope walls and (b) the inside of the cylinder showing the rough Photograph cylinder walls. of the false base and loadcells that were used in the experiment. Experimental apparatus positioned in a strong box on the UWA geotechnical centrifuge. Change in pressure and stress during Stage 1 loading. Incremental change in u during Stage 2 loading. Incremental load / stress distribution in second stage of loading. Relationship between vertical effective stress and void ratio from the Rowe cell test. Figure 6.9 Relationship between void ratio and permeability from Rowe cell. Figure 6.10 Comparison between measured and calculated pore pressure in Stage 1. Figure 6.11 Comparison between the measured and calculated load distribution in Stage 1. Figure 6.12 Evolution of G o and q u against time for the kaolin with 25% cement mix. Figure 6.13 Comparison between measured and calculated pore pressure in Stage 2. Figure 6.14 Comparison between the measured and calculated load distribution in Stage 2. xiv

17 Figure 7.1 Figure 7.2 Figure 7.3 Figure 7.4 Figure 7.5 Figure 7.6 Figure 7.7 Figure 7.8 Figure 7.9 Figure 7.10 Figure 7.11 Figure 7.12 Figure 7.13 Figure 7.14 Figure 7.15 Figure 7.16 Figure 7.17 Particle size distribution of backfills tested. Evolution of permeability against time for different mine backfills. Evolution of cohesion against time for different mine backfills. Minefill 2D results of barricade stress against time for different backfill types. Development of pore pressure against time for different mine backfills. Pore pressure isochrones for different mine backfills. Influence of drawpoint permeability on pore pressure at the base of a stope with consolidating fill. Pore pressure isochrones for consolidating fills with various drawpoint permeabilities. Barricade stress against time for different drawpoint permeabilities with consolidating fills. Pore pressure against time for consolidating fills with different permeabilities. Barricade stress against time for consolidating fills with different permeabilities. Pore water pressure against time for consolidating fill with different binder contents. Barricade stress against time for consolidating fills with different binder contents. Comparison between applied shear stress and cohesion for a boundary element. Contour of cohesion at the end of filling for the (a) the 3.0% cement and (b) the 1.5% cement case. Total vertical stress calculated for the (a) 3.0% cement and (b) the 1.5% cement case. Influence of filling rate on consolidating fill pore pressures. xv

18 Figure 7.18 Figure 7.19 Figure 7.20 Figure 7.21 Figure 7.22 Figure 7.23 Figure 7.24 Figure 7.25 Figure 7.26 Figure 7.27 Figure 7.28 Figure 7.29 Figure 7.30 Figure 7.31 Figure 7.32 Figure 7.33 Influence of filling rate on consolidating fill barricade stress. Relationship between pore pressure and barricade stress in a consolidating fill. Pore pressure against time for non-consolidating fills with different drawpoint permeabilities. Barricade stress against time for non-consolidating fills with different drawpoint permeabilities. Pore pressure profile at the end of filling for (a) kdp=10k stope and (b) kdp=0.1k stope. Pore pressure against time for non-consolidating fills with different permeabilities. Barricade stress against time for non-consolidating fills with different permeabilities. Pore pressure against time for non-consolidating fills with different cement contents. Barricade stress against time for non-consolidating fills with different cement contents. Barricade Stress and pore pressure against time for non-consolidating fill with a bonded and unbonded interface Pore pressure against time for non-consolidating fills with different filling rates. Barricade stress against time for non-consolidating fills with different filling rates. Development of effective stress within an element of consolidating and non-consolidating fill against time. Development of effective stress against time in a consolidating fill. Development of effective stress against time in a non-consolidating fill. Development of effective stress against time at different elevations in a non-consolidating fill. xvi

19 LIST OF TABLES Table 5.1 Table 5.2 Table 5.3 Material properties adopted for CeMinTaCo - Minefill-2D comparison. P.F.-A material properties (from Helinski et al. 2007) adopted for back analysis of in situ test results. Material properties adopted in the investigation of the arching Table 6.1 Material properties for kaolin with 25% cement content. Table 7.1 Table 7.2 Comparison of hydraulic fill and paste fill properties. Material Properties. xvii

20 Introduction CHAPTER 1 INTRODUCTION Many underground hard-rock mining operations adopt an open stoping technique, which involves the extraction of ore in large underground blocks called stopes. Stope sizes are dictated by geotechnical conditions, but the extraction of an orebody generally requires many, often hundreds of stopes. In order to maintain geotechnical stability on both a local and regional scale, significant pillars containing valuable ore must be left between stopes, but this can significantly reduce the quantity of ore recovered. To increase recovery, many mines choose to re-fill previously mined stopes. The filling process involves placing mine waste materials into previously mined stopes, in order to provide a number of services to the mining operation. These services include: Providing support to the surrounding rockmass Creating a working surface for production activities Disposal of mining waste products. The primary reason for adopting a mine backfill strategy is to increase the quantity of ore that may be recovered and reduce the amount of ore dilution that occurs during stoping. In addition, mine backfill can be used to improve ground conditions by replacing poor natural host rock with an engineered material, in regions that are sensitive to mining. Mine backfilling can be carried out in a number of different ways including hydraulic fills, which use the coarse component of the tailings stream; paste backfill, whose source is full-stream tailings, and rockfill, which may be generated from quarried rock or mining waste rock. The main advantage of hydraulic fill and paste fill over rockfill is their ability to be transported hydraulically. This provides benefits regarding material handling costs, but once placed within a stope the transportation water can reduce stability if not managed appropriately. 1.1

21 Introduction This thesis is focused on tailings-based backfill, which includes both hydraulic and paste fills. These are grouped under the term tailings-based backfill throughout this thesis. Figure 1.1 provides an illustration of the processes involved at a typical tailingsbased backfill site. This figure illustrates the interaction of mining, processing and filling activities. The relevant features of Figure 1.1 with respect to the backfill process are as follows (the numbers refer to the key in Figure 1.1): 3. Shows ore being extracted from a stope. 27. Shows the concentrator, where the ore is crushed and the commodity extracted. 36. Shows the backfill plant, which is where the tailings from the concentrator are post-processed to generate the desired backfill product (this often includes cycloning, thickening, filtration and cement mixing). 23. Shows the underground backfill delivery borehole/ pipeline system. 6. Shows the backfill slurry being deposited into a stope. 4. Shows a stope being blasted, which leads to the adjacent backfill mass being exposed vertically, and the overlying backfill mass being exposed horizontally. The focus of this work is to improve the understanding of the processes involved during the deposition of mine backfill into a stope. Figure 1.2 presents a schematic showing backfill being deposited into a stope. This figure shows a typical stope with a drawpoint that would previously have been used to extract ore from the stope. Fill would be deposited into the stope from the top and containment barricades (also referred to as bulkheads) would be constructed in the drawpoint to retain the fill from flowing out of the stope and into the active mining environment. These barricades are typically constructed from permeable bricks or sprayed fibrecrete. The terminology presented in Figure 1.2 will be used throughout this thesis. Figure 1.1 illustrates that, during the extraction of ore around existing fill masses, the material is exposed vertically and horizontally. In order to maintain stability during these exposures, small proportions of binder (cement) are often added to the tailings 1.2

22 Introduction mix. As conveyed throughout this thesis, the addition of cement to the fill mass results in additional complexities when attempting to characterise the deposition behaviour. Traditionally the use of tailings-based backfill has involved the removal of fines from the tailings stream (referred to in the industry as classification ) to create a coarse material, which is transported through pipelines in a turbulent manner with large amounts of water (Thomas and Holtham 1989). The purpose of removing the fines is to increase the hydraulic conductivity of the material so, when placed, transportation water can drain away freely. Recently there have been significant developments in the field of tailings-based mine backfill with the introduction of full-stream tailings into the underground environment. This type of fill is transported with lower water contents than hydraulic fills and the presence of fines allows the material to be transported at slower velocities without creating segregation in the reticulation system. This material is termed paste backfill and is comprehensively addressed by Landriault (1995, 2006). The main focus of this thesis is to investigate the processes and mechanisms associated with the placement and consolidation of tailings-based backfill, and develop a sound methodology for understanding the mechanisms, and interaction of mechanisms, that occurs during the filling process. The thesis examines the influence of these mechanisms on total stresses applied to containment barricades as well as the development of effective stress within cemented mine backfill during the hydration process. Only by applying a rigorous approach to these problems, can certainty be developed regarding these areas of concern. In the mining industry there has, in the past, been an acceptance of operational rules of thumb, which were developed through experience at other sites, or through experience at the site of interest. These rules of thumb can result in a successful outcome, but as noted by Baldwin (2004) each tailing stream is unique and the resulting paste geomaterial behaviour can and does vary dramatically from one operation to another. Therefore, without a fundamental understanding of the processes involved, it is impossible to determine when subtle characteristics associated with a given situation will result in the rules of thumb becoming invalid. In this situation, a variation from the expected behaviour can result in catastrophic consequences such as the failure of 1.3

23 Introduction containment barricades and inrush of fill material, or the failure of a fill mass during exposure. Between the period of December 2003 and December 2004, there were seven tailingsbased fill barricade failures worldwide; in 2006 there were at least five barricade failures. Due to confidentially reasons barricade failures are often not reported in literature. One example is that reported by Revell and Sainsbury (2007). These authors present a number of different examples of barricade failures. Included in this document are two examples where rapid filling rates resulted in excessive loading of barricade structures. These failures resulted in a very large energy release with paste fill flowing up to 250 m from the original bulkhead location. Figure 1.3 presents a photograph of a failed barricade from this paper. In addition, this paper discussed various barricade (or bulkhead) designs and presents details relating to the structural failure mechanisms. Another hydraulic fill barricade failure, that was documented in a coroner s report (Coroner s Report, 2001), is that at the Bronzwing mine in Western Australia where three miners were killed. The overall conclusion of this investigation suggested that inadequate stope drainage was the aspect that resulted in excessive loads on the barricade structure. In addition to addressing the problem of barricade loads, by developing a model that rigorously captures the most important mechanisms associated with cemented mine backfill processes, filling conditions can be varied throughout the whole spectrum of tailings-based fill types without having to adopt simplifying assumptions to achieve a result. This approach provides an understanding of which parameters control the behaviour and which fundamental relationships need to be satisfied in order to deem various rules of thumb appropriate. 1.1 SIGNIFICANCE OF CONSOLIDATION TO MINE BACKFILL Tailings-based backfill that is transported hydraulically, is a multi-phase system consisting of a solid phase and water phase. Due to the large compressive stiffness of the pore water, relative to the soil structure, the application of load (due to the accretion of overlying material) creates an increase in the pore fluid pressure. Should there be no dissipation of pore fluid pressure, there would be no increase in effective stress and the 1.4

24 Introduction situation is said to be undrained. If the pore pressure is dissipated immediately, any applied load would be immediately placed on the soil matrix in the form of effective stress, and the situation is said to be drained. Various mine sites have fill types that possess different mineralogy and particle size distribution, while filling rates and stope sizes vary from site to site. As a result, the degree of consolidation that occurs during filling also varies. To complicate the consolidation process further, most mine backfills contain a small component of cement, which acts to modify the consolidation properties by increasing the stiffness and reducing the permeability. It is important to appreciate that throughout this thesis, consolidation is defined as the transfer of stress from the water phase to the soil phase. This should not be confused with the compression of the soil matrix or the bonding of material, through cement hydration, as has been noted throughout mine backfill literature. An appropriate definition of consolidation is particularly important in relation to stiff cemented soil where only small amounts of compression is required to mobilise large stresses. Given the theoretical developments that are generated in this work the results will be applied to mine backfill problems such as; Providing a rigorous technique for estimating loads placed on barricade structures Providing an understanding of in situ curing conditions relative to those in the laboratory 1.2 PROJECT METHODOLOGY The overall objective of this thesis was to develop a means of representing the cemented mine backfill deposition process. As will be outlined throughout this thesis, the cemented mine backfill process involves the interaction of a number of complex mechanisms, and in order to achieve the desired outcome simplification of many of these mechanism was required. The methodology adopted is to develop an understanding of the consolidation behaviour of cementing soils through an assessment of past research in relevant fields. On this 1.5

25 Introduction basis an assessment was undertaken of the applicability and limitations of previous work to the mine backfill situation. Using previous work, a rational approach to simulating the cemented mine backfill deposition process is formulated. The second component of this project focuses on the utilisation of existing literature as well as experimental testing, to formulate suitable models to represent various mechanisms that occur during the mine backfill deposition process. Areas investigated include the characterisation of strength, stiffness and permeability of the material prior to cementation, but unlike in conventional soil mechanics, a major focus is placed on the evolution of these properties due to cement hydration. Hydrating cement acts to develop a structure that increases the material stiffness and yield strength, yet the application of stress can potentially destroy this cemented structure. Furthermore, the growth of cement hydrates has been shown to reduce the material permeability. In addition, the cement hydration reaction creates a net volume reduction, which is termed self desiccation. In later chapters this volume change is shown to have a significant influence on the overall consolidation behaviour and must be incorporated into the understanding of the mine backfill deposition process. Cemented mine backfill placement essentially involves the interaction of three timedependent relationships, which include filling rate, consolidation rate and hydration rate. In order to appropriately link these mechanisms, they are coupled numerically. The first numerical stage included incorporation of the cementing soil s material characteristics into the one-dimensional, large strain, tailings consolidation program MinTaCo (Seneviratne et al., 1996). This modified model was renamed CeMinTaCo, and is used in a sensitivity analysis to investigate the interaction of mechanisms during typical mine backfill runs. From this sensitivity analysis, the most significant characteristics associated with the consolidation of cemented mine backfill were identified. A new two-dimensional (plane strain and axi-symmetric) fully coupled consolidation model named Minefill-2D is then presented. Minefill-2D incorporates all of the relevant cemented mine backfill mechanisms, as well as the ability to simulate the progressive accretion of material and any stress redistribution onto the surrounding stiff rockmass. This model is verified against a number of established analytical solutions as well as 1.6

26 Introduction laboratory experiments (including both element testing and centrifuge modelling) and in situ data. Having gained appropriate confidence in Minefill-2D, a sensitivity study was undertaken. This study investigates the fundamental difference in mechanisms between full-stream tailings backfill (paste fill) and classified-tailings backfill (hydraulic fill). A sensitivity study was undertaken for both full-stream and classified-tailings backfills, to highlight what are likely to be important, and less important, characteristics when dealing with the various fill types. The results of the sensitivity study are used to provide some guidance when designing and managing filling operations. 1.7

27 Background & Literature Review CHAPTER 2 BACKGROUND & LITERATURE REVIEW 2.1 INTRODUCTION The purpose of this chapter is to provide an overview of the literature that is relevant to this thesis. Firstly, there is a discussion regarding the state of the art in mine backfill. This provides an overview of existing methods being applied in the mining industry and highlights a number of areas where further research can deliver an improved understanding. This is followed by a review of previous work that is considered to be relevant to this thesis. Specifically, topics addressed include consolidation theory, structured-soil mechanics, and cement technology. In addition to the overview of previous work, at the end of each section there is a brief description of how the literature has been applied in the context of mine backfill throughout this thesis. 2.2 MINE BACKFILL LITERATURE In conventional surface tailings disposal, consolidation is important since this mechanism dictates the settlement of the tailings mass and therefore the quantity of material that can be placed into a storage facility. In addition, the stress history of tailings is important when determining the undrained shear strength of the material. As a result, authors such as Gibson (1967), Williams (1988), Toh (1992), Seneviratne et al. (1996) and Newson et al. (1996) have thoroughly investigated the consolidation behaviour of surface tailings facilities. In an underground environment, the degree of settlement is not of major importance and since the material is often cemented, the undrained shear strength is less likely to be influenced by stress history. Therefore the relevance of consolidation might be questioned Influence of consolidation on barricade stresses In the underground backfill environment, the surrounding rockmass is significantly stiffer than the material being deposited. Rankin (2004) investigated numerically the 2.1

28 Background & Literature Review development of stress in the backfill during filling and found that much of the vertical stress can be redistributed to the surrounding rockmass. This work neglected pore pressures in the calculation of the stress distribution and as shown later in the thesis, this approach can lead to a gross oversimplification of the process. To understand how stress is redistributed to the surrounding rockmass requires an understanding of the effective stress. And in order to understand effective stress, an understanding of the consolidation process is required. To demonstrate the significance of consolidation (or specifically the influence of pore water pressure) on the stress distribution in a backfill mass, Helinski et al. (2006) undertook a series of numerical simulations using the finite difference program FLAC (Fast Lagrangian Analysis of Continua). This analysis involved filling a plane strain stope (20 m wide by 50 m high), with fully hydrated cemented paste backfill, assuming either fully drained or undrained conditions. The fully drained case neglected the influence of pore water pressure, while the undrained case assumed that the material is placed without any consolidation. Neglecting the influence of pore water pressure in the fully drained case is considered a valid representation of the best case scenario as the water table is assumed to have been drawn to the bottom of the stope, and with a low air entry suction value (for non-plastic tailings), this would result in atmospheric pressures existing throughout most of the fill mass. Material properties adopted in this analysis were those quoted by Rankin et al. (2001) for Cannington paste fill. These included a unit weight of 20 kn/m 3,Young s modulus (E) of 60 MPa and Poisson s ratio (ν ) of These parameters equate to a shear modulus (G) of 24 MPa and a drained bulk modulus (K) of 40 MPa. The friction angle (φ ) adopted was 25º and, to demonstrate the influence of bond strength (or lack thereof), an artificially high cohesion (c ) of 25 MPa was adopted. Figure 2.1 presents the calculated total vertical stress down the centreline of the stope at the end of filling, when the material has been placed in both a drained and an undrained manner. Also presented in Figure 2.1 is the total vertical stress assuming no stress redistribution to the surrounding rockmass. Figure 2.1 demonstrates that there is a significant difference between the total vertical stress down the centreline of a stope, if filling is carried out under fully consolidated 2.2

29 Background & Literature Review (drained) or fully unconsolidated (undrained) conditions. With fine-grained material (with a high air entry suction value) drawing the water table down through the fill mass may cause suctions to develop within the fill mass. The development of suctions would increase the amount of arching in the drained case, increasing the influence of pore pressure on the arching process. Even with fully-hydrated cemented backfill, if there is no consolidation there is very little stress redistribution to the surrounding rockmass, even with an inflated value of cohesion. In order to mobilise any shear stress at the fill/rock interface, shear strains are required. To generate shear strain the material must settle, but under undrained conditions the compressive stiffness of the bulk material is that of water, which is very high, and therefore, very little settlement occurs. It is not until water is squeezed out of the fill mass that soil compression (settlement) can occur and shear strains at the interface can occur, generating the arching effect. The lower vertical stress for the drained case in Figure 2.1, is due to this arching effect. It is interesting to note that, in the lower 10 m of the stope in the drained case, there is a linear increase in vertical total stress. The reason for this is that, towards the stiff base of the stope, the total amount of settlement (vertical deformation) is reduced, resulting in less shear strain being mobilised at the interface and therefore less shear stress. As a result less stress redistribution or arching occurs towards the base even in a drained situation. In addition, as the name implies, a certain vertical height is required to accommodate the arch in the material, so that arching only takes effect above a certain distance from the base. The results from this numerical study can be extended to the total horizontal stress placed on the barricade for the two extreme cases. It should be noted that in both cases the pore pressure immediately behind the barricade is set to zero. The total horizontal stress calculated at the barricade location is plotted against height up the barricade in Figure 2.2 for both the drained and undrained cases. This Figure illustrates that if filling is carried out undrained, barricade stresses are very high ( 800 kpa) while drained filling results in much lower barricade stresses ( 80 kpa). Figure 2.1 demonstrates that without consolidation, there is little stress redistribution and high vertical total stresses. In addition to these high total vertical stresses within the 2.3

30 Background & Literature Review stope, the undrained filling case also results in higher horizontal total stress for a given vertical total stress. This may be understood with reference to Figure 2.3, which illustrates Rankin s lateral earth pressure theory. This theory relates the vertical total stress ( σ ), vertical effective stress ( σ ), pore pressure (u) to the horizontal total stress v v ( σ h ) in accordance with Rankin s lateral earth pressure coefficient K 0. For most uncemented tailings K 0 is typically in the range of If all of the self-weight stress were supported by the water phase, the horizontal total stress would be equal to the vertical total stress. As consolidation occurs and the selfweight stress is transferred off the water phase and onto the soil structure, the horizontal total stress becomes less than half of the vertical total stress, for typical K o values. Consolidation also influences the horizontal effective stress within a stope. In order to generate frictional shear strength between the fill mass and the surrounding rockmass, horizontal effective stress is required. If all of the self weight vertical stress is being carried by the water phase, the horizontal total stress and pore pressure would be equal. In this case, the horizontal effective stress would be zero. Consolidation reduces the pore pressure, increasing the horizontal effective stress and allows some frictional shear strength to exist at the rock/fill interface. Gibson (1958) investigated analytically the amount of consolidation in a deposit of a saturated soil where the thickness of the deposit is increasing with time. He derived a relationship between the development of excess pore pressure (u ex ), the coefficient of consolidation (c v ), the filling rate (m) and the duration that filling has been ongoing (t), in a one-dimensional situation. Applying this analytical solution, Gibson (1958) developed a chart to relate a nondimensional time term (T) to the excess pore pressure (u ex ). In this solution, u ex is represented by a gradient of u ex against depth relative to the gradient of u ex that would be created with no consolidation. This ratio is defined as (du/dz)/γ. If this ratio is equal to unity, the total stress and pore pressure are equal (meaning that there is no consolidation) while if equal to zero there is no excess pore pressure (i.e. complete consolidation). The non-dimensional time constant is defined as; 2.4

31 Background & Literature Review T = 2 m. t c v (2.1) Gibson s chart to relate the degree of consolidation that occurs during placement to the non-dimensional time constant is reproduced as Figure 2.4. The relevance of this figure to tailings backfill is discussed further later. The situation analysed is well suited to the case of tailings-based backfill placement into an open stope. While it might be argued that the placement of minefill into a stope does not strictly conform to the one-dimensional assumption due to the potential for arching to the surrounding rockmass, neglecting arching during the early stages of placement can provide a reasonable representation of most situations. The other point of question may relate to the base boundary conditions. In most situations it is reasonable to consider free-draining conditions at the barricade location. But, as illustrated in Figure 1.2, the drawpoint flow area is often significantly smaller than that of the stope. Furthermore, as filling progresses away from the base, the distance to this boundary increases, making drainage towards the top boundary more likely. As a result, it may be more appropriate to ultimately assume an impermeable condition at the base. Gibson (1958) analysed both permeable and impermeable boundary conditions at the base. Qiu and Sego (2001) undertook a series of laboratory experiments on full-stream gold and copper tailings. One component of this work included large strain consolidation testing of this material to determine c v. The tests indicated c v values of 14 m 2 /yr and 25 m 2 /yr for the gold and copper tailings, respectively, over the density range typical for paste backfill. Vick (1983) suggests that c v for classified tailings (which would be representative of hydraulic fill) ranges between 1500 m 2 /yr and 300,000 m 2 /yr and c v for full-stream tailings ranges from 3 m 2 /yr to 300 m 2 /yr. To develop an understanding of the degree of consolidation likely to occur during filling in typical mine backfill operations, these suggested c v values were combined with a filling rate of rise of 5 m/day (a typical filling rate) and a 40 m high stope to calculate the respective dimensionless time factor (T). The location of the various material types is superimposed onto Gibson s consolidation chart in Figure

32 Background & Literature Review Figure 2.4 therefore indicates that during the placement of hydraulic fill it is unlikely that excess pore pressures would develop unless very high filling rates are adopted. In contrast, for full-stream tailings (paste fill), it indicates that it is very unlikely that consolidation would occur. This suggests that, following the logic outlined earlier, loads applied to barricade structures can be extremely high in full-stream tailings backfill in an uncemented state. It should be noted that Gibson s chart only considers excess pore pressures, neglecting hydrostatic pore pressures. However, as discussed later in this document, the presence of hydrostatic type pore pressures (generated as a result of a flow restriction through the drawpoint area) also make the influence of pore water pressure relevant to a hydraulic filling scenario. To the author s knowledge, the only case where the influence of pore pressure has been incorporated into the analysis of mine backfill deposition mechanics is in the work described by Kuganathan (2002). This work presented an analytical solution for estimating barricade stresses in hydraulic fill stopes, which incorporates steady state seepage-induced pore pressures 1 within the stope drawpoint. This solution is based on a limit state analysis, which incorporates the influence of pore pressures only within the drawpoint of a stope. Being a limit state method, this approach assumes the mobilisation of the ultimate material strength at the rock/fill interface and there is no consideration of the influence of pore pressures on the stress distribution within the stope, nor is there consideration of excess pore pressures that may be created during filling. Therefore, while this technique may provide a reasonable indication of barricade stresses under some conditions, these limitations can lead to oversimplification in many cases (particularly cases involving fine-grained full-stream tailings backfill). Another approach that has previously been adopted to establish an understanding of the stresses placed on barricades is direct stress measurement using diaphragm-type earthpressure cells. Revell (2002) and Belem et al. (2004) used total pressure cells to measure the loads placed on paste fill retaining structures during filling. Based on the 1 Steady-state seepage pore pressures will be properly defined later. Briefly, this is the pore pressure profile that is reached when steady-state seepage is established within the stope, in equilibrium with the boundary total head conditions (the boundaries being the top fill surface and the barricade). 2.6

33 Background & Literature Review measurements, it was concluded that the amount of load transferred to the wall reduced as the cement hydration proceeded. Clayton and Bica (1993) demonstrated that the stress measurements from earth-pressure cells are typically lower than the true values; this is called under-registration. The degree of under-registration is related to the relative stiffness between the cell and the surrounding soil. As hydration proceeds, the stiffness of a cemented soil increases significantly, and therefore the degree of under-registration in such circumstances could also change. Therefore, questions may arise as to whether the reduction in stress measured by Revell (2002) and Belem at al. (2004) is a true reduction in barricade stress or if it is simply a result of the change in under-registration due to the progress of hydration. Stone (personal communications 2007) suggests that the biggest problem facing the mining industry with regard to mine backfill is uncertainty over barricade loads. The need for further research into loads being placed on mine backfill retaining structures has also been recognised by Le Roux (2004) who suggests that there is a need for a renewed focus on barricade design with high rates of filling. McCarthy (2007) suggests that mine backfill barricades are a problem in the mining industry and that the problem is technically complex and there is a need for more research in this area Influence of consolidation on in situ strengths It has been documented that in situ backfill strengths are often significantly greater than those measured in the laboratory, for the same mix (Cayouette, 2003, Revell 2004). It has also been well established that the application of effective stress to a cementing soil prior to or during hydration can increase the material strength (Blight and Spearing 1996, Consoli 2000, Rotta 2003). The improvement in strength is said to be a result of soil matrix compression (which leads to an increased density) as well as an improvement in the intimacy of the contact points. This topic has been researched experimentally by a number of different authors such as Blight and Spearing (1996), Le Roux at al. (2002) and Belem et al. (2006). 2.7

34 Background & Literature Review The work by Blight and Spearing (1996) focused on investigating the influence of closure strains 2 on the strength of mine backfill. This work demonstrated that as the strain rate is increased there is an associated increase in strength. As this work was carried out in the context of strains induced by ground movement in classified tailings backfill, a strain criterion was adopted and there was no need for an effective stress consideration. The loading rate adopted by these authors is less likely to be relevant to a large open stoping situation where the application of total stress during filling is usually dependent on the self weight of the overlying fill mass. Le Roux et al.(2002) investigated the impact of applying load in a one-dimensional situation to a sample during curing. The results indicated that higher cement contents reduced the degree of compression for the same loading sequence. The deficiency with this work was that the rate of loading adopted was in accordance with the rate of application of self weight total stresses in a typical filling situation rather than that of effective vertical stress. In order to develop a rational approach to the loading rate that should be applied, it is the rate of development of effective stress in the field that must be matched, rather than the total stress. As demonstrated in this thesis, this is particularly relevant during the early stages of loading where the pore pressures in a stope can increase at the same rate as the total stress, resulting in no change in effective stress during the early stages of hydration. Belem (2006) undertook a series of column filling tests. The columns used in this work were 3 m high, and 300 mm square in plan. Three columns were tested: the first had impermeable vertical boundaries, the second had an impermeable top half and a permeable bottom half and the third had completely permeable boundaries. These columns were filled with paste backfill containing cement. At the end of the tests, the resulting cemented material was investigated. This investigation indicated that drainage created a significant increase in density which resulted in an increase in material strengths. These tests were meant to represent possible conditions within a stope, but due to the significant reduction in drainage path length associated with the boundary 2 Closure strains refer to the inward movement of the walls of a stope after the fill is placed and the hydration process is occurring. 2.8

35 Background & Literature Review the rate of effective stress development is not considered representative of the field situation 1. Therefore, in order to improve the understanding of the mine backfill deposition process and to start to develop a rational approach for understanding the interaction of cement hydration and the application of effective stress, an understanding of the mine backfill consolidation process is required. This aspect has been recognised by Le Roux (2004) who suggests that it is necessary to understand the influence of hydrating cement on the consolidation properties of the paste fill and how this influences the final material properties and affects the performance of the material Influence of consolidation on exposure stability During the removal of stopes adjacent to a cemented fill mass (as illustrated in Figure 1.1 point number 3), there is a reduction in confining stress, which reduces the stability of the fill mass. If the fill mass has insufficient cohesive strength, fill failure can occur, resulting in dilution of the ore being mined in the adjacent stope. A number of authors have proposed analytical solutions for estimating vertical exposure strength requirements. The most commonly adopted analytical solutions include the upper bound mechanisms by Mitchell and Wong (1982) and those based on the limit state arching theory of Marston (1930) and Terzaghi (1943) (such as those presented by Winch 1999 and Aubertin et al. 2003). The interesting point about these two commonly adopted limit state techniques is the strength parameters used to represent the contact between the fill mass and the surrounding rockmass. In the upper bound mechanism proposed by Mitchell and Wong.(1982), it is assumed that the interface is cohesive, while the technique presented by Winch (1999) and Aubertin et al. (2003) is based on a frictional contact strength only. During the filling process, the interaction between the development of shear strength and the application of shear stress may modify the cohesive properties at this interface. Such interaction is dependent on the material properties, boundary conditions, filling 1 The limitations of using scaled models (whether on a geotechnical centrifuge or at 1g) for this type of investigation is that the timescale of consolidation/drainage is reduced by reducing the scale, but the timescale for hydration is not. This is explained in much more detail in Chapter

36 Background & Literature Review rate and the consolidation rate, but without appropriately understanding the filling process it is difficult to establish an understanding of this important characteristic Summary This section has presented previous work in the field of mine backfill and demonstrated the need for a soil mechanics approach to understanding the mine backfill deposition behaviour. The remainder of this chapter focuses on work carried out in the fields of consolidation, structured-soil and cementation which is considered relevant to the cemented mine backfill application. 2.3 CONSOLIDATION A solution for the process of consolidation in a saturated soil was developed by Terzaghi, on the basis of a number of simplifying assumptions, such as: the pore water is infinitely stiff relative to the soil skeleton, such that an application of external stress results in generation of a pore pressure equal to that stress the permeability (hydraulic conductivity) and compressibility of the soil does not change during a loading increment Darcy s law applies i.e. the rate of water flow in the soil depends on the permeability and the gradient in the total head. For slurries consolidating under self-weight stresses, many authors, such as Carrier (1982), pointed out that the assumption of constant permeability and compressibility of the matrix is not correct, due to the large changes in void ratio that occur as consolidation proceeds, resulting in significant change in compressibility, and even more significant change in permeability. The Terzaghi model was extended by Gibson (1958) to simulate the progressive sedimentation of material, as discussed in the previous section. This model was based on small-strain theory and restricted to material properties that remain constant throughout the consolidation process. The main advancement in this work was to take account analytically of an increase in drainage path length as well as the inclusion of self-weight stresses. 2.10

37 Background & Literature Review In order to take account of the significant nonlinearity in large-strain consolidation problems, researchers began investigating finite strain consolidation models. This included work by Mikasa (1965) and Gibson et al. (1967, 1981). The methodology uses a Lagrangian coordinate system where the boundaries move in accordance with the evolving soil dimensions. Through applying this theory numerically, the authors were able to rigorously account for variations in geometry as well as variations in permeability and stiffness during compression. Based on this work, Gibson et al. (1981) demonstrated that conventional small-strain theory had the potential to significantly underestimate excess pore pressures. Tan and Scott (1988) continued the comparison of small- and large-strain theory, suggesting that Terzaghi s small-strain solutions were only applicable for strains less than 20%. With modern developments in computational efficiency, numerical programs specifically focused on solving the large-strain consolidation equations for the purpose of understanding the mine tailings deposition process, have been generated (Williams et al., 1989, Tao, 1992 and Seneviratne et al., 1996). In addition to the numerical and analytical developments, significant research effort has been dedicated to understanding material parameters including oedometer testing, constant and falling head permeability tests as well as Rowe cell testing that captures volume and permeability changes under various confining stresses. Based on results from this type of testwork, authors such as Carrier et al. (1983) developed models to represent the large strain compressive behaviour of soil Consolidation behaviour of cementing soil The development of a one-dimensional consolidation model for soil undergoing cementation (CeMinTaCo) is described in detail in Chapters 3 and 4. However, a brief overview is given here, to show where it fits with respect to other models in the literature. The basis for this model is the large-strain consolidation equation derived by Gibson et al. (1981). The governing equation is derived through combining equilibrium of the soil and water phases using Darcy s law to represent flow. Combining these equations and maintaining continuity, the following governing equation was derived to represent onedimensional large strain consolidation of uncemented slurry. 2.11

38 Background & Literature Review δu δσ ( ) v δ k 1+ eo δu δk δσv + 1+ eo { t e a + = δ w 1 e a δ 43 δ γ + δ δa { δt ( A) ( D) ( B) ( C) (2.2) where a is a Lagrangian coordinate, u is pore pressure, k is hydraulic conductivity (permeability), and σ v and σ v are the vertical effective and total stresses, respectively. In this equation, term A is the rate of change in pore pressure as a result of a rate of application of total stress (term B), term C is the volumetric strain, which is dictated by the hydraulic conductivity (k) of the material, and term D is the current stiffness of the material. During the consolidation of uncemented mine tailings from an initial slurry state, both the stiffness (compressibility) and the permeability of the material change as the void ratio reduces. When cement is added, these changes still occur but a number of other mechanisms associated with cement hydration are introduced. These include the development of cement-induced stiffness and strength, a reduction in permeability and the introduction of a new mechanism that is referred to as self desiccation. The modified governing equation is presented here: δu e δσ 1 v ( t, Cc, e, v ) t σ K w e δ δ (A ) ( t, C ) δσ v δv ( t, C, e, ) sh c δσ + v c σ v = 14 δe δt 3 { δt (E) (B) ( e ) δk ( e ) δσ k v δ eff 1 + e (,,, )( 1 ) 0 δu eff + t Cc e σ v + e δe δa γ w 1 + e δa δa (D) (C) (2.3) In this equation, the modified terms are identified using the same labels as the equivalent unmodified terms (in Equation 2.2) but there is an additional term (term E) that does not have an equivalent term in the unmodified equation. Due to the soil matrix stiffness potentially approaching that of water, the change in pore pressure (term A in Equation 2.2) resulting from a change in total stress, requires 2.12

39 Background & Literature Review δσ modification to take account of the cemented matrix stiffness ( v ) and the bulk δe modulus of water (K w ) to satisfy strain compatibility. The volumetric strain term (term C in Equation 2.2) requires modification to take into account the fact that the permeability (k) is affected not just by the normal void ratio reduction due to consolidation, but also by the formation of cement gel in the void space. The stiffness term (term D in Equation 2.2) requires modification to express the material δσ stiffness ( v ) as a function of cement hydration, current stress state and previous δe stress excursions. An additional term (term E) needs to be introduced to take account of volumetric δ changes ( δt V sh ) associated with the cement hydration process (the self-desiccation process referred to above). The derivation of the modified material models is presented in Chapter 3 while the derivation of the modified governing equation for one-dimensional consolidation of a cementing soil (Equation 2.3) is presented in Chapter STRUCTURED SOIL The term structured soil refers to any soil that has a true cohesive strength. This may include artificially-cemented soils or natural soils that may have been cemented through natural processes, such as calcite precipitation. Clough et al. (1981) pioneered the research into cemented soils by investigating experimentally the impact of cementation on both naturally-cemented and artificiallycemented soils. This work demonstrated that cementation creates true cohesion but has little impact on the friction angle. It was also shown that density, grain-size distribution, and grain shape all have a significant influence on the behaviour of cemented soils. Clough et al. (1989) continued this work on cemented soils with experimental investigations into the cyclic loading of cemented soils. 2.13

40 Background & Literature Review In the late 1970 s - early 1980 s during the construction of offshore oil and gas platforms on the North West shelf of Australia, piling problems were encountered. As discussed in Jewell et al. (1988), the major reason for these problems was associated with a lack of understanding regarding the behaviour of structured soils. In response to these problems, a significant focus was placed on understanding the behaviour of structured soils. Leroueil and Vaughan (1990) were the first to present a comprehensive framework for understanding structured soils, with a particular focus on the behaviour of residual soils. They discuss how the shape of the yield surface varies with curing stresses. The different failure modes that would occur through loading along different stress paths were also discussed. In this framework it was shown that shearing would produce a localised failure plane, while compressive stresses would destroy the structure more uniformly, leading to volumetric contraction. The authors also introduced the concept of the structure-permitted space, which is illustrated in Figure 2.5. This is a region in volumetric compression space (e - p ) where only material with structure can exist. Coop and Atkinson (1993) presented a framework for understanding the behaviour of cemented carbonate sand. This work showed that when sheared, the materials in either a cemented or uncemented state approach the same critical state. Also, they suggest that the cemented friction angle is slightly lower than the uncemented equivalent. This is attributed to surface coating. They demonstrate that, as with overconsolidated soils, shearing under low stress results in high stress ratios with post-yield strain softening, while shearing under high mean stress results in the cementation having little influence on the ultimate strength. It was also shown that cementation can significantly increase the elastic compressive stiffness. Cuccovillo and Coop (1997) investigated the yielding and pre-failure deformation of cemented soils. They demonstrated that a cemented soil showed two major yield points in loading, these being the stress where the material stiffness starts to reduce below the small strain stiffness (termed Y1 yield stress) and the point where significant reduction in stiffness is observed (termed Y2 yield stress). Y1 is said to be the first onset of structural breakdown. The rate of stiffness change at Y2 was shown to be a function of 2.14

41 Background & Literature Review the state of the soil fabric. It was shown that a loose calcarenite reduces in stiffness significantly more than dense silica sandstone. Asaoka et al. (2000) investigated the significance of structure in clayey soil on the consolidation/ compression behaviour. It was concluded that prior to yield, the higher stiffness of the structured soil (relative to the destructured soil) resulted in faster rates of consolidation. However, as the material was loaded beyond its yield point (Y2), the stiffness of the structured soil was less than that of the destructured soil (under the same stress) and, as a result, consolidation of the structured material occurred over a longer period with greater settlement. More recently, there has been renewed interest in the behaviour of soils cemented artificially for the purpose of soil improvement. This research effort has been primarily driven by Consoli and his co-workers, as detailed below. Consoli et al. (2000) showed that the stress state during curing plays a significant role in the mechanical behaviour of the soil. Schnaid et al. (2001) investigated the triaxial behaviour of cemented soils experimentally. They showed that the shear strength of a cemented soil can be appropriately determined from the unconfined compressive strength and the uncemented friction angle. For the confining stresses used in the testwork, the secant modulus is unaffected by the confining stress, suggesting that the stiffness is more a measure of the bond strength. Rotta et al. (2003) investigated isotropic yielding of a cemented soil. This work involved an experimental investigation of material cemented at different densities, under different stress levels. They introduced the concept of the incremental yield strength, which is considered to be the contribution of cementation to the increase in yield stress of the material. The focus of this work was to develop a rational approach to determining the material characteristics that influence this incremental yield strength. It was demonstrated that this value is dependent on the degree of cementation and the material state. Finally, Consoli et al. (2006) combined the results of Schnaid et al. (2001) and Rotta et al. (2003) to develop a unified framework for understanding the strength of cemented soils. This work demonstrated that the incremental isotropic yield stress and initial bulk 2.15

42 Background & Literature Review modulus can be linearly related to the unconfined compressive strength for a cemented material. Yin and Fang (2006) undertook experimental studies into the influence of cementtreated clay columns on the consolidation of an otherwise untreated clay mass. These results indicated that the presence of the cement-treated material played a significant role in accelerating the consolidation of the mass. This was primarily attributed to the increase in material stiffness. A number of different constitutive models have been developed to represent the behaviour of structured soils (Gens and Nova, 1993; Lagioia and Nova, 1995; Rouainia and Wood, 2000; Kavvadas and Amorosi, 2000). Comparison with experimental data indicates that these models provide a good representation of the soil behaviour. But in order to provide this representation, significant mathematical detail is required. While these types of models are considered superior to those presented in this thesis, at the time of writing this thesis, such complexity was considered a second order effect in the context of this work. Liu and Carter (2002, 2005) present a modification of the well known Cam-Clay model to represent the behaviour of structured soil. This model is referred to as the Structured Cam-Clay model. The concept behind this model is that the yield surface for the cemented soil is simply an expansion of the original yield surface for the uncemented soil, and the magnitude of this expansion is dependent on the degree of cementation. This concept is illustrated in Figure 2.6. As the soil is loaded, the model allows for the degradation of the structured yield surface and hardening of the uncemented yield surface. This can occur at the yield point (virgin yielding) as well as for loading excursions within the yield surface (sub-yielding), but beyond a particular stress level (Y1 as defined by Cuccovillo and Coop, 1997). This logic is the same in both the compression and shearing stress paths Modelling structured soil behaviour In order to characterise the material response for one-dimensional compression modelling, a modified version of the Structured Cam-Clay model was adopted. This model provides the flexibility to represent the compression behaviour initially in accordance with the uncemented Cam-Clay model and to take account of the presence 2.16

43 Background & Literature Review of cementation through an increased yield surface. The Structured Cam-Clay model also allows for the yield surface to be degraded (potentially back to that of the uncemented soil) in accordance with the destructuring functions suggested by Carter and Liu (2005). To represent the size of the yield surface, the methodology presented by Rotta et al. (2003) and Consoli et al. (2006) is used. The concept of an incremental yield stress is incorporated to separate the cemented yield stress from the uncemented yield stress. The magnitude of the incremental yield stress is said to be a function of the degree of cementation and material state in accordance with the function suggested by Rotta et al. (2003). Furthermore, based on the findings of Consoli et al. (2006), the unconfined compressive strength and small-strain bulk stiffness is said to be proportional to the incremental yield stress along the isotropic and one-dimensional stress paths. Details of this approach are presented in Section CEMENTATION Combining Sections 2.3 and 2.4, a rational methodology for the consolidation analysis of a cemented soil can be developed. However, in order to appropriately represent the cemented mine backfill process, a model that can appropriately represent the consolidation of a cementing soil is required. In this work, previous work in the field of cement and concrete research was taken into account. Pioneering work in the field of cement research is described in a series of publications by Powers and Brownyard (1947). These publications were the culmination of a research program, by the Portland cement association, aimed at understanding the behaviour of Portland cement paste. This work was later summarised in a single concise document by Brouwers (2004). This, and subsequent work by Powers (1958, 1979), developed the first model for understanding cement hydration. When the cement particles are undergoing hydration, a number of chemical reactions take place. These reactions result in the growth of hydrates that effectively act to connect particles. An illustration of this process (taken from Illstron et al., 1960) is presented in Figure 2.7. Powers and Brownyard (1947) suggest that the cemented structure is made up of solid particles and cement gel. With this, they introduce the concept of non-evaporable water, which is bound within the 2.17

44 Background & Literature Review solid material, and gel water, which exits between gel particles. Due to the large surface area of the very fine gel particles, van der Waals forces bind gel water within the gel phase. Based on their research, Powers and Brownyard (1947) determined that the specific gravity of the unhydrated cement is 3.17 while that of the hydrated gel solids is 2.43 and that of the gel including pores is This indicates that, when combined with water in the hydration process, the unhydrated cement volume increases by approximately 80% (including gel products). It was also found that the weight of chemically-bound water (termed non-evaporable water) used in cement hydration is 23% of the weight of unhydrated cement. Furthermore, it was found that due to the change in volume stoichiometries during the cement reactions, there is a net reduction in volume from the unhydrated cement and water to the final hydrated cement product. This change in volume (in cm 3 ) was shown to be 27% of the weight of non-evaporable water. In conventional concrete literature, this volume reduction is termed self desiccation as it acts to desaturate lean concrete mixes. This mechanism is important with respect to conventional concrete mechanics because of the way that it influences shrinkage cracking (termed autogenous shrinkage ). Researchers such as Powers and Brownyard (1947), Hua et al. (1995), Koenders and Van Breugel (1997), Bentz (1995) and Brouwers (2004) investigated the impact of this mechanism on the shrinkage of conventional concrete. Illstron (1979) presents the rate of hydration for the various compounds that make up cement paste. This work indicated that the four main compounds react at vastly different rates, ranging from C 3 S, which achieved 70% of its ultimate strength after 28 days, to C 2 S which has achieved only 5% of its strength after 28 days. Rather than simulating the rate of hydration for each individual compounds, other researchers have developed empirical relationships to represent the rate of hydration for the overall cement product (Rastrup, 1956, Guo, 1989 and Sideris, 1993). These authors term the rate of hydration maturity and essentially fit various curves to the development of cement related characteristics (maturity) against time. The growth of cement hydrates increase the material stiffness and strength, due to the bonding of particles. This has been well documented by authors such as Powers and 2.18

45 Background & Literature Review Brownyard (1947), Illstron (1979) and Sideris et al. (2004). The strength achieved is said to be a function of the cement content as well as the water-cement ratio. For a saturated soil, this is consistent with the findings of the cemented soil literature, which suggests that the strength is dependent on the density of the cemented soil (Consoli. et al. 2006). During the hydration process, some of the water is converted from a free liquid to either solid or gel product, which forms a component of the soil structure and occupies some of the previous void space. As already mentioned, Powers and Brownyard (1947) suggest that the hydrated solid and gel is 80% greater than the original unhydrated cement volume. Just as with a reduction in void space from soil compression, the infilling of voids by cement gel acts to reduce the permeability of the material. This aspect has been researched in the concrete literature for the purpose of reinforced concrete corrosion resistance (Garboczi and Bentz,1995, Breysse and Gerard, 1997, and Bentz et al. 1998). Garboczi and Bentz (1995) present the concept of critical porosity. This is defined as the point where the cement has enlarged sufficiently that the combination of the cement solids and the gel structure create a seal across the entire cross-sectional area of the sample. Since the cement gel is composed of platelets with very large surface areas, this situation produces a significant reduction in permeability; in fact, at this point the material is considered to be impermeable. Based on the volumetric changes suggested by Powers and Brownyard (1947), Figure 2.8 was developed to illustrate the relationship between void ratio and cement content required to achieve the critical porosity (as described by Garboczi and Bentz, 1995). Also presented in Figure 2.8 is the range over which typical mine backfills are produced. This indicates that, due to the relatively low density and small cement contents, it is very unlikely that a typical mine backfill would ever approach critical porosity. Therefore, while the presence of cementation acts to reduce the permeability (and should be taken into account), this reduction is not expected to render the material impermeable. 2.19

46 Background & Literature Review Cementation behaviour In order to represent the cementation process, research in the field of concrete technology (which was presented in the previous section) was investigated. A brief overview of how this logic is applied has been provided in this section. While each of the maturity functions (discussed in the previous section) appears to provide a reasonable fit to experimental data, the exponential relationship suggested by Rastrup (1956) was adopted to represent the maturity of cement throughout this thesis. This work provides a simple exponential relationship between cement hydration and time. Investigations presented later in this thesis indicate that the rate of change of strength, stiffness, permeability and volume can all be appropriately represented using the same maturity relationship. Details of this approach are provided in Section 3.2. Combining the total volumetric changes recommended by Powers and Brownyard (1947) with the maturity function presented by Rastrup (1956), a function is developed to represent the rate of volumetric change that occurs with time due to the self desiccation mechanism. This approach is detailed in Section 3.4. To represent the influence of cement hydration on permeability, the relationship between void ratio and permeability suggested by Carrier et al (1983) is combined with the volumetric changes during cement hydration as recommended by Powers and Brownyard (1947) and the maturity relationship of Rastrup (1956). Details of this relationship are provided in Section SUMMARY This chapter has presented an overview of previous work in the field of mine backfill. In addition, some simple examples were presented to demonstrate the significance of some of the assumptions inherent in existing solutions. Specifically, these examples demonstrate that gaining an understanding of the degree of consolidation that occurs during placement is essential in attempting to determine the stress distribution around a stope. This chapter continues with a description of literature relevant to understanding the consolidation that takes place during the deposition of cemented mine backfill. The fields covered included consolidation, structured soil and cement hydration. Following a 2.20

47 Background & Literature Review description of background literature, a brief description is provided in each of these areas to explain how this previous work is applied to the cemented mine backfill problem throughout this thesis. The next chapter will expand on this brief description and develop these ideas to form a unified framework to represent the individual mechanisms relevant to the cemented mine backfill deposition process. 2.21

48 Behaviour of Cementing Slurries CHAPTER 3 BEHAVIOUR OF CEMENTING SLURRIES 3.1 INTRODUCTION During the placement of mine backfill, the material initially behaves in accordance with the uncemented material characteristics, but as cement hydrates the behaviour of the material changes. Due to the increase in stiffness, reduction in permeability, and the self desiccation mechanism, the change in material behaviour can have a significant influence on the consolidation response. This chapter presents a description of the behaviour of a tailings material undergoing simultaneous consolidation and cementation, and develops equations to characterise this behaviour. These equations will form the basis of the numerical models presented later in the thesis. 3.2 STRENGTH AND STIFFNESS Terms A, D and E in the governing consolidation equation (Equation 2.3) are all influenced by the stiffness of the material. Therefore, it is important that an appropriate model be developed to represent the evolution of the material stiffness throughout the filling process. This model must take account of the response of the material prior to the formation of any cementation as well as the evolution of the material properties with time. Due to the interaction of filling and cement hydration, this model must be capable of representing the formation of cement bonds as well as the possible breakdown of these bonds as a result of stresses that exceed the current bond strength Uncemented material response As the eventual goal is to adopt the Structured Cam-Clay model to represent the behaviour of the material in a cemented state, a convenient method of representing the compression behaviour of the uncemented soil is through the Cam-Clay model. This relationship is represented by Equations 3.1 and 3.2. σ ( ) v i e = λ. ln σ v( i 1) (3.1) 3.1

49 Behaviour of Cementing Slurries σ v( e = κ. ln σ v( i i) 1) (3.2) where e is the change in void ratio in the current time increment, λ and κ are the conventional Cam-Clay parameters describing the gradient of the compression curve, and σ v(i-1) and σ v(i) are the vertical effective stresses at the start and end of the increment respectively. The normally consolidated relationship (Equation 3.1) applies to loading of the material on or above the uncemented compression line while the elastic compression relationship (Equation 3.2) applies for material undergoing compression at stress levels below the uncemented compression line (i.e. material that has been overconsolidated) Stress-strain behaviour of cemented fill To incorporate the effect of cementation on strength, a convenient starting point is the Structured Cam-Clay model developed by Liu and co-workers at Sydney University (Liu et al., 1998; Liu and Carter, 2002; and Carter and Liu, 2005). In this approach, structure (which could include cementation) has the effect of increasing the isotropic (or one-dimensional) compression yield stress in a manner analogous to overconsolidation. In the case of cemented mine backfill, the yield stress in compression is a function of void ratio and cementation, and consequently it changes with time as both of these change. A considerable extension to the Structured Cam- Clay model is required in this case, to deal with the combined effects of growth of structure (e.g. cement gel) as hydration occurs and damage to this structure due to possible yielding with increasing effective stress. The principle that has been adopted to determine the cement contribution to compression resistance follows the concept suggested by Rotta et al. (2003). Rotta et al. (2003) propose the concept of the incremental isotropic yield stress ( p y ) and define this as being the difference between the primary yield stress and the isotropic curing stress. The concept of incremental yield stress has been illustrated in Figure 3.1, which presents a plot of mean effective stress (p ) versus void ratio (e) for soil in uncemented and cemented states during isotropic compression. As mine backfill material is placed and consolidated along the normally consolidated line, it is assumed that the curing 3.2

50 Behaviour of Cementing Slurries stress can be appropriately represented by the yield stress of the material in an uncemented state. Therefore, the incremental yield stress is said to represent the difference between the yield stresses for the uncemented and cemented material. Rotta et al. (2003) suggested that p y is a measure of the bond strength, and Consoli et al. (2006) continued this concept to show that p y is proportional to the unconfined compressive strength (q u ). Given these findings, it is considered reasonable to assume that this proportionality would continue along the one-dimensional compression stress path. Therefore, the incremental one-dimensional vertical yield stress ( σ vy, the preconsolidation stress) for a cemented soil has been assumed to be adequately represented by the superposition of an uncemented and a cemented component (the p y contribution). Furthermore, based on the findings of Consoli et al. (2006) it has been assumed that σ vy can be linearly related to q u. During the mine backfill deposition process, previously placed fill is subjected to mechanical processes that cause changes to the one-dimensional yield stress ( σ vy ). These include: conventional soil hardening due to void ratio reduction (dh); increases in yield stress with time due to cementation (dhyd); a potential reduction in strength due to plastic deformation effectively, yielding of the cement bonds as compression occurs simultaneously with hydration (dd). These characteristics are accounted for by cumulating the changes in each of these individual characteristics over a particular timestep (dt): σ dt vy dh + dhyd dd = dt (3.3) Hardening Hardening in the model results from void ratio reduction as for conventional uncemented soil and also from the hydration process. 3.3

51 Behaviour of Cementing Slurries The conventional soil strain hardening term (dh) applies to an increase in the uncemented yield strength as a result of the compression of the soil matrix. This hardening is a function of the uncemented soil properties λ and Γ: Γ e dh = exp λ κ p (3.4) where λ and κ are as defined above (Equations 3.1 and 3.2), Γ corresponds to the void ratio on the normal consolidation line at a vertical effective stress of 1 kpa, and e p is the plastic change in void ratio. The additional, hardening (strength increase) that occurs due to hydration (dh yd ) is assumed to be a function of cement content, tailings density at the time of the hydration increment and the time from the start of hydration. It has been well documented (Leroueil and Vaughan, 1990; Consoli et al., 2000; Li and Aubertin, 2003; and Rotta et al., 2003) that an increase in either cement content or density increases the strength of a cemented soil. Rotta et al. (2003) developed an empirical equation to relate the incremental isotropic yield strength ( p y ) to both cement content and void ratio: p' y X.Cc + Y e = exp Z.Cc + W (3.5) where C c is cement content (weight of cement per unit weight of solids), e is void ratio and X, Y, Z and W are dimensionless constants and p y is in kpa. As it stands, this equation implies that there is some cement component of strength even when the cement content is zero. In order to ensure that there is zero cement component of strength at zero cement content, the Y constant has been replaced by a cement power term and the function adopted is shown in Equation 3.6. In addition, a constant multiplier A (with units of kpa) has been introduced. p' y = 0.1 X.C c + Cc e A.exp Z.Cc + W (3.6) Assuming that σ vy, q u and p y are all proportional (as discussed earlier), data on any of the stress paths may be used to derive the constant terms (X, Y, Z and W), and by adjusting the constant A (according to the ratio of proportionality between the various 3.4

52 Behaviour of Cementing Slurries cemented strength components) the cement component of strength along other stress paths may be determined. An example of this is given in Figures 3.2(a) and 3.2(b), which show how Equation 3.6 can be fitted to a series of unconfined compression test results on CSA hydraulic fill and Cannington mine paste fill data (Rankin, 2004), respectively. This indicates that Equation 3.6 can appropriately represent the development of cementation in a range of typical cemented mine backfill materials. For one-dimensional compression analysis the most direct method of determining all constants (A, X, W and Z) is through regression analysis on a series of one-dimensional compression tests. The maturity relationship adopted to represent the progress of hydration with time is an exponential relationship originally presented by Rastrup (1956) and republished by Illston (1979). This relationship is presented as: d m = exp * t (3.7) where m is the degree of maturity (0 at the start of the process, 1 at the end), d is a maturity constant (day -1/2 ), t * is the time (in days) since initial set. While it is acknowledged that Equation 3.7 is not dimensionally independent, to maintain consistency with previous work, the published form was preserved with t* always specified in units of days and d in terms of day 1/2. A series of unconfined compression tests was carried out at different stages of hydration to assess the development of this bond strength with time. Figure 3.3 shows q u (normalised by dividing by the maximum q u ) against the time in hours for both Cannington paste fill (PF) (Rankin, 2004) and CSA hydraulic fill (HF). Based on regression of the two data sets in Figure 3.3, maturity constants (d) of 0.9 day 1/2 and 2.6 day 1/2 provided a very close match to the hydraulic fill and the finer paste fill, respectively, with the duration until initial set (t o ) being 4 hours (0.16 days) in both cases. The maturity relationship (Equation 3.7) may be combined with the strength increment relationship (Equation 3.6) to determine the increment of bond strength (dhyd) over a given time interval ( t): 3.5

53 Behaviour of Cementing Slurries dhyd = exp d d exp * * t + t t 0. 1 X.C + c Cc e.a. exp Z.Cc + W (3.8) It should be noted that the change in bond strength is incremented in accordance with the material state at t *, the time at the start of that increment. This ensures that any strain hardening of the soil matrix is accounted for when evaluating hardening due to hydration over the next time increment Damage due to yielding during hydration (dd) As hydration may be occurring simultaneously with an increase in effectives stress (due to consolidation) the newly-forming structure may experience damage due to the evolving yield stress being exceeded. This damage may occur as a result of loading within the yield surface as well as loading on the yield surface (virgin yielding). The damage relationship adopted here follows the approach used in the Structured Cam- Clay model (Liu et al., 1998; Liu and Carter, 2002; and Carter and Liu, 2005). In this approach, incremental plastic volumetric strain induces damage, which is manifest as a reduction in the size of the yield surface. The function adopted to account for plastic volumetric strain in the model follows the work of Carter and Liu (2005) where the plastic component of strain may be represented by Equation 3.9. dε p v η = 1 Μ * α λ * * ( κ ) dpc + α b dpc (1 + e) p s 3 (3.9) where the asterix (*) indicates uncemented properties, η is the stress ratio (q/p ), M is the stress ratio at critical state, p c is the applied effective stress, b is a constant representing the structural breakdown, and α is a measure of the kinematic hardening given by: p c pu α = p s pu (3.10) where p u is the stress at which kinematic hardening or destruction occurs, and p s is the isotropic stress on the yield surface. 3.6

54 Behaviour of Cementing Slurries Given the plastic strain increment, the associated reduction in compressive yield strength may be determined as: ( 1+ e) b p s dεv p = s dd ln c p ( ) * * p o λ κ 1 + b ln s c p po (3.11) where c is the constant separating the limiting compression lines of the cemented and uncemented soils (for the very low cement contents commonly used in mine backfill this term is equal to zero), and p o is the stress required to place the uncemented soil in the same state on the normal consolidation line. While changes in Poisson s ratio (due to cementation) can modify the stress path in onedimensional compression, CeMinTaCo has been simplified by replacing all mean stress terms in Equations by vertical effective stress (σ v ), and setting the stress ratio term (η) to zero Unconfined compression strength (q u ) As explained earlier, it is assumed that the incremental one-dimensional yield stress is linearly related to q u. In this analysis, the total one-dimensional yield stress and the equivalent uncemented one-dimensional yield stress are monitored. By subtracting the latter from the former, and applying the constant of proportionality, q u is determined. This assumption has little impact on the overall consolidation behaviour. However, it is common to use q u when referring to material strengths in the mining industry therefore it is useful to gain an understanding of the impact of the various mechanisms on q u throughout the filling process Stiffness The previous section addressed the change in yield stress due to strain hardening, cement hydration and damage. As with strength, these characteristics also influence the material stiffness and in order to undertake consolidation analysis it is therefore essential to characterize any material stiffness changes that occur. In an approach similar to that used for strength, it is assumed that the stiffness of the cemented soil is a combination of the stiffness due to the uncemented soil skeleton and that due to the 3.7

55 Behaviour of Cementing Slurries cementation. The uncemented stiffness is determined in accordance with Equations 3.1 and 3.2, while the cemented component of stiffness is assumed to be proportional to the cemented component of strength ( σ vy, q u or p y ). A series of experiments was carried out to assess the validity of the assumption that the cement induced stiffness and cement induced strength could be linearly related. These experiments involved the measurement of small strain shear stiffness (G o ) using bender elements prior to unconfined compression testing of these specimens. Figure 3.4(a) shows the results of incremental shear stiffness (G o(inc) ) relative to q u for a variety of combinations of CSA hydraulic fill mixes. Figure 3.4(b) illustrates the relationship between q u and Young s Modulus for Cannington Paste fill as published by Rankin (2004). Figures 3.4(a) and 3.4(b) indicate that for a range of material strengths and material types there appears to be a linear correlation between the cement component of stiffness and cemented strength (q u ). Therefore, if σ' vy or q u are known, it is reasonable to assume that a constant of proportionality may be applied to calculate the cement component of the stiffness. These Young s modulus or shear modulus values can be converted to constrained modulus values using Poisson s ratio and these may be combined with the uncemented constrained modulus values to give total values of constrained modulus for every stage of hydration. Assuming that the strength and stiffness are proportional, it may be useful to utilise nondestructive stiffness measurement techniques such as bender elements (Baig et al., 1977) to assess the rate of cementation development with time. Experiments on CSA hydraulic fill indicate that the maturity factor (d in Equation 3.7) to represent the development of stiffness with time was 1.0 which is very close to that determined for the development of strength with time (0.9) Stress-strain behaviour: summary This section has presented the details of how the various constitutive aspects have been related in order to characterize the mechanical response of the cemented mine tailings during filling. Combining these aspects, the stiffness term in Equation 2.3 can be 3.8

56 Behaviour of Cementing Slurries determined as a function of material density (i.e. void ratio e), cement content (C c ), hydration duration (t) and effective stress (σ v) as illustrated in Equation δσ ' v = ' f ( e, Cc, t, σ v) δe (3.12) In order to demonstrate its applicability, the proposed constitutive relationship was used to simulate a series of one-dimensional compression experiments on cemented CSA hydraulic fill. In these experiments the specimens were prepared at different densities and allowed to cure for different periods of time prior to loading them in onedimensional compression. The material constants d, X, W and Z (from Equation 3.8) were determined from q u and bender element experiments. The parameters λ * and κ * (from Equation 3.9) were determined from one-dimensional compression tests on uncemented material and through modifying the terms A (from Equation 3.6) and b (from Equation 3.9 and 3.11) the one-dimensional compression response could be adequately represented. A comparison between the experimental results and the proposed model is presented in Figure 3.5. Note that different initial void ratios were used in the three tests, which explains why the 16-day result plots above the 5-day result, initially. Once the cementation bonds are broken, all three results tend to converge to the same compression line. Figure 3.5 indicates that, given suitable experimental results, the proposed constitutive relationship provides a good representation of the material behaviour when subject to curing, compression and cementation breakdown. 3.3 PERMEABILITY Term C in Equation 2.3 is highly dependent on the material permeability. This is the term that controls the rate water is expelled from the system. As a result, permeability can have a significant influence on the overall consolidation behaviour Uncemented permeability During the compression of a soil matrix, the void volume reduces, which can lead to a reduction in permeability. Carrier et al. (1983) developed a relationship that has been shown to provide a good representation of the relationship between void ratio and 3.9

57 Behaviour of Cementing Slurries permeability for mineral waste materials. This function was adopted for this study and is presented as equation 3.13 k ( e) d k ck = ( 1+ e) (3.13) where k is the permeability, e is the void ratio and c k and d k are constants Cemented permeability The hydration of cement is associated with a growth of cement products. These products are in the form of solid cement hydrates as well as cement gel. This product growth fills some of the void volume, which further reduces the permeability. Due to the relatively low permeability of the cement gel itself, it is suggested that in addition to the growth of cement solids the entire gel volume should be taken into account in determining the reduction in permeability. Powers and Brownyard (1947) suggest that when combined with water, the solids and gel volume created (after full hydration) are 80% greater than the initial unhydrated cement volume. In order to account for this characteristic, Equation 3.13 is modified to be in terms of effective void ratio (e eff ). The calculation of effective void ratio is based on the void space determined in the conventional manner as well as that calculated in accordance with the hydrating cement products. This concept is illustrated in Equations 3.14 and e eff = f ( e, C, t) c ( e ) d k ck eff k = ( 1+ e) (3.14) (3.15) The rate at which the growth of cement products takes place is simulated using the maturity relationship (Equation 3.7). A series of permeability experiments was conducted to assess the applicability of this relationship to cementing tailings. These tests were conducted in a permeability cell where the cell pressure was maintained at 520 kpa. The hydraulic gradient was established by setting the back pressure at the top of the sample to 510 kpa and that at 3.10

58 Behaviour of Cementing Slurries the base to 490 kpa. Testing at these elevated back pressures ensured full saturation throughout the test. As curing progressed, permeability measurements were taken at regular intervals. At the completion of the test, the sample dimensions were measured and, based on the initial dry weight, the void ratio could be calculated. The results of tests on cemented hydraulic fill with cement contents of 2%, 5% and 10% are presented in Figure 3.6, which shows the calculated effective void ratio against measured permeability for the different experiments, along with the model estimate. Figure 3.6 indicates that a reasonable fit to the measured data may be achieved using the proposed method. However, it is suggested that the constant terms (in Equation 3.15) representing compression and those representing cement growth may vary. Further work may be required to develop the understanding of the contribution of these two mechanisms to the reduction in permeability. 3.4 SELF DESICCATION The process known as self desiccation has been well documented with respect to its impact on concrete behaviour. The basis of this process is that following cement hydration, the resulting hydrated volume is less than the combined volume of the unhydrated constituents (cement and water). Researchers such as Powers and Brownyard (1947), Hua et al. (1995), Koenders and Van Breugel (1997), Bentz (1995) and Brouwers (2004) have investigated the impact of this mechanism on the shrinkage of conventional concrete. Most conventional concrete masses have lean (low) water contents and are placed in thin horizontal layers resulting in low total vertical stress. Therefore, the volume reduction of the cement/water constituents can result in development of negative pore pressure and desaturation of the mixture hence the term self desiccation. However, cemented mine backfills have much higher water contents (and lower cementwater ratios) than conventional concrete and can be subjected to high self-weight total stresses due to rapid rates of rise in typical stope-filling operations. In fine-grained (paste) fills, this can result in high positive pore pressures. As a result, the processes involved in self desiccation act, in these circumstances, to reduce the build-up of positive pore pressure rather than desaturating the material and creating negative pore pressures. Consequently there is no self desiccation per se. Thus, when reference is 3.11

59 Behaviour of Cementing Slurries made to self desiccation in this thesis, this refers to reduction in pore pressure resulting from cement hydration, rather than desaturation (desiccation) of the material. The term self desiccation has been used to preserve consistency with the mechanism of hydration-induced water volume reduction, rather than implying any actual drying out (desaturation). In saying this, given the appropriate conditions, this mechanism does have the potential to generate negative pore pressures and potentially desaturate the mass. The aims of the work described in this section are to show that the self-desiccation process can have a significant effect on the behaviour of the backfill (during the hydration process), to derive a model for describing the process and to devise a laboratory testing procedure to enable the model parameters to be determined for any fill/cement combination Cementation reactions The reactions associated with cement hydration involve the chemical combination of cement and water. If it is assumed that an enclosed volume of the soil-cement-water slurry prior to cement hydration contains a water volume of V w, and an unhydrated cement volume of V cu. After hydration, the hydrated cement volume is V ch, such that V ch V cu = V hyd. In this reaction, the increase V hyd is less than the volume of water used in hydration, V wh. In keeping with the terminology used in the concrete literature, this loss of volume is denoted V sh (the chemical shrinkage volume). For the purposes of the calculations that follow, the total water volume used in hydration (V wh ) can conveniently be thought of as being composed of two parts an amount converted directly into solid volume equal to V hyd, and a volume equal to V sh that is lost from the system as if removed via an internal water sink. V wh = V hyd + V sh (3.16) Thus, using this approach, V sh represents an apparent water volume lost from the system due to the hydration reaction, whereas V hyd represents water volume that is substituted by solid volume, and hence has no overall effect on total volume or water pressure. 3.12

60 Behaviour of Cementing Slurries All of this assumes that the soil voids can compress to accommodate the lost volume ( V sh ) in a completely unrestrained way, and V sh, when integrated over the total volume, would give the total shrinkage. This would be the case in a slurry where the soil matrix has zero stiffness, and the voids can compress without any change in effective stress or any change in the pressure in the remaining water. Thus, it is only in this case that V sh in Equation 3.16 represents the apparent unrestrained water volume lost via the internal sink, and, when integrated, gives the overall slurry shrinkage. Conversely, in the hypothetical case of a soil matrix with infinite stiffness (assuming a fully-saturated state and no inflow of water allowed), no overall volume change can occur, and the chemical shrinkage can only be accommodated by a volume expansion of the remaining water equal to V sh, leading to a drop in pore pressure equal to the bulk modulus of water multiplied by V sh /(V w V wh ). For the general case of a soil matrix of finite stiffness, some of the volume loss is accommodated by soil matrix compression (and hence some increase in effective stress), and some by expansion of the remaining water (and hence some reduction in pore pressure). This will be discussed further in the next section. It should be remembered that mine backfill slurries are fully saturated, typically with initial water content (mass of water per unit dry mass of soil) of 100% or greater, and cement content (mass of cement per unit dry mass of soil) typically 2 5%. Therefore, the water-cement ratio is much greater than for conventional concrete (for 100% water content, and 2% and 5% cement content, the water-cement ratio would be 50 and 20, respectively, in mass terms, corresponding to about 160 and 62, respectively, in volume terms). Thus, the actual volume of water involved in hydration is relatively small, and hence volumetric strains in the water can be calculated relative to the original total volume of water (V w ), rather than the final volume (V w V wh ). In fact, in the numerical implementation of the equations, all calculations are performed in incremental fashion, so that volumes are continually updated, and strains are therefore calculated using the appropriate water volume. It should also be noted that, following the convention used in soil mechanics, compressive stresses and strains are considered positive, while tensile stresses and strains are considered negative. Thus, volume reduction is considered positive (and hence chemical shrinkage V sh is positive). 3.13

61 Behaviour of Cementing Slurries Powers and Brownyard (1947) found experimentally that, for a fully hydrated system, V sh for a cement paste could be related to the mass of chemically-combined water (W n ) through Equation 3.17: V sh = W n (3.17) where V sh is the volume reduction in cm 3 and W n is in gram (and thus the constant has units of cm 3 /g). From a series of laboratory experiments, they found that W n could be related to the proportion of the compounds that make up the cement product and the mass of unhydrated cement (W c ) in accordance with Equation W n /W c = 0.187X 3 C S X 2 C S X 3 C A X 4 C AF (3.18) where X is the proportion by mass of the subscript compound in the cement. For the proportions contained in most General Portland cements, they established empirically that the W n can be approximately related to W c via Equation 3.19: W n /W c = 0.23 (3.19) Combining Equations 3.17 and 3.19 allows the shrinkage volume (in cm 3 ) that would occur in a General Portland cement paste over the full hydration period to be determined. This relationship is shown in Equation 3.20 as a function of the original mass (in g) of cement: V sh = W c (3.20) Impact on pore pressure As mentioned above, the apparent unrestrained volume change in the water resulting from hydration ( V sh ) could occur under undrained conditions only if the soil skeleton were of zero stiffness, and this volume change would result in an equal compression of the soil skeleton. To calculate the actual volume changes and pore pressure changes, it is necessary to consider the water and soil matrix stiffnesses, and use principles of strain compatibility and stress equilibrium to calculate the actual behaviour. The change in pore pressure is a function of the difference between the shrinkage volume ( V sh ), as defined in Equation 3.16, and the actual reduction in void volume 3.14

62 Behaviour of Cementing Slurries ( V v ) resulting from soil matrix compression. The difference between these two volumes is denoted V rel : V rel = V v V sh (3.21) Effectively, strain compatibility requires that the water must expand by V rel to accommodate the fact that the actual void volume reduction V v is less than V sh (and hence V rel as defined by Equation 3.21 is negative, signifying expansion). Initially, when the soil matrix has a very low stiffness, the void volume reduction ( V v ) is close to V sh, and hence there is very little pore pressure change. However, in the case of soil containing cement, an increase in stiffness comes about not just as a result of ongoing compression, as with uncemented soils, but also due to the formation of cement bonds so that as hydration proceeds the pore pressure reduction can be quite substantial. A major difference between self desiccation and evaporative desiccation is that, with evaporation, the water sink is at the (top) boundary, which sets up internal hydraulic gradients to feed water to the evaporation process. However, in the hydration process, internal sinks are set up within every pore throughout the material. Therefore the mechanism is purely intrinsic and the incremental reduction in pore pressure is dependent on the hydration time and not on any length scale in the problem Analytical model An analysis relating fundamental material properties to the reduction in pore pressure is discussed below. The analysis assumes that: the material is in an undrained state (with respect to water flows across the external boundary); the soil compressibility is linear, corresponding to the current small-strain bulk modulus, at any stage of hydration (though changing with ongoing hydration); soil particles are incompressible; the water bulk modulus (K w ) is constant; the material is fully saturated at all stages of the process; and 3.15

63 Behaviour of Cementing Slurries the water density is independent of pressure. In the experimental work described later, full saturation at all stages has been assured by using high initial back pressure, such that positive pore pressure exists at all stages, even following the pore pressure reduction resulting from the hydration process. Equilibrium of the pore water system requires: u = εv. Kw = Vrel Vw Kw (3.22) where u is the change in pore pressure in the current increment, ε v is the increment of volumetric strain in the water required to maintain strain compatibility with the soil skeleton, K w is the bulk modulus of the water, V rel is the relative pore volume reduction (as defined by Equation 3.21), and V w is the total volume of the pore water. Since V rel is negative (expansion), both ε v (expansion) and u (pore pressure reduction) are also negative. The change in soil bulk volume is proportional to the change in effective stress. With a constant total stress, the change in effective stress ( σ ) is equal in magnitude and opposite in sign to the change in pore pressure: σ = u (3.23) The incremental volumetric strain in the soil matrix ( ε v-soil ) is a function of the change in effective stress ( σ ) as well as the bulk modulus of the soil matrix (K s ): V v ε σ v soil = = VT K (3.24) s where V T is the total volume of the combined soil and water (bulk volume) and V v is the actual change in the void volume due to compression (which is identical to the change in the bulk volume V T, since the soil particles are taken to be incompressible). Combining the behaviour of the pore water (Equation 3.22) with the behaviour of the soil matrix (Equation 3.24) via Equation 3.23 gives: V v. VT K s = V V rel. w K w (3.25) 3.16

64 Behaviour of Cementing Slurries Equation 3.21 may then be substituted into Equation 3.25 to derive a relationship between the actual incremental contraction of the pore volume ( V v ) and the chemical shrinkage volume ( V sh ): Vv = Vsh. Kw Vw Ks K + w VT Vw (3.26) which indicates, as expected, that V v = V sh when K s = 0. By combining Equations 3.26, 3.24 and 3.23 and rearranging, a relationship can be obtained between the incremental change in pore pressure ( u), the bulk stiffnesses of the soil (K s ) and water (K w ), the porosity of the material (a function of V w and V T ) and the incremental change in volume associated with the hydration reaction ( V w ): Vsh KwKs Vsh K u =. =. w Vw. VT Ks Kw VT ( n + Kw Ks ) (3.27) + VT V w This gives u 0 as K s 0, and u K w { V sh /(n.v T )} as K s, as expected Experimental demonstration of effect of self desiccation A series of preliminary tests was carried out to demonstrate the validity and relevance of the self-desiccation concept as applied to cemented tailings backfill. These experiments used a silty silica sand hydraulic fill (HF) from the CSA mine and a silt-sized paste fill (PF) from Kanowna Belle (KB) mine. These materials were mixed with 5% General Portland cement from the Kandos Cement Plant (Kandos, NSW, Australia) and Cockburn Cement (Perth, WA, Australia), respectively. In this thesis, the cement content is defined as the mass of dry cement divided by the total dry mass of solids. Particle size distribution curves for the two tailings materials are presented in Figure 3.7. The specific gravity (G s ) of CSA material is 2.81 while that for the KB material is The tests were carried out on samples set up in a triaxial cell in the conventional manner. The specimens were prepared using the dry sand preparation technique explained by Ismail et al. (2000). This technique involves preparing the specimens dry 3.17

65 Behaviour of Cementing Slurries before purging with CO 2 and back-pressure saturating the samples. While this sample preparation technique does not represent the mine filling process, the technique was adopted to ensure consistency between samples. Both samples were prepared at a void ratio of After saturation in the triaxial cell, the cell pressure was increased to 550 kpa and the back pressure to 500 kpa. The purpose of the high back pressure was to ensure positive pore pressure and full saturation throughout the test, given the large pore pressure reductions expected from the self-desiccation process. For both tests, the Skempton B-value was checked and found to be greater than At this point, the back pressure valve was closed and the pore pressure was monitored with time. The results of the tests are presented in Figure 3.8, which shows the applied total stress, the pore pressure and the effective stress, plotted against time from the start of the test. As may be seen in Figure 3.8, even with cement content as low as 5%, the hydration process creates a significant reduction in pore pressure, with both material types. With a constant total stress, this pore pressure reduction is associated with an effective stress increase of equal magnitude. The figure shows that the rate and final amount of pore pressure reduction for the CSA HF specimen are significantly greater than for the finer KB PF specimen. Consequently the impact of the self-desiccation process depends on material type, as well as other factors discussed below. These tests provide a graphic illustration of the changes in pore pressure that result from the cement hydration process and the resulting change in effective stress, even where the samples are subjected to undrained boundary conditions. Therefore, it is apparent that this self-desiccation phenomenon needs to be considered when analysing the behaviour of cemented mine backfill, particularly where filling rates are rapid and finegrained (i.e. low permeability) tailings are used, resulting in the hydration process occurring under undrained conditions Material properties influencing self desiccation Equation 3.27 indicates that the reduction of excess pore pressure is sensitive to the water and soil bulk moduli (K s and K w ) as well as to the rate of water consumption and the total volume of water consumed during the hydration process. 3.18

66 Behaviour of Cementing Slurries Material stiffness Due to the growth and strengthening of hydrates, the soil matrix undergoes an increase in stiffness during hydration. A non-destructive test that is often used in soil mechanics to monitor the small strain shear stiffness (G max, also called G o ) of a soil matrix involves the measurement of shear wave velocity (Dyvik and Olsen, 1989, Baig et al. 1997, Fernandez and Santamarina, 2001). This technique consists of generating a shear wave pulse at one end of a sample using a piezoceramic bender element, and measuring the arrival time at the opposite end of the sample using a second bender element. Figure 3.9 shows an example of the data from one of the tests carried out in this study. In this case, the transmitting bender element is excited by a single sine wave pulse, nominally of 10 V amplitude, and the arrival of this shear wave at the other end of the sample is picked up by the receiver bender element. Based on the time of transmission and the length of the sample, the shear wave velocity (V s ) can be obtained. From this value of V s and the bulk density of the material (ρ), the value of G max may be inferred using Equation G max = ρv. 2 s (3.28) This test can be carried out at intervals during the hydration process to monitor the development of the shear modulus with time. The corresponding small strain effective bulk modulus K max can be related to G max via the Poisson s ratio (ν): 2( 1+ ν Kmax = G max 3 ( 1 2ν )) (3.29) In this paper, this value of K max is assumed to be equivalent to the soil matrix stiffness K s mentioned earlier (e.g. Equation 3.24), which is equivalent to assuming that soil matrix stiffness is linear over the range of strain relevant to this work. Santamarina et al. (2001) and Jamiolkowski et al. (1994) suggest that a small strain drained Poisson s ratio of 0.1 to 0.15 is appropriate for many soils, and thus, for the interpretation of the results in this paper, a small strain Poisson s ratio of has been adopted. It should be noted that varying the Poisson s ratio over this range has minimal impact on the results. 3.19

67 Behaviour of Cementing Slurries At the University of Western Australia, bender elements are fitted as standard in triaxial setups, allowing shear wave velocity (and hence G max ) to be determined routinely. Measuring the compression wave velocity V p (and the equivalent E max ) could also be used to indicate the progress of hydration, but doing so in the triaxial apparatus was not possible with the equipment available. Water consumption during hydration The process that determines the rate at which pore water volume is consumed is very complex and is made particularly difficult to quantify theoretically due to: the hydration of cement involving at least 8 different chemical reactions; each reaction consuming different volumes of water; each reaction producing a different hydrate volume; each reaction commencing at a different time after the start of hydration; each reaction occurring at a different rate; only cement surfaces exposed to pore water reacting; the cement being made up of different proportions of each constituent; the reactions being dictated by the random collision of various cement constituents; not all of the total cement content in the mix may react. Cement technology researchers have developed detailed microscopic models to predict this process for the purpose of concrete shrinkage predictions (Bentz, 1995). These are complex models that involve the input of many fundamental cement properties, and further discussion of them is beyond the scope of this work. The other complicating factor associated specifically with mine backfill is that in addition to different cement types, different tailings mineralogy and chemicals contained in the tailings after processing may have an impact on the chemical reactions that take place. Therefore, it is suggested that the most practical method of determining the net volumetric change and the rate at which this change occurs is through direct experiment with each cement/tailings combination. Furthermore, it is suggested that 3.20

68 Behaviour of Cementing Slurries rather than adopting the total volume change (6.4% of the unhydrated cement weight, Equation 3.20) as determined by Powers and Brownyard (1947), the volume change should be defined as a variable (E h ) for each particular cement/tailings combination. Therefore, Equation 3.20 is re-written as Equation 3.30, where E h is defined as the total volumetric change V sh per unit mass of cement W c : V sh = E h. W c (3.30) Experimental derivation of parameters By measuring the incremental pore pressure reduction and monitoring the material stiffness, the rate of water volume consumption may be back-calculated using the proposed analytical solution (Equation 3.27). The rate of hydration (d in Equation 3.7) and hydration efficiency (E h ) are considered fundamental material properties. Therefore, once determined, these parameters may be incorporated into a coupled analysis model to account for the impact of this mechanism on the consolidation and filling process. Experimental procedure A series of pore pressure reduction experiments was carried out to verify the proposed theory, provide examples of how the experimental process may be conducted and demonstrate how the relevant material parameters may be derived. The material used in these experiments was again silty sand (hydraulic fill) from the CSA mine and silt (paste fill) from Kanowna Belle. These materials were mixed with General Portland cement from the Kandos Cement Plant (Kandos, NSW, Australia) and the Cockburn Cement Company (Perth, WA, Australia), respectively, in various proportions. The experiments were conducted in a triaxial cell, with the specimens being prepared using the dry sand preparation technique explained by Ismail et al. (2000). During saturation, the amount of water added to the system was measured (as this would be the volume of water subject to the volumetric changes). As was shown in a previous section, (Figure 3.8) the hydration process results in a reduction in water volume, which leads to a reduction in pore pressure and a corresponding increase in effective confining stress. This increase in effective stress could lead to yielding of the hydrating matrix, which could invalidate the assumption that the small strain stiffness K max is the relevant bulk stiffness K s for the soil. Also, 3.21

69 Behaviour of Cementing Slurries depending on the initial back pressure, the reduction in pore pressure could lead to air coming out of solution, thereby changing the bulk modulus of the pore fluid. To avoid any of these potential problems associated with a decreasing pore pressure, the back pressure and cell pressure were initially set at values well above those recommended by Bishop and Henkel (1962) for complete saturation. To avoid the possibility of yielding due to increasing effective stress, the effective stress was kept low by regularly restoring the back pressure to its original value by opening the drainage valve at various stages during the test. This restoration of back pressure means that, strictly speaking, the experiment was not conducted under undrained conditions, but since the material properties are only determined during the undrained stages (i.e. while the back pressure valves are closed) the application of Equation 3.27 remains valid. At different stages during the tests, shear wave velocity measurements were made, using bender elements, to monitor the evolution of stiffness (G max ) with time. Figure 3.10 presents the results of one of the tests on the CSA HF (hydraulic fill) material. This shows the actual pore pressure behaviour i.e. reduction in pore pressure while the drainage valve was shut, followed by restoration of the initial back pressure in the brief intervals when the valve was opened. From this, the cumulative pore pressure change was determined to be of the order of 800 kpa for this test. The actual effective stresses during the test are also shown, with the procedure adopted limiting the effective stress to a maximum of less than 200 kpa. An identical test on an uncemented specimen was carried out prior to those on the cemented specimens to assess the compliance of the system. The system indicated a pore pressure change of less than 5 kpa for the uncemented specimen over a 3 day period, indicating that the system was free of any leaks. Stiffness development From the measurements of G max made as hydration proceeded, Equation 3.29 was used with a Poisson s ratio of to determine the soil matrix small strain bulk modulus K max, which was taken to be equivalent to K s. Figure 3.11 shows how this calculated value of K s increased with time during the various experiments. 3.22

70 Behaviour of Cementing Slurries The curves shown fitted to the data in Figure 3.11 are based on the exponential maturity relationship (for cement hydration) published in Illston et al. (1979). For this application, this relationship takes the form: d K s = K s i + K s f.exp * (3.31) t where K s-i is the initial bulk modulus and K s-f is the increase in bulk modulus at the completion of the hydration period, d is a maturity constant, and t * is the time since the commencement of hydration. The curves in Figure 3.11 were obtained using d = 0.9 day 1/2 with all cement contents. The time until initial set was found to be reasonably consistent at about 4 hours for all these tests. Pore pressure reduction The test procedure used in these tests involved opening the drainage valve at regular intervals during the test, thereby re-applying the initial back pressure. The data from pore pressure reduction in the undrained phases that followed each of these reapplications of back pressure can be combined to form a continuous pore pressure reduction curve for each test, as shown in Figure By dividing the pore pressure reduction into one-hour increments, the incremental rate of pore pressure reduction was determined for the duration of the test. Figure 3.12 shows this incremental reduction rate plotted against time for the CSA hydraulic fill material with different cement contents. While there is some fluctuation in the pore pressure measurements, it can be seen that the rate of reduction diminishes with time over the duration of the test (from the start of initial set). Figure 3.12 also indicates that the rate of pore pressure reduction increases with an increase in cement content. It should be noted that the pore pressure fluctuation is temperature sensitive (fluctuating on a 24 hour cycle), suggesting that these tests should have been conducted in a temperature-controlled environment. Pore water volume decrease In order to incorporate the self-desiccation mechanism into a finite element (or other numerical) computer code, the incremental water volume change with time is required. By substituting the instantaneous bulk modulus and the pore pressure reduction over a 3.23

71 Behaviour of Cementing Slurries given time period into the analytical solution (Equation 3.27) and rearranging, the pore water volume change over that given time period may be back calculated. Direct measurement of water volume consumption was also attempted in these experiments. However, the volume measuring system used proved to have insufficient resolution and accuracy, given that the volumes involved were of the order of tenths of a cm 3 per day. An improved system of volume-change measurement is a priority for inclusion in future experiments. After calculating the rate of water volume change throughout the experiment as described above, the results can be divided by the relevant cement mass to determine a rate of volume change per unit mass of cement. The results of this analysis are presented in Figure 3.13 as the rate of water volume consumption per unit mass cement ( V w /W c ) plotted against time for tests with three different cement contents. The maturity model presented in Illston et al. (1979) was combined with Equation 3.30 (for total water consumption) to estimate the total water volume change after a given hydration time (t). This relationship has been differentiated and divided by the mass of unhydrated cement (W c ) to derive a function for the rate of volume change per unit mass of cement. This function is presented as Equation 3.32: δ ( V W ) δ( V W ) w δt c = sh δt c = 1 2 Eh. d ( t *) 1.5 d.exp t * (3.32) The same maturity constant (d = 0.9 day 1/2 ) as that found for the rate of stiffness development was substituted into Equation 3.32, and the efficiency term (E h ) was adjusted to achieve the best fit to the experimental data, resulting in a best-fit value of E h = cm 3 /g. The derived curve is compared with the experimental data in Figure In this case, the fit was obtained by taking t as applying from the start of the test, rather than the initial set; slightly different parameters would be obtained if the latter had been used. Cumulative pore pressure reduction Combining the experimentally derived terms for hydration efficiency (E h = cm 3 /g) with the maturity constant (d), the rate of pore pressure change can be determined. This rate may be integrated over a given time period to predict the 3.24

72 Behaviour of Cementing Slurries cumulative pore pressure drop. The experimental results are compared with the analytical solution in Figure 3.14 for CSA material, with d = 0.9 day 0.5 and E h = cm 3 /g. Figure 3.14 indicates that the predicted pore pressure reduction due to cementation can be estimated accurately using the proposed analytical solution with appropriate values of d and E h. The values of d and E h have been shown to be unique for a given cement/tailings combination over the range of typical cement contents. The value of E h determined for the CSA fill (0.035 cm 3 /g) is somewhat less than the value of cm 3 /g suggested by Powers and Brownyard (1947) for cement paste. Kanowna Belle paste fill experiments Experiments were carried out using silt sized Paste backfill material from the Kanowna Belle (KB) mine (with cement contents of 2% and 5%) to assess the applicability of the proposed approach to a different type of minefill. The experimental technique used was identical to that described for the CSA test work. From the results of these experiments, values of d and E h of 2.5 day 1/2 and cm 3 /g, respectively, were determined. These values were substituted into Equations 3.31 and 3.32 before combining them in Equation 3.27 to predict the cumulative drop in pore pressure with time and this prediction is compared with experimental results in Figure It can be seen that the analytical solution compares well with the experimental results in this figure. It should be noted that, again, the maturity constant (d) representing the rate of hydration appears similar for both the rate of pore water volume consumption as well as the development of shear stiffness with time. For the KB Paste backfill the E h term of cm 3 /g corresponds closely to the value of cm 3 /g suggested by Powers and Brownyard (1947) for cement paste, whereas a significantly lower value (0.035 cm 3 /g) appears relevant for the CSA hydraulic fill. 3.5 TEMPERATURE As cement hydration is an exothermic reaction, in a bulk filling situation hydration of cemented mine backfill can lead to temperature increases. However, as cement contents in minefill are often very low, temperatures typically range from 20 30ºC in a typical cemented mine backfill situation. Temperature increases greater than 5ºC act to reduce the water density, increasing the water volume. This was taken into consideration, as a 3.25

73 Behaviour of Cementing Slurries volume increase has the potential to negate volumetric reductions from self desiccation. Assessment of the magnitude of volumetric change over this range indicates the potential for a maximum 0.1% increase in water volume throughout a typical filling period. In comparison with volumetric changes associated with the self desiccation process, this change was shown to be a second order influence and was therefore not addressed in this thesis. Turcry et al. (2002) demonstrated that thermal volumetric changes can simply be superimposed onto chemical volumetric changes to achieve a net volumetric change. Therefore, to incorporate temperature variation into the analysis of the influences of any volumetric changes, it could simply be incorporated as an independent mechanism in the analysis. Temperature variations also have the potential to influence the rate of hydration. Therefore, rather than superimposing the influence of temperature changes at the analysis stage, consideration was given to incorporating the influence of temperature in the experimental process. This work is ongoing, but to investigate the appropriateness of carrying out the hydration test with an insulated specimen a numerical analysis was carried out to assess the appropriateness of a fully insulated assumption in a typical mine backfill scenario. This study utilised the numerical code Temp/W 1 to assess the likelihood of heat transfer to the surrounding rockmass in a typical mine backfill scenario. The analysis involved establishing an initial temperature of 30ºC throughout a 10 m wide, 40 m tall plane-strain stope with a boundary condition of 20ºC. The material properties adopted included a thermal conductivity of 1 J/s/m/ K and a heat capacity of 3 MJ/m 3 / K, which are considered suitable for a saturated soil at a void ratio of 1.0. Figure 3.16 presents the calculated temperature profile laterally across the analysed half-space after 20 days (a typical filling period). The results indicate that only the outer 1 m of the fill mass is significantly influenced by the heat exchange at the fill-rockmass boundary, and the majority of the material remains in an insulated state. Based on this 1 Temp/W is a part of the GeoStudio suite of programs from Geo-Slope International Ltd, Calgary, Alberta, Canada,

74 Behaviour of Cementing Slurries result, it may be more appropriate to undertake hydration testwork (as discussed in Section 3.6) in a fully insulated environment, which would address both water volumetric changes (through a modified E h in Equation 3.32) and the influence of temperature on hydration rate (through a modified d term in Equation 3.7). 3.6 MATERIAL CHARACTERISATION TECHNIQUE This chapter has addressed details of the mechanisms that are considered to be relevant to the deposition and consolidation of cemented mine backfill. Being a complicated interaction of different mechanisms, it is important to characterise the influence of different materials on each of these mechanisms via fundamental material properties. Keeping in mind the properties required, an experimental technique was devised to capture most of the important material properties. This technique generally only requires a hydration test, a triaxial test, and a Rowe cell test. The hydration test is similar to that described in Section Using the technique described an understanding of the development of small-strain stiffness against time as well as the self-desiccation characteristics can be obtained. In addition, a hydraulic gradient can be established across the sample, at any time during hydration, to measure the permeability of the material and assess how this changes with cement hydration. Figure 3.17 presents an illustration of the experimental setup for a hydration test. The hydration test can be combined with a conventional consolidated drained triaxial test to determine the shear strength parameters such as cement induced bond strength and frictional characteristics. If equipped with a local strain measurement system, it is possible to use this experiment to determine non-linear elastic stiffness parameters and, if the sample is strained to sufficient levels, the rate of cementation breakdown with plastic strain can also be determined. Finally one-dimensional compression (or Rowe cell) testing can be used to define the stiffness and permeability characteristics during the compression of the material in either a cemented or uncemented state. 3.27

75 Behaviour of Cementing Slurries 3.7 CONCLUSION Background citations and experimental data have been presented to demonstrate the mechanisms and material models that are used throughout this thesis. In addition, experimental techniques have been presented for determining material properties that are considered to most significantly influence the cemented mine backfill deposition process. With this basis of understanding, the remainder of this thesis is focused on the combination of these mechanisms and how they influence the overall filling behaviour. 3.28

76 One-dimensional Consolidation Modelling CHAPTER 4 ONE-DIMENSIONAL CONSOLIDATION MODELLING 4.1 INTRODUCTION In Chapter 2, Gibson s governing equations for one-dimensional consolidation were introduced and the influence of cement hydration on these equations was discussed. In Chapter 3, a description of the different processes that are expected to occur during filling with cemented mine backfill was presented, and equations to describe these processes were developed. This chapter is focused on incorporating these mechanisms into Gibson s one-dimensional consolidation equations. These modified equations are then solved using a modified version of the one-dimensional finite element tailings consolidation program MinTaCo. This program has been renamed CeMinTaCo, and is used in a sensitivity study to demonstrate the interaction of the different consolidation mechanisms. 4.2 MODEL DEVELOPMENT Modelling the behaviour of uncemented tailings: the MinTaCo Program In previous work carried out some 10 years ago at UWA by others, a finite element program was developed to model the consolidation and evaporation behaviour of mine tailings, within the context of conventional tailings deposition in above-ground tailings storage facilities (TSFs). This program, named MinTaCo (Mine Tailings Consolidation) forms the basis of the new program. The new program has been named CeMinTaCo, to indicate it deals with cemented mine tailings consolidation. A full description of the MinTaCo model is provided by Seneviratne et al. (1996), and a summary of some of its features that are relevant to cemented backfill is provided in the following section: MinTaCo is a one-dimensional model, which uses a large-strain formulation with Lagrangian coordinates and Gibson s consolidation equations (Gibson 1967) to deal with the large volume changes. The form of the Gibson consolidation equation was presented as Equation 2.2: 4.1

77 One-dimensional Consolidation Modelling δu δσ ( ) v δ k 1+ eo δu δk δσv + 1+ eo { t e a + = δ w 1 e a δ 43 δ γ + δ δa { δt ( A) ( D) ( B) ( C) (2.2bis) where a is a Lagrangian coordinate, u is pore pressure, k is hydraulic conductivity (permeability), σ' v and σ v are the vertical effective and total stresses, respectively. In this equation, term A is the rate of change in pore pressure as a result of a rate of application of total stress (term B), term C is the volumetric strain, which is dictated by the hydraulic conductivity (k) of the material, and term D is the current stiffness of the material. As with tailings placed into surface TSFs, paste fill placed underground may undergo large settlements as it drains and consolidates. Incorporating a large strain formulation into the model was regarded as important. MinTaCo provided this. Fresh tailings slurry can be added at any desired rate, and this rate can be changed at any stage during filling. Details of this aspect can be found in Toh (1992) and Seneviratne et al (1996). The properties of the fresh layers can be different from preceding layers. The settled density of the material is taken as the starting point for consolidation. Thus if very wet (low solids content) slurry were used, the model is able to account for the generation of bleed water and update the initial void ratio of the fill to account for this. The base of the storage area can be perfectly permeable, perfectly impermeable, or any state in between. The input data required to run the program are: the material parameters; the filling schedule and the drainage conditions. The material parameters are: The specific gravity G s of the tailings material. The initial settled density of the tailings. The k e (permeability void ratio) and e σ' v (void ratio effective stress) relationships, which are generally very non-linear, are expressed using power functions suggested by Carrier (1983): 4.2

78 One-dimensional Consolidation Modelling e = a c ( σ v ) dk ( e) ck k = 1+ e bc (4.1) where a c, b c represent soil compression constants and c k, d k represent permeability constants. The large volume changes that occur during paste fill consolidation referred to earlier mean that large void ratio changes occur and it is essential to account for the effects of these changes on parameters such as permeability. The air entry suction value the point where desaturation starts to occur during drying. This allows an important feature of a consolidating fill mass, development of a partially saturated matrix, to be accounted for. Estimates of shear strength and its variation with time may be made using the Cam Clay model, so that values of the Cam Clay parameters (λ, κ, M, Γ) are required for the material. Drainage occurs in the vertical direction only (upwards or downwards, depending on hydraulic gradient), and strains are vertical only. The MinTaCo program has been used extensively for modelling a wide variety of tailings filling operations. Some examples of its application may be found in Fahey and Newson (1997) and Fahey et al. (2002) Modelling the behaviour of cemented tailings: the CeMinTaCo Program Section 2.2 showed that regardless of the ultimate cured strength, the loads applied to (backfill) barricades during the filling process are highly dependent on the degree of consolidation. Furthermore, it was demonstrated that in an uncemented state, very little consolidation is likely to occur in paste fill during a typical filling sequence. As a result, barricade stresses are more appropriately calculated assuming undrained conditions. However, as discussed in Chapter 3, the addition of cement to backfill complicates the rate of pore pressure change and in most cases where paste fill is used, the behaviour is likely to be neither fully drained or fully undrained, but somewhere in between. Use of a model such as that described in this thesis makes it possible to determine where a particular fill is located between these two extremes. 4.3

79 One-dimensional Consolidation Modelling Because it provides full coupling between filling rates, boundary drainage, and stiffness and permeability changes within the tailings, the MinTaCo program appeared to provide the ideal basis for the development of a program to model the consolidation behaviour of backfill. However, to be of general application to the backfilling problem, additional features were required, relating particularly to the effect of adding cement in various quantities to the tailings. During the consolidation of uncemented mine tailings from an initial slurry state, the material behaviour that is most important are the changes in soil stiffness and permeability that occur due to the reduction in void ratio as consolidation progresses. The rate of increase of the fill stiffness is important as it governs, inter alia, the amount of stress transfer due to arching that can occur. In the case of cemented mine backfill, a number of other mechanisms associated with cement hydration are introduced, which also need to be addressed during modelling. These include: the development of an appropriate material stiffness that takes account of soil volumetric changes, cement hydration and damage that may occur to cement bonds during the filling process (and thus, changes are required in term D of Equation 2.2); changes in permeability, not only with changes in void ratio, but also with the growth of cement gel in the voids (and thus, changes are required in term C in Equation 2.2); self desiccation of the hydrating cement paste the water volume changes that occur due to chemical reaction in the hydration process (an additional term in Equation 2.2); the large increase in stiffness of the cementing soil matrix, leading to the matrix bulk stiffness being comparable to that of water, which must be taken into account in estimating pore pressure changes due to increases in total vertical stress. (and hence changes are required in term A in Equation 2.2); as shown by Black and Lee (1973), when the stiffness of a soil matrix becomes similar to that of water, the change in pore pressure due to load application cannot be 4.4

80 One-dimensional Consolidation Modelling estimated using conventional approaches but must account for the relative stiffnesses CeMinTaCo governing equations The following section provides the derivation of the governing equations for the large strain consolidation of a cementing soil. The description provided follows that of Gibson et al. (1981), but these equations are modified to take into account the influence of cement hydration. In the derivation, convective forces are ignored and the motion of pore fluid relative to the solids is assumed to be governed by Darcy s law. For this analysis, an updated Lagrangian coordinate system is adopted. Figure 4.1 presents the definition of this coordinate system over a consolidation timestep t to t+ t. With reference to Figure 4.1, a is the original element height, x is the equivalent height of soil solids, and ξ is the real coordinate system, which is required for the calculation of hydraulic gradients. These terms can be related through: da dx = (1 + e dξ = ) (1 e) o + (4.2) As illustrated in Figure 4.2, the weight of fluid flow out of an element of thickness δ a is given by: a [ nγ ( ν ν )] δa w w s (4.3) where n is the porosity, ν w is the velocity of water ν s is the velocity of soil and γ w is the unit weight of water. The change in water volume in an element of height δ a as a result of self desiccation over time ( t ) is be given by: where ( Vsh desiccation. a V 1 (4.4) sh ( + e ) t 0 ) is the change in volume per bulk unit volume of solids as a result of self 4.5

81 One-dimensional Consolidation Modelling Assuming the water volume is independent of the water pressure, Equations 4.3 and 4.4 can be combined to determine a relationship between the change in stored water in an element of height a with time ( ( + e ) V f t ). a V V sh f + [ nγw( νw νs )] δa = 1 t a t (4.5) 0 Assuming laminar flow conditions, the fluid velocity ( ν w ( ν s ) can be determined using Darcy s law, which is defined as: ) relative to the soil velocity n ( v v ) = w s k γ w u ξ ex (4.6) where ( ν w ν s coefficient of permeability and ) is the relative velocity between the soil and the fluid, k is the u ex ξ is the excess pore pressure gradient. Combining Darcy s law with the coordinate transformation relationship (Equation 4.2) Equation 4.5 becomes: a V sh k 1+ e u + 0 ex w V a = ( 1+ e ) t a γ 1+ e a t 0 f (4.7) In most, if not all, stopes free-draining barricades are constructed at the base. This free draining condition acts as a base drain and draws down the phreatic surface. The gradual drawdown of the phreatic surface combined with the accretion of overlying material makes the it difficult to define excess pore pressures. Due to these reasons, it is inconvenient to undertake calculations in terms of excess pore pressures and it is more suitable to perform calculations in terms of total pore pressure (u). When converting from u ex to u Equation 4.7 becomes: a V sh k + w 1+ e u 1+ e + γ o V a = w ( 1+ e ) t a γ 1+ e a 1+ e t 0 0 f (4.8) In conventional soil mechanics, it is common to assume that the stiffness of the water phase is significantly greater than that of the soil skeleton and as a result the volumetric 4.6

82 One-dimensional Consolidation Modelling soil compression is considered to be equal to removed water. However, in the case of cementing soil, the soil stiffness may be comparable to that of water. In order to take account of the relative stiffness between the soil and water phases, Hooke s law can be applied to the water phase to derive pore pressure changes. If the soil particles are assumed to be incompressible, this may be written as: u t = t V V f f V t V f s K w V + = a t e a t e f ( 1+ e0 ) Vs (1 e0 ) K w (4.9) where Vs is the change in soil volume in an element of height a. δσ Assuming a constant stiffness ( δe may be represented as: ) over the timestep ( t ), the constitutive relationship V a t s ε = t s σ = v t δe δσ 1 σ u δe = v ( e + 1) t t δσ ( e 1) 1 (4.10) where and σ v and σv are the change in vertical effective and total stress, respectively, εs is the change in vertical strain in the element. Substituting Equations 4.8 and 4.10 into Equation 4.9 and rearranging: δσ δt v δσ + v δe δu = 1 δt ( 1+ e ) o e K w δσ v δe δ k δa γ w δσ + v δe 1+ eo 1+ e δv δt sh δu δk + δa δa (4.11) δ σ v If K w is significantly greater than δe and ( δ Vsh ) is equal to zero Equation 4.11 takes the form of Gibson s large strain consolidation equation (Equation 2.2) for conventional soils. δσ v As explained in Chapter 3 the material stiffness ( 1+ e 0 ) δe permeability (k) and self desiccation induced volumetric shrinkage ( δ V sh ) can all be represented by functions involving various combinations of effective stress ( σ v ), void ratio ( e ) cement 4.7

83 One-dimensional Consolidation Modelling content ( C c ), time ( ) t and effective void ratio ( e ) eff. Substituting these dependent variables into the appropriate terms of Equation 4.11 gives Equation 2.3, which has been implemented and solved using CeMinTaCo. δu e δσ 1 v ( t, Cc, e, v ) t σ Kw e δ δ (A) ( t, C ) δσ v δv ( t, C, e, ) sh c δσ + v c σ v = 14 δe δt 3 { δt (E) (B) ( e ) δk( e ) δσ k v δ eff 1+ e u eff ( 1 e )( t, C, e, ) o δ + + o c σ v + 14 δe δa γw 1+ e δa δa (D) (C) (2.3bis) In this equation, the modified terms are identified using the same labels used to identify the equivalent terms in the unmodified equation (Equation 2.2), but there is also an additional term (E), which does not have an equivalent term in the unmodified equation. As the stiffness of the cemented soil matrix may be comparable to that of pore water, the change in pore pressure (term A in Equation 2.2) due to a change in total stress, is δσ modified to take account of the stiffness of the cemented matrix ( v ) and that of δe water ( K ). This formulation incorporates strain compatibility to achieve an w appropriate distribution of total stress. The volumetric strain term (term C in Equation 2.2) is modified to take into account the fact that the permeability (k) is affected not just by normal void ratio reduction due to consolidation, but also by the formation of cement gel in the void space. This aspect was addressed in Section 3.3. The stiffness term (term D in Equation 2.2) is modified to take account of the fact that δσ the material stiffness ( v ) is now a function of cement hydration, current stress state δe and previous stress excursions as documented in Section

84 One-dimensional Consolidation Modelling 4.9 In addition to these modified terms, an additional term (term E) has been included to quantify the impact of volume changes ( t V sh δ δ ) associated with the self desiccation mechanism, as discussed in Section NUMERICAL IMPLEMENTATION The solution to Equation 2.3 is obtained through implementation into the onedimensional tailings consolidation program MinTaCo. This program, which has been renamed CeMinTaCo in its modified form, solves these equations using an implicit finite element formulation for the space variable, and an explicit finite difference time marching scheme. Figure 4.3 shows the geometric layout adopted in the finite difference solution to Equation 2.3. Each finite element is represented using a single nodal point. Node i has nodal points i-1 and i+1 in the adjacent elements with the vertical spacing between these points being a 1 and a 2 respectively. Assume a time increment that is defined as t where t = t j+1 -t j. The finite difference representation of Equation 2.3 is given by: { } ( ) ( ) [ ] { } { } ( ) ( ) j i j shi f f v j i w f j i j i f f f j i f f f j i f f f e V S a a t S e K e S u u D K a S u a a K a a D S u D K a S j i,, 2 1,, 1 1, , , , + + σ + + = δ δ + + δ δ + + δ δ (4.2) where the coefficients are defined as: ) ( a a a a t + = δ ) ( 4 a a t + = δ ( ) ( ) 1 1, 1, 2 1, 1 1, = j i j i j i j i perm k k a k k a K ( ) j i j i v f e e S, 1, 1 d d + = + σ

85 One-dimensional Consolidation Modelling γ = + + 1,, 1, 1 1 j i j i w j i f e e k K γ = , 1, 1 1, 1,, 1, 2 1,, 1, 1 1, 1, 1 1, j i j i j i j i j i j i j i j i j i j i j i j i w f e e k e e k a e e k e e k a D where K w is the bulk modulus of the water phase and sh V is the volumetric change that occurs over the time increment ( t) due to self desiccation. This may be calculated as: ( ) = *.exp * t d t d W E t V h c sh (3.32bis) where W c is the weight of cement per unit volume of material, t* is the time since the commencement of hydration, E h is the efficiency of hydration (as defined in Section 3.4) and d is the hydration maturity constant. The duration of each consolidation timestep is initially estimated based on Terzagi s time factor for individual layers. This time factor is then used along with a user-defined allowable strain level to make an initial estimate for the allowable time increment. Using the defined timestep, a solution (based on a void ratio convergence criterion) is sought through a maximum of 40 successive iterations. Should the solution not converge, a smaller timestep is established and the calculation repeated. After converging to an acceptable solution, the maximum induced strain is determined and compared with a user-defined tolerance. Should the tolerance be exceeded, the time increment is halved and the calculation repeated until the strains obtained are less than the allowable strains. Over each timestep, the material properties are assumed to remain constant, but at the completion of each timestep, the material properties are updated in accordance with the time increment and strains that occurred during that timestep.

86 One-dimensional Consolidation Modelling 4.4 MODEL VERIFICATION Compressibility In order to demonstrate its applicability in modelling compressibility, the proposed approach has been used to simulate a series of one-dimensional compression tests on cemented CSA hydraulic fill. In these experiments, the specimens were prepared at different densities and allowed to cure for different times prior to loading. The material constants d, X, W and Z (in Equation 3.5) were determined from the measured values of q u and from G o values obtained from bender elements. The parameters λ * and κ * (in Equation 3.1 and 3.2) were determined from one-dimensional compression tests on uncemented material, and through modifying the terms A (in Equation 3.5) and b (in Equation 3.11), the one-dimensional compression response could be adequately represented, as was previously presented in Figure Self desiccation To verify the self-desiccation aspect of the model, a hydration test was carried out, and the CeMinTaCo program was used to reproduce the reduction in pore pressure induced by self desiccation observed in the experiment. The test involved preparing a fully saturated sample of CSA hydraulic fill, at a void ratio of 0.7 and cement content of 5%, in the form of a triaxial test sample. This was mounted in a triaxial cell, and enclosed in a latex membrane in the usual way. The sample was subjected to a total cell pressure of 850 kpa and an initial back pressure of 830 kpa. Then, the back-pressure valve was closed, so that the hydration process could take place in a completely undrained state. The results are shown in Figure 4.4 as a plot of measured pore pressure versus time. In this case, the self-desiccation mechanism has reduced the pore pressure from the initial back pressure value of 830 kpa to a final value close to zero. (This suggests that it might have been appropriate to start from an even higher back pressure in this case, to ensure a final pore pressure well above zero). The response fitted using the CeMinTaCo program is also shown in Figure 4.4, which indicates that the program is capable of reproducing the observed experimental results quite well. It should be noted that the CeMinTaCo output was modified in accordance with the Poisson s ratio to convert from a onedimensional situation to an isotropic situation. 4.11

87 One-dimensional Consolidation Modelling This experiment shows how effective the self-desiccation mechanism can be in reducing pore pressure (and hence in increasing effective stress). In this case, this occurs in the absence of any external drainage effects, but in a real stope, it would combine with any consolidation drainage to potentially produce a faster pore pressure reduction than would otherwise be the case. 4.5 SENSITIVITY STUDY A limited sensitivity study was undertaken to illustrate the effect of varying some of the input parameters on the response when modelling the filling of a stope. The filling strategy used in the study was based on a common paste fill schedule, and involved filling an initial plug at 0.4 m/hr for 16 hours, followed by a 24-hour rest period, and then completing filling the remaining 30 m at a rate of 0.4 m/hr. The base-case set of input parameters used in the study is given in Table 4.1; these parameters correspond to typical paste backfill properties, and except where otherwise indicated these parameters are used in all the examples that follow. Proper simulation of the three-dimensional geometry of a real stope and drawpoint (illustrated schematically in Figure 1.2) would require a three-dimensional FE program, or at least a two-dimensional or axi-symmetric program. However, since CeMinTaCo is only one dimensional, a means of simulating the restriction to drainage resulting from the reduced drawpoint cross-section was required. The method adopted is illustrated in Figure 4.5, which consisted of introducing a 5 m thick layer with reduced permeability ( 1 / 8 of the value adopted for the bulk of the material at a corresponding void ratio) at the base of the stope. Note, however, that the material in this region had zero cement content, so none of the effects of self desiccation apply in this region. In the following sections, the effect of changing a number of parameters is investigated. These parameters include cementation, permeability, and damage Influence of cementation To illustrate the effect of cementation on the consolidation response, analysis was first carried out using uncemented material. Then, the analysis was repeated with cement content (C c ) of 5%, in one case with the self-desiccation mechanism disabled in the model, and the other with it enabled. 4.12

88 One-dimensional Consolidation Modelling Figure 4.6 presents the results of these analyses as plots of pore pressure (2 m above the base drainage layer) versus time. Also shown is a plot of the total vertical stress versus time at the same point in the profile. These plots indicate that for the case without any cement, the increase in pore pressure is similar to the increase in total stress, and hence very little effective stress is generated during filling. After the completion of filling, the rate of dissipation of pore pressure is slow, and very little consolidation has occurred at the end of the period modelled (250 hours). This indicates that, in the absence of cementation, paste fill barricade stresses would be well represented by the undrained case that was discussed on Section 2.2. For the second case, it may be seen from Figure 4.6 that, even with the self-desiccation mechanism disabled, pore pressures are significantly less than for the uncemented case once hydration begins. The effect of adding cement is to produce an increase in soil stiffness (after the start of hydration) and a reduction in permeability, as previously discussed. Since the rate of pore pressure reduction (consolidation) is dictated by the product of stiffness and permeability, this result indicates that the effect of the increase in stiffness outweighs the effect of the reduction in permeability, and there is some increase in the rate of pore pressure dissipation, even during filling. However, it should be noted that there are still significant excess pore pressures present at the end of filling. Due to the increased stiffness, these dissipate somewhat more rapidly after completion of filling than in the previous case. In the third case, with self desiccation enabled, there is a significant increase in the degree of pore pressure reduction that takes place, indicating the potential importance of the self-desiccation mechanism in promoting dissipation of pore pressure. It should be noted that the dissipation of pore pressure would act to increase the effective stress, promoting arching, which would further reduce the pore pressure. This will be shown with reference to in situ measurements later, and also when two-dimensional modelling results are presented in Chapter Influence of permeability To illustrate the influence of permeability on the overall filling response, analyses were carried out using the filling sequence and material properties described above, with C c of 5%, but using three different permeability relationships (i.e. three different values of 4.13

89 One-dimensional Consolidation Modelling the permeability parameter c k in Equation 3.15). The resulting three permeability functions (denoted k 1, k 2 and k 3 ) are plotted against curing time in Figure 4.7. In this plot, the change in permeability with time shown for each case is due only to cement growth, whereas in a modelling situation, the change could be greater with the added effect of void ratio reduction due to compression. Figure 4.8 shows the pore pressure during and following filling for a point 7 m above the base (i.e. 2 m above the lower-permeability drawpoint region) for the three cases considered. Figure 4.9 shows the pore pressure profile down through the stope at the end of filling. Also shown in Figure 4.9 is the final steady state pore pressure (SSPP) for the k 1 case (the SSPP lines for the other two cases are practically coincidental). In Figure 4.8, the final steady state equilibrium has been reached at about 230 hours for the k 1 case, whereas changes were still occurring for the other two cases at this stage. In Figure 4.9, the line labelled k 1 SSPP refers to the steady state pore pressure that results from maintaining a water table in the stope at m height (the final filled height) and zero pore pressure at the base of the drawpoint, with the permeability in the lower 5 m being about 8 times less than the permeability in the stope proper for each case. Note that the permeability in the stope is not uniform with depth, so the ratio of 8 refers to average values. In Figure 4.9, the difference between the pore pressure at the end of filling and the SSPP line is the excess pore pressure at this stage. Thus, there are excess pore pressures in the stope for each of the three cases at the end of filling, but these are different for the three cases. These results appear to be counterintuitive, since conventional consolidation theory suggests that high permeability material should dissipate pore pressures more quickly than low permeability material. Thus, in Figure 4.8, while the lowest permeability case (k 3 ) shows the highest pore pressure in the first filling stage, it shows pore pressures very much less than the higher permeability cases during the rest period and at all times thereafter. Examination of the pore pressure plot at the end of filling for this case in Figure 4.9 shows that from the surface down to about 25 m above the base, the pore pressure gradient corresponds to the total overburden stress gradient i.e. there is no pore pressure dissipation in this region at this stage, and hence the effective stresses are zero. However, below about 25 m, the pattern changes completely. In this region, 4.14

90 One-dimensional Consolidation Modelling hydration and self desiccation are occurring, setting up high negative excess pore pressures. Though this results in a very steep downward hydraulic gradient (from 25 m down to 13 m), the low permeability prevents sufficient internal water flow from dissipating these negative pore pressures. If later pore pressure isochrones for this case were plotted, these would show the point of minimum pore pressure gradually moving upwards until it reached the surface (as hydration progressed). Then, slow internal flows would gradually move the pore pressures onto the steady state line. For the highest permeability case (k 1 ), the same internal volume change occurs due to hydration, and thus the potential pore pressure reduction resulting from this is the same. However, the higher permeability in this case means that high internal hydraulic gradients are not sustainable, due to the ease of generating internal water flow to smooth out the pore pressure profile. Thus, at the end of filling, the pore pressures for the k 1 case are not very different from the SSPP values. There is still evidence of the self desiccation process occurring in this plot i.e. the slight concave-upward curvature of the pore pressure profile from about 10 to 20 m would not be present if self desiccation was not influencing the process. The intermediate permeability case (k 2 ) shows behaviour similar to the k 1 case, commensurate with the fact that the permeability is not very much lower than for the k 1 case, as shown in Figure Typical damage scenario As discussed throughout this thesis, the filling process involves the interaction of three time-dependent processes: the rate of filling, cement hydration and consolidation. Researchers such as Le Roux at al. (2002) and Belem et al. (2006) have investigated the mine backfill process experimentally. In this work, the authors apply effective stress to curing cemented paste fill at a rate equivalent to the accumulation of total stress from the fill self weight. Through adopting a total stress approach, rather than an effective stress approach, the third of the time-dependent processes (consolidation) has been neglected. This section presents a numerical investigation of the interaction of the three time-dependent processes with specific emphasis on the influence that damage (from excessive vertical effective stress on fragile cement bonds during the early stages of hydration) has on the consolidation process. 4.15

91 One-dimensional Consolidation Modelling The purpose of this analysis is to select a material that possesses an ultimate strength that is suitable for eventual vertical exposure, and determine if this material can be damaged during a typical filling sequence. The focus of the analysis is the early stages of hydration, where fragile cement bonds may be damaged by the application of compressive stress. The material properties from Table 4.1 were adopted, but in order to produce a material with an ultimate q u that is equal to the final vertical effective stress, the void ratio has been increased to The property that dictates the response of the material to damage is the damage coefficient (b) in Equation 3.11; in this analysis, damage coefficients of 0.05 and 3.0 have been adopted. These values are considered appropriate for representing the entire range of damage coefficients for mine backfill. The impact of this variation on the structural breakdown has been demonstrated in Figure 4.10, which presents the results of a simulated one-dimensional compression test on a fully hydrated sample. Figure 4.10 indicates that prior to yield, the behaviour is largely independent of b, but after yield the rate of cementation breakdown is very sensitive to the value of b. The analysis has considered two materials, one with the value of the permeability term a given in Table 4.1, and the other with the value of a increased by two orders of magnitude. These are meant to represent a paste fill example and a hydraulic fill example, respectively. Paste fill modelling The results of the paste backfill modelling are presented in Figures 4.11 and Figure 4.11 shows the development of pore pressure (u), vertical total stress (σ v ) and vertical effective stress (σ v ) against time, at a point 2 m above the base of the stope, using both damage coefficients (b). The results of the simulation with b = 3 are plotted as lines, while those with b = 0.05 are plotted as symbols. Figure 4.11 indicates that in a typical paste fill situation, compressive damage is unlikely to influence the consolidation behaviour. The main reason for independence is as follows: The application of total stress (due to the accumulation of overlying material) is resulting in an equal increase in pore pressure, and therefore there is no change in effective stress, and no possibility of damage being caused. 4.16

92 One-dimensional Consolidation Modelling Due to the low coefficient of consolidation (associated with the fine grained nature of paste fill) the cement hydration is required to achieve consolidation (i.e. pore pressure reduction, rather than conventional consolidation ). As a result, the hydration timescale dictates the timescale of consolidation (or application of effective stress). Therefore, softer/weaker material consolidates more slowly, allowing bonds to mature appropriately, while stiff/strong material rapidly develops sufficient strength to overcome the associated rapid application of effective stress. Figure 4.12 presents the application of vertical effective stress (σ v ) and onedimensional yield stress (σ vy ) against time for the element. Initially both σ v and σ vy are very low. After reaching initial set σ vy increases at a significantly faster rate than σ v therefore eliminating the likelihood of damage. This would typically be the case in a paste fill situation. Also presented in Figure 4.12 is the calculated unconfined compressive strength (q u ) for the in situ material and that for material cured under no stress (as would be the case in the laboratory). Comparison of these indicates that the application of effective stress during filling can actually increase the material strength (by reducing the final density) rather than damaging fragile cement bonds. This behaviour is in accordance with that observed by Blight and Spearing (1996), who investigated the effect of stope lateral strain (i.e. stope closure) on cementing backfill, and showed that such strain (i.e. the resulting effective stress increase), resulted in higher final strengths. It is also in accordance with many field observations (Revell, 2004, Cayouette, 2003), where the unconfined compression strengths obtained from cores taken from filled stopes are often significantly greater than the control samples taken from the material as it is filled and cured under zero confining pressure. Hydraulic fill modelling It has been demonstrated that in a typical paste fill situation the damage coefficient, which represents the rate of cementation breakdown with strain, has little influence on the consolidation and hydration behaviour because in this case it is the hydration process that generates effective stress. However, in the case of hydraulic fill, the material often has a much higher permeability. As a result (if it is assumed that 4.17

93 One-dimensional Consolidation Modelling immediate consolidation occurs) the rate of development of effective stress is more closely related to the filling rate. In order to simulate a typical hydraulic filling situation, the same material properties as those adopted for the paste fill example are adopted, but the permeability is increased by two orders of magnitude. Furthermore, rather than a filling rate of 0.5 m/hr with a single long rest period (as in the paste fill case) a constant filling rate of 3 m/day was adopted without a rest period. This is expected to be indicative of typical hydraulic filling rates, when taking account of fill and rest periods that are commonly adopted to avoid piping type failures (Cowling et al. 1987). The results of this modelling are presented in Figures Figure 4.13 presents the development of pore pressure (u), vertical total stress (σ v ) and vertical effective stress (σ v ) against time for a point 2 m above the base of the stope. Again the results of modelling with a damage coefficient b = 3 are presented as lines while those with a damage coefficient b = 0.05 are presented as symbols. It is clear from this figure that, as in the paste fill example, the damage coefficient has little influence on consolidation in a typical hydraulic fill situation. This is most likely to be related to the fact that (as indicated in Section 2.2 using Gibson s (1958) analytical solution) the combination of permeability and stiffness immediately after placement of hydraulic fills results in excess pore pressures dissipating rapidly. Hence, water pressures in a hydraulic fill stope are dictated by the restriction at the drawpoint, rather than the dissipation of excess pore pressures. This point was also evident in the high permeability example in Section Figure 4.14 presents the development of one-dimensional yield stress (σ vy ) and applied vertical effective stress (σ v ) against time in an element 2 m above the stope floor. Unlike with the paste-fill case, the application of vertical total stress (from the accretion of material) creates an immediate increase in vertical effective stress. This acts to compress the soil, increasing σ vy even prior to the onset of cement hydration. This creates some initial hardening of the material and, as with the paste-fill case, the onset of cement hydration causes σ vy to increase significantly faster than σ v. Again this reduces the likelihood of damage. 4.18

94 One-dimensional Consolidation Modelling Also presented in Figure 4.14 is the calculated q u against time for material in situ and that expected for the material cured under zero applied stress. As with the paste-fill case, q u for material cured in situ is greater than that for material cured under zero stress. But it is important to note that even with the reduced filling rate (relative to the paste fill situation), the increase in q u of the in situ material relative to that cured under zero stress is significantly greater. The increased ratio is a result of the soil compression that occurred immediately after deposition. This compression increased the material density, which leads to the higher strengths. Summary Overall, it can be concluded that, under most conditions, the interaction of effective stress and the growth of fragile cement bonds during filling is unlikely to adversely influence the consolidation behaviour or damage the fragile cement bonds in either a paste or hydraulic fill situations. In fact, modelling indicates that in most cases this interaction will actually lead to higher material strengths in situ due to soil compression Strain requirements One component that is often incorporated into tailings consolidation models is large strain consolidation theory. This is important when analysing the consolidation of large storage facilities containing compressible tailings. But in a tailings-based backfill situation material is either cycloned (to remove fine particles) or, if placed as full-stream tailings, combined with cement to avoid the material liquefying after placement. In addition to reducing the risk of liquefaction, the removal of fines from a tailings stream (as in a hydraulic fill) increases the material stiffness (in an uncemented state) and therefore reduces the amount of compression, while, as noted by Le Roux et al. (2005) the presence of cementation in full-stream tailings backfill (paste fill) acts to reduce the compression that occurs during the filling process. For these reasons largestrain numerical formulation may be unnecessary when undertaking consolidation analysis of mine backfill. To investigate this aspect, the vertical strain calculated for the paste fill example presented in Section is plotted against time in Figure This figure indicates that vertical strain levels of 4% occurred for the cemented paste example. 4.19

95 One-dimensional Consolidation Modelling As hydraulic fill can be placed without any cement, it is important to consider the likely strains that would be generated for a typical uncemented hydraulic fill. The values of uncemented compression parameters (λ = 0.06, κ = 0.006) that were adopted for the previous study are considered to be greater than the values relevant to a typical hydraulic fill, and hence using these parameters would overestimate strains in a hydraulic fill situation. Based on Rowe cell testing of hydraulic fills, compression parameters of λ = 0.035, κ = are considered more appropriate. These compression parameters were adopted, along with the other material properties for the hydraulic fill example in Section 4.5.3, and zero cement content, in an analysis to investigate the degree of compression likely to occur in a typical uncemented hydraulic fill situation. The calculated axial strain is plotted against time in Figure 4.15, indicating that a maximum strain of 6% occurred in this example. The axial strains calculated for both the paste and hydraulic fill examples are both significantly less than 20%, which was specified by Tan and Scott (1988) as the strain levels requiring large strain formulation. This result indicates that the large strain approach (involving a Lagrangian coordinate system and very small timesteps) adopted in CeMinTaCo is unnecessary, and it would appear that a conventional Cartesian coordinate system can provide a suitable representation of most mine backfill situations. This is the approach adopted in the two-dimensional consolidation program, which is presented in Chapter Comparison with data from in situ monitoring of filled stopes To determine how well the CeMinTaCo program can reproduce the behaviour in an actual mine backfilling situation, the program was used to simulate the deposition of a fine-grained cemented paste fill at the Cayeli mine in Turkey. The properties of the asplaced material adopted in the modelling were in accordance with those in the field. These included a placed void ratio of 1.0, a cement content of 8%, and a fully hydrated q u of 1 MPa. However, some of the other relevant material properties could not be obtained, and thus, in order to gain a reasonable estimate of appropriate material properties, those determined for a similar tailings material with the same cement content were adopted. This material had grain size distribution, and mineralogical and cement 4.20

96 One-dimensional Consolidation Modelling characteristics, similar to those encountered at Cayeli and was therefore expected to have similar properties. The values chosen in this way include the efficiency and rate of hydration (E h = 0.032, d = 1.5), the ratio of q u to σ vy (6), the uncemented compression parameters (λ = 0.06, κ = 0.009) and permeability parameters (k m/s), the ratio between cemented stiffness and strength (1300) and the damage coefficient (b = 0.5). The method adopted to account for the flow restriction due to the drawpoint is the same as that used earlier in the parametric study, and is illustrated in Figure 4.5. The modelling was carried out by increasing the fill height at the same rate as that adopted in the field. The filling rate was a constant rate of rise of 0.4 m/hr for the first 24 hours followed by a 9-hour rest period, and then filling the remainder of the stope at a rate of 0.4 m/hr over a 100-hour period. Figure 4.16 shows a plot of pore pressure versus time obtained from the modelling, compared to the field measurements. The monitoring location for the in situ measurements was 1.0 m above the stope floor, and the CeMinTaCo results plotted refer to the same elevation. In Figure 4.16, the response during the initial stage of filling is linear (and, though not shown, coincides with the total stress increase during this period). However, the onset of initial set coincides with a reduction in the rate of pore pressure increase, such that from about 20 hr onwards, the pore pressure is actually reducing for both the measured and model values even as filling continues (up to 24 hr). When filling recommences (at approximately 33 hr) the initial pore pressure behaviour appears to be reasonably well modelled, but as filling continues the model and in situ results start to diverge. For the in situ case, it is likely that, due to consolidation, some of the fill/rock interface strength is mobilised, resulting in a stress redistribution to the surrounding rockmass (arching). This reduces the total vertical stress imposed on the material at the monitoring point, resulting in a lower pore pressure increase than would otherwise have occurred. In fact, any tendency for pore pressure increase beyond this point is completely counteracted by on-going drainage (and self desiccation), with the result that the pore pressure at the monitoring point continues to reduce. Clearly, the one-dimensional CeMinTaCo model is not able to account for the arching mechanism, and in this case it predicts an increase, rather than a decrease, in pore pressure when filling recommences. 4.21

97 One-dimensional Consolidation Modelling While many of the material parameters used in the modelling have not been derived directly for the material being modelled, the ability of the model to reproduce the significant characteristic of the filling process based on properties of similar material illustrates that the model is capturing the most significant mechanisms associated with mine backfill placement. However, it is also clear that a two-dimensional model (plane strain or axi-symmetric), or even a full three-dimensional model, is required to capture the complete behaviour. 4.6 CONCLUSION Overall, this section has demonstrated that the mine backfill process is a complex interaction of mechanisms. This interaction of mechanisms can actually create circumstances that produce counterintuitive outcomes, as was demonstrated in the permeability sensitivity study (Section 4.5.2). For example, contrary to rules of thumb used in industry, filling a stope with low-permeability material can result in very low pore pressures being present in the fill at the end of filling pore pressures much lower than those in a free-draining fill. Therefore, in order to predict the overall response, the individual mechanisms need to be fully coupled into a program such as CeMinTaCo. It would be unwise to speculate about the impact of a single mechanism on the overall response and it would be unwise to attempt to superimpose the impact of individual mechanisms in an effort to understand the cumulative response. This work has demonstrated that compressive yielding during placement is unlikely to occur in a typical mine backfill situation. In addition, analysis of typical strains levels during filling indicate that, under normal conditions, small-strain formulation is sufficient to capture the consolidation behaviour of mine backfill. Comparison with in situ monitoring demonstrated that the one-dimensional model (CeMinTaCo) was capable of accurately representing the early age behaviour; but diverged from in situ measurements during the later stages of filling. This is believed to be a result of stress redistribution to the surrounding rockmass. To appropriately address this mechanism, a two- or three-dimensional model is required. The development of a new fully-coupled two-dimensional finite element model is presented in Chapter 5 of this thesis. 4.22

98 One-dimensional Consolidation Modelling 4.23

99 Two-dimensional consolidation analysis (Minefill 2D) CHAPTER 5 TWO-DIMENSIONAL CONSOLIDATION ANALYSIS (MINEFILL-2D) 5.1 INTRODUCTION In Chapter 4, a computer code (CeMinTaCo) for modelling the behaviour of backfill material undergoing consolidation and cement hydration during and following placement in a stope was presented. Being one-dimensional, the model can not, of course, deal with any of the two-dimensional or three-dimensional aspects of the behaviour in a real stope. For example, in comparing the numerical output from CeMinTaCo with the in situ measurements, e.g. as presented in Section 4.5.6, one drawback that becomes evident is the inability of the one-dimensional model to appropriately capture the redistribution of stress to the surrounding rockmass (arching), and thus it cannot take account of the reduced vertical stress that can result from arching. It is likewise incapable of representing the stope drawpoint in a geometrically correct fashion. Without being able to represent the stope drawpoint correctly, artificial base boundary conditions are required to represent the drainage restrictions through the drawpoint, such as those described in Figure 4.3. In addition, a one-dimensional model cannot appropriately represent the horizontal stresses placed on barricades. In order to take these aspects into account, a two- or three-dimensional model is required. While the one-dimensional nature of CeMinTaCo has these drawbacks, it has shown that some aspects of cemented mine backfill behaviour that were previously thought to be important were, in fact, not so important after all in most situations. These were the requirement to use large-strain formulation, and the possibility of yielding of cement bonds as they formed due to the development of excessive confined vertical compressive stresses. With regard to the first aspect, the sensitivity study in Chapter 4 demonstrated that the presence of cementation (in paste fill) or the removal of fines (in hydraulic fill) result in strain levels that are far less than 20% (strains in the order of 6% were calculated). Tan and Scott (1988) suggest that for strains less than 20%, a small-strain formulation 5.1

100 Two-dimensional consolidation analysis (Minefill 2D) provides accurate solutions. Therefore, it is considered acceptable to perform the calculations using the conventional Cartesian coordinate system rather than the Lagrangian coordinate system that was used in CeMinTaCo. With regard to the second aspect, a study into the influence of structural damage from excessive compressive stress indicates that, provided the material has sufficient strength to support the ultimate stress state, effective stress generated during the early stages of hydration is unlikely to damage cement bonds as they form. Therefore, it is considered appropriate to undertake calculations where compressive yield of the cemented structure is neglected and a Mohr Coulomb yield surface is used to represent the behaviour of the cemented material. It should be noted that compressive yield of the material in an uncemented state is taken into account to address any compression that occurs prior to the onset of hydration, which was shown to be relevant in Section This chapter begins by outlining the unique requirements of a model to represent the mine backfill deposition process. This is followed by a description of the governing equations and numerical formulations developed within the program Minefill-2D. An overview of the material models adopted in this program is then provided. Minefill-2D is then compared with various well-established analytical solutions and CeMinTaCo to verify the performance of the model. Finally, a comparison against in situ measurements is undertaken to verify the applicability of the program to the mine backfill deposition process. Many of the basic ideas incorporated into Minefill-2D are the same as those incorporated into CeMinTaCo, and these ideas have been thoroughly explored in previous chapters. Nevertheless, there is a considerable amount of repetition of this material in this chapter; this has been done for the sake of completeness, and to make this chapter more coherent. 5.2 PROGRAMMING REQUIREMENTS The main features required in this model included the following: fully coupled analysis i.e. full coupling between compression, water flow, and the cementation processes; 5.2

101 Two-dimensional consolidation analysis (Minefill 2D) calculations in terms of total water head; ability to vary boundary conditions on the upper surface, to enable fresh material to be added, and to deal with various water outflow or inflow conditions; ability to take account of water accumulation above the fill surface (influencing surface total stresses and pore pressures); a constitutive model that takes account of cement hydration; a permeability model that takes account of cement hydration; a self-desiccation model; strain softening of the fill mass due to interface shear during filling. In order to achieve these requirements, a number of commercially-available programs, including FLAC, Plaxis and AFENA, were examined. None of these programs proved to be suitable due primarily to problems associated with simulating the accretion of soft soil whose properties evolve with time under fully coupled conditions. Specifically this related to dynamic waves generated during the consolidation of soft material disrupting the calculation scheme (in FLAC), problems associated with undertaking calculations in terms of total water head and problems associated with establishing boundary conditions along the surface nodes and then including these surface nodes back into the calculation scheme at a later stage. Because of these problems, it was decided that the most appropriate approach would be to develop a new two-dimensional (plane-strain or axi-symmetric) model, which specifically addressed the described criteria. This program was coded in Visual Fortran 90 and named Minefill-2D. 5.3

102 Two-dimensional consolidation analysis (Minefill 2D) 5.3 PROGRAMMING METHODOLOGY Introduction This section presents the relevant numerical components incorporated into the program Minefill-2D. It includes an introduction of the numerical technique, a description of the calculation sequence, an outline of the governing equations, as well as a description of how other numerical difficulties were addressed. Throughout this section, all relationships are formulated for the condition of plane strain analysis. Section presents a description of how the equations are converted for axi-symmetric analysis The finite element method The numerical technique adopted is the finite element method. As described in Potts and Zdravković (1999) the finite element method involves 6 main steps. These include: Element discretisation Primary variable approximation Element equations Global equations Boundary conditions Solution to the global equations Element discretisation The first step in the finite element formulation is to discretise the problem geometry into small domains, (elements). These individual element are then connected by a series of points (nodes). The most important feature of defining a suitable discretisation of the problem geometry is to increase the number of elements in regions where unknowns vary rapidly, such as displacements (shear strains) at the fill/rock interface. In two-dimensional problems, triangular or quadrilateral elements are commonly adopted. Throughout this thesis, quadrilateral elements were adopted with 8 boundary 5.4

103 Two-dimensional consolidation analysis (Minefill 2D) nodes to represent displacement and 4 boundary nodes to represent pore pressures, as illustrated in Figure 5.1. Primary variable approximation The primary unknown variables adopted in Minefill-2D are displacement and pore pressure. Stresses and strains are determined as a function of the calculated displacements field. In the two-dimensional analysis presented, global displacements û and vˆ are determined in the x and y direction respectively (typically the conventional symbols adopted for displacements are u and v but to avoid confusion with pore pressures and Poisson s ratio these modified symbols were used). Across each element, the displacements are assumed to vary in accordance with a polynomial shape function, where the order of the polynomial depends on the number of nodes in the element. Displacement ( û, vˆ ) at any point within an element are defined in accordance with nodal displacements and the matrix of shape functions [ N d ] such that: u ˆ = vˆ [ N ]{ uˆ,uˆ,...,uˆ,vˆ,vˆ,..., v } d ˆ n n n n n n 8 (5.1) where û and vˆ are the displacements at any point within the element and û ni the displacements (in the x and y directions respectively) at nodal points i., vˆ ni are If displacements vary quadratically across an element, strains and therefore effective stresses vary linearly across the element. To ensure that effective stress and pore pressure vary in the same way across an element, it is conventional to adopted 4-noded elements to represent pore pressure variations. Therefore, pore pressures (u) within an element are related to the four nodal pore pressures by: [ u ] = [ N ]{ u,u,...,u } p n1 n2 n4 (5.2) where uni is the nodal pore pressure at location i and N p is the shape function. To assist with the numerical formulation, most finite element programs (including Minefill-2D) uses isoparametric elements, where the global coordinates (x, y) of a point in an element are expressed as a function of the global nodal coordinates (x i, y i ) and 5.5

104 Two-dimensional consolidation analysis (Minefill 2D) local shape (interpolation) functions N i (s,t). For the elements shown in Figure 5.2, the global coordinates of a point in the element can be expressed by coordinate interpolation of the form: x 8 = 1 N i ( s t), xi 8 = ( ) and y N i s t 1, yi (5.3) where s and t are local coordinates which vary from -1 to 1 across each element. The purpose of introducing this coordinate system is to allow a solution to be sought through Gaussian integration. The term isoperimetric come from the fact that the geometry is approximated using the same shape function as that for displacements, which simplifies the element equations. Element equations a. Co-ordinate transformation The element equations govern the deformation of each element. The formation of element equations combines compatibility with equilibrium and the constitutive relationship. Using the primary variable approximation, presented previously, the compatibility equations can be represented as: N1 ε x x ε y 0 = γ xy N1 εz y 0 0 N1 y N1 x N8 x 0 N8 y 0 0 u ˆ1 N 8 v&& 1 y... N8 uˆ 8 x v&& 8 0 (5.4) which can be more conveniently expressed as: { ε} = [ B]{ d} n (5.5) where [ ] B contains the derivatives of the shape functions [N i ], and { d} n contains a list of the nodal displacements for a single element. The shape functions [N i ] depend only on the local coordinates (S and T). Therefore, in order to calculate the derivatives of these shape functions relative to the global coordinate system (x and y), a chain rule is 5.6

105 Two-dimensional consolidation analysis (Minefill 2D) required to relate the x and y derivatives to derivatives with respect to S and T. Using the chain rule: Ni S T Ni T N = J i x T Ni y (5.6) where J is defined as the Jacobian matrix: J x = S x T y S y T (5.7) the global derivatives of the shape functions (used in Equation 5.4) can be obtained by inverting Equation 5.6. Time-dependent consolidation requires the material constitutive model to be combined with equilibrium and Biot s consolidation equations. Coupling these leads to the development of the governing equations of finite element consolidation as follows. b. Constitutive model Assuming elastic behaviour over a given loading increment ( σ ), Hooke s law states that the relationship between stress and strain can be represented as: { σ } = [ D ]{ ε} (5.8) ' ' where { σ } = [ σ, σ, τ ] T x y xy and { ε} = [ ε ε, γ ] T x, y xy are the incremental effective stress and strain vectors in plane strain respectively, and [ D ] is the assumed relationship between these vectors. [ D ] is based on the drained Young s modulus (E ) and the drained Poisson s ratio (ν ) such that: [ D ] E (1 ν ) (1 + ν )(1 2ν ) E ν = (1 + ν )(1 2ν ) 0 E ν (1 + ν )(1 2ν ) E (1 ν ) (1 + ν )(1 2ν ) E 3(1 2ν ) (5.9) 5.7

106 Two-dimensional consolidation analysis (Minefill 2D) Terzaghi s principle of effective stress states that: { σ} = { σ } + { u} (5.10) where σ is the change in total stress, σ is the change in effective stress and u is the change in pore pressure. Substituting Equation 5.8 into Equation 5.10 gives: { σ} = [ D ]{ ε} + { u} (5.11) where ε is the strain matrix. c. Continuity The equation for pore fluid continuity is: x x + y y ε Q = t v (5.12) where x, and y are the components of pore fluid velocity in the coordinate directions and Q is any source or sink term. Assume the pore fluid flow is in accordance with Darcy s law: x kxx = y k yx h kxy h x k yy y (5.13) or { } = [ k]{ h} where k ij is the coefficient of hydraulic conductivity for the soil, [ k ] is the hydraulic conductivity matrix and h is the hydraulic head, defined as: Vector { i } { i, i } T g gx gy ( x. i + y i ) u h. = + gx gy γ (5.14) w = is the unit vector parallel to, but in the opposite direction to, gravity and γ w is the unit weight of water. d. Equilibrium and governing equations 5.8

107 Two-dimensional consolidation analysis (Minefill 2D) Rather that solving for force equilibrium, a more convenient formulation is brought about through considering conservation of energy, (i.e. internal ( W ) and external work ( L ) must be equal): W L = 0 (5.15) The internal work is given by the integration of the increment of total stress multiplied by the increment of strain across the element: W = 1 2 σ Vol T { ε} { } dvol (5.16) Using Equation 5.11, Equation 5.16 can be split into soil matrix and pore pressure terms, and re-written as: W Vol T T [{ ε} [ D ]{ ε} + { ε} { u} ] dvol = 1 2 (5.17) The work done by the incremental applied loads ( L ) can be divided into contributions from body forces and surface tractions, and can be expressed as: T T L = { d} { F} dvol + { d} { T}dSrf (5.18) Vol Srf Combining the above, the equilibrium condition is satisfied during the consolidation step when [ K ]{ d} + [ L]{ u} = { } E R E (5.19) where d is the nodal displacements vector, and T = Vol (5.20) [ K ] [ B] [ D ][ B] dvol E which is termed the element stiffness matrix, and [ B ] is the derivative of the shape functions as discussed previously. [ L E ] is termed the element volume matrix and is defined as: 5.9

108 Two-dimensional consolidation analysis (Minefill 2D) T [ L ] = { m}[ B] [ N ] E Vol p dvol (5.21) where [N p ] is the matrix of shape functions for pore fluid pressure interpolation and T { m} = { } Using the principle of virtual work, the continuity equation (5.6) can be written as: T ε { } { ( u) } + v u dvol Q u = 0 t Vol (5.22) Substituting Darcy s law (Equation 5.13) into Equation 5.22 gives: Vol T { h} [ k] { ( u) } ε + v u dvol = Q u t (5.23) where [ k ] is the permeability matrix and { h} takes account of both elevation head { } g is the gradient of total water head. h i and total pore pressure { u} so that calculations can be carried out in terms of total water head rather than excess pore pressures. It is important for Minefill-2D to carry out analysis in terms of total water head, as the combination of on-going filling and drainage (through base barricades) make it difficult to define hydrostatic conditions. The sink term ( Q ) becomes particularly important when accounting for self-desiccation volumetric changes. If ε v t is approximated as ε v t, equation 5.23 can be re-written as: [ L ] { d} T n E E n E + t [ Φ ]{ u} = [ n ] Q (5.24) where Φ E = T [ E] [ k][. E] d Vol Vol γ (5.25) w represents the element permeability matrix, 5.10

109 Two-dimensional consolidation analysis (Minefill 2D) n E = T [ E] [ k]{ ig } dvol Vol (5.26) represents flows due to gravitational forces, and [ E] T N p N p N p =,, x y z (5.27) represents the derivative of the shape functions for pore water pressure interpolation. Equations 5.24 and 5.19 are solved using a time-marching process such that if the nodal pore pressure { u } n and displacements { d} n are known at time t 1, then the solution for nodal pore pressures and displacements is sought at time t 2 = t 1 + t. If a finite difference approach is adopted, and assuming a linear interpolation in time, the resulting equation is: t t 2 1 [ ] t [ Φ ]{ u} dt = [ Φ ] β( { u} ) + ( 1 β) ({ u} ) E n E n 2 n 1 (5.28) Booker and Small (1975) demonstrated that, in order to form a stable solution to Equation 5.28, the value of β must be greater than or equal to 0.5. To maintain an implicit time-marching solution, a value of 1.0 was adopted for β throughout this work. Substituting equation 5.28 into 5.24 gives: ( ) t [ L ]{ d} t[ Φ ]{ u} = [ Φ ]({ u} ) + Q + [ n ] E n E n E n 1 E (5.29) Combining equations 5.13 and 5.23, the governing equations for finite element consolidation analysis can be developed. These governing equations are presented as Equation 5.30: [ K E ] [ LE ] T [ L ] t [ Φ ] E { d} { u} n = { RE } ([ n ] + Q + [ Φ ]{ u} ) t E n E E n 1 (5.30) where [ K E ] represents the element stiffness matrix, [ E ] submatrix, [ Φ E ] represents the permeability submatrix, { R E } L represents the element volume is the vector of boundary stresses, [ n E ] represents flow due to gravitational forces, Q represents an internal sink 5.11

110 Two-dimensional consolidation analysis (Minefill 2D) term, { u} n is the vector of nodal total pore pressure increments, { d} n is vector of nodal displacement increments. Global equations The global system of finite element equations for the consolidation problem is simply the assembly of terms from Equation 5.30, across the entire problem domain in accordance with corresponding nodes. [ KG ] [ LG ] T [ L ] t [ Φ ] G { d} { u} n = { RG } ([ n ] + Q + [ Φ ]{ u} ) t G n G G n 1 (5.31) where: N [ KG ] = [ K E ] i= 1 N [ LG ] = [ L E ] i= 1 N [ ΦG ] = [ ΦE ] i= 1 N [ RG ] = [ R E ] i= 1 N [ ng ] = [ n E ] i= 1 i i i i i (5.32) (5.33) (5.34) (5.35) (5.36) where N is the number of elements in the problem domain. Extension to axi-symmetric conditions To model the complexities of the stope drawpoint geometry would require the development of a full three-dimensional version of the two-dimensional (plane strain) model. This is beyond the scope of this thesis. The plane-strain Minefill-2D model is capable of providing very good representation of the behaviour in many stopes, especially where the length-to-breath ratio is high. However, in some situations, an axisymmetric model might provide a better representation of reality. In addition, Chapter

111 Two-dimensional consolidation analysis (Minefill 2D) presents the results of an axi-symmetric centrifuge test, and clearly an axi-symmetric model would be more appropriate for modelling this test. All of the previous discussion relating to the development of Minefill-2D was based on a plane-strain formulation. Axi-symmetric analysis follows the same calculation methodology as that for plane strain conditions, but rather than analysing an element of unit depth, the analysis is carried out on a one-radian slice through an axi-symmetric geometry (i.e. through a cylinder) as illustrated in Figure 5.3. As is well documented in the literature (Naylor et al., 1981, Potts and Zdravković,1999, Smith and Griffiths, 1998), rather than calculations being carried out in terms of x and y coordinates (as is the case in plane strain) calculations are carried out using a cylindrical coordinate system (r, z, θ). As the calculations progress outwards from the centreline, the thickness of the slice is always equal to the radius (since a one-radian slice is considered). In order to account for the increase in thickness, a number of minor numerical adjustments are required. These include the following: The conversion of surface stress into nodal forces needs to be modified to account for the increasing radius and therefore increased force applied to the surface nodes with an increase in radius. The terms in the stiffness matrix for both the undrained and consolidation calculation steps need to be multiplied by the respective Gauss-point radius. The volume submatrix [ L E ] must be multiplied by the respective Gauss-point radius to account for the increase in volume that occurs as the radius increases. These modifications were made to Minefill-2D to allow the program to be used in either plane-strain or axi-symmetric mode. 5.13

112 Two-dimensional consolidation analysis (Minefill 2D) Boundary conditions Initial conditions The methodology adopted in Minefill-2D is to simulate the continuous placement of material by activating discrete layers of material at a defined rate. The initial placement of each layer involves an undrained step. As this step is assumed to occur over an infinitely short time and as the material stiffness of each new layer is initially very low, it is assumed that the layer being placed demonstrates completely undrained conditions (i.e. within the new layer, the increase in total stress and pore pressure with depth are equal). The existing fill mass is loaded with a vertical stress that is equal to the weight of the new layer. The response of the existing layer to this vertical force is calculated with an undrained calculation step. The reason for undertaking this undrained step is to provide a consistent match between model geometry and applied self weight, and to independently establish the stress distribution throughout the matrix in accordance with strain compatibility between the water and soil phases. The undrained loading step in Minefill-2D is undertaken using effective stress parameters. When undertaking undrained analysis Equation 5.19 simplifies to: [ K ]{ d} = { R } E n E (5.37) or in global form: [ K ]{ d} = { R } G ng G (5.38) While the formation of the element stiffness matrix remains the same, the constitutive matrix [ D ] is modified to [ ] D, which accounts for the compressive stiffness of the water phase through its bulk modulus K w. Therefore, in an undrained situation the plane strain stiffness matrix [ D ] takes the form: 5.14

113 Two-dimensional consolidation analysis (Minefill 2D) [ D] E (1 ν ) + K (1 + ν )(1 2ν ) E ν = + K (1 + ν )(1 2ν ) 0 W w E ν + K (1 + ν )(1 2ν ) E (1 ν ) + K (1 + ν )(1 2ν ) 0 w W 0 0 E 3(1 2ν ) (5.39) After the placement of each new layer, Equation 5.38 is solved to derive the nodal displacements and, like with the consolidation case, Equation 5.4 is used to derive the strains increment ( ε). These strains are then used to determine the associated changes in effective stress, total stress and pore pressure in accordance with σ = D. ε σ = D. ε u = K w. ε (5.40) (5.41) (5.42) As discussed previously, a fully-coupled analysis requires the pore pressures to be calculated at the element nodal points rather than the integration points. Therefore, pore pressures calculated at the integration points must be converted to nodal pore pressures for the consolidation calculation phase. A number of stress-recovery techniques have been proposed by researchers such as Zienkiewicz and Zhu (1992). These authors note that if the variation of properties is linear across the element, then a straightforward averaging technique would provide accurate results. As the flow calculations are carried out using 4-noded elements, the shape functions vary linearly across the element and linear interpolation is suitable. Therefore, in order to recover the nodal pore pressures, the integration-point pore pore-pressure tensor is multiplied by the inverse of the shape function to calculate the contribution of each integration point to the particular node. The contributions of all integration points (from elements surrounding the particular node) are averaged to recover the appropriate nodal point value. These values can then be used during the consolidation calculation phase. Phreatic surface control During the deposition of saturated slurry material, the solids may immediately settle, creating a free surface of water above the solids mass. Also, due to the bulk unit weight 5.15

114 Two-dimensional consolidation analysis (Minefill 2D) being greater than that of water, undrained placement creates a hydraulic gradient that is steeper than hydrostatic. This gradient causes upward water flow, which leads to water ponding on the surface. A surface water pond applies a total stress and (an equal) pore pressure at the fill surface. The magnitude of the total stress and pore pressure is proportional to the depth of the pond, and since they affect the total stress distribution throughout the fill mass and the hydraulic gradients, it is necessary to accurately take account of the accumulation of water above the fill surface. In Minefill-2D, changes in surface ponding are accounted for by monitoring the water exchange through the surface layer, in a manner almost identical to that employed in CeMinTaCo (and in the original MinTaCo). The characteristics that are taken into account in estimating the water exchange include flows through the surface layer, volumetric changes that occur in the surface layer and any self-desiccation volumetric changes. Based on the cumulative impact of these three mechanisms, the change in phreatic surface elevation is determined. During the placement of a new layer, any existing ponded water is transferred directly to the surface of the new layer. Often when delivering mine backfill to a stope, the water content required for transportation results in the solids settling (almost immediately) and free water accumulating on the surface. If this is the case, any surplus water is added to the existing surface water and consolidation calculations begin at what is defined as the settled density. All modelling described in this thesis was carried out assuming completely saturated conditions. Therefore, the only relevance of the phreatic surface is that it defines a surface on which the pore pressure is equal to atmospheric pressure. As a result, if base drainage is occurring (without the addition of an equal quantity of water at the surface), the phreatic surface would eventually be drawn below the fill surface. As discussed by Fredlund and Rahardjo (1993), in order to maintain equilibrium, water above the phreatic surface develops negative pore pressures that increase in magnitude with height according to the unit weight of water. Full saturation assumes that the pore suctions at the fill surface are always less than the air-entry suction of the fill, no matter how large these suctions become. In real stope filling, desaturation can occur, though it is 5.16

115 Two-dimensional consolidation analysis (Minefill 2D) generally where high cement contents are adopted, or it occurs late in the process, well after the development of maximum barricade loads. Therefore, at this stage, extension of the model to deal with unsaturated behaviour has not been attempted, but this is certainly a desirable aspect that could be investigated in future work. Boundary node control Changes in boundary conditions occur during the transition from an undrained loading calculation step to a consolidation calculation step. During this change in calculation routine, the pore pressures at the controlled boundaries change from the value calculated during the undrained step to that specified by the boundary condition. This change in pore pressure can be accounted for by reassigning the nodal pore pressure values, but this change in pore pressure must be reflected in a change in effective stress and associated strains. Also, as discussed in the previous section, the initial placement of material can create a surface water pond or an upward hydraulic gradient which allows water to accumulate on the fill surface. Any accumulated water would apply a total stress and pore pressure to the surface nodes, with the magnitude being a function of the water depth. This condition cannot be managed by eliminating the surface nodes from the calculation scheme, as later they must be reintroduced into the calculation scheme after the placement of the next layer. In both cases, the initial and eventual nodal pore pressures are known, and therefore the technique that is commonly adopted to apply known nodal displacement increments can be utilised to address these issues. The following section presents how this logic can be applied to the situation of changing nodal pore pressures along a boundary. Assume the problem to be solved is: k... ki... kn { u} ( ) [ Φ ]{ u}... k k... + t 1 j... 1n 1 G ng k { } [ ]{ ( } ) = + Φ u t ij... k u... jn j G ng j knj... knn { u} n... + [ Φ ]{ u} G ( ) ng t n (5.43) 5.17

116 Two-dimensional consolidation analysis (Minefill 2D) When progressing from an initial condition ({ u } Undrained the boundary condition ({ u } BC ) the change in pore pressure { u} j accordance with: ) to a condition specified by can be determined in { u} j = { u cons } = { u} BC { u} Undrained (5.44) This situation occurs when progressing from the undrained calculation step to the boundary condition of atmospheric pressure at the barricade location or due to a change in surface nodal pore pressure and total stress from a change in surface pond elevation. Therefore, { u} = { } j u cons can be simply substituted into the j th row of the consolidation matrix and all other terms in the j th row of the [k] matrix can be removed. Also, as the value of { u} j is now known, it can be subtracted from both sides of the equation such that: k kn1 { u} [ Φ ]{ u} k n 1 G ng 1 1 j { u} j = cons k { u} + [ Φ ]{ u} nn... n G ( ) t k.(... + [ Φ ]({ u }) t) { u } cons ( ) ( [ ]({ }) ) ng t knj ΦG ucons j t n G j (5.45) Given this procedure, the pore pressure change can be incorporated into the calculation scheme such that it is appropriately reflected in changes to effective stress and strain in addition to pore pressures. Furthermore, by maintaining the terms in the calculation matrices, they can be included into the conventional calculation scheme when required Solution to the global equations As will be described in Section 5.4, a non-linear constitutive equation is adopted to represent the cemented mine backfill. In order to solve the non-linear constitutive relationship, the visco-plasticity technique (Zienkiewicz and Cormeau, 1967) was adopted. The associated numerical code is taken from Smith and Griffiths (1998). 5.18

117 Two-dimensional consolidation analysis (Minefill 2D) The visco-plasticity technique allows the material to be loaded to a stress state that is beyond the yield surface. If the yield function [F y ] is positive (i.e. yielding has occurred) this function is combined with the flow rule Q and viscosity parameter ( ) σ vp determine the visco-plastic strain rate ( ε& ) in accordance with: µ to Q ε& vp = µ. F y. σ (5.46) Ideally, µ should be determined experimentally, but as the main interest is in determining steady-state stress and plastic strains, the transient stress path is not important. It will be shown later (in Equation 5.48) that when determining stress states and unbalanced forces, µ cancels, making the result independent of the chosen value. The visco-plastic strain rate vp ε& is combined with a pseudo-time step ( ) to t cr determine the increment of plastic strain vp ε. The time step used in the time-marching process ( t) must be limited to maintain stability. For the Mohr-Coulomb yield surface, which is adopted in Minefill-2D, it has been shown that the maximum stable timestep ( t cr ) is given by: ( 2ν ) 2 1 t cr = µ G (5.47) 2 ( 1 2ν + sin φ) where G is the shear modulus, ν is the Poisson s ratio and φ is the friction angle. The visco-plastic strains are combined with the material stiffness to evaluate the stress increment σ. σ = D. ε µ. φ δq σ [ F] D tcr (5.48) where D is the elastic stiffness matrix. In addition, the last term in Equation 5.48 is used to derive the unbalanced body stresses. These body stresses are integrated over each Gauss point to determine unbalanced body forces, which are redistributed to other nodes in the finite element mesh during subsequent iterations. The solution is iterated until no Gauss-point stress 5.19

118 Two-dimensional consolidation analysis (Minefill 2D) state violates the yield criterion (within a certain tolerance). The convergence tolerance adopted throughout this thesis was During each calculation step, it is assumed that the material properties remain constant but these properties are updated after each increment of load or time. A flaw that exists with this approach is the implementation of the strain-softening criteria into the viscoplasticity solution scheme. Inherent in the visco-plasticity solution is the assumption of perfect plasticity, and therefore body forces are calculated based on the assumption of plastic strains not absorbing (or releasing) energy. But the degradation of material strength with plastic strain does result in an energy release. Therefore, a rigorous solution should take account of this energy release when calculating the body forces. By updating the yield strength (taking account of this strength degradation) at the end of each increment, and mapping the stress state back onto the yield surface during the following timestep the energy release is, to some degree, taken into account. Detailed and rigorous treatment of this aspect is beyond the scope of the thesis but future work may consider applying a secant stiffness solution algorithm, which is better suited to managing strain softening. To minimise the likelihood of numerical drift, the maximum strain increment is maintained below in any calculation increment. If this tolerance is exceeded in the undrained load calculation, the load increment is reduced, or if exceeded in the consolidation calculation the consolidation timestep is reduced, and the calculation repeated to ensure that this tolerance criterion is satisfied. Currently this process is carried out manually, but future versions of Minefill-2D will combine the coefficient of consolidation with the element size to derive a suitable timestep in a similar way to that suggested by Yong et al. (1983) for the one-dimensional consolidation situation. This approach would increase the efficiency of this process by maximising the timestep increment without exceeding the strain criteria. 5.4 MATERIAL BEHAVIOUR Influence of cementation on governing equations Immediately after placement, and before the cemented mine backfill has reached initial set, the material is assumed to behave in accordance with the uncemented material 5.20

119 Two-dimensional consolidation analysis (Minefill 2D) properties. However, as demonstrated in Chapter 4 (using CeMinTaCo), the time-scale associated with consolidation may be similar to that of the hydration process. As a result, the cement hydration process must be fully coupled with the consolidation process. As discussed previously (in Chapters 3 and 4), the cement-hydration process influences the consolidation behaviour. This influence was shown to be most significantly associated with: Stiffness: Aspects that can influence the material stiffness include the initial uncemented density, cement hydration, and damage to the cement bonds due to excessive strain. The evolution of these influences the constitutive matrix [ D ], which influences the global stiffness matrix [ K G ]. Strength: This can be influenced by cement hydration as well as by destruction of cement bonds due to excessive stress. Strength or yield stress influences the constitutive matrix [ D ] and the global stiffness matrix [ ] selection of stiffness properties. K G as it governs the Permeability: This can be influenced by material density, particle size distribution and cement hydrate growth. These mechanisms interact to influence the permeability matrix [ Φ G ]. Self desiccation: This refers to the volume changes that occur during the hydration process (as discussed in Chapter 3) and can be taken into account through the internal sink term Q. Therefore, in order to take account of the cement hydration processes during the consolidation process, the governing consolidation equations (Equation 5.31) are solved such that the relevant terms are a function of time, material state (void ratio), and cement content (t, e and C c ): 5.21

120 Two-dimensional consolidation analysis (Minefill 2D) [ KG ( t, e, Cc )] [ LG ] T [ L ] t. [ Φ ( t, e, C )] G G c { d} { u} ng = ng { RG } ([ n ( t, e, C )] + Q( t, e, C ) + [ Φ ( t, e, C )]{ u} ) t G c c G c ng (5.49) Details of the cemented material relationships incorporated into Equation 5.49 were discussed previously in Chapter 3, and are discussed further in the following section Constitutive model, [ K ([ D ( t, e, )]) ] G C c The overall approach to the material model used in Minefill-2D is similar to that described in Section 3.2, where the cemented and uncemented material behaviour is superimposed to represent the overall response, and the small strain stiffness is linearly related to the material strength while the secant stiffness is degraded in accordance with the proximity of the loading surface to the yielded surface. Section 3.2 focused on a model to represent one-dimensional loading, while the description that follows here focuses on the response of the material under two-dimensional loading conditions. In what follows, there is considerable repetition of material previously dealt with in Chapter 3; this has been done for completeness, and to make it easier to follow the developments. In order to represent the behaviour of the material after placement but prior to initial set of the cement, a power law was adopted to relate the void ratio to the applied effective stress. This power law takes the form of: a c b ( ) c e = σ (5.50) where e is the void ratio and σ is the mean effective stress, while a c and b c are curve fitting constants. This function has been successfully applied to the compression behaviour of uncemented mine tailings (Fahey and Newson, 1997 and Fahey et al., 2002). Note that this differs from the Cam Clay approach to representing material compression used in Chapter 3 (Equations 3.1 and 3.2). By differentiating Equation 5.50 and combining the result with well known elastic relationships, the uncemented shear stiffness G (uncem) can be derived such that: 5.22

121 Two-dimensional consolidation analysis (Minefill 2D) G ( uncem) σ e + 1) = e 2 1 ( + ν ) = 2a ( e + 1) b ( 1+ ν ) e ac ( c c c 1 1 b (5.51) where ν is the drained Poisson s ratio. Once the initial set point is reached, it is also necessary to take account of the influence of cementation on the behaviour. The material model used in Minefill-2D assumes a Mohr-Coulomb failure criterion, where the size of the yield surface is governed by the material state and degree of hydration. The shear stiffness is dependent on the size of the yield surface and the mobilised stress relative to the yield stress. The compressive stiffness is then related to the shear stiffness in accordance with an assumed value of Poisson s ratio. This is a much simpler approach than that used in CeMinTaCo, where a model similar to the Structured Cam Clay model was used to take account of possible yielding on the compression side of the yield surface, an aspect that, as explained earlier, has not been incorporated into Minefill-2D. In the Mohr-Coulomb yield surface, it is assumed that the friction angle is independent of cementation, and during hydration, only the cohesive component evolves. This is consistent with the findings of Clough et al. (1981) and Schnaid et al. (2001), who suggest that cementation has little influence on the friction angle. The cohesive component of strength increases as a result of cement hydration and decreases due to damage in accordance with: Hyd c = t D p εs (5.52) where c is the change in the effective cohesion, hydration with time and p strain ( ε S ). D ε p S Hyd t is the change in c due to is the degredation in c with time due to plastic shear This differs from the approach taken in CeMinTaCo where, firstly, the damage term is a function of the vertical compressive strain, and secondly, in addition to a damage term degrading the cement contribution to the yield surface, a hardening term increases the 5.23

122 Two-dimensional consolidation analysis (Minefill 2D) size of the uncemented yield surface. This hardening term is not included in Equation 5.52, but, as the cohesive strength is a function of the cement content and void ratio (in accordance with Equation 5.53), any soil compression will manifest in an increase in Hyd over subsequent timesteps. Soil hardening is accounted for in the hydration function by calculating the hydration component as a function of both void ratio (e) and cement content C c, expressed as a percentage. It was shown in Section 3.2 that the unconfined compressive strength (q u ) can be related to e and C c by Equation (3.6). Since the friction angle is assumed to be constant, cohesion (c ) is linearly related to q u. This implies that a modified version of Equation 3.6 can be used to relate C c and e to c (in kpa). The modification involved the introduction of another constant term (A c ) which is ratio between c and q u. 0.1 X. C + C e c = A c c c exp Z. Cc + W (5.53) where A c, X, Z and W are curve fitting constants. As in CeMinTaCo, the exponential relationship proposed by Rastrup (1956) (Equation 3.7) is used to relate the cumulative evolution of cement hydration (or maturity, m) against time. By differentiating Equation 3.7 and combining this with Equation 5.53 the rate of development of cohesion with time can be represented. This function is c 1 = t d d X. C + C e.exp. Aexp c c 1 (5.54) ( ).5 t * t * Z. Cc + W If the material is strained beyond yield, progressive breakdown of the bond strength can occur. This mechanism has been accounted for by reducing c linearly as a function of the plastic shear strain p ε S (i.e the D ε p S term in Equation 5.52). The breakdown of cementation can be characterised using a triaxial test. An example showing the stress-strain plot from a triaxial test on cemented paste fill is presented in Figure 5.4 (a). Figure 5.4 (b) shows the assumed evolution of the Mohr-Coulomb yield surface during this test. 5.24

123 Two-dimensional consolidation analysis (Minefill 2D) Figure 5.4 (a) shows that as the material is loaded beyond yield, there is a progressive reduction in the shear strength until it plateaus. The strength reduction is considered to be a result of a progressive breakdown in the cement bonds until eventually all of the bond strength is destroyed and the shear strength is purely a function of the frictional strength and confining stress. The impact of cementation breakdown on the yield surface is demonstrated in Figure 5.4 (b), where the gradient of the yield surface remains constant (due to the assumption of a constant friction angle), but c is degraded between the fully cemented and uncemented surfaces. The rate of breakdown of c is assumed to be linearly related to the plastic shear strain according to the behaviour in triaxial compression. In Section 3.2.6, it was shown that the cement-induced component of stiffness can be linearly related to q u. Therefore, the cement-induced component of stiffness can also be linearly related to c, assuming a constant friction angle. This assumption is convenient for modelling since, by evolving the cohesive intercept in accordance with Equation 5.52, the cement-induced component of stiffness can be linearly related to this value in accordance with a constant rigidity term. To represent the pre-yield response, a non-linear stiffness function was adopted. This function degrades the material tangential stiffness linearly as the shear stress approaches yield in accordance with: G τ f τ = G0 1 mob t(cem) (cem) (5.55) max where τ mob is the mobilised shear stress, τ max is the yield stress, G t(cem ) is the cement contribution to the tangential shear stiffness, G 0(cem) is the cement component of the small strain shear stiffness and f is a curve fitting constant. If the uncemented soil contribution to the material stiffness is very low and f is equal to 1, infinite strain is required to reach the ultimate shear strength (τ max ). Thus the peak is never reached and softening never occurs. For a model that has a similar drawback, Fahey and Carter (1993) suggested the introduction of a constant term f, which if less than 1, ensures that the material fails at finite strain. The actual value for f can be derived from a triaxial stress-strain curve. 5.25

124 Two-dimensional consolidation analysis (Minefill 2D) Figure 5.5 compares the adopted model with experimental data from local strain gauges on a cemented backfill sample loaded in a triaxial compression. The comparison suggests that for this particular material, the proposed model provides a reasonable representation with f = Others (Fahey and Carter, 1993) suggest that the secant stiffness degrades in accordance with a hyperbolic function while the tangential stiffness degrades in accordance with the square of the hyperbolic function. While a more complex model may provide an improved representation, the linear relationship was adopted because it provides modelling convenience and appears to represent the experimental data reasonably well. After the cement-induced component of stiffness is calculated, it is directly added to the uncemented stiffness (from Equation 5.51) to determine an appropriate stiffness for the cemented soil mass. The superposition of the cemented and uncemented properties provides a convenient method of addressing the evolution from an uncemented material to a fully-cemented material. If required, the approach is also suitable for simulating the breakdown of the cementation due to excessive shear stress. Modelling has assumed a constant Poisson s ratio. Therefore, after an appropriate shear stiffness is evaluated, this value can be used to derive the bulk modulus in accordance with well documented elastic relationships. It is recognised that this approach neglects the potential for strain localisation but with appropriately sized boundary elements, this approach is considered to be reasonable for this thesis Permeability model, [ Φ ( t, e, C )], [ n ( t, e, C )] G c G c The permeability function adopted in Minefill-2D is the same as that presented in Section 3.3. This model is a modified version of that originally suggested by Carrier et al. (1983), but in this case the void ratio term is modified to account for both cement hydrate growth as well as soil compression. This relationship was previously presented as Equation 3.15 and is repeated below: c k = k ( e ) eff d k 1 + e (3.15 bis) 5.26

125 Two-dimensional consolidation analysis (Minefill 2D) Self desiccation, Q(t,e,C) The process of self desiccation was addressed in Section 3.4, where a relationship between the rate of volume change in an element Q ( t e, ), C c, the cement weight per element (W c, ), the efficiency of hydration (E h ) and a constant to represent the rate of hydration (d) was presented. This relationship was implemented into Minefill-2D as an internal sink term and is repeated below: Q 1 d d c (3.32 bis) ( t, e, C ) = E h. Wc..exp 2 * * t 1.5 t 5.5 MODEL VERIFICATION Comparison with analytical/numerical solutions In the following section, Minefill-2D is compared with a range of analytical and numerical solutions to verify its performance. The first simulation involved an elastic, weightless, one-dimensional consolidation problem, with 2-way drainage the most basic problem encountered in any undergraduate textbook treatment of Terzaghi s consolidation solution. This analysis assumed a Young s modulus of 100 MPa and a permeability of 1x10-6 m/hr. Figure 5.6 presents an illustration showing the problem geometry. The proportion of excess pore pressure at the various elevations after 30 and 50 hours of consolidation are shown in Figure 5.7. Also shown in Figure 5.7 is the well-known analytical solution to this problem, for the same times. This demonstrates that the conventional consolidation behaviour can be well represented by Minefill-2D. To assess the performance of Minefill-2D with respect to self-weight consolidation, a comparison between the Minefill-2D program and the commercially-available program Plaxis (Vermeer and Brinkgreve, 1998) was undertaken. The development and dissipation of excess pore pressures due to the deposition of a fresh layer of material was simulated using these two programs. This analysis involved placing a 4 m thick layer of material with a saturated unit weight of 19.5 kn/m 3, a Young s modulus of 100 MPa and a permeability of 1x10-6 m/hr. The problem is illustrated in Figure

126 Two-dimensional consolidation analysis (Minefill 2D) Immediately after placement, the base and top boundaries were set to atmospheric pressure and consolidation was initiated. For the Minefill-2D case, the initial pore pressure profile was determined using an undrained step (based on self-weight loading) followed by the top and base boundary conditions being reset, in accordance the technique described previously in this chapter. Figure 5.9 indicates that the undrained calculation step (in Minefill-2D) provides an accurate method of establishing the initial conditions, and the subsequent consolidation calculations are consistent with results from Plaxis. To assess the performance of the self-desiccation mechanism in Minefill-2D, the model was compared with the analytical solution (Equation 3.27). The problem simulated was what was referred to as a Hydration Test in Section Modelling represented a sample placed into a triaxial cell where the cell pressure was increased to 500 kpa with the back pressure valves closed. The material properties included a void ratio of 1.05, a cement content of 5%, an initial effective bulk modulus of 20 MPa and an ultimate bulk modulus of 420 MPa. The rate of hydration was assumed to be in accordance with Equation 3.7, with a hydration coefficient (d) value of -1.5 days 1/2, and an efficiency of hydration (E h ) of 6.4%. The initial set time was 12 hours. This example is illustrated in Figure Figure 5.11 compares the variation in pore pressure (u) and the development of effective stress (σ ) against time, for an element test as determined using Minefill-2D and the analytical solution presented in Section for this problem. The analytical solution for undrained self desiccation (Equation 3.27) is presented as symbols while the Minefill-2D results are presented as lines. Figure 5.11 indicates that the self-desiccation component of the model is performing in the appropriate manner. It should also be noted that cement-induced development of stiffness against time for Minefill-2D was also compared with the measured results and found to provide a match. The combination of these is evidence that the cementation component of Minefill-2D is providing accurate results. The final modelling carried out to assess the performance of Minefill-2D (against analytical solutions) was a falling head permeability test. The purpose of this was to ensure the algorithm controlling the elevation of the phreatic surface above the fill mass 5.28

127 Two-dimensional consolidation analysis (Minefill 2D) is operating appropriately and also to ensure that flow calculations are performed appropriately in terms of total water head. Modelling involved establishing a 4-m thick saturated soil layer with 0.8 m of water above the layer and atmospheric pressure specified along the base boundary. The material was assigned a Young s modulus of kpa (to ensure that volumetric changes were minimal) and a permeability of 5x10-5 m/s. An illustration showing this problem is presented in Figure Figure 5.13 shows a comparison between the elevation of the phreatic surface (above the fill surface) calculated using Minefill-2D and that calculated according to Darcy s law, against time. Figure 5.13 indicates that the change in phreatic surface elevation determined using Minefill-2D is consistent with that calculated using Darcy s law. This demonstrates that the algorithm controlling the movements of the phreatic surface above the fill surface and the component controlling flows due to gravitational forces, are providing accurate results Comparison with CeMinTaCo Because CeMinTaCo is a modification of the well tried tailings consolidation program MinTaCo, which takes account of the influence of cementation on the consolidation process, this provides an excellent basis to validate the performance of the new finite element program Minefill-2D. Furthermore, because CeMinTaCo uses a Lagrangian coordinate system and takes full account of yielding in one-dimensional compression, this comparison provides an opportunity to investigate the significance of these characteristics on the numerical results. The material properties adopted for this comparison are those deemed typical for a cemented paste backfill. These properties are presented in Table 5.1. Using these properties, a one-dimensional filling situation was simulated, adopting an impermeable base condition. This simulation involved the accretion of material at a constant rate of 4 m/day for a period of 4 days. Figure 5.14 presents the development of total vertical stress (σ v ) and pore pressure (u) at a point 2.0 m above the base against time. 5.29

128 Two-dimensional consolidation analysis (Minefill 2D) The results presented in Figure 5.14 indicate that the pore pressure calculated using CeMinTaCo is greater than that calculated using Minefill-2D. It is also clear that the point where the curves representing the pore pressure and total vertical stress diverge also differs for the two models. Examination of the output from the two models indicates that during the very early stages of strength and stiffness development, these material properties begin to change (i.e. reach initial set ) at a slightly different times in the two programs. In CeMinTaCo, the cemented strength and stiffness are dependent on the difference between the cemented and uncemented yield surfaces in one-dimensional compression, while in Minefill-2D the cemented strength and stiffness are independent of the uncemented yield surface. Therefore, in CeMinTaCo during the early stages of cement hydration, any compression of the soil matrix hardens this material and softens the cemented yield surface, effectively merging these surfaces. However, in Minefill-2D, hardening of the uncemented soil simply acts to increase the density and therefore increase the influence of cementation in the next timestep. The overall influence of this behaviour is to effectively delay the initial set point, but the calculated behaviour is essentially the same beyond this point. This is demonstrated in Figure 5.15, which again presents the calculated pore pressure and vertical stress, for the one-dimensional accretion of material at 4 m/day, but in this case the initial set point for the Minefill-2D example has been delayed an additional 0.4 days. By making this adjustment the results from the two programs are equal. While this initial set point has been shown to have an influence on the result of the modelling, and is therefore an aspect that should be addressed, it is suggested that curing samples under effective stresses induced by self desiccation (as suggested in Chapter 3), and adopting the measured initial set, Minefill-2D can provide a good representation of the behaviour Stope mesh details Element size To investigate the influence of mesh size on the modelling results, and choose an appropriate mesh size for the sensitivity study in Chapter 7, a convergence study was 5.30

129 Two-dimensional consolidation analysis (Minefill 2D) undertaken. This study adopted typical paste backfill material properties and involved identical simulations of the filling process using Minefill-2D in plane strain mode with various mesh sizes. The stope geometry simulated was 10 m wide and 40 m tall with a 6 m high drawpoint, 5 m in length. Mesh sizes adopted in the analysis included: A coarse mesh consisting of 5 elements horizontally across the stope width, 2 elements along the drawpoint length, 3 elements representing the drawpoint height and 20 elements to represent the stope height. This mesh is presented in Figure 5.16a. A medium mesh consisting of 10 elements horizontally across the stope, 5 elements along the drawpoint, 6 elements representing the drawpoint height and 50 elements representing the stope height. This mesh is presented in Figure 5.16b. A fine mesh consisting of 40 elements horizontally across the stope, 10 elements representing the drawpoint length, 10 elements representing the drawpoint height and 80 elements representing the stope height. This mesh is presented in Figure 5.16c. These meshes were used to simulate the same filling sequence, which consisted of filling the stope at a constant rate of 0.5 m/hr for 12 hours, at which time filling was suspended for 24 hours prior to a second filling at a constant rate of rise of 0.5 m/hr from 6 m to the top of the 40 m high stope. In this analysis, all boundary nodes (apart from those along the fill surface) were fixed against displacement in both the vertical and horizontal direction. Nodes along the barricade boundary were maintained at zero pore pressure. The calculated pore pressure, at the centre of the stope floor is plotted against time for each of the meshes in Figure 5.17, while the calculated barricade stress is plotted against time for each mesh in Figure These figures indicate that the coarse mesh produces considerable different results to the other meshes, but the results from the medium and fine mesh appear very close. To investigate the influence of element size throughout the mesh the vertical total stress (σ v ) contours at the completion of filling for the coarse, medium and fine meshes are 5.31

130 Two-dimensional consolidation analysis (Minefill 2D) shown in Figures 5.19 a, b and c respectively. Again, comparison of these images indicates that the coarse mesh produces significantly different results to the fine and medium mesh. Figures 5.19 b and c are very similar with the fine mesh indicating slightly higher stresses than the medium mesh. The accurate results with the medium sized mesh are due to the relatively low pore pressure and effective stress gradients throughout the simulated geometry. Considering the minor variation in results between the fine and medium mesh and the significant difference in computational time, it is considered most suitable to adopt the medium mesh in the remainder of the calculations in this chapter as well as the sensitivity study presented in Chapter 7. Interface behaviour In Minefill-2D, the interface between the fill and surrounding rockmass was represented using conventional elements where the boundary nodes (corresponding to the interface) are fixed against displacement in both directions. The significance of deformation at this interface is evident in Figure 5.19, where the σ v contours change sharply in direction near the stope boundaries, indicating a stress discontinuity. Reducing the element size reduces the region of influence such that it is difficult to identify shear planes in the fine mesh. As shear planes are most likely to form immediately adjacent to the interface, the boundary elements were reduced in size so that any yielding was concentrated at the interface. Apart from the influence on the stress transfer to the surrounding rockmass, the development of shear planes in these elements would have minimal influence on the overall consolidation behaviour. An alternative approach would have been to introduce interface elements to concentrate any yielding along a defined plane. This may be considered in future developments Comparison with in situ measurements To assess the ability of Minefill-2D to capture the important aspects associated with the mine backfill deposition process, the model output was compared with in situ measurements. In this analysis, the calculated pore pressure at the centre of a stope is compared with actual pore pressures measurements during filling at site Paste Fill A 5.32

131 Two-dimensional consolidation analysis (Minefill 2D) (PFA) in August This is the same material used in the sensitivity study presented in Chapter 7. The plan dimensions of the stope were 15 m x 18 m and 50 m tall. Using data collected on the log sheets from the paste-fill plant, the volume of placed material was combined with the actual stope cross sectional area (at various elevations) to determine the elevation of the fill surface against time. This approach is considered valid as this material typically does not experience significant volumetric changes during placement and subsequent consolidation. The filling sequence consisted of filling the first 10 m at a vertical rate of rise of m/hr prior to a 24-hour rest period. After the rest period, filling continued at a vertical rate of rise of m/hr until the stope was filled. It should be noted that the rate of rise adopted in the modelling was varied to match the actual rate for each individual layer. While the axi-symmetric geometry could have been more appropriate to represent the stope geometry, the plane strain version of Minefill-2D was adopted to allow the drawpoint to be represented. Based on a numerical comparison between an equivalent axi-symmetric and plane strain stope, an 11 m wide plane-strain stope was deemed appropriate to represent a stope of 15 m x 18 m plan dimensions. Pore pressure (u cl ) in the field was measured using a vibrating wire piezometer that was installed on the floor of the stope prior to the commencement of filling. Readings were taken on an automatic data logger at 2 minute intervals throughout the filling process. The material used to fill the stope was PFA mixed with 3.1% cement and delivered at a density of 75% solids by weight. Material properties used in the back analysis were derived using a 1-D compression test, a hydration test and a triaxial test. Laboratory testwork was actually carried out for PFA material at the same density (75% solids by weight) but containing 3% cement, prior to field testing (Helinski et al., 2007). Due to the close match of the tested material to the actual mix adopted, further testing was not undertaken with 3.1% cement. The material properties adopted for the model are presented in Table 5.2. Figure 5.20 presents a comparison between the measured pore pressure and that calculated using Minefill-2D. Also shown in Figure 5.20 is the total vertical stress (σ v ) that would be applied to the stope floor if no arching occurred. 5.33

132 Two-dimensional consolidation analysis (Minefill 2D) Because of the low permeability and stiffness of the PFA material (in the uncemented state) soon after placement, u cl initially increases at the same rate as σ v. This is an indication that no consolidation is occurring, and that the fill mass is fully saturated and it also provides confidence that the vibrating wire piezometer is fully saturated, and measuring water pressures accurately. Soon after the material reaches initial set, u cl diverges from σ v. However, as fill continues to be deposited, and the increase in u cl due to the accretion of material is greater than the reduction from consolidation, u cl continues to increase. After 35 hours, filling stops, but as consolidation continues u cl decreases rapidly. When filling resumes (at 59 hours), there is an increase in u cl, but as filling extends up into the stope, some of the fill self weight is redistributed to the surrounding rockmass. As a result, the incremental increase in σ v at the piezometer location reduces. This results in u cl plateauing and then reducing at the later stages of filling. Overall, Figure 5.20 indicates that using independently-determined material properties Minefill-2D provides a very good representation of the pore pressure in the centre of the stope floor during filling, which indicates that Minefill-2D appears to be representing the consolidation behaviour of a cemented paste backfill accurately Investigation of the arching mechanism A study was undertaken using Minefill-2D to investigate the significance of the arching mechanism in a typical mine backfill scenario. Minefill-2D was used to simulate a 13 m wide, 40 m tall plane-strain stope that was filled at a constant rate of rise of 0.4 m/hr. The material properties adopted in this study where considered typical for a cemented paste backfill and were the same for both scenarios analysed. These properties are presented in Table 5.3. To investigate the significance of stress redistribution onto the surrounding rockmass ( arching ), analysis was undertaken assuming boundary nodes that were fully fixed in both directions ( fixed BC ) and boundary nodes that were fixed against horizontal displacement but free to displace in a vertical direction ( free BC ). The fixed-bc and free-bc cases are illustrated in Figure 5.21a and b, respectively. The calculated pore pressure (u) and total vertical stress (σ v ) on the stope centre line 1 m above the stope floor are plotted against time during filling in Figures 5.22 for both 5.34

133 Two-dimensional consolidation analysis (Minefill 2D) cases. Also shown in Figure 5.22 is the vertical total self-weight stress from the overlying fill calculated assuming no arching. Figure 5.22 shows that during the early stages of deposition both u and σ v are equal to the vertical self-weight stress for both cases. This is because there is no consolidation, and even with consolidation the ratio of fill height to width is insufficient to create any noticeable stress redistribution away from the centre of the stope. After about 12 hours, u diverges from σ v (indicating consolidation) but the ratio of consolidated fill height to width is insufficient to create a stress redistribution. After 30 hours, 12 m of fill is in place and, of this, the bottom 6 m has achieved a considerable amount of consolidation. In the fixed-bc scenario, the rate of increase in σ v is less than that for the free-bc case, because some of the applied vertical stress from the accretion of fill material is redistributed to the fixed boundary (which represents stiff rockmass) as arching. It is interesting to note that, even though the consolidation characteristics are the same for both scenarios, the calculated u values also diverge at this point. This is because arching, which is occurring in the fixed BC case, is reducing the amount of total stress transferred to the stope floor during the accretion of additional material. Finally, it is interesting to note that in the free-bc case, σ v is not equal to the total selfweight stress, as would be expected in a true one-dimensional case. The reason for this result is a stress redistribution that is occurring around the drawpoint opening. This stress redistribution acts to spread some of the vertical stress around the drawpoint opening, which actually reduces σ v in the centre of the stope floor. This will be discussed in further detail below. Contours of σ v at the end of filling for the fixed BC and free BC case are presented in Figures 5.23a and b respectively. In addition, the σ v along the centreline for both cases and that due to self-weight stress without arching is presented in Figure Comparison of these figures indicates that for the upper m, the total vertical stress for both scenarios is approximately the same. This is a consequence of reduced consolidation in this area and an insufficient height-to-width ratio to generate arching. But progressing further from the top of the stope, the contour plots are significantly different. Figures 5.23a and 5.24 indicate that in the fixed-bc case, σ v (along the centre 5.35

134 Two-dimensional consolidation analysis (Minefill 2D) line) remains relatively constant at approximately 200 kpa for the entire height of the stope. This is an indication that significant arching is occurring. Figures 5.23b and 5.24 indicates for the free-bc case no arching occurs throughout the stope, resulting in an increase in stress with depth that is equal to the self-weight stresses. Approaching the drawpoint, the rate of stress increase with depth reduces, which is a consequence of arching around the relatively soft drawpoint opening. Even though stress cannot be transferred vertically along the stope walls, a semi-circular stress arch is established between the corner of the stope floor (opposite the drawpoint) to above the drawpoint, as illustrated in Figure 5.23b. This section has demonstrated that stress redistribution to the surrounding rockmass can make a significant contribution to reducing the vertical stress in a typical mine backfill stope. Two extreme cases were presented, but the trends are applicable for stopes of different plan dimensions. As the stope plan area increases, the situation tends towards the free-bc case,where little arching occurs, while a reduction in stope plan area would cause the result to trend towards the fixed-bc case, or, in the case of even narrower stopes than that presented, would promote additional stress redistribution leading to even lower vertical stresses. 5.6 CONCLUSION This chapter has presented the basis of the two-dimensional cemented tailings consolidation program Minefill-2D. The program provides results that are consistent with well-established analytical solutions to drainage-, consolidation- and cementationtype problems. When compared with in situ monitoring data, Minefill-2D was shown to provide a very good representation of the mine backfill deposition process. Overall, this assessment provides confidence that Minefill-2D is performing appropriately and can be used to represent the mine filling process. Finally, a brief study was undertaken to investigate the arching mechanism in a typical mine backfill situation. This study revealed that stress arching to the stiff surrounding rockmass can make a significant contribution to reducing vertical total stresses in a typical mine backfill stope. 5.36

135 Centrifuge Modelling CHAPTER 6 CENTRIFUGE MODELLING 6.1 INTRODUCTION A centrifuge modelling experiment was undertaken to demonstrate experimentally some of the points that have been made in this thesis and to verify the performance of Minefill-2D for representing the consolidation and arching processes in a cementing backfill. In this experiment, a 3-D stope was represented by a cylindrical container i.e. an axi-symmetric representation. This axi-symmetric geometry was chosen for practical experimental reasons outlined later, but also because the axi-symmetric geometry could be modelled numerically using Minefill-2D. Centrifuge modelling (Schofield 1980) is an experimental technique commonly adopted in geotechnical research. The concept behind centrifuge modelling is that by rotating a scale model, the centrifugal forces increase the gravitational forces, increasing the stress levels within the soil mass. By increasing the gravitational forces the model size can be proportionally reduced while still creating an equivalent self-weight stress distribution. In soil mechanics, it is important to reproduce similar stress conditions, as soil behaves differently (particularly with respect to volume changes during shearing) under different stress levels. In the language of centrifuge modelling, a centrifuge imposes an acceleration level of N times the acceleration due to the earth s gravity (g) i.e. an acceleration of Ng. Provided the soil in the model is of the same density as that in the prototype, an acceleration of Ng increases the unit weight by a factor of N, such that at a depth z in the model, the vertical stress is the same as that at a depth Nz in the prototype. The factor N is therefore thought of as being the length scaling factor of the model test. Since the time-scale for consolidation depends on the square of the drainage path length, the time for consolidation in the model is N 2 times faster than in the prototype. Therefore, the centrifuge is an ideal tool for investigating problems involving consolidation. However, in this case, the interest is in consolidation and cement hydration in mine backfill, where the time-scales of the two processes are similar, and hence where these two processes are coupled. However, unlike for consolidation, the time-dependency of cement hydration does not depend on any length scale, and hence 6.1

136 Centrifuge Modelling the time for hydration in the prototype is not reduced in the model. Therefore, if the time-scales of consolidation and hydration are similar in the prototype, they cannot be similar in a centrifuge model in which the same materials are used, and therefore the coupling between these processes cannot be studied directly in a centrifuge model. The aim of the centrifuge experiment was to investigate the interaction between consolidation and the total stress distribution for a consolidating soil undergoing cementing in a model that represents an idealised stope. This test specifically focused on how consolidation influenced the stress transferred through the soil mass and that transferred as shear to the surrounding stiff container. This concept is fundamental to all of the work discussed in this thesis. The aim of this work had originally been to conduct an experiment that coupled the time-dependent processes of loading, consolidation and cement hydration. Coupling of these processes proved to be impossible due to the small scale of the model, as explained above. Although the stress field could be scaled up in the experiment, the consolidation time was still dictated by the actual drainage path length in the model. This created very high hydraulic gradients that accelerated conventional drainage-type consolidation, such that the time-scale for consolidation was very much less than that for hydration. As a result, the material completely consolidated prior to the commencement of hydration. 6.2 EXPERIMENTAL APPARATUS The experimental apparatus is designed to capture the important aspects relating to the distribution of stress around a stope during the placement of fill material. A schematic showing a section view of the apparatus is presented in Figure 6.1. The apparatus consists of a hollow cylinder (620 mm high and 180 mm in diameter with an average wall thickness of 6 mm), machined on the inside to provide a rough interface with the fill material. The cylinder is fitted with six axial and six hoop Wheatstone bridge strain-gauge sets spaced at 100 mm centres along the vertical axis of the cylinder. Each strain-gauge set consists of 4 gauges spaced at 90 intervals around the cylinder circumference. The readings from each of the strain gauges in the set are 6.2

137 Centrifuge Modelling averaged to provide the value at that particular elevation. The Wheatstone bridges are completed in each case by external resistors. The purpose of the strain gauges is to measure the hoop and axial strains in the cylinder. As will be discussed later, the axial and hoop strains can be combined to determine the axial and hoop stress in the cylinder. As the strain gauges are sensitive to any temperature variations, each strain gauge site is fitted with a thermocouple for ongoing temperature measurements. Photographs of the strain gauged cylinder are shown in Figures 6.2 (a) and (b). A floating base is inserted into the bottom of the cylinder. This base fits into a smooth section of the cylinder to ensure a water-tight O-ring seal. The base rests on three loadcells that measure the load carried by the base throughout the test. A drainage hole is drilled into the centre of the base, with a filter placed immediately above this surface. The drainage hole is connected to a pore pressure transducer to monitor the change in pore pressure at the base location throughout the experiment. A photograph of the base arrangement showing the floating base, loadcells and the base stand is presented in Figure 6.3. The purpose of the floating base resting on stiff loadcells is to provide a true measure of the stress transferred vertically through the fill mass to the base. Due to the high stiffness of the base loadcells, the displacement of the floating base is negligible, relative to the soil stiffness. This boundary can therefore be considered as being rigid, and the loads measured by the loadcells considered equal to those placed on a rigid boundary, such as the base of a stope. It would have been useful to also measure the stresses at discrete points within the fill mass. However, the measurement of stress within a soil mass is very difficult, since this generally requires inclusion of transducers with different relative stiffnesses. As discussed in Sections 2.2, this is particularly problematic in cemented materials, where the soil stiffness can become significantly greater than the diaphragm of an earth pressure cell. These problems have been well documented by authors such as Clayton and Bica (1993), and Take and Valsangkar (2001). 6.3

138 Centrifuge Modelling During testing, the experimental apparatus was placed within an aluminium strong box, which was mounted on the swinging platform of the geotechnical centrifuge. Figure 4 presents a photograph of the apparatus in place on the centrifuge. 6.3 CALIBRATION The process of calibrating the load cells and strain gauges attached to the cylinder walls was carried out on the centrifuge, where known weights were accelerated to known levels, to create a known force (or stress). Details of this calibration process are presented below. Base readings All of the model testing discussed later was carried out at 100g. Therefore, the first stage of calibration involved placing the empty cylinder on the centrifuge and accelerating the centrifuge to 100g. The increment of strain measured on each instrument when ramping up from 1g to 100g was due purely to the weight of the apparatus itself. This value was deducted from all subsequent experimental results recorded in the model tests. The empty apparatus was also subjected to different g- levels to determine base-line readings to be deducted from calibration measurements at different g-levels. Loadcell calibration For the calibration of the base loadcells, various weights were placed on the floating base and the centrifuge accelerated to 100g. Knowing the weight and the radius to the weight as well as the angular velocity, the force could be calculated. The force increments were then used to form a linear correlation with the loadcell output. Calibrating the loadcells using the centrifuge rather than at 1g meant that the same logging system as that used in the experiment was used as well as taking into account any friction loss between the O-ring and cylinder. Strain gauges One of the potential concerns regarding the strain gauge output was the influence of temperature on the output. As only half Wheatstone bridge strain gauges were used in either direction, all bridge outputs had to be adjusted for temperature changes. To calibrate for the effect of temperature, the cylinder was filled with warm water (at a 6.4

139 Centrifuge Modelling temperature of 40 C) and left stationary (at 1g) overnight. During this period, the cylinder temperature (as measured by the thermocouples mounted on the outer surface of the cylinder at each site) and bridge output was logged. Due to the high thermal conductivity of the aluminium cylinder, this temperature measurement was considered representative of the average cylinder temperature. Temperature measurements indicated that the water initially heated the cylinder to 40 C and overnight the cylinder temperature reduced to 20 C. As the stress conditions remained constant over this period the strain gauge half bridges could be calibrated for temperature variations. This calibration was then used to correct the bridge output for temperature variations throughout the calibration and testing stages. The strain gauges used were manufactured from aluminium and as the cylinder was also aluminium the temperature correction was minimal. As strains can be linearly related to the strain gauge electrical resistivity (via a gauge factor) and strains can be linearly related to applied stresses or forces the calibration and the interpretation strategy adopted in the study was to simply relate the strain gauge voltage output to an applied force or stress. To calibrate the apparatus for axial force (F), a top cap was placed over the empty cylinder and various weights were stacked onto this top cap. Once the weights were in place, the centrifuge was accelerated to 50, 100, 150 and 200g to vary the axial force applied to the cylinder. This process applied an axial force (F) without any change in internal radial pressure (P). For calibration of radial stress the cylinder was filled with water before applying 50, 100, 150 and 200g. After deducting the influence of the cylinder self-weight stresses, this procedure provided an increase in radial pressure (P) without changing the axial force (F). When applying only an axial force (F) a voltage change was measured across the axial and hoop bridges. If we denote the axial and hoop bridge voltage change as V AF and V HA, respectively these can be related to F via calibration factors A F and H F in accordance with: = F ( ) V = F. ( ) V. AF A F HA H F (6.1) 6.5

140 Centrifuge Modelling By accelerating the water-filled container an internal pressure (P) is generated which induces axial and hoop bridge outputs of V AP and V HP respectively. After deducting the apparatus self-weight voltage changes, P can be related to the axial and hoop bridge outputs (V AP and V HP respectively) via calibration factors A P and H P in accordance with: V = P. ( ) V = P. ( ) AP A P HP H P (6.2) The changes in bridge voltages due to both an axial force and radial pressure are given by: V + A = VAF VAP V P = VHA + VHP (6.3) Substituting 6.1 and 6.2 into 6.3 V V A H AF = H F A H P P F P (6.4) Using this approach calibration factors A F, A P, H F and H P were derived. To interpret the experimental results Equation 6.4 must be rearranged such that F and P can be derived from the measured values of V A and V H. Inverting the matrix of calibration factors and rearranging Equation 6.4 gives: F 1 = P AF H P H F A P H H P F AP V AF V A H (6.5) Therefore, the bridge outputs were simply adjusted for temperature variations and the apparatus self-weight prior to direct substitution into Equation 6.5 to calculate the axial force and radial stress throughout the experiment. Pore pressure transducer During the calibration with the water-filled cylinder, the standpipe pore-pressure transducer was in place. From the calculated water pressure at the transducer location, the calibration factor supplied with the transducer was verified. The previously-described calibration routine provided suitable calibration factors for the various instruments. This calibration yielded excellent consistency, providing confidence in the performance of the data collection system. 6.6

141 Centrifuge Modelling 6.4 EXPERIMENT Only one experiment was undertaken in this investigation. The aim of this experiment was to investigate the interaction between consolidation and stress distribution in a typical mine backfill situation Material In a centrifuge model of thickness d representing a full-scale prototype of thickness D (where d = D/N, and N is the acceleration multiplier), the time-scale for consolidation is reduced by a factor N 2 compared to the time-scale for the prototype. However, the time-scale for hydration is unaffected by the g-level, so that the time until initial set, and the total time for hydration, are the same for the model and the full-scale prototype. Thus, if the time-scales for consolidation and hydration are similar in the full-scale prototype, they are completely different for the model, assuming that the same material is used in the model as in the prototype. In an effort to prolong the consolidation time (with the aim being to investigate the interaction of consolidation / stress arching and cement hydration), a material with a low coefficient of consolidation was required, as the use of conventional mine tailings (even a fine grained paste fill) would result in very rapid consolidation at the scale of the centrifuge experiment. In order to prolong the consolidation rates, commerciallyavailable kaolin clay was adopted for this test. The aim of the experiment was to investigate the interaction of the loading, consolidation and cementation time-dependent processes. Therefore, cement was added to the kaolin mix. Due to the high compressibility of the kaolin clay and the high water contents required to achieve a flowable mix, 25% cement was required to achieve an appropriate development of stiffness with time. Without sufficient cementation, it would have been difficult to identify the influence of cementation on the overall consolidation behaviour. To maximise the strength gain for minimum cement content, and minimise the material permeability, the water content was maintained at the minimum level that the mix would be sufficiently free flowing to remove entrained air. The water content adopted 6.7

142 Centrifuge Modelling was 62%, which corresponded to a placed void ratio of 2.20, assuming fully saturated conditions. As will be shown in this chapter, these high cement contents altered the coefficient of consolidation such that consolidation was complete prior to the onset of initial set. Thus, even with the use of the kaolin clay, the interaction of consolidation and hydration could not be investigated in this experiment. Nevertheless, some interesting results are presented Experimental procedure The experiment involved filling the cylinder with the kaolin/cement/water mix in two layers. The first of the layers was 250 mm high and the second 240 mm high. Prior to the placement of the first layer, 5 mm of water was placed in the base of the cylinder to assist with the removal of air during the filling process. The first layer was placed in 5 sub-layers, each 50 mm high, with each layer being tamped 20 times to ensure that all entrained air was removed. After placement of the first layer, water was added above the material. This water filled the cylinder until it reached the overflow valves at the top of the cylinder, where it was directed out of the strong box. The water level in the cylinder was kept constant by continually adding water to maintain an overflow, to make up for any water lost via evaporation. The high water level also provided a back pressure within the soil, which assisted with ensuring full saturation throughout the consolidation period. With the first layer in place, the centrifuge was ramped up to 100g and this was maintained for 20 hours. After 20 hours the centrifuge was stopped, resulting in a total stress reduction in the soil at all depths. Initially the total stress reduction created an equivalent reduction in pore pressure, and therefore there was no change in effective stress. But due to the short drainage path, and increased material stiffness, stopping the centrifuge allowed the negative pore pressures to increase to hydrostatic levels at 1g. This led to a reduction in effective stress. Should the total stress again be increased (through ramping up the centrifuge), the stress distributed to the surrounding cylinder would be different to that before ramping down, as there has been a change in shear stiffness at the soil / cylinder interface that was 6.8

143 Centrifuge Modelling brought about due to cement hydration (this was demonstrated numerically by Rankin, 2004). To remove the influence of any changes in stress distribution from the stress cycling, the centrifuge was again ramped up to 100g where new baseline readings were taken, which were subsequently used to determine the incremental change in stress due to the application of the second layer. A second layer of material (with the same mix proportions as the first) was then added above the original material. This layer was 240 mm thick and was placed in the same way as described for the first layer. The centrifuge was again ramped up to 100g and the material was allowed to consolidate until equilibrium was achieved Experimental results The results of the experiment have been divided into two sections, namely Stage 1 loading and Stage 2 loading. Stage 1 loading contains data collected during the consolidation of the initial layer and Stage 2 loading contains data gathered during the placement and consolidation of the second layer. Stage 1 loading During the placement of the first layer, the relationship between degree of consolidation (as measured by the base pore pressure measurement) and the distribution of total stress around the cylinder was investigated. These results are presented in Figure 6.5, which shows the vertical force resulting from the soil and overlying water weight within the cylinder ( Total soil force ), as well as the total force measured on the base load cells ( Base load cells force ) and the cylinder (wall) axial load ( Cylinder axial force ) plotted against time. Also plotted on the right axis of Figure 6.5 is the measured pore pressure at the base of the cylinder ( Base u ), plotted against time. Initially, after the material is placed and the centrifuge reaches the operating speed, the measured pore pressure at the base of the cylinder was 600 kpa, which corresponds to the total self-weight stress of the overlying material (assuming no arching). This indicates that at this stage, the material is fully saturated and in an undrained state (i.e. no consolidation has occurred). It can also be seen that initially the entire load is being transferred through the saturated soil to the base loadcells, and no arching is occurring. This is verified by the fact that no load is transferred axially through the cylinder (apart from the cylinder self-weight). 6.9

144 Centrifuge Modelling As consolidation takes place (indicated by the reduction in base u), there is a gradual reduction in load measured on the base and an increase in the axial load on the surrounding cylinder walls. This demonstrates that without consolidation there can be little arching, but as consolidation occurs (even with a very low-strength clay material) arching can create a significant amount of stress distribution onto the surrounding cylinder. At approximately 2.25 hours, the pore pressure at the base of the cylinder has reached hydrostatic levels, and the system is therefore in equilibrium at this stage. As the pore pressure reaches a constant value, there is no further change in effective stress and no further change in any other measurements. This demonstrates that it is consolidation, and not cement hydration bond strength, that is most important for arching. Stage 2 loading During the second loading stage, a 240-mm layer of slurry was placed over the original layer. At the time of placement of the second layer, the original layer had been allowed to cement to an unconfined compressive strength of approximately 300 kpa. The incremental changes in pore pressure, base stress and axial stress that resulted from the application of this second layer and subsequent ramping back up to 100g are presented in Figures 6.6 and 6.7. Figure 6.6 shows an incremental increase of 95 kpa in the pore pressure at the base of the cylinder. The total vertical stress generated by the new layer was 105 kpa, so even after developing a significant cemented strength, most of the applied load is still being supported by the water phase and not being distributed to the surrounding cylinder through arching. Figure 6.7 shows the increment of force applied from the second layer ( Applied force increment ) as well as the incremental change in force measured by the base loadcells ( Base loadcells force ) and that measured as axial force in the cylinder ( Cylinder (wall) axial load ). The results indicate that even with cemented material in the lower part of the cylinder (which is expected to have q u in excess of 300 kpa), immediately after placement almost all of the applied stress is transferred to the base. But as consolidation takes place (which is indicated by a reduction in base u) force is transferred off the base and onto the surrounding cylinder. 6.10

145 Centrifuge Modelling Using the strain gauges at the #5 location, the total horizontal stress increment ( σ h #5 ) applied to the cylinder was monitored and is plotted, using the right hand axis, in Figure 6.7. This strain-gauge set was installed 80 mm above the floating base, making the location adjacent to the cemented layer (Layer 1). The measurements indicate that immediately after the placement of the second layer, the increase in horizontal total stress is 100 kpa, which is almost equal to the applied total vertical stress (105 kpa). Therefore, even within the cemented mass, the horizontal stress increase is approximately the same as the applied vertical stress if no consolidation takes place. But, as consolidation takes place, σ h reduces significantly such that after complete consolidation σ h reduces to approximately 30 kpa, or 30% of the applied total stress increment. 6.5 NUMERICAL BACK ANALYSIS As explained previously, it was not possible to conduct a centrifuge experiment in which the time-scales of consolidation and hydration would be similar, and hence it was not possible to study the entire interaction of mechanisms. Nevertheless, the experiment has shown an interesting interaction between consolidation and the distribution of stress around a stope-shaped container. The purpose of this section is to use the numerical program (Minefill-2D) to simulate the consolidation behaviour, and replicate the distribution of stress that was measured during the experiment Material characterisation Consolidation in Stage 1 of the experiment was primarily conventional drainage-type consolidation (rather than self desiccation), so back analysis of the results is most sensitive to the consolidation characteristics of material in an uncemented state. For the purposes of the numerical modelling, the one-dimensional consolidation properties of the material were determined using a Rowe Cell consolidation test. The Rowe Cell is a one-dimensional loading apparatus for measuring the consolidation characteristics of soil. Load increments are applied via a flexible membrane, rather than via a solid piston, as in a standard oedometer apparatus. With the Rowe Cell setup used at UWA, the permeability can be directly determined at the end of each loading increment. The test is carried out using one-way drainage, with the pore pressure 6.11

146 Centrifuge Modelling response at the undrained boundary being measured directly. The test is performed under elevated back pressure, which helps ensure full saturation (and also ensures fast response in the base pore pressure transducer). The material used in the element testing was identical to that used in the centrifuge experiment. The material consisted of 75% commercially available kaolin clay and 25% ordinary Portland cement, by dry weight, which was mixed to a water content of 62%. Axial stresses of 220, 250, 300, 350, 400, and 500 kpa were applied with a constant back pressure of 200 kpa. Throughout the consolidation period, the pore pressure at the base (the undrained end of the sample) and the settlement of the sample were measured to determine the confined modulus and permeability over a range of densities. Direct permeability measurements were taken by establishing a hydraulic gradient across the sample after completion of consolidation under axial effective stresses of 50, 100, 200 and 300 kpa. The results of these tests are presented in Figures 6.8 and 6.9. Figure 6.8 presents the relationship between applied vertical effective stress and void ratio, and Figure 6.9 presents the relationship between permeability and void ratio. Also presented in these figures are the material relationships that were adopted in the numerical back analysis. While the relationship between vertical effective stress and void ratio departs from the experimental results at higher stress levels, over the range of vertical effective stresses encountered in Stage 1 of the test (0-150 kpa) the relationship provides a good representation. Note that normally a linear relationship in semi-logarithmic space (e log σ v ) would be used to describe such a relationship, but in this case the linear relationship shown is more than adequate for the purpose required. Stage 2 of the experiment involved the consolidation of both cemented and uncemented layers. Therefore, the consolidation characteristics of Layer 1 (taking account of cement hydration) at the time of the application of the second layer were required. To characterise the cemented material properties, a hydration cell and triaxial test (after 77 hours of hydration) was carried out on kaolin with 25% added cement. Using the experiments, the influence of cementation on the material behaviour was determined. The relevant material properties are presented in Table 6.1. Figure

147 Centrifuge Modelling presents the experimental measurements of small strain shear stiffness (G o ) and unconfined compressive strength (q u ) as well as the relationship assumed in the back analysis plotted against time. After 22 hours of hydration (the time when the second layer is applied in the centrifuge test) the material is expected to have a G o of 180 MPa and a q u of 300 kpa. In addition, an internal friction angle of 23º (Randolph and Hope, 2004) was adopted, assuming that the friction response was in accordance with that of pure kaolin. One aspect that complicates the derivation of appropriate cemented material properties in Stage 2 is the significant density change that occurs due to conventional drainagetype consolidation in Stage 1. Any density increase would lead to higher cementinduced strength/stiffness than that measured in the element test where no (drainagetype) consolidation took place. To address this complexity, the stiffness and strength results were extrapolated to different densities using the exponential relationship between void ratio and strength that was defined in Section 3.2.3, for Cannington Paste backfill. To account for the effect of cement hydration on the material permeability, the relationship between void ratio and permeability for the uncemented material was maintained, but the influence of cement hydrate growth was taken into account via the effective void ratio term as described in Section Numerical back analysis The program Minefill-2D, which was presented in Chapter 5, was used in axisymmetric mode for back analysis of the experiment results. The material relationships are those described in Section Figure 6.10 presents a comparison between the measured base pore pressure and that predicted using Minefill-2D during Stage 1. This figure indicates that the experimental pore pressure reduction is only slightly more rapid than that calculated using Minefill- 2D. This provides confidence that Minefill-2D is providing an accurate representation of the consolidation behaviour (albeit conventional drainage-type consolidation). Figure 6.11 presents a comparison between the experimental and numerical results for the distribution of vertical stress between the floating base and the surrounding cylinder. 6.13

148 Centrifuge Modelling The experimental results are represented by solid lines while the numerical results are represented by symbols. This comparison indicates that Minefill-2D provides a good representation of the initial stress distribution as well as the redistribution of stress during the consolidation period. Initially, both experimental and numerical results indicate that without consolidation all of the soil weight is transferred through the saturated soil to the floating base. But as consolidation takes place, the force transferred to the base reduces and that transferred through the surrounding cylinder (through arching) increases. The transfer of force off the base and onto the surrounding cylinder continues as the pore pressure reduces (or as consolidation takes place), but when the pore pressure plateaus, this force transfer stops. It can be seen that the slightly faster consolidation rates measured in the experiment are associated with a slightly faster increase in axial stress in the cylinder. The calculated incremental change in pore pressure during Stage 2 is compared with the experimental measurements in Figure Again the calculated increase in pore pressure due to the application of Layer 2 and the subsequent reduction in pore pressure are well represented. Figure 6.14 presents a comparison between calculated and measured incremental changes in vertical forces acting on the floating base and transferred to the surrounding cylinder when the centrifuge was restarted after Layer 2 was added. In addition, the measured and calculated total horizontal stress at the strain gauge #5 level in the cylinder is shown on the right axis. The measured results are presented as solid lines while the calculated results are represented by symbols. The calculated incremental change in total stress distribution slightly overestimates the measured amount of arching. The overestimation of arching could have resulted from an inappropriate relationship to represent the influence of density on cement-induced strength and stiffness. This could have led to the model overestimating the actual material stiffness, which would have promoted additional arching. It should be noted that the bulk modulus of the material used in this experiment is at the lower end of what would be expected in a real cemented mine backfill situation. Should this stiffness be increased, the transfer of stress (through the cemented layer) due to the undrained application of total stress would reduce in accordance with strain 6.14

149 Centrifuge Modelling compatibility between the soil and water phases. Strain compatibility has been taken into account when establishing the initial conditions in Minefill-2D to address this aspect. 6.6 CONCLUSION This chapter has presented a centrifuge experiment that was designed to investigate the interaction of consolidation, cement hydration and the distribution of stress. However, where the time-scales of consolidation and cement hydration are similar in a full-scale stope (and hence these processed are coupled), the times-scales are very different in a reduced-scale model, since the consolidation time is reduced (by a factor N 2 ), but the hydration time is unaltered. Thus, it was not possible to devise an experiment where these processes could be fully coupled. However, the results have experimentally confirmed a number of key aspects relating to this thesis. These include: The distribution of stress is heavily influenced by consolidation and largely independent of the cement-induced bond strength. Even in a material with an unconfined compressive strength of 300 kpa, if saturated, the application of stress initially results in the load being supported by the water phase, with very little arching occurring. Even in a material with an unconfined compressive strength of 300 kpa, if saturated, the undrained application of vertical stress results in an increase in horizontal total stress of equal magnitude. As consolidation takes place, the material is able to mobilise shear strength at the soil/boundary interface and redistribute some of the vertical stress onto the surrounding stiff medium. Minefill-2D is capable of providing a reasonable representation of the conventional consolidation and arching behaviour, using material parameters measured in element testing. 6.15

150 Sensitivity Study CHAPTER 7 SENSITIVITY STUDY 7.1 INTRODUCTION The preceding chapters have described the development of a rigorous numerical model for simulating the mine backfill deposition process. This model is based on fundamental material properties and, through comparison with well established analytical solutions, was shown to provide a good representation of individual mechanisms. It was demonstrated experimentally that the model is capable of accurately coupling the interaction between consolidation and stress development in conditions similar to those that are likely to be encountered in a stope filling environment. This provides confidence that the Minefill-2D program is capable of providing a good representation of the cemented mine backfill process and that the tool can be used with confidence. This section uses Minefill-2D to assess the sensitivity of the overall filling response to various characteristics. The aim of this work is to understand the backfill process and provide strategies for managing the process that are based on sound logic. Sections 7.2 involves a comparison between hydraulic and paste fill. This is followed by two sensitivity analyses, one on material that consolidates immediately after placement (typically hydraulic fill) and another on material that does not consolidate immediately after placement (typically paste fill). Throughout the sensitivity analysis, emphasis is placed on the resulting barricade loads, but the final section (Section 7.5) considers the effect of the application of effective stress to in situ material during curing. 7.2 COMPARISION OF HYDRAULIC FILL AND PASTE FILL In the mining industry, slurry mine backfills are commonly divided into two main groups, paste fill and hydraulic fill. As Minefill-2D undertakes analysis using fundamental material properties, it provides an opportunity to investigate the relationship between paste and hydraulic fills without introducing simplifications that pre-empt the final outcome. When considered from a fundamental soil mechanics point of view, hydraulic fill and paste fill are essentially the same product. The main difference is that hydraulic fill 7.1

151 Sensitivity Study generally contains less fines than paste fill. The typical consequences of this difference are highlighted in Table 7.1 In order to investigate the significance of these characteristics on the overall filling response, an experimental and numerical study was undertaken. This involved testing 4 different cemented mine backfills using the (previously described) hydration test, triaxial test and Rowe Cell test to determine both cemented and uncemented material properties. Testing was carried out on two hydraulic fills and two paste fills. Hydraulic Fill A (HFA) is from a zinc mine, Hydraulic Fill B (HFB) is from a copper mine, Paste Fill A (PFA) is from a gold mine tailings and Paste Fill B (PFB) is from a nickel mine Experimental results The experimental program commenced with particle size distribution analysis of each tailings specimen. The results of this analysis are presented in Figure 7.1. As expected, Figure 7.1 indicates that the hydraulic fill materials have far less fines than the paste fills. The aim of this investigation is to assess how the tailings characteristics influence the filling behaviour. Therefore, in order to maintain consistency, testing was carried out with each of the materials combined with 3% ordinary Portland cement and each mixed with water to achieve an equivalent void ratio of 0.9, assuming fully saturated conditions. Each mix was subject to a hydration test to determine the cement hydration properties (as discussed in Chapter 3) followed by a triaxial test to determine the strength properties. Rowe Cell testing was also undertaken on the tailings material (without cement) to determine properties that represent the behaviour prior to the onset of cement hydration. A summary of the material properties for the various fill types is presented in Table 7.2. From Table 7.2, it can be seen that the final unconfined compressive strengths (q u-f ) are very similar for the four samples, even though the materials have different rates of hydration (d), efficiency of hydration (E h ), and hydraulic conductivity parameters (c k and d k ). Figures 7.2 and 7.3 show how the hydraulic conductivity (k) and cohesion (c ) evolve with time, respectively. 7.2

152 Sensitivity Study Modelling In order to assess the impact of the various material properties on the filling process, Minefill-2D was used (in plane strain mode) to simulate the filling of a plane strain stope 20 m wide and 40 m high. A drawpoint height of 5 m was adopted with a barricade offset distance of 5 m. A boundary condition of atmospheric pore pressure was assigned along the boundary that represents the barricade. To allow direct comparison between the various materials, a standard filling sequence was adopted. This sequence consisted of filling the first 8 m over a 16-hour period (0.5 m/hr) followed by a 14-hour rest period, and then filling the remaining 32 m over a period of 64 hours (0.5 m/hr). In an actual stope, the drawpoint width is typically less than the side length of the stope, whereas in the plane strain representation it occupies the full side length. This means that the actual drawpoint represents a greater choke to outflow than the plane strain representation. In order to account for this, the hydraulic conductivity in the drawpoint area was halved. Modelling was undertaken using the material properties presented in Table 7.2 to assess the impact of tailings type on the consolidation behaviour and on the resultant barricade stresses. Figure 7.4 shows a plot of the total horizontal stress, developed at a point immediately behind the barricades, for the various fill materials, using the described filling sequence. This indicates that barricade stress reaches 108 kpa for PFA, 150 kpa for both HFB and HFB and 240 kpa for PFB. Thus, even with fills that reach the same ultimate strength (q u-f ), stresses applied to barricades can vary significantly. Furthermore, there is no obvious relationship between any one material property and the resulting barricade stresses. For example, barricade loads for PFA are the lowest, even though the hydraulic conductivities of HFA and HFB are higher, while that of PFB is lower. Also, HFA and HFB show a faster rate of hydration (lowest d value) and a higher efficiency of hydration (highest E h value), when compared with the paste fill materials, but ranks in the middle in terms of ultimate barricade stress. 7.3

153 Sensitivity Study The reasons for the stress variation may be better understood with reference to the development of pore pressure at the opposite side of the stope to the barricade. This is presented in Figure 7.5 along with the steady state seepage pore pressure that is created when the water table is maintained at the fill surface and atmospheric pore pressures are maintained at the barricade boundary. This is calculated in accordance with the relationship presented by Helinski and Grice (2007). Pore pressures greater than steady state indicate that the material has not fully consolidated, while pore pressures equal to this value indicate that the material has completely consolidated. This is a somewhat artificial situation, since ongoing water flow without further addition of water to the stope would result in lowering of the water table (with the possibility of further consolidation as the equilibrium situation changes) but it does provide a reference for assessment of excess pore pressures. Comparison between Figures 7.4 and 7.5 indicates that there is a clear relationship between the development of pore pressure and the stresses placed on barricades. This is logical, as higher pore pressures are associated with less consolidation and lower effective stress. As discussed in Chapter 2, with less effective stress, less interface shear strength is mobilised resulting in higher total vertical stresses in the stope. In addition, the conversion from total vertical stress to total horizontal stress adjacent to the drawpoint is dependent both on the proportion of the load being carried by the soil skeleton (effective stress) and that carried by the pore water (pore pressure), in accordance with Equation 7.1: σ = σ. h v K o + u (7.1) where σ h is the total horizontal stress, σ v is the vertical effective stress, K o is the lateral earth pressure coefficient ( ) and u is the pore pressure. Therefore, if all of the total vertical stress is supported by the water phase ( u = σ ) the vertical and horizontal total stresses would be equal, but if the pore pressure is zero, the horizontal total stress would approximately 30% to 50% of the total vertical stress. The other aspect to note about Figure 7.5 is with respect to the development of pore pressure (for the different mine backfill materials) relative to the steady state seepage pore pressure. Comparing the pore pressures for the four cases with the steady state v 7.4

154 Sensitivity Study seepage pore pressure, it is clear that both HFA and HFB hydraulic fills exhibit close to steady state seepage pore pressures throughout the filling process, indicating immediate consolidation, PFB develops pore pressures that are greater than steady state seepage pore pressures indicating that consolidation is not complete, and PFA exhibits pore pressures that are even less than steady state seepage pore pressures. This may be more clearly depicted in Figure 7.6, which shows the pore pressure isochrones along the stope centre line at the completion of filling. Also shown in Figure 7.6 is the line representing the steady state seepage pore pressures for the stope. The reason for the three different types of behaviour is as follows: HFA and HFB Due to the initial high value of the coefficient of consolidation (i.e. higher permeability and stiffness compared to the paste fill materials), excess pore pressures dissipate immediately and the pore pressures in the fill mass are the steady state seepage pore pressures resulting from the reduced flow area in the drawpoint. It is also interesting to note that the efficiency of hydration for the HFA hydraulic fill is double that of the HFB hydraulic fill but the pore pressures and barricade loads are almost identical. This suggest that this mechanism plays little role in the consolidation of hydraulic fills. PFA For PFA, the initial low stiffness and low hydraulic conductivity result in very little conventional drainage-type consolidation prior to initial set. Close inspection of Figure 7.5 indicates that during the early stages of filling, pore pressures in PFA are higher than in HFA and HFB. This is reflected in higher barricade loads during this period. However, this material has a high propensity for self desiccation after initial set, where the water volume reduction from self desiccation combines with the rapidly increasing material stiffness to reduce the pore pressures. For higher permeability materials, this would be counteracted by an inflow of water from above that would restore steady state seepage pore pressures (as shown for the hydraulic fills), but for PFA, the permeability is so low that volumes being consumed by the self-desiccation mechanism are greater than the inflow from above. Therefore, the very steep hydraulic gradients being generated by the low pore pressures can be maintained. This suggests 7.5

155 Sensitivity Study that very low pore pressures, below the steady state line, may be produced by self desiccation in association with low hydraulic conductivity. PFB Like PFA, the initial value of the coefficient of consolidation of PFB is very low (i.e. low permeability and high stiffness), and therefore drainage-induced consolidation is insufficient to dissipate excess pore pressures. However, unlike PFA, the prosperity for self desiccation is too low to give a significant pore pressure reduction, with the result being significant pore pressure development. Also, even though the material is gaining stiffness, the low permeability is preventing any conventional dissipation of excess pore pressures. The resulting high pore pressures (low levels of consolidation) are reflected in high barricade loads. This situation seems to be most prominent when the tailings being used to form the paste have high active clay content. Clay particles reduce the coefficient of consolidation (suppressing conventional consolidation) and have also been shown to adversely influence the cement hydration process. This is the case with PFB Comparison of hydraulic fill and paste fill This analysis has identified two significantly different responses depending on whether the material undergoes immediate consolidation or if very little consolidation takes place prior to the onset of hydration. Broadly, it may be assumed that hydraulic fills consolidate immediately while paste fills require cement hydration to achieve consolidation, but this outcome will be dependent on both the coefficient of consolidation and the filling rate. Therefore, both of these factors must be taken into account when characterising the expected behaviour. One method of characterising the combination of material properties and filling rate is through Gibson s (1958) analytical solution that was introduced in Section 2.2. The following two sections describe sensitivity studies that investigate the behaviour of firstly consolidating fills and secondly non-consolidating fills. 7.3 CONSOLIDATING FILL This section refers to fill types that when first deposited, at the specified rate of rise, have a coefficient of consolidation that is sufficient to dissipate any excess pore 7.6

156 Sensitivity Study pressures while filling is in progress. This characteristic is most commonly associated with hydraulic fills, but is equally applicable to coarse paste fills that are placed with low rates of rise. The analysis carried out to investigate the sensitivity of consolidating fills has used the HFB parameters, which were presented in Table 7.2. In each case the stope geometry simulated was a 40 m tall, 13 m wide plane-strain stope, with a 5m long and 5 m high drawpoint. The 13 m wide plane-strain stope was selected as this dimension is expected to provide a similar vertical stress distribution to a stope with plan dimensions of 20 m x 20 m, which is considered typical, and the plane-strain configuration allows the drawpoint to be represented. In most consolidating fill situations, fill rates are often much slower than 0.5 m/hr, which was adopted in Section 7.2 for direct comparison with paste fills. Therefore, in order to provide more realistic results, the analysis in this section is carried out using a constant fill rate of 3 m per day or approximately m/hr Influence of stope geometry Stopes often have different configurations with regard to plan dimensions and the number and size of drawpoints. Different configurations will lead to differences in the restriction to flow at the base of the stope. This section is focused on investigating the influence of the drawpoint restriction on barricade loads. To represent different drawpoint restrictions the stope geometry has been maintained constant but the drawpoint permeability was modified by an order of magnitude. This modification has the equivalent impact as modifying the number of drawpoint openings or the installation of drains through this region. In addition, to demonstrate the extreme situation, an impermeable barricade was simulated. The development of pore pressure at a point 2 m above the stope floor on the opposite side of the stope has been plotted against time for each of these cases, in Figure 7.7. Figure 7.7 indicates that the pore pressure at the opposite side of the stope to the drawpoint is heavily influenced by the restriction created at the base of the stope. It should be noted that the reduced pore pressures (at the base of the stope) coincide with a significant change in pore pressure distribution throughout the stope rather than a significantly different phreatic surface elevation. This point is demonstrated in Figure 7.8, which presents the pore pressure isochrones along the centre line of the stope for 7.7

157 Sensitivity Study the different cases. It can be seen that the phreatic surface elevation is effectively the same for each of the cases, but the rate of pressure increase (with depth) is significantly reduced as the restriction to flow through the drawpoint reduces (or the drawpoint permeability increases). The impact of the different drawpoint restrictions on barricade stress is illustrated in Figure 7.9, which presents the total horizontal stress placed on the barricade against time for the different cases. Figure 7.9 indicates that the reduction in pore pressure and increase in effective stress associated with the reduced drawpoint restriction significantly influences loads applied to consolidating fill barricade structures. Even with the same phreatic surface elevation, the different drawpoint restrictions can have a significant influence on the distribution of total stress and hence on barricade loads. This is most significant in the extreme case of the impermeable barricade. In this case there is no water flow and the resulting hydrostatic pore pressures leads to very high barricade stresses. This result is consistent with the analytical analysis results published by Kuganathan (2002), who also suggested that the installation of engineered drainage systems in the stope drawpoint can minimise barricade stresses Influence of permeability To investigate the significance of changes in the permeability of a consolidating fill material, the HFB permeability was modified by an order of magnitude in both a positive (k=10 k HFB ) and negative (k=0.1 k HFB ) direction. It should be noted that, with the change in permeability, the coefficient of consolidation remained sufficiently large to ensure that there was no build up of excess pore pressures during filling. Figure 7.10 indicates that, until approximately 220 hours, the material permeability has little influence on the pore pressure that develops in a stope. At 220 hours, the highpermeability material allows the phreatic surface to fall below the fill surface, which leads to reduced pore pressures. But for the same phreatic surface elevation, the pore pressures are independent of the permeability. The reason for the independence is that, provided the permeability is sufficient to dissipate the build up of excess pore pressures, in situ pore pressures would be dictated by the relative flow resistance between the 7.8

158 Sensitivity Study stope and drawpoint. Provided the relative flow resistance (between the stope and drawpoint) is constant, for a given water table elevation, the pore pressure profile will be similar. Should the permeability be further reduced, there is potential to accumulate excess pore pressures, which would change the deposition behaviour. This is discussed in Section The impact of fill mass permeability on barricade stress is presented in Figure 7.11, which shows the development of barricade stresses against time for the various cases. As with the pore pressure, it can be seen that for the same phreatic surface elevation the barricade loads remain largely independent of permeability. It is interesting to note that, for the k=10 k HFB case, when the phreatic surface falls below the fill surface at approximately 220 hours, there is an associated significant decrease in barricade stress. The reduction in pore pressure is associated with an increase in effective stress, which acts to mobilise more shear stress (within the fill mass) and reduce the total stress transferred to the barricade Influence of cementation The following sensitivity study investigates the influence of cementation on the barricade loads in a consolidating fill. Again the HFB material is adopted but the cement content is varied between 0%, 1.5%, 3% and 8%. Figure 7.12 shows the development of pore pressure at the base of the stope (on the opposite side of the stope to the barricade) against time for the different cement contents. Based on the results, it appears that the development of pore pressure against time in a consolidating fill is largely independent of cement content. This is expected to be due to the high initial coefficient of consolidation, which rapidly creates and sustains steady state conditions (as discussed in Section 7.2.2). Consequently cementation is not required in the consolidation process. Figure 7.13 presents the development of barricade stresses in a consolidating fill mass against time with varying cement contents. It can be seen that between cement contents of 3 and 8 %, the presence of cementation has little influence on the calculated barricade stresses, but as the cement content drops to 1.5 %, there is an increase in barricade 7.9

159 Sensitivity Study stress. The barricade stress for the 1.5% case is similar to the 0% case. This increase in stress is a result of the weaker material (associated with the lower cement contents) yielding at the fill/rock interface. To demonstrate this point, Figure 7.14 presents the calculated shear stress and cohesive strength against time for an element at the interface between the fill and the rockmass, 7 m above the stope floor. This result indicates that with 3% cement, the cohesive component of strength is sufficient to support the applied shear stress, and no softening occurs. But in the 1.5% cement case, there is some strain softening and subsequent breakdown of the cementation at the fill/rock interface, which is indicated by the reduction in cohesion from approximately 80 hours onward. Another illustration of this cementation breakdown is shown in Figures 7.15 (a) and (b), which show contours of cohesion for the 3.0% and 1.5% cases, respectively. Figure 7.15 (a) shows relatively constant cohesion horizontally across the stope while Figure 7.15 (b) shows a dramatic reduction in cohesion at the fill/rock interface. A consequence of this softening is that stress that was previously supported in shear by the boundary element is redistributed, increasing the vertical stress within the fill mass, and therefore increasing the barricade stresses. The influence of strain softening on the vertical total stress is illustrated in Figure 7.16 (a) and (b), which show vertical total stress contours at the completion of filling for the 3 % cement and 1.5 % cement cases, respectively. Comparison of these figures indicates that strain softening (associated with the 1.5% case) results in a 150 kpa increase in vertical total stress at the base of the stope. This increase in total vertical stress does not induce an associated increase in pore pressure, since the coefficient of consolidation is sufficient to dissipate any excess pore pressures that are created, but this increase in total vertical stress creates an associated increase in horizontal effective stress, which contributes to barricade stresses. In addition to the implications of interface strain softening on barricade stress, this mechanism should also be considered when assessing fill exposure stability (as discussed in Section 2.2.3). For example, the assumption of a fully cohesive fill/rock interface (Mitchell and Wong 1982) would not be valid in the 1.5% cement example, and instead a friction-only interface should be considered when undertaking exposure stability analysis for this case. By reducing the filling rate, such that the development of 7.10

160 Sensitivity Study shear strength exceeded the application of shear stress, it could be possible to avoid yield at the interface, which would result in increased fill stability at the time of exposure Influence of filling rate The following section presents an investigation into the influence of placement rate on material that might be considered to be consolidating fill. Again the HFB parameters (from Table 7.2) have been adopted, but the rate of fill rise is varied from a constant 0.06 m/hr to 4 m/hr. The development of pore pressure is presented against time for each of the cases in Figure Figure 7.17 indicates that the maximum attained pore pressure for all filling rates up to 0.6 m/hr is relatively constant at 200 kpa. However, for filling rates of 2 m/hr and 4 m/hr, pore pressures reach a higher maximum before reducing to around the same constant value. These higher pore pressures are excess pore pressures resulting from the higher filling rates. Figure 7.18 presents the calculated barricade stresses against time for the different filling rates. As with the development of pore pressure, the maximum barricade load remains relatively constant (at approximately kpa) up to a filling rate of 0.6 m/hr. But with the filling rates of 2 m/hr and 4 m/hr the peak barricade stress is significantly greater. The higher barricade stresses are a result of the excess pore pressures, which change the loading mechanism Consolidating fill: discussion The modelling results presented indicate that aspects such as drawpoint restriction, cement content and filling rate can influence loads applied to barricade structures for consolidating fill. But, apart from the drawpoint restriction, barricade stresses appear relatively constant over a range of cement contents and filling rates. It was demonstrated that if these factors vary beyond a given thresholds, there is a step-change, where the deposition behaviour is modified. Specifically, the change in mechanism involves strain softening at the rock/fill interface and the development of excess pore pressures. The discrete change in behaviour results in a change to barricade stresses. Therefore, when estimating barricade stresses with consolidating fill, it is first necessary to define if the 7.11

161 Sensitivity Study fill/rock interface is likely to yield during deposition and secondly to define the rate of rise that would allow excess pore pressures to develop. Provided that excess pore pressures are not generated and the calculation of vertical stress within the stope takes account of the fill/rock interface behaviour, barricade stresses should remain relatively independent of these factors. Section showed that steady state seepage pore pressures are dependent on the elevation of the phreatic surface and the restriction to flow through the drawpoint. Helinski and Grice (2007) showed that the restriction to flow through the drawpoint can vary significantly between stopes due to the presence of macro pores, which can dominate the drainage behaviour through the drawpoint region. Comparison between Figures 7.8 and 7.9 indicates a trend between barricade stresses and the pore pressure on the floor of the stope opposite the drawpoint. To examine this relationship, the calculated pore pressure was plotted against the barricade stress in Figure 7.19, for each of the cases analysed in Section This figure indicates a unique relationship between barricade stress and this pore pressure. The significant dependence on pore pressure is problematic from a design point of view (as it is difficult to accurately predict pore pressures), but since it is very easy to measure positive water pressure accurately, these measurements can be used to efficiently manage filling activities. For example, based on an assumed drawpoint restriction, the required barricade capacity can be estimated. As the most significant assumption in the design is the drawpoint flow restriction, pore pressure measurements can be used in operation to manage filling operations such that the actual pore pressures do not exceed those assumed in the design. For example, consider the case presented in Section If the design assumes a drawpoint resistance that is equivalent to k dp = k st, an ultimate barricade stress of 118 kpa would be expected. Applying the relationship between pore pressure and barricade stress presented in Figure 7.19, filling should be undertaken such that the pore pressure at the opposite side of the stope floor to the barricade does not exceed 196 kpa (the estimated peak pore pressure for this condition). If the pore pressures increased at a rate faster than expected, filling should be suspended prior to the pore pressures reaching 196 kpa. Filling would then continue, ensuring that this target is not surpassed. 7.12

162 Sensitivity Study Alternatively, should pore pressures remain low, filling could be accelerated, ensuring that excess pore pressures are not generated. The relationship presented in Figure 7.19 can be used along with the peak pore pressure to estimate the ultimate barricade stress Consolidating fill: conclusion Based on the consolidating fill sensitivity study, it can be concluded that the important aspects to consider in determining barricade stress level are: Should the placement rate be limited to ensure that no excess pore pressures develop, the calculated barricade loads would be largely independent of filling rate and permeability. A step change in barricade stress was shown to occur depending on whether or not the material yields at the fill/rock interface during placement. For both the yielding and non-yielding cases, the barricade stresses are largely independent of cement content. The restriction to flow through the drawpoint dictates the pore pressure distribution within a consolidating fill stope. This pore pressure distribution significantly influences the effective stress and therefore barricade stresses. For the same stope geometry with different drawpoint restrictions, a unique relationship exists between pore pressure and barricade stress. This unique relationship can provide a useful means of managing filling activities. 7.4 NON-CONSOLIDATING FILL The definition of non-consolidating fill means that, during fill deposition, very little conventional drainage-type consolidation occurs. This scenario would most frequently be associated with paste fill, but could be equally applicable to fine hydraulic fills that are placed at fast rates of rise. For the purpose of the non-consolidating fill sensitivity study, PFA material properties (from Table 7.2) were adopted. The filling sequence involved the first 8 m of material being placed over a 16-hour period (0.5 m/hr), followed by a 14-hour rest period, and then filling the remaining 32 m over a period of 64 hours (0.5 m/hr filling rate). The stope geometry adopted represents a 13 m wide, 40 m high plane strain stope with a 5m 7.13

163 Sensitivity Study long drawpoint. Through the drawpoint the fill permeability is reduced by 50% to represent the reduction in drawpoint flow area. The aspects that were covered in the consolidating fill sensitivity study have been addressed here also. These include the influence of stope geometry, permeability, cementation and filling rate Influence of stope geometry This study involved varying the permeability of the stope drawpoint area, which in turn varied the restriction to conventional drainage-type consolidation through this region. In this study the drawpoint permeability was increased (k dp = 10 k stope ) and decreased (k dp = 0.1 k stope ) by an order of magnitude. Figure 7.20 presents the development of pore pressure against time during filling for a point on the stope floor on the opposite side of the stope to the drawpoint. This figure indicates that during the early stages of filling, the pore pressure is relatively independent of the drawpoint permeability. The reason for this is that the dissipation of pore pressure, at the opposite side of the stope to the drawpoint, is primarily dictated by self desiccation rather than conventional drainage-type consolidation. At the later stages of filling, when water migrates down to the base of the stope, the restriction to flow at the drawpoint becomes more influential on the pore pressures. The influence of the drawpoint permeability on barricade stress is presented in Figure 7.21, which shows the development of barricade stress with time for the different cases. This result indicates that, even during the early stages of filling, the drawpoint restriction can influence barricade stresses. This is also the case later in the filling cycle. This is due to the hydraulic gradient that exists through the drawpoint region. With higher resistance to flow through the drawpoint the hydraulic gradient is steeper, which effectively results in lower effective stresses and less stress being transferred to the surrounding rockmass. This is illustrated in Figures 7.22 (a) and (b), which presents pore pressure contours at the completion of filling for the k dp =0.1 k stope and k dp =10 k stope cases respectively. Figure 7.22a shows an almost linear reduction in pore pressure when progressing across the stope floor, but Figure 7.22b shows much higher, almost constant, pore pressures within the stope and a very steep hydraulic gradient in through the drawpoint. It is this pore pressure profile that creates the difference in barricade stress. 7.14

164 Sensitivity Study Influence of permeability To investigate the influence of permeability on non-consolidating fill deposition, sensitivity modelling was undertaken using PFA material properties, but with the hydraulic conductivity increased (k=10 k PFA ) and decreased (k=0.1 k PFA ) by an order of magnitude. Figure 7.23 presents the evolution of pore pressure with time at a point on the stope floor at the opposite side of the stope to the drawpoint. This result suggests that permeability significantly influences the consolidation behaviour. Soon after placement, a reduction in permeability creates an increase in pore pressure. This is consistent with conventional consolidation theory. But interestingly, during the later stages of filling a reduction in permeability is associated with lower pore pressures. The reason for this unusual response is that, after cement hydration begins to create an increase in material stiffness, the consolidation behaviour is dictated by the selfdesiccation mechanism. If the propensity to self desiccation is high, very large hydraulic gradients can be created in the fill mass (due to the material being at different stages of hydration). If the permeability is low, these hydraulic gradients can be sustained, effectively suppressing the development of pore pressures. But if the permeability is increased, the hydraulic gradients will cause water to flow, recharging voids that were previously depleted due to self desiccation. This will re-establish steady state seepage pore pressures. An example of this is demonstrated in Figure 7.23 for the k=10.k PFA case. Here the permeability is high enough for water to flow through the fill mass, and pore pressures are dictated by the build up that occurs at the drawpoint as discussed in Section 7.3. Figure 7.24 presents the calculated barricade stress against time for the different material permeabilities. The barricade stress trends closely follows those for pore pressure, with lower permeabilities initially creating higher barricade stresses (due to a reduction in conventional drainage-type consolidation) but as filling continues the lower permeability material produces lower barricade stresses. 7.15

165 Sensitivity Study Influence of cementation To investigate the influence of cementation on the filling response, modelling involving PFA with cement contents of 1.5% and 4.5% in addition to the base case of 3.0% was undertaken. Figure 7.25 presents the development of pore pressure with time for the different cement contents, at point on the stope floor on the opposite side of the stope to the barricade. This figure indicates that even minor variation in cement content can have a significant influence on the development of pore pressure within a paste-fill stope. The significant impact is due to the increased stiffness achieved by the higher cement contents as well as the increase in self-desiccation volumes that come about from higher cement contents. Figure 7.26 presents the calculated barricade stress against time for PFA with the various cement contents. As with pore pressures, changes in cement content significantly influence barricade stresses for non-consolidating fill. In this particular case, an increase in cement content from 3% to 4.5% results in a barricade stress reduction of over 50%, while a reduction in cement content from 3% to 1.5% results in a 150% increase in barricade stress. Again, the change in barricade stresses can be attributed to the influence of cementation on the consolidation behaviour, which in turn influences the total stress distribution. In addition to the influence that cementation has on the consolidation behaviour, a reduction in cement content also increases the likelihood of yielding at the rock/fill interface. As discussed in Section 7.3.3, yielding at the rock/fill interface can increases the vertical total stress within the stope, which increases barricade stresses. To investigate the influence of the interface behaviour, an analysis was undertaken using the base case material properties (PFA with 3% cement) but in this analysis the cohesive bond along the rock/fill interface was set to zero. The calculated barricade stresses and pore pressure at the opposite side of the stope to the drawpoint are presented in Figure 7.27, along with the results for the fully bonded case. Figure 7.27 indicates that yielding at the fill/rock interface can increase barricade stresses, but unlike the consolidating fill case, this yielding is associated with an increase in pore pressure. This is because with non-consolidating fill material the increased vertical total 7.16

166 Sensitivity Study stress creates an increase in excess pore pressure, and due to the low coefficient of consolidation these pressures cannot be dissipated rapidly Filling rate During the deposition of cemented mine backfill three different time scales interact, these being the rate of hydration, rate of consolidation and rate of placement. In order to investigate the influence of the third timescale (rate of placement) a series of numerical experiments were undertaken. These experiments used PFA material with filling rates of 0.2 m/hr, 2.5 m/hr as well as the base case of 0.5 m/hr. The filling sequence adopted involved filling the first 8 m followed by a 14 hour rest period before filling the remaining 32 m. The development of pore pressure, at the opposite side of the stope to the barricade, is plotted against time in Figure As expected increasing the filling rate caused an increase in pore pressures. Increasing the filling rate increases the rate of total stress application but as pore pressures are being dissipated primarily as a result of self desiccation (which is independent of the pore pressure magnitude) faster filling rates will create an overall increases increase in pore pressure. The reverse occurs when filling rates are reduced. In the 0.2 m/hr case the rate of application of total stress is reduced but the rate of (self desiccation induced) pore pressure reduction remains constant resulting in lower pore pressures. But, the other influence of slowing filling rates is to extend the loading timescale to be comparable to the timescale associated conventional drainage-type consolidation. In this case, drainage-type consolidation acts to restore steady state seepage pore pressures leading to an increase in pore pressures. The calculated barricade stress against time is presented in Figure 7.29 for the different filling rates. Again the trend of the pore pressure and barricade stress plots are similar, with the highest filling rates being associated with the highest barricade stresses. The higher stresses can be attributed to reduced consolidation Non-consolidating fill: discussion As with consolidating fills, the overall result of this study indicates that barricade stresses are closely related to the degree of consolidation (or the pore pressures). But it is interesting to note that material properties that appeared to have little influence on the 7.17

167 Sensitivity Study behaviour of consolidating fill, such as cement content and permeability, had a significant impact on the behaviour of non-consolidating fills. The fundamental reason for the significant influence of these characteristics is their influence on the consolidation mechanism. As with consolidating fills, the significant influence of pore pressures on barricade stresses poses a problem for mine backfill designers, since pore pressures are very difficult to predict numerically. However, this dependence presents the opportunity to manage the situation using in situ pore pressure measurements. Due to the complex interaction of mechanisms in a non-consolidating fill a unique relationship cannot be developed between pore pressure and barricade stress. But pore pressure measurements can provide an indication of the field situation varying from the design. Using fully-coupled numerical modelling, and the associated laboratory experiments to define the material characteristics (as outline in Chapter 3), a reasonable understanding of the likely behaviour during filling can be developed. This provides a rational approach to defining an initial filling sequence. From the analysis, barricade stresses can be estimated as well as providing an understanding of the expected pore pressure regime. As illustrated in Section 7.4, the modelling results can be significantly influenced by a number of different characteristics and it is usually necessary to assess the performance of the model results in situ. Clayton and Bica (1993), Take and Valsangkar (2001) and Fourie et al. (2007) suggest that the direct measurement of stress within a soil can be problematic due to the inclusion of a loadcell that possesses a different stiffness to the soil medium. This problem is exacerbated when attempting to measure stress in a soil, such as a cementing minefill, in which the stiffness changes (often by an order of magnitude) with time. Therefore, managing filling operations based on loadcell measurements is considered unreliable. However, as demonstrated in this thesis, with non-consolidating fills most variations from the design assumptions (such as delayed initial set, permeability changes, excessive drawpoint flow resistance, fill/rock interface softening or inappropriate material stiffness development) result in higher pore pressures. Therefore, during filling in situ pore pressure measurements may be compared with modelling results to assess if 7.18

168 Sensitivity Study the proposed sequence is suitable. Should the measured pore pressures vary from the predicted value, the schedule can be adjusted accordingly. As barricade stresses progressively increase during filling, the information gathered during the early stages of filling can be used to manage filling activities in the later stages, where barricade stresses may approach their maximum. This approach may not clearly identify the root cause of any problem, but in most cases it can identify if the actual situation varies from the design assumptions and hence avert barricade failure Non-consolidating fill: conclusion The two-dimensional mine backfill consolidation program Minefill-2D was used to undertake a sensitivity study on cemented mine backfill that would be unlikely to consolidate during the filling process without the assistance of cement hydration. This study highlighted a number of interesting aspects that should be considered when using this type of fill. These include: As with consolidating fills, the degree of consolidation (or increase in pore pressure) has a significant influence on barricade stresses. The resistance to flow through the drawpoint region can influence loads applied to barricade structures. This suggested that the use of free-draining barricades help to reduce the barricade stresses during filling. During the initial placement of non-consolidating fill, an increase in permeability may increase the amount of conventional drainage-type consolidation, reducing pore pressures and barricade loads. Contrary to conventional consolidation theory, a reduction in permeability can actually lead to higher consolidation and lower barricade stresses after cement hydration is initiated. The most significant factor influencing loads applied to barricade structures from non-consolidating fills is cement content. Non-consolidating fills are highly dependent on cementation to achieve consolidation due to the stiffness increase and self-desiccation characteristics that cementation imparts. Other properties that influence these characteristics, such as placed density and 7.19

169 Sensitivity Study mineralogy, can have a comparable influence on consolidation and barricade stresses. A number of different factors were shown to influence stresses applied to nonconsolidating fill barricade. The most significant of these factors result in higher pore pressures. Therefore, it is suggested that fully-coupled numerical analysis, combined with appropriate in situ monitoring, can provide a safe and efficient means of managing filling activities. 7.5 DEVELOPMENT OF EFFECTIVE STRESS DURING CURING Comparision between consolidating and non-consolidating fill Coring of in situ cemented backfill has shown in situ strengths to be frequently greater than those measured in the laboratory, for the same mix (Revell 2004, le Roux et al. 2002, Belem et al. 2002). The higher in situ strengths are expected to be a result of different curing conditions. One aspect that differs between material cured in situ and that cured in the laboratory, is the level of effective stress during curing. Application of effective stress during curing has been shown to increase material strengths by increasing the number of contact points and improving the intimacy of the contacts (Blight 2000, Rotta et al. 2003, Consoli et al. 2000). While the development of total stress to an element within a stope is relatively easy to predict, it is the rate that effective stress develops relative to the hydration period that must be appropriately understood to develop a more representative approach to sample preparation. For example, application of effective stress at the same rate as the total stress will result in an initial compression of the soil matrix and hydration at an increased density, while application of the entire self-weight stress at the completion of filling may result in crushing of weak cement bonds, and may thus have a detrimental, rather than a positive, effect on strength. As Minefill-2D is a fully coupled model, it can be used to estimate the rate and magnitude that effective stress develops in material within a stope. Given the rate of effective stress development in situ, the significance of this with respect to the final strength of the material can be understood. 7.20

170 Sensitivity Study To investigate the impact of different fill types on the rate at which effective stress develops, the Paste fill B (PFB) and Hydraulic Fill A (HFA) modelling results, from Section 7.2, are plotted in Figure This shows a plot against time of the development of vertical effective stress (σ v ) at a point located 12 m above the stope floor, at the opposite side to the drawpoint, for the HFA (HFA σ v ) and PFB (PFB σ v ). Also plotted in Figure 7.30 are the total self-weight stress (σ v ) and the effective selfweight stress (σ v ) that would develop in the absence of any arching. Assuming the same density, for the same filling sequence, this would be equal for both fill types. The other information presented in Figure 7.30 is the magnitude of decrease in pore pressure for the two materials due to self desiccation in isolation ( u SD only) (using Equation 3.27). The first point to note is that effective stress develops in HFA material immediately after placement, while no effective stress develops in PFB until approximately 6 hours. Also, in the first 30 hours of curing, the rate of development of effective stress in the HFA material is almost double that in PFB. Finally, the rate of effective stress development is relatively constant with the HFA material, while that with PFB is initially very slow but then increases exponentially Development of effective stress in consolidating fill Figure 7.30 suggests that the rate of development of effective stress in the HFA material is in accordance with the effective self-weight stress. The reason is that the coarse nature of HFA causes immediate dissipation of excess pore pressures, but due to the restriction (to flow) created at the drawpoint a phreatic surface is established within the fill mass. This phreatic surface creates approximately hydrostatic pore pressures within the stope and, if arching is neglected, this would result in effective stress developing in accordance with the effective unit weight of the material. If arching occurs as filling progresses, the effective stress applied is less than the effective self-weight stress. The significance of this increases as the stope plan area is reduced, with the consequence of reduced vertical total stress and a reduced rate of development of vertical effective stress. Another factor that could influence this response is the restriction at the drawpoint. As illustrated in Section 7.3.1, the resistance to flow through the drawpoint modifies the gradient of the pore pressure isochrones 7.21

171 Sensitivity Study within the stope. Using the effective unit weight and the filling rate to define the effective self-weight stress assumes hydrostatic pore pressures. A reduction in flow resistance through the drawpoint area would act to reduce pore pressures leading to an increase in vertical effective stress. To investigate the applicability of this theory for different filling rates, the effective stress at the same point was monitored for different filling rates using HFA. Figure 7.31 presents the development of vertical effective stress against time for a point 12 m above the base of the stope with different filling rates. Also presented in Figure 7.31 are the self-weight stresses, for each filling rate, if arching is neglected. In each case, the actual effective stress is very similar to the effective self-weight stress. The rate of development of effective self-weight stress is dependent on the filling rate and the effective unit weight of the material and independent of the rate of cementation. Obviously, the maximum effective stress in this case depends on the amount of material placed above the location of interest. It is also interesting to note that, for the HFA material, the calculating the effective stress using the dissipation of pore pressure that would occur due to self desiccation in isolation significantly overestimates the effective stress for this material. This is because with the high permeability of HFA, only very small hydraulic gradients are required to recharge water volumes removed through self desiccation. These pores are recharged and steady state seepage pore pressures are re-established Development of effective stress in non-consolidating fill Figure 7.30 indicates that the rate of development of vertical effective stress in PFB material is approximately equal to the rate that pore pressure is dissipated as a result of self desiccation alone. This is because the low coefficient of consolidation allows very little conventional (drainage-type) consolidation to take place. Furthermore, with little conventional consolidation taking place, the application of total self-weight stress (from fill accretion) creates an equivalent increase in pore pressure and no change in effective stress. As the only mechanism causing dissipation of any significant proportion of pore pressure is self desiccation, this mechanism alone can appropriately capture the rate at which effective stress develops in the soil matrix. 7.22

172 Sensitivity Study To investigate this theory in more detail, modelling was undertaken using PFB and the same fill/rest schedule as before, but this time with filling rates varying from 0.05 m/hr to 1.0 m/hr. The calculated vertical effective stress is plotted against time, for a point 12 m above the base of the stope, in Figure Also presented in Figure 7.32 is the dissipation of pore pressure as a result of self desiccation occurring in isolation. As this characteristic is material dependent, the relationship is consistent for all cases. Figure 7.32 indicates that, the development of vertical effective stress is similar for all filling rates greater than 0.05 m/hr, and that these are close to the magnitude of pore pressure reduction from self desiccation alone. This is particularly the case during the early stages of hydration, where the effective stress level has the greatest influence on the cured strength. The exception is the slowest filling rate of 0.05 m/hr. At this filling rate, the time required to fill the stope is of the same order as the time required for conventional drainage-type consolidation to take place. With reference to Gibson s (1958) consolidation chart (Figure 2.4) this situation corresponds to a dimensionless time factor (T=m 2 t/c v ) equal to 0.5. Figure 2.4 suggests that this time factor corresponds to (du/dx)/γ equal to 0.15, indicating drained filling conditions. This essentially changes the situation to that of a consolidating-type fill, where the effective stress is similar to the effective self weight. To investigate the spatial variation around a stope, the base case (PFB with a filling rate of 0.5 m/hr) was selected and the development of vertical effective stress at different elevations was monitored, and the results plotted in Figure Also presented in Figure 7.33 is the total vertical self-weight stress (from the accumulating fill mass) as well as the reduction in pore pressure from self desiccation alone. Figure 7.33 indicates that for non-consolidating fills, the development of vertical effective stress throughout a stope can be appropriately represented by the self desiccation mechanism in isolation Curing of fill: discussion and conclusion From the above discussion, it is clear that effective stress should be applied to laboratory control samples during curing at the same rate that they develop in situ, 7.23

173 Sensitivity Study otherwise the cured strengths of the laboratory samples will not be the same as the in situ cured strengths. One approach to doing so is to simulate each individual filling sequence using a tool such as Minefill-2D, and, based on the results, the laboratory specimen could be loaded to create an equivalent stress regime throughout the curing period. However, the results from the previous sensitivity analyses can also provide some useful guidance in formulating an appropriate curing technique. For material with a high uncemented coefficient of consolidation relative to the filling rate (such as the HFA case presented above), the development of vertical effective stress was shown to be in accordance with the effective self weight vertical stress. This logic assumes: Excess pore pressures are immediately dissipated Hydrostatic pore pressures are established within the fill mass due to the restriction at the drawpoint There is no arching. It is also important to note that the maximum effective stress depends on the depth of the sample within the fill mass. For material with a very low coefficient of consolidation relative to the filling rate (such as the PFB case presented above), it is expected that effective stress develops due to the drop in pore pressure that occurs from self desiccation occurring in isolation. In this case, the setup similar to the hydration experimental setup described previously (Section 3.6) can be used to allow the effective stress to develop as hydration proceeds. In this setup, high total stress is applied to the saturated sample enclosed in a membrane, which generates pore pressure practically equal to the applied total stress, and thus there is initially practically zero effective stress, just as in the stope. However, the process of hydration causes pore pressures to reduce (and effective stresses to increase) due to the self-desiccation mechanism, in a manner that exactly mimics what happens within the stope. Thus, at all stages of the test, the effective stress develops at exactly the same rate as it does within the stope assuming of course that the material is sufficiently finegrained to prevent any conventional consolidation occurring prior to hydration. 7.24

174 Sensitivity Study Modelling demonstrated that the rate of development of vertical effective stress is the same throughout the fill mass in the stope, which suggests that a single experiment may suitably define the material strengths throughout the stope. This logic assumes: The material remains saturated in the field No conventional drainage-type consolidation takes place. It is important to note that an increase in the coefficient of consolidation can have the effect of increasing or decreasing the rate of development of effective stress. Conventional consolidation acts to restore steady state seepage pore pressures. Therefore, if the self-desiccation mechanism is unable to reduce pore pressures below the steady state condition (as explained in Section 7.2.2), conventional consolidation acts to assist with the dissipation of pore pressures and thus, in this case, this increases the rate of development of effective stress. This is the case where a filling rate of 0.5 m/hr is adopted with PFB. On the other hand, should the self-desiccation mechanism be capable of reducing the pore pressures below steady state (as was demonstrated with PFA in Section 7.2.2), conventional consolidation causes water to flow downwards, recharging the pores, and re-establishing steady state seepage pore pressures. This reduces the rate that effective stress develops. 7.6 CONCLUSION The tools developed throughout this thesis have been used in this chapter to investigate the behaviour of tailings-based mine backfill. This investigation addressed a comparison between a range of tailings-based fill types, focusing on barricade stresses and the development of effective stress during curing. At the completion of each section, a specific conclusion section was provided. Some of the major conclusions that resulted from this analysis are presented below. Regardless of the fill properties, the most significant factor influencing barricade stresses is consolidation. Reduced consolidation resulted in higher barricade stresses. Broadly speaking, tailings-based fills can be divided into two groups: fills that consolidate immediately after placement (consolidating fills) and those that are unlikely to consolidate without the influence of cementation (non-consolidating fills). The fundamental difference between these fill types is that the mobilisation of strength in 7.25

175 Sensitivity Study consolidating fills is dependent on the rate of deposition, while the mobilisation of strength in non-consolidating fills is dependent on the rate of cement hydration. Pore pressures in consolidating fills are largely independent of cementation, permeability (for a given phreatic surface elevation) and filling rates, but are influenced by the flow restriction through the drawpoint at the base of a stope. Reducing this flow restriction can significantly reduce pore pressures throughout the stope, thereby increasing effective stresses and reducing barricade stresses. Cementation, permeability, drawpoint restriction and filling rate can all have a significant influence on the barricade stresses from non-consolidating fill. A variation in any of these factors results in a pore pressure change, which leads to higher barricade stresses. 7.26

176 Concluding Remarks and Recommendations of Future Work CHAPTER 8 CONCLUDING REMARKS AND RECOMMENDATIONS FOR FUTURE WORK 8.1 CONCLUDING REMARKS This thesis has presented an investigation into the mine backfill deposition process that is based on fundamental soil mechanics principles. The main feature of the work was to investigate and numerically couple three time-dependent processes that interact during the cemented tailings backfill process, these being: the loading rate (or filling rate), the conventional consolidation rate and the cement hydration rate. Based on the interaction of these different processes, a number of useful results were obtained that are relevant to the cemented mine backfill process. These results and some concluding remarks are contained in this chapter. 8.2 MAIN OUTCOMES The first significant result from this work was to highlight the importance of consolidation in estimating barricade stresses. It was demonstrated numerically that stresses applied to mine backfill barricade structures can vary by an order of magnitude depending on the degree of consolidation that occurs during filling. The significance of consolidation on the total stress distribution was also demonstrated experimentally using geotechnical centrifuge modelling. Furthermore, it was demonstrated that, without the presence of cement, the degree of consolidation during filling for typical tailings-based backfills can range from fully drained to fully undrained conditions. Investigation of the fundamental characteristics that influence the consolidation of cemented mine backfill showed that even with the minor amounts of cement typically added to mine backfill (2% to 10%), the material properties can change significantly. Specifically these changes include: An increase in stiffness, which can be greater than an order of magnitude. 8.1

177 Concluding Remarks and Recommendations of Future Work A reduction in permeability, which can also be greater than an order of magnitude. A volumetric reduction, which, while only very small, can lead to a significant drop in pore pressure when combined with the high material stiffness achieved through cement hydration (this is the so called self-dessication effect). By modifying the tailings consolidation program MinTaCo, the time-dependent process of cement hydration was successfully coupled with filling and conventional consolidation to assess the influence of cementation on the filling process. This modified program (termed CeMinTaCo) demonstrated that: The cement-induced increase in stiffness and self desiccation can make a significant contribution to the mine backfill consolidation process Because of the substantial influence of cementation on the consolidation behaviour, cement content can have a major influence on the consolidation of some cemented mine backfills. Contrary to conventional consolidation theory, the combination of cementation with low permeability material can act to generate lower pore pressures (higher consolidation) than higher permeability material. To investigate the influence of stress arching (onto the surrounding rockmass) during filling, a new two-dimensional consolidation program (termed Minefill-2D) was developed. Like CeMinTaCo, Minefill-2D coupled the three time-dependent processes, but, unlike CeMinTaCo, Minefill-2D also takes account of the influence of the stiff surrounding rockmass on the stress distribution. In addition, Minefill-2D allowed the stope drawpoint geometry to be incorporated (albeit in plane strain), which allowed stresses applied to barricade structures to be determined. This new model was compared with results from a series of laboratory tests and shown to provide a good representation of the process. To investigate the ability of Minefill-2D to represent the consolidation behaviour in an actual filling situation, modelling results were compared with in situ measurements. A comparison was carried out between the measured pore pressure in the centre of the stope floor and that predicted using Minefill-2D, using material properties that were 8.2

178 Concluding Remarks and Recommendations of Future Work independently derived using the material characterisation technique described in Section 3.6. This comparison indicated that Minefill-2D can provide a very good representation of the consolidation behaviour. A sensitivity study to investigate barricade stresses using Minefill-2D indicated: Broadly speaking, tailings-based fills can be divided into two groups: fills that consolidate immediately after placement ( consolidating fills ) and those that are unlikely to consolidate (during the filling period) without the influence of cementation ( non-consolidating fills ). The fundamental difference between these fill types is that the mobilisation of strength in consolidating fills is dependent on the rate of deposition, while the mobilisation of strength in nonconsolidating fills is dependent on the rate of cement hydration. Provided that no excess pore pressures are generated during deposition (i.e. consolidating fills as defined in Chapter 7) pore pressure is largely independent of cementation, permeability (for a given phreatic surface elevation) and filling rates, but is influenced by the flow restriction through the drawpoint at the base of the stope. Reducing this flow restriction can significantly reduce pore pressures throughout the stope, resulting in an increase in effective stress and a reduction in barricade stresses. Cementation, permeability and filling rate can all have a significant influence on the barricade stresses imposed by a non-consolidating fill. A variation in any of these characteristics results in a pore pressure change, which leads to changes in barricade stresses. As consolidation is the characteristic that most significantly influences barricade stresses (in both fill types), it is recommended that the most appropriate means of managing the risk of barricade failure is through in situ pore pressure monitoring strategies. The recommended management strategies for consolidating fills differ from those for non-consolidating fills. A sensitivity study to investigate the development of effective stress during curing using Minefill-2D indicated: 8.3

179 Concluding Remarks and Recommendations of Future Work The application of effective stress (at rates similar to those experienced in situ) during curing increases the final strength of the material. This was primarily due to an increase in density, which is consistent with the results of previous experimental studies. The development of effective stress during curing in a consolidating fill can be closely related to the accumulation of effective self-weight stress from the overlying fill mass The development of effective stress during curing in a non-consolidating fill can be closely related to the reduction in pore pressure from self desiccation in isolation. 8.3 RECOMMENDATIONS FOR FUTURE WORK The main focus of this thesis was to develop a framework for understanding the cemented mine backfill deposition process that may be used to assess the significance of various aspects and help with the interpretation of in situ monitoring results. In achieving the final outcome, a series of assumptions and simplifications were made to firstly represent the material behaviour and secondly simulate the behaviour. Much of this work should be revisited with the view of refining some of the material characteristics that were shown to be most critical. Specifically material modelling should focus on: Improved techniques for quantifying the self-desiccation process, including directly quantifying volumetric changes that occur during the hydration process and taking account of temperature changes during the hydration process. An improved model to represent the influence of cement hydration and soil compression on the permeability of the material. Additional experimental and constitutive modelling to more appropriately represent the variation in material strength and stiffness during the cement hydration process. Minefill-2D is a new finite element model that was developed specifically for the purpose of representing the cemented mine backfill deposition process. In its current 8.4

180 Concluding Remarks and Recommendations of Future Work state, the program is considered suitably rigorous for the applications in this thesis, but nevertheless improvements to some of the calculation algorithms would probably result in increased calculation speed and accuracy. Specifically these improvements might include: An improved time-stepping algorithm. This algorithm would calculate the most appropriate time-stepping size based on the element size, coefficient of consolidation and information from previous calculations in a manner similar to that adopted by Yong at al. (1983). Implementation of a constitutive model that takes account of yielding due to volumetric compression as well as a more rigorous approach to numerically accounting for strain softening. This would be useful when investigating the behaviour of very weak material. Implementation of interface elements to more appropriately represent the behaviour of the interface between the fill and the surrounding rockmass. Extension of the geometry to more appropriately represent the stope drawpoint. This may include extension from two to three dimensions or coupling of the axi-symmetric version of Minefill-2D (to represent the stope) with another axisymmetric version of Minefil-2D to represent the drawpoint. The stress distribution around a stiff fill mass can be influenced by the deformation behaviour of the barricade structure. Consideration should be given to implementing beam elements to represent any flexibility in the barricade structure. The combination of slow filling rates and high self-desiccation rates can lead to the development of large matrix suctions. As discussed by Grabinski and Simms (2006) these suctions have the potential to desaturate the fill matrix which could change the modelling response. Consideration should be given to taking account of matrix desaturation in the numerical analysis. This thesis demonstrated that devising a centrifuge experiment in which the three timedependent processes can interact is very difficult, and in order to achieve this, full-scale field testing is required. While the repetitive nature of stoping and backfilling provides 8.5

181 Concluding Remarks and Recommendations of Future Work opportunities to undertake full scale parametric studies, full scale field testing introduces problems regarding the suitability of instrumentation. Gathering quality data from cemented mine backfill stopes can be difficult and care should be taken to address the following concerns; It is well documented (Clayton and Bica, 1993, Take and Valsangkar 2001) that the deformation of earth pressure cells can lead to under registration (i.e. the cell measures less than the actual stress). The degree of under registration depends on the stiffness of the cell relative to the surrounding soil. As cemented mine backfill can gain very high stiffness during the hydration process, care should be taken to ensure that the cell stiffness matches the material stiffness appropriately. In the centre of a large backfill mass, the cement hydration process can lead to temperature changes that are in the order of 20ºC. With fluid-filled pressure cells, this can cause the internal fluid to expand, leading to an artificial pressure increase in the cell. Should this type of pressure cell be adopted, care must be taken to ensure the fluid has an appropriately low coefficient of thermal expansion to eliminate or minimise this error The measurement of positive pore pressure can be successfully achieved using vibrating wire piezometers, but when (and if) pore pressures become negative, the porous disk at the face of the piezometer can desaturate, creating a capillary block. In order to gather accurate negative pore pressure measurements, care should be taken to select a porous disk with an appropriate pore size to avoid desaturation. Also, to minimise the likelihood of desaturation, the porous disk should be saturated with a low-viscosity fluid under vacuum. Grabinski at al. (2007) adopted heat dissipation sensors in an attempt to measure pore water suctions, but are yet to report on the success of this approach. An obvious model verification strategy is to use in situ monitoring results to further verify the performance of the modelling approach presented in this thesis. However, prior to undertaking such back analysis, it is considered imperative that a number of assumptions regarding boundary conditions should be more clearly defined. Aspects that should be investigated include pore pressure accumulation immediately behind 8.6

182 Concluding Remarks and Recommendations of Future Work barricade structures (assumed to be zero in this analysis) and the pore pressure boundary condition within the stope at the fill / rock interface. 8.7

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189 References Le Roux, K.A. Bawden, W.F. and Grabinski, M.W.F. (2005). Field properties of cemented paste backfill at the Golden Giant Mine. Proceedings of the 8 th International Symposium on Mining with Backfill, Beijing, September, Leroueil, S. and Vaughan, P.R.(1990). The general and congruent effects of structure in natural soils and weak rocks. Géotechnique 40(3), pp LI, L. and Aubertin, M. (2003). A general relationship between porosity and uniaxial strength of engineering materials. Canadian Journal of Civil Engineering, August 03, Vol. 30, No.4, Liu, M.D. Carter, J.P. Desai, C.S. and Xu, K.J. (1998). Analysis of the compression of structured soils using the disturbed state concept. University of Sydney, Department of Civil Engineering, Research Report R770. Liu, M.D. and Carter, J.P. (2002). A Structured Cam-Clay model. Canadian Geotechnical Journal, Vol??, No 39, Liu, M.D. and Carter, M.D. (2005). Some applications of the Sydney Soil Model. Proceedings of the 16 th International Conference on Soil Mechanics and Geotechnical Engineering, Osaka, September, Proceedings, vol. 2, Marston, A. (1930). The theory of external loads on closed conduits in the light of latest experiments. Bulletion No.96, Iowa Engineering Experiment Station, Ames, Iowa. McCarthy, P. (2007). Digging Deeper. AMC Newsletter, March 07. Mitchell, R.J. and Wong, B.C. (1982). Behaviour of cemented sands. Canadian Geotechnical Journal, Vol. 19, Mikasa, M. (1965). The consolidation of soft clay, a new consolidation theory and its application. Japanese Society of Civil Engineers (Reprint from Civil Engineering in Japan 1965): Naylor, D.J. Pande, G.N. Simpson, B. and Tabb, R. (1981) Finite elements in geotechnical engineering, Pineridge press, Swansea, U.K. ISBN Potts, M.D. and Zdravković, L. (1999). Finite element analysis in geotechnical engineering (theory), Thomas Telford, ISBN

190 References Potvin, Y. Thomas, E. and Fourie, A. (eds.). (1995). Handbook on Mine Fill. Australian Centre for Geomechanics, ISBN Powers, T.C. and Brownyard, T.L. (1947). Studies of the physical properties of hardened Portland cement paste. Bull. 22, Res. Lab. of Portland Cement Association, Skokie, IL, U.S.A., reprinted from J. Am. Concr. Inst. (Proc.), Vol. 43, , , , , , , Powers, T.C. (1956). Structure and physical properties of hardened Portland cement paste. Bull. 94, Res. Lab. of Portland Cement Association, Skokie, ILK, U.S., J. Am. Ceram. Soc. 41, 1-6 Powers, T.C. (1979). The specific surface area of hydrated cement obtained from permeability data. Materials and Structures, Vol. 12, No. 3, , Springer. Qiu, Y. and Sego, D.C. (2001). Laboratory properties of mine tailings. Canadian Geotechnical Journal, Feb 2001, No.38, Randolph, M. F. and S. Hope (2004). Effect of cone velocity on cone resistance and excess pore pressures. IS Osaka - Engineering Practice and Performance of Soft Deposits, Osaka, Japan, n/a: Rankin, R. (2004). Geotechnical characterisation and stability of paste fill stopes at Cannington mine. PhD thesis, James Cook University. Rastrup, E. (1956). The temperature function for heat of hydration in concrete. Proceedings of the RILEM Symposium on Winter Concreting, Copenhagen, Danish National Institute for Building Research, Session B Revell, M. (2002). Underground mining at Aurion gold Kanowna Belle. AusIMM Bulletin, May/June, Revell, M.B. (2004). Paste How strong is it? Proceedings of the 8 th International Symposium on Mining with Backfill, September, Beijing, The Nonferrous Metals Society of China, Revell, M. and Sainsbury, D (2007) Paste bulkhead failures, Minefill 07, Montreal, Paper #

191 References Rouainia, M. and Wood, D.M. (2000). Kinematic hardening constitutive model for natural clays with loss of structure. Géotechnique, 50(2), Rotta, G.V. Consoli, N.C. Prietto, P.D.M. Coop, M.R. and Graham, J. (2003). Isotropic yielding in an artificially cemented soil cured under stress. Géotechnique 53(5), Santamarina, J. C., Klein, K. A., and Fam, M. (2001). Soils and Waves Particulate Materials: Behaviour, Characterisation and Process Monitoring. Wiley, Chichester, England. Schnaid, F, Prietto, P.D.M. and Consoli, N.C. (2001). Characterization of cemented sand in triaxial compression. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 127, No. 10, Schofield, A.N. (1980). Cambridge Geotechnical Centrifuge operations. Géotechnique 30(3), pp Seneviratne, N., Fahey, M., Newson, T.A. and Fujiyasu, Y. (1996). Numerical modelling of consolidation and evaporation of slurried mine tailings. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 20, No. 9, Sideris K. (1993). The cement hydration equation. Zem-Kalk-Gips;12:E337-55, Edition B. Sideris, K.K. Manita, P. and Sideris, K. (2004). Estimation of the ultimate modulus of elasticity and Poisson s ratio of normal concrete. Cement & Concrete Composites, No (not Vol??) 26, Smith, I.M. and Griffiths, D.V. (1998). Programming the Finite Element Method. 3 rd edition. John Wiley and Sons, ISBN Tan, T.S. and Scott, R.F. (1988). Finite strain consolidation a study of convection. Soils and Foundations, Vol. 28, No. 2, Take, W.A. and Valsangkar, A.J. (2001). Earth pressures on unyielding retaining walls of narrow backfill width. Canadian Geotechnical Journal, Vol. 38, No. 6,

192 References Terzaghi, K. (1943). Theoretical Soil Mechanics. John Wiley & Sons, New York. Thomas, E.G. and Holtham, P.N. (1989). The basics of preparation of de-slimed mill tailings hydraulic fill. Innovations in Mining Backfill Technology, Hassani et al. (eds), Balkema, Rotterdam Toh, S.H. (1992). Numerical and centrifuge modelling of mine tailings consolidation. PhD thesis,. Turcry, P. Loukili, A. Barcelo, L. and Casabonne, J.M. (2002). Can the maturity concept be used to separate the autogenous shrinkage and thermal deformation of cement paste at early age? Cement and Concrete Research, Vol. 32, Vermeer and Brinkgreve (1998). Plaxis Finite element code for soil and rock analysis. Balkema, Rotterdam. Vick, S.G. (1983). Planning, design and analysis of tailings dams. John Wiley and Sons, New York. Winch, C.M. (1999). Geotechnical characterisation and stability of paste backfill at BHP Cannington Mine. Undergraduate thesis, School of Engineering, James Cook University, Australia. Williams, D.J. Carter, J.P. and Morris, P.H. (1989). Modelling numerically the lifecycle of coal mine tailings. Proc. 12 th Int. Conf. Soil Mech. Found. Engrg, 3, Rio de Janeiro, Yin. J. H and Fang. Z, (2006). Physical modelling of consolidation behaviour of a composite foundation consisting of a cement-mixed soil column and untreated soft marine clay. Géotechnique 56(1), Yong, R.N. Siu, S.K.H and Sheeran, D.E. (1983). On the stability and settling of suspended solids in settling ponds. Part 1. Piecewise linear consolidation analysis of sediment layer. Canadian Geotechnical Journal, Vol. 20, Zienkiewicz, O.C. and Cormeau, I.C. (1967). Viscoplasticity, plasticity and creep in elastic solids. A unified numerical solution approach. Int. J. Num. Meth. Eng., No.8,

193 References Zienkiewicz, O.C. and Zhu, J.Z. (1992), The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. International Journal for Numerical Methods in Engineering, Vol. 33,

194 Figures

195 Ch 1 Introduction - Figures Figure 1.1. Schematic of a typical mine tailings based backfill system (contributed by Cobar Management Pty Ltd). 1.1

196 Ch 1 Introduction - Figures Fill deposition point m Stope m Saturated fill material 5-6 m Containment barricade 5-6 m 5-6 m Drawpoint Figure 1.2. Schematic showing a typical stope filling situation (with typical dimensions). Figure 1.3. Photograph showing a failed barricade (from Revell and Sainsbury 2007). 1.2

197 Ch 2 Background Literature Review - Figures Height above base (m) Drained Self weight stress σ v σ v 10 5 Undrained Vertical total stress, σ v (kpa) Figure 2.1. Stress distribution down the centreline of a stope assuming drained and undrained filling. 7 6 Height up barricade (m) Drained analysis σ x Undrained analysis Barricade stress, σ x (kpa) Figure 2.2. The impact of drained and undrained filling on barricade stress. F2.1

198 Ch 2 Background Literature Review - Figures σ v =σ v + u σ h =σ v.k 0 + u Figure 2.3. Conversion from vertical total stress to horizontal stress Classified tailings Vick (1983) Impermeable base Full-stream tailings Vick (1983) (du/dx)/γ' at surface Permeable base Cu tailings, Qiu and Sego (2001) Ag tailings, Qiu and Sego (2001) T=m 2 t/c v Figure 2.4. Gibson's(1958) consolidation chart with typical minefills. F2.2

199 Ch 2 Background Literature Review - Figures Void ratio, e Structure permitted space Compression of bonded material Compression of destructured material Mean stress, p Figure 2.5. Comparison between structured and unstructured compression behaviour. Deviator stress, q Equivalent unstructured yield surface Critical state line Structured yield surface Loading surface p 0 p c p s Mean stress, p Figure 2.6. Comparison between structured and unstructured yield surfaces. F2.3

200 Ch 2 Background Literature Review - Figures Figure 2.7. Powers illustration of the Cement hydration process (from Illstron et al. 1979). 70 Cement content required (%) Critical porosity Typical cemented minefill operating range Void ratio, e Figure 2.8. Relationship between void ratio and binder content to achieve critical porosity and typical mine backfill range. F2.4

201 Ch 3 Behaviour of Cementing Slurries- Figures Mean effective stress, p Yield stress increment Δp y Cemented yield p y Uncemented yield Cemented compression curve Void Ratio, e Uncemented yield Figure 3.1. Incremental yield stress as it is defined in this thesis. Unconfined compression strength, q u (kpa) Lines: Eq. 3.6 Points: Data C c = 10%, 28 day C c = 5%, 7 day Void ratio, e Figure 3.2 (a). Relationship between void ratio and q u for CSA hydraulic fill. F3.1

202 Ch 3 Behaviour of Cementing Slurries- Figures Unconfined compression strength, q u (kpa) C c = 4% C c = 2% C c = 6% Lines: Eq. 3.6 Points: Data (All at 28 days) Void ratio, e Figure 3.2 (b). Relationship between void ratio and q u for Cannington paste fill from Rankin (2004). 1 CSA H.F. Cannington P.F. q q u u(max) = exp 0.9 t q u /q u(max) q q u u(max) = exp 2.6 t Time, t (day) Figure 3.3. Normalised q u against time for CSA hydraulic fill and Cannington paste fill. F3.2

203 Ch 3 Behaviour of Cementing Slurries- Figures 2000 Incremental Go (MPa) R 2 = Unconfined compression strength, q u (MPa) Figure 3.4 (a). Incremental small strain shear stiffness against q u for CSA hydraulic fill. 250 Young's modulus, E (MPa) R 2 = Unconfined compression strength, q u (MPa) Figure 3.4 (b). Young's modulus (at large strains) against q u for Cannington paste fill. F3.3

204 Ch 3 Behaviour of Cementing Slurries- Figures 1.1 C c = 5%, 1 day 1 C c = 5%, 16 day Void ratio, e C c = 5%, 5 day Uncemented Lines: model Points: data Vertical effective stress, σ' v (kpa) Figure 3.5. Comparison between one-dimensional compression experiments and the model results. 8.0E E E-06 Permeability, k (m/s) 5.0E E E E E-06 10% 5% 2% Model 0.0E Effective void ratio, e eff Figure 3.6. Comparison between e ff and permeability. F3.4

205 Ch 3 Behaviour of Cementing Slurries- Figures 100% 90% 80% Percentage passing 70% 60% 50% 40% 30% KB Paste CSA HF 20% 10% 0% Size (microns) Figure 3.7. Particle size distribution curves. 600 Confining 500 Pressure (kpa) KB PF u KB PF σ' Time, t (hr) CSA HF σ' CSA HF u KB PF: Kanowna Bell Paste Fill CSA HF: CSA mine Hydraulic Fill Figure 3.8. Pore water pressure (u ) and effective stress changes in triaxial samples hydrating under constant total stress and undrained boundary conditions. F3.5

206 Ch 3 Behaviour of Cementing Slurries- Figures Sent wave amplitude Received wave amplitude Time, t (μ Seconds) Figure 3.9. Typical result from bender element test Total stress u Pressure (kpa) Cumulative u drop u backup to minimise effective stress p' Time, t (hr) Figure Typical pore water pressure (u ) and effective stress changes in a triaxial sample (CSA hydraulic fill material with 5% cement) hydrating under constant total stress and undrained boundary conditions (with periodic re-establishment of back pressure, to minimise effective stress change). F3.6

207 Ch 3 Behaviour of Cementing Slurries- Figures Soil bulk modulus, K s (MPa) % Binder (Maturity relation, eqn 3.31) 10%Binder (from Go experiment) 5% Binder (Maturity relation, eqn 3.31) 5% Binder (from Go experiment) 2% Binder (Maturity relation, eqn 3.31) 2% Binder (from Go experiment) Time, t (hr) Figure The development of bulk stiffness Ks with time for CSA hydraulic fill: experimental data (symbols) and Equation 3.31 (lines). Incremental u reduction (kpa/hr) % Binder 5% Binder 2% Binder Time, t (hr) Figure Rate of pore water pressure (u ) reduction with time after initial set for various cement contents for CSA hydraulic fill. F3.7

208 Ch 3 Behaviour of Cementing Slurries- Figures Normalised water consumption rate (cm3/cem gram/hr) % Binder 5% Binder 2% Binder Time, t (hr) Figure Normalised apparent water loss rate plotted against time for different cement contents for CSA hydraulic fill: experimental data compared with Equation Cumulative pore pressure reduction, Δu (kpa) % Theoretical 10% Experiment 5% Theoretical 5% Experiment 2% Theoretical 2% Experiment 0% Experiment Time, t (hr) Figure Comparison of experimental reduction of pore water pressure (u ) against time and adjusted theoretical solution for CSA hydraulic fill. F3.8

209 Ch 3 Behaviour of Cementing Slurries- Figures Cumulative pore pressure reduction, Δu (kpa) % Binder Prediction 2% Binder Experiment 5% Binder Preciction 5% Binder Experiment Time, t (hr) Figure Predicted and measured reduction in pore water pressure (u ) for KB paste backfill Temperature (ºC) t BC =20ºC Monitoring location t 0 =30ºC 5 0 m 5 m x-coordinate (m) Figure Temperature variation across stope half-space after 20 hours. F3.9

210 Ch 3 Behaviour of Cementing Slurries- Figures Cell Bender elements Cell pressure control Sample enclosed in membrane Top back-pressure control Bender Element processing system Base back-pressure control Pore pressure transducer Figure Hydration test setup. F3.10

211 Ch 4 One Dimensional Consolidation Modelling - Figures a + da ξ(a+da,t) δa δξ δx 1 δx 1 a ξ(a,t) Figure 4.1. Schematic representation showing the relationship between a, ξ and x in the convective coordinate system. n ( v w v s ) γ w δa V a t sh n a ( v v ) γ + [ n( v v ) γ ] a w s w w s w Figure 4.2. Schematic representing pore water continuity across an element a. F4.1

212 Ch 4 One Dimensional Consolidation Modelling - Figures i+1 a 2 i a 1 i-1 Figure 4.3. Schematic showing mesh used in CeMinTaCo finite difference approximation Pore pressure, u (kpa) Experiment: CSA HF, C c = 5%, e = 0.7 CeMinTaCo Time, t (hr) Figure 4.4. Comparison between the self desiccation pore pressure reduction in a hydration test and CeMinTaCo output. F4.2

213 Ch 4 One Dimensional Consolidation Modelling - Figures Typical geometry stope geometry Typical stope Drainage through through drawpoint draw-point Idealised onedimensional stope Idealised onedimensional stope Vertical drainage Vertical drainage Figure 4.5. Idealisation of the base boundary conditions used to represent a stope in CeMinTaCo. 600 Pore pressure, u (kpa) Total vertical stress No cement C c = 5%, no self desiccation C c = 5%, with self desiccation Time, t (hr) Figure 4.6. CeMinTaCo output illustrating the influence of the cement induced mechanisms on the pore pressure response. F4.3

214 Ch 4 One Dimensional Consolidation Modelling - Figures 1.0E-06 k 1 Permeability, k (m/s) 1.0E E-08 k 2 k 3 1.0E Curing time, t (hr) Figure 4.7. Variation in permeability against time k 1 Pore pressure, u (kpa) k Time, t (hr) k 3 Figure 4.8. Pore pressure against time for the different cases analysed. F4.4

215 Ch 4 One Dimensional Consolidation Modelling - Figures Height above base, h (m) k 3 k 1 SSPP k Pore pressure, u (kpa) k 2 5 m Stope Drawpoint Figure 4.9. Pore pressure isochrones for the different permeability cases analysed b= e b= Vertical effective stress, σ v ' (kpa) Figure e against σ v for different damage parameters. F4.5

216 Ch 4 One Dimensional Consolidation Modelling - Figures Pore pressure, u / Effective stress, σ' v / Total stress, σv (kpa) σ v Time, t (hr) u σ v ' Figure CeMinTaCo output for different damage parameters. 400 Stress, σ v / Strength, q u, σvy' (kpa) One-dimensional yield stress σ v q u (in situ ) q u (unstressed ) Time, t (hr) Figure Development of material strength against time for different damage parameters. F4.6

217 Ch 4 One Dimensional Consolidation Modelling - Figures Pore pressure, u / Effective stress, σ' v / Total stress, σv (kpa) Time, t (hr) σ v u σ v ' Figure CeMinTaCo output for different damage parameters in free draining material Stress, σ v / Strength, q u, σ' vy (kpa) One-dimensional yield stress q u (in situ) σ v ' q u ( without σ v ' ) Time, t (hr) Figure Development of material strength for different damage parameters with free draining fill. F4.7

218 Ch 4 One Dimensional Consolidation Modelling - Figures 7% 6% Hydraulic fill, 0% cement 5% Vertical strain, εv 4% 3% Paste fill, 5% cement 2% 1% 0% Time, t (hr) Figure Axial strain levels for different filling scenarios Pore pressure, u (kpa) u, CeMinTaCo u, In situ measurement Time, t (hr) Figure Comparison between CeMinTaCo and in situ pore pressure measurements. F4.8

219 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures 1 y z x Displacement only nodes Displacement and pore pressure nodes Figure 5.1. Element geometry adopted for plane-strain displacement and pore pressure finite element calculations in this thesis. (a) (b) Figure noded isoparametric element (taken from Potts and Zdravković, 1999) showing (a) the parent element and (b) the global element. F5.1

220 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures Displacement only nodes 1 radian Displacement and water pressure nodes r 2 CL r 1 r 1 r 2 z θ r Figure 5.3. Element geometry adopted for axi-symmetric displacement and pore pressure finite element calculations in this thesis Peak strength Residual strength Cemented yield surface Shear stress, τ (kpa) Shear stress, τ (kpa) Uncemented yield surface Plastic shear strain to destroy i Axial strain, ε q (%) Triaxial stress path Mean stress, p (kpa) (a) (b) Figure 5.4. (a) shear stress against axial strain and (b) shear stress against mean stress for a triaxial test. F5.2

221 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures G t(cem) / G 0(cem) Experimental Model t/t max Figure 5.5. Tangent shear stiffness normalised by small strain shear stiffness against shear stress normalised by the peak shear strength. 1 m u=0 E = 100 MPa, k=1e-6 m/hr 4 m u=0 Figure 5.6. Illustration of one-dimensional consolidation problem. F5.3

222 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures Depth (m) Initial pressure Analytical 30 hr Analytical 50 hr Minefill-2D 30 hr Minefill-2D 50 hr Excess pore pressure normalised against initial value, u ex /u ex0 Figure 5.7. Comparison between Minefill-2D and the analytical solution for one-dimensional consolidation analysis. 1 m u=0 E = 100 MPa, k=1e-6 m/hr, γ=19.5 kn/m 3 4 m u=0 Figure 5.8. Illustration showing the one-dimensional self weight consolidation problem used in the Minefill-2D verification. F5.4

223 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures Depth (m) Initial pressure 0 hr Plaxis 6 hr Plaxis 20 hr Minefill-2D 6 hr Minefill-2D 20 hr Excess pore pressure, u ex (kpa) Figure 5.9. Comparison between Minefill-2D and Plaxis for a self weight consolidation problem. 500 kpa 500 kpa Impermeable 500 kpa Figure Numerical simulation undertaken to verify the performance of the self desiccation mechanism. F5.5

224 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures 600 Pore pressure, u / Mean stress, p' (kpa) Minefill-2D u Analytical p' Time, t (hr) Figure Comparison between Minefill-2D and the analytical solution for self desiccation. Phreatic surface height E = 1x10 20 kpa, k=5x10-5 m/sec 4 m u=0 Figure Numerical geometry for comparison between Minefill 2D and Darcy's law for a falling head permeability test. F5.6

225 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures Minefill-2D Phreatic surface height (m) Analytical Time, t (sec) Figure Comparison with Minefill-2D and Darcy's law for the flow through the surface layer of the fill. 300 Pore pressure, u/ Vertical total stress, σv (kpa) σ v, CeMinTaCo u, Minefill-2D σ v, Minefill-2D u, CeMinTaCo 4 m/day Time, t (hr) u Figure Comparison between Cemintaco and Minefill 2D. F5.7

226 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures Pore pressure, u/ Vertical total stress, σv (kpa) σ v, CeMinTaCo u, Minefill-2D σ v, Minefill-2D u, CeMinTaCo 4 m/day u Time, t (hr) Figure Comparison between Cemintaco and Minefill 2D with a modified "initial set" point. (a) (b) (c) Figure Finite element mesh used to represent (a) coarse mesh, (b) medium mesh and (c) a fine mesh. F5.8

227 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures Centre-line pore pressure, u -cl (kpa) u Medium mesh Coarse mesh Fine mesh Time, t (hr) Figure Calculated pore pressure in the centre of the stope floor for different mesh shapes Barricade stress, σx (kpa) σ x Medium mesh Coarse mesh Fine mesh Time, t (hr) Figure Calculated barricade stress in the centre of the stope floor for different mesh shapes. F5.9

228 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures σ v (a) (b) (c) Figure Vertical total stress contours at the completion of filling for the (a) coarse mesh, (b) medium mesh and (c) the fine mesh. Vertical total stress, σv / Centre-line pore pressure, u cl (kpa) σ v, No arching u cl, In situ measurement u cl, Minefill-2D Time, t (hr) Figure Comparison between Minefill-2D and in situ measurements. F5.10

229 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures 13 m 13 m 40 m 5 m 5 m 5 m 5 m (a) (b) Figure Illustration showing the boundary conditions adopted for the (a) fixed-bc and (b) free-bc case in the "arching" analysis. Vertical total stress, σv/ Pore pressure, u (kpa) u σ v σ v, fixed-bc u, fixed-bc Self weight stress σ v, free-bc u, free-bc Time, t (hr) Figure Comparison between u and σ v in a stope with fixed and free vertical displacement boundary conditions. F5.11

230 Ch 5 Two Dimensional Consolidation analysis (Minefill 2D) - Figures σ v σ v (a) (b) Figure σ v contours for a stope with (a) fixed vertical displacement boundary conditions and (b) with free vertical displacement boundary conditions Height (m) σ v, fixed-bc Self weight stress 5 0 σ v, free-bc Total vertical stress, σ v (kpa) Figure Total vertical stress along the stope centreline for the fixed and free BC. F5.12

231 Ch 6 Centrifuge Modelling - Figures Water overflow line 180 Rough wall Base plate Strain gauge set O-ring seal 5 Base load cells 6 Figure 6.1. Schematic showing a section through the sample container. Pore pressure transducer Figure 6.2.(a) Photograph of strain gauged cylinder that was used to represent the stope walls and (b) the inside of the cylinder showing the rough cylinder walls. F6.1

232 Ch 6 Centrifuge Modelling - Figures Figure 6.3. Photograph of the false base and loadcells that were used in the experiment. Figure 6.4. Experimental apparatus positioned in a strong box on the UWA geotechnical centrifuge. F6.2

233 Ch 6 Centrifuge Modelling - Figures Total soil force Base load cell force 700 Vertical force (kn) Base u Pore pressure, u (kpa) Cylinder axial force Time, t (hr) Figure 6.5. Change in pressure and stress during Stage 1 loading. 100 σ v, Layer 2 Pore pressure increment, Δu (kpa) u Base Δu Pore pressure transducer Time, t (hr) Figure 6.6. Incremental change in u during Stage 2 loading. F6.3

234 Ch 6 Centrifuge Modelling - Figures Vertical force increment (kn) Figure 6.7. Incremental load / stress distribution in second stage of loading. Figure σ h #5 Base loadcells force Cylinder (wall) axial force (#6) Applied force increment Time, t (hr) #5 #6 σ h Horizontal total stress increment, Δσh (kpa) Fitted relationship used in the modelling Void ratio, e Test data Effective vertical stress, σ v (kpa) Figure 6.8. Relationship between vertical effective stress and void ratio from the Rowe cell test. F6.4

235 Ch 6 Centrifuge Modelling - Figures Permeability, k (m/s) 1.0E E E E-08 Direct measurement From c v obtained from displacement rate From c v obtained from pore pressure dissipation Fitted relationship used in the modelling 1.0E Void ratio, e Figure 6.9 Relationship between void ratio and permeability from Rowe cell Minefill-2D Base pore pressure, u (kpa) Experiment u Time, t (hr) Figure Comparison between measured and calculated pore pressure in Stage 1. F6.5

236 Ch 6 Centrifuge Modelling - Figures Applied force 14 Base loadcells Vertical force (kn) Minefill -2D Base Force Minefill-2D Axial Force Base Cylinder (wall) axial load (#6) Time, t (hr) Figure Comparison between the measured and calculated load distribution in Stage 1. Small strain shear stiffness, Go (MPa) Application of layer 2 q u fit G o fit Go measurement qu measurement Time, t (hr) Unconfined compressive strength, q u (kpa) Figure Evolution of G o and q u against time for the kaolin with 25% cement mix. F6.6

237 Ch 6 Centrifuge Modelling - Figures 100 σ v, Layer 2 Pore pressure increment, Δu (kpa) u Base u Pore pressure transducer Minefill-2D, Base u Time, t (hr) Figure Comparison between measured and calculated pore pressure in Stage 2. Vertical force Increment ( kn) Δσ h Base loadcells force Cylinder (wall) axial force (#6) Minefill-2D, Incremental axial force Minefill-2D, Incremental base force Minefill-2D, Incremental σ h Applied force increment #5 σ h Time, t (hr) # Increment of horizontal total stress, Δσh (kpa) Figure Comparison between the measured and calculated load distribution in Stage 2. F6.7

238 Ch 7 Sensitivity Study - Figures HFA HFB Portion passing PFA PFB Size (micron) Figure 7.1. Particle size distribution of backfills tested. 1.0E-05 HFA Permeability, k (m/s) 1.0E-07 HFB PFA 1.0E-09 PFB 1.0E Time, t (hr) Figure 7.2. Evolution of permeability against time for different mine backfills. F7.1

239 Ch 7 Sensitivity Study - Figures PFA Cohesion, c' (kpa) HFB PFB HFA Time, t (hr) Figure 7.3. Evolution of cohesion against time for different mine backfills PFB Barricade stress, σx (kpa) σ x HFB PFA HFA Time, t (hr) Figure 7.4. Minefill 2D results of barricade stress against time for different backfill types. F7.2

240 Ch 7 Sensitivity Study - Figures Steady state seepage pore pressure PFB 250 HFA Pore pressure, u (kpa) u HFB 50 PFA Time, t (hr) Figure 7.5. Development of pore pressure against time for different mine backfills PFB Steady state seepage pore pressure Height, h (m) PFA HFA HFB Pore pressure, u (kpa) Figure 7.6. Pore pressure isochrones for different mine backfills. F7.3

241 Ch 7 Sensitivity Study - Figures Pore pressure, u (kpa) u Impermeable barricade k dp =0.1 k stope k dp =k stope k dp =10 k stope Time, t (hr) Figure 7.7. Influence of drawpoint permeability on pore pressure at the base of a stope with consolidating fill Height, h (m) Impermeable Barricade 10 5 k dp =10 k stope k dp =k stope k dp =0.1 k stope Pore pressure, u (kpa) Figure 7.8. Pore pressure isochrones for consolidating fills with various drawpoint permeabilities. F7.4

242 Ch 7 Sensitivity Study - Figures σ x Impermeable barricade Barricade stress, σx (kpa) k dp =0.1 k stope k dp =k stope k dp =10 k stope Time, t (hr) Figure 7.9. Barricade stress against time for different drawpoint permeabilities with consolidating fills. 250 k=0.1 k HFB 200 u Pore pressure, u (kpa) k=k HFB 50 k=10 k HFB Time, t (hr) Figure Pore pressure against time for consolidating fills with different permeabilities. F7.5

243 Ch 7 Sensitivity Study - Figures σ x k=0.1 k HFB Barricade stress, σx (kpa) k=10 k HFB k=k HFB Time, t (hr) Figure Barricade stress against time for consolidating fills with different permeabilities % cement 3.0% cement 200 Pore pressure, u (kpa) % cement 1.5% cement 50 u Time, t (hr) Figure Pore water pressure against time for consolidating fill with different binder contents. F7.6

244 Ch 7 Sensitivity Study - Figures % cement 160 σ x 1.5% cement Barricade stress, σx (kpa) % cement 8.0% cement Time, t (hr) Figure Barricade stress against time for consolidating fills with different binder contents Shear stress, τ /Cohesion, c' (kpa) τ 3.0% cement, cohesion 3.0% cement, shear stress 1.5% cement, shear stress % cement, cohesion Time, t (hr) Figure Comparison between applied shear stress and cohesion for a boundary element. F7.7

245 Ch 7 Sensitivity Study - Figures Interface shear induced softening (a) (b) Figure Contour of cohesion at the end of filling for the (a) the 3.0% cement and (b) the 1.5% cement case. (a) (b) Figure 7.16 Total vertical stress calculated for the (a) 3.0% cement and (b) the 1.5% cement case. F7.8

246 Ch 7 Sensitivity Study - Figures m/hr Pore pressure, u (kpa) m/hr 2 m/hr 0.12 m/hr 0.06 m/hr 50 u Time, t (hr) Figure Influence of filling rate on consolidating fill pore pressures Barricade stress, σx (kpa) m/hr 2 m/hr 0.6 m/hr 0.12 m/hr 0.06 m/hr. 50 σ x Time, t (hr) Figure Influence of filling rate on consolidating fill barricade stress. F7.9

247 Ch 7 Sensitivity Study - Figures Pore pressure, u (kpa) Kdp=Kstope Kdp=0.1 Kstope kdp=10 Kstope 50 u σ x Barricade stress, σ x (kpa) Figure Relationship between pore pressure and barricade stress in a consolidating fill u Pore pressure, u (kpa) k dp =0.1 k stope k dp =k stope 50 k dp =10 k stope Time, t (hr) Figure Pore pressure against time for non-consolidating fills with different drawpoint permeabilities. F7.10

248 Ch 7 Sensitivity Study - Figures σ x Barricade stress, σx (kpa) kdp=0.1 k stope kdp=k stope kdp=10 k stope Time, t (hr) Figure Barricade stress against time for non-consolidating fills with different drawpoint permeabilities. (a) (b) Figure Pore pressure profile at the end of filling for (a) kdp=10k stope and (b) kdp=0.1k stope. F7.11

249 Ch 7 Sensitivity Study - Figures u k=10 k PFA Pore pressure, u (kpa) k=k PFA k=0.1 k PFA Time, t (hr) Figure Pore pressure against time for non-consolidating fills with different permeabilities Barricade stress, σx (kpa) σ x k=10 k PFA k=k PFA 20 0 k=0.1 k PFA Time, t (hr) Figure Barricade stress against time for non-consolidating fills with different permeabilities. F7.12

250 Ch 7 Sensitivity Study - Figures u Pore pressure, u (kpa) % cement 1.5% cement % cement Time, t (hr) Figure Pore pressure against time for non-consolidating fills with different cement contents. 300 Barricade stress, σx (kpa) σ x 1.5% cement 3.0% cement % cement Time, t (hr) Figure Barricade stress against time for non-consolidating fills with different cement contents. F7.13

251 Ch 7 Sensitivity Study - Figures Barricade stress, σx / Pore pressure, u (kpa) u, Bonded interface σ x, Bonded interface u, Cohesionless interface u σ x σ x, Cohesionless interface Time, t (hr) Figure Barricade Stress and pore pressure against time for non-consolidating fill with a bonded and unbonded interface u Pore pressure, u (kpa) m/hr 0.5 m/hr 0.2 m/hr Time, t (hr) Figure Pore pressure against time for non-consolidating fills with different filling rates. F7.14

252 Ch 7 Sensitivity Study - Figures m/hr σ x Barricade stress, σx (kpa) m/hr 0.2 m/hr Time, t (hr) Figure Barricade stress against time for non-consolidating fills with different filling rates. 500 Vertical effective stress, σv' / Vertical total stress, σv / Pore pressure, u (kpa) σ v(self weight) HFA, σ v ' HFA, -Δu S.D. only PFB, Δu S.D. only σ v(self weight) PFB, σ v ' Time, t (hr) Figure Development of effective stress within an element of consolidating and nonconsolidating fill against time. F7.15

253 Ch 7 Sensitivity Study - Figures Vertical effective stress, σv' (kpa) Effective self weight 1 m/hr σ v ' 0.5 m/hr (minefill-2d) σ v ' 1.0 m/hr (minefill-2d) Effective self weight 0.5 m/hr Effective self weight 0.05 m/hr σ v ' 0.05 m/hr (minefill-2d) Time, t (hr) Figure Development of effective stress against time in a consolidating fill m/hr Self desiccation -Δu Vertical effective stress, σv' (kpa) m/hr 0.15 m/hr 0.05 m/hr Time, t (hr) Figure Development of effective stress against time in a non-consolidating fill. F7.16

254 Ch 7 Sensitivity Study - Figures 600 Vertical effective stress, σv' (kpa) σ v from fill self weight without arching 2 m 19 m 25 m 29 m Self desiccation -Δu 15 m Time, t (hr) Figure Development of effective stress against time at different elevations in a nonconsolidating fill. F7.17

255 Tables