Jia, Yudan (2011) Numerical modelling of shaft lining stability. PhD thesis, University of Nottingham.

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1 Jia, Yudan (2011) Numerical modelling of shaft lining stability. PhD thesis, University of Nottingham. Access from the University of Nottingham repository: -_Y._Jia.pdf Copyright and reuse: The Nottingham eprints service makes this work by researchers of the University of Nottingham available open access under the following conditions. Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in Nottingham eprints has been checked for eligibility before being made available. Copies of full items can be used for personal research or study, educational, or notfor-profit purposes without prior permission or charge provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. Quotations or similar reproductions must be sufficiently acknowledged. Please see our full end user licence at: A note on versions: The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher s version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. For more information, please contact eprints@nottingham.ac.uk

2 Num erical Modelling of Shaft Lining Stability Prepared by Yudan Jia BEng in Civil Engineering MSc in Structural Engineering subm itted to for the degree of Doctor of Philosophy October 2010

3 This thesis is dedicated to m y parents, sisters, brother, m y husband and our baby.

4 Abstract ABSTRACT This research proj ect focuses on the application of num erical m odelling m ethods to rock m echanics problem s, com bining theoretical, experim ental and num erical m odelling work. Specifically, practical finite difference m odelling approach for analysing shaft lining stability through the Marl and Potash strata at Boulby m ine UK has been developed using the com m ercially available software FLAC 2D / FLAC 3D (I TASCA, 2008). A soft rock Marl occurs close to the bottom of the two deep shafts at the m ine. Both shafts concrete linings through this stratum have suffered considerable pressure, which has caused gradual failure of the shaft lining. So far, both shaft linings through the Marl stratum have been rest ored twice after sunk in 1970s and a further third relining is now required and being planned. The in situ observations, the rock engineers experience, and the available in situ m easurem ents at the m ine have been significantly helpful in the validation of the num erical m odelling. Many factors at the m ine site have, however, m ade this num erical m odelling research challenging, including com plicated lining structures, com plex lining failure conditions and the scarcity of laborat ory t est data for the weakest rock m aterial - the Marl, which easily weathers on exposure. Based on a com prehensive literature review, a database of m aterials properties relevant to t his research has been produced. The m ethodology of obtaining appropriate rock m ass input m aterial properties to use in num erical m odelling based on laboratory test data has been studied. I n three- dim ensional m odels in this research, two m odelling m ethods have been developed t o sim ulate each stage in the shaft linings: the continuous m odel for all shaft linings and independent m odels for each shaft lining. The num erical m odelling results im ply that: Firstly, in the independent three- dim ensional m odels, the m odelling results were difficult to understand due to the com plexity of the structures i

5 Abstract representing the shaft relining system s and difficulty in defining appropriate properties for the interface elem ents. Therefore, the continuous three- dim ensional m odel that gives the analysable m odelling results is recom m ended by the author for this research. By this m ethod, the effect of the historic changes in the stress field on each shaft lining s stability can be investigated from initial shaft construction to subsequent relining phases. Secondly, the weak rock Marl should not be the only reason for the shaft linings failure through this stratum. The roadway approxim ately 10 m beneath the Marl strat um was also a key factor for the stability of the shaft linings. The weak Marl cannot carry the stress redistribution around the shaft caused by the roadway excavation, which was an uneven loading acting on the circular shaft linings. This uneven loading introduced high shear and t ensile stresses which threatened the stability of the circular concret e structures. Thirdly, the interface m aterials between high strength concrete blocks in shaft relinings im proved the flexibility of the lining system s successfully, but decreased the strength of the whole lining system s as weak j oints. I n addition, the single ring concrete blocks ( the first and third relinings) are a m ore effective lining than the double rings (the second relining), and the third relining would perform better than the previous ones. As a recom m endation for the further sim ulation, it is worth attem pting to sim ulate the longer term deform ation and stress conditions of the shaft concret e lining system s using the Creep m odel built in FLAC 2D / FLAC 3D codes. Additionally, deeper research work com bined with in situ investigation can be done to decrease the uncertainty of the input m aterial properties to m ake the num erical m odels as close to the real engineering situation as possible. ii

6 Acknowledgements ACKNOW LEDGEMENTS First of all I would like to express m y sincere thanks and gratitude to m y supervisors Dr. David Reddish and Dr. Rod Stace for their academ ic guidance, encouragem ent and financial support throughout the PhD course. I would also like to thank Prof. Hai- Sui Yu and Prof. Yang Ju for t heir supervisions, help and encouragem ent during this research. Acknowledgem ents are also given to Mr. Allan William s and Mr. Mike Keen, the rock engineers of Boulby m ine, Cleveland Potash Ltd for their support during the progress of t he research proj ect. Thanks m ust go to Dr. Philip Rowsell, Mr. Mark Dale and Mr. Craig Cox for their generous help and collaboration during the laboratory tests for t his research. I am thankful to all friends at the Nottingham Centre for Geom echanics with whom I have had a wonderful tim e throughout three years PhD study. Sincerely thanks m ust go t o m y parents, m y husband Yat e, m y sisters and brother without whose support and encouragem ent I would not have been what I am now; especially to m y husband Yat e, who I believe is a great husband and will be a great father. The research work outlined in this thesis was largely funded by Cleveland Potash Ltd. Part-funding was also gratefully received from the National Basic Research Proj ect of China (Grant No. 2010CB226804, 2002CB412705), the New Century Excellent Talents Program of the Ministry of Education of China ( Grant No. NCET ) and Beijing Key Laboratory Research Proj ect ( Grant No. JD ), who have provided financial support with part of the tuition fees. Finally, I would like to thank the I nstitute of Materials, Minerals and Mining ( I OM 3 ) and South Midlands Mining and Minerals I nstitute (SMMMI ) for the awards that provided part of m y research and living expenses. iii

7 List of Contents LI ST OF CONTENTS Abstract Acknowledgements List of Contents List of Figures List of Tables Notation i iii iv viii xiv xvi CHAPTER 1 I NTRODUCTI ON 1.1 Introduction Problem Definition Aim s and Objectives Technical Challenges Research Outline 9 CHAPTER 2 GENERAL LI TERATURE REVI EW 2.1 I n Situ State of Ground Stress Stress Distribution around Excavations Rock Mass Classification System s I ntroduction Rock Quality Designation (RQD) Rock Mass Rating (RMR) System Coal Mine Classification Rating (CMCR) Rock Tunnelling Quality I ndex, Q Conclusions Shaft Stability Problem s Previous Rock Mechanics Research at Boulby Mine History of Shafts at Boulby Mine The Design for the Original Lining of the Shafts The Design for the First Relining of the Shafts The Design for the Second Relining of the Shafts The Design for the Third Relining of the Shafts Conclusions and Assum ptions I n Situ Stress Measurem ents at Boulby Mine 65 iv

8 List of Contents 2.8 I n Situ Deform ation Measurem ents at Boulby Mine Chapter Sum m ary 69 CHAPTER 3 LABORATORY DETERMI NATI ON OF GEOTECHNI CAL PARAMETERS 3.1 Determ ination of Rock Mass Strength I ntroduction Geological Strength I ndex (GSI ) Hoek-Brown Failure Criterion RocLab Software Rock Materials from Boulby Mine Laboratory Tests Data Collection Materials Properties Used in Modelling Laboratory Tests for Concretes used at Boulby Mine I ntroduction Laboratory Tests Results and Analysis Material Properties Used in Modelling I nterface Problem s in the Shaft Lining Modelling I ntroduction I nterfaces between Epoxy Resin and Concrete I nterfaces between Cem ent Mortar and Concrete I nterfaces between Plywood Pack and Concrete Other Param eters used in the Shaft Lining Modelling Material Properties of Polyurethane and Verm iculite Material Properties of Cem ent Grout Chapter Sum m ary 109 CHAPTER 4 I NTRODUCTI ON OF FLAC 2 D / FLAC 3 D 4.1 I ntroduction Fields of Application Fundam ental Com ponents of a Problem Finite Difference Grid Boundary Conditions I nitial Stress Conditions Constitutive Models 119 v

9 List of Contents Material Properties Chapter Sum m ary 123 CHAPTER 5 TW O- DI MENSI ON AL NUMERI CAL MODELLI NG OF SHAFTS LI N I N G SYSTEMS 5.1 I ntroduction Param etric Study Geom etry of the Model and Mesh Definition Boundary and I nitial Stress Conditions Material Properties Stress Relaxation and Modelling Sequence Modelling Results of the Param etric Study The Effect of the Properties of the Marl The Effect of the Extent of the Weathered Marl The Effect of the Ground Stress Field The Possible Point Loading on the Original Lining Model Configurations Modelling Results and Discussion Modelling for the Shaft Original Lining and Relinings Model Configurations I nterfaces between Concrete Blocks Modelling Results and Discussion Conclusions 159 CHAPTER 6 THREE- DI MEN SI ON AL NUMERI CAL MODELLI NG OF SHAFTS LI N I N G SYSTEMS 6.1 I ntroduction Modelling Methodology - A Continuous Model for the Original Lining and All Relining System s Modelling Methodology - I ndependent Models for the Original Lining and All Relining System s Modelling Methodology - Excavation and Relining Sequences Model Configurations Dom ain and Mesh Design Dim ensions Used in the Models 176 vi

10 List of Contents Support for the Roadway Detailed Engineering Design Modelling Boundary and I nitial Stress Conditions Material Properties Surrounding Rock Concrete and Cem ent Grout I nterfaces Polyurethane and Verm iculite Modelling Results Results of the Continuous Model Results of the I ndependent Models Conclusions 225 CHAPTER 7 CONCLUSI ONS AN D RECOMMENDATI ONS 7.1 Conclusions Recom m endations 236 REFEREN CES 238 APPENDI X I I I Sum m ary of Boulby Mine Rock Materials Laboratory Tests Data Mohr-Coulom b/ Hoek-Brown Properties of Rock Materials at Boulby Mine Laboratory Tests Data of the Concrete Segm ental Linings from Boulby Mine vii

11 List of Figures LI ST OF FI GURES Figure 1.1 Location of Boulby mine 3 Figure 1.2 Stratigraphic section 5 Figure 2.1 Results of stress measurements: vertical stress (1973) 14 Figure 2.2 Results of stress measurements: average horizontal stress 15 Figure 2.3 Results of stress measurements: vertical stress (1978) 17 Figure 2.4 Variation of ratio of average horizontal stresses to vertical stress 18 Figure 2.5 Equations for the stresses in the material surrounding a circular hole in a stressed elastic body 21 Figure 2.6 Variation in ratio of tangential stress to vertical applied stress z with radial distance r along horizontal axis for k 0 =0 22 Figure 2.7 Estimated support categories based on the Tunnelling Quality Index Q 37 Figure 2.8 Strata sequence of Boulby potash mine 43 Figure 2.9 Detailed geology of the Permian strata at Boulby mine 44 Figure 2.10 Indicative longitudinal section through original rock-shaft lining 49 Figure 2.11 First relining for the man shaft, section 52 Figure 2.12 First relining, plan 53 Figure 2.13 Damaged manshaft before the second relining 54 Figure 2.14 Second relining, plan 55 Figure 2.15 Second relining, section 56 Figure 2.16 Damaged manshaft before the third relining 59 Figure 2.17 Third relining, plan 60 Figure 2.18 Plastic zone becoming bigger with relining 61 Figure 2.19 Conceptual relationship between strength of lining required and practical concrete lining 64 Figure 2.20 Recorded stress in row 7 in the second relining 67 viii

12 List of Figures Figure 2.21 Instrumentation layouts at man shaft through Upper Halite stratum 68 Figure 3.1 RocLab software user interface 77 Figure 3.2 Mohr-Coulomb strength envelopes for the Marl obtained from tests data 84 Figure 3.3 Samples of concrete from Boulby mine 86 Figure 3.4 Test set up for UCS and Young s modulus 87 Figure 3.5 Test set up for triaxial compressive tests 87 Figure 3.6 Zone dimension used in stiffness calculation 95 Figure 3.7 Diagram of direct shear test 101 Figure 3.8 Marine plywood and concrete samples used in direct shear test 102 Figure 3.9 σ τ curves obtained from the direct shear tests: shear force perpendicular to the texture of the plywood surface 103 Figure 3.10 σ τ curves obtained from the direct shear tests: shear force parallel to the texture of the plywood surface 103 Figure 3.11 Stress-strain curve for the plywood pack used in relining systems 105 Figure 4.1 General solution procedure 113 Figure 4.2 Gradually changed mesh: fine mesh in the vicinity of excavation (inside red dashed line), coarse mesh in other parts of the model 114 Figure 4.3 Sudden changes in neighbour zone size 115 Figure 4.4 Geometry for an example water tunnel 116 Figure 4.5 Example of boundary conditions 118 Figure 4.6 Determination of material properties for Mohr-Coulomb model 123 Figure 5.1 Deformed shape of 25 mm diameter rockbolt following rupture at end of shear test 125 Figure 5.2 A horizontal slice in Marl in the two-dimensional model (not to scale) 127 ix

13 List of Figures Figure 5.3 Finite difference grid used in the two-dimensional models 128 Figure 5.4 Boundary and initial stress conditions of the two-dimensional numerical model 130 Figure 5.5 Conceptual plastic zone around the shaft 133 Figure 5.6 Weathered Marl simulated in the two-dimensional models 133 Figure 5.7 Mohr-Coulomb strength envelopes for the Marl 135 Figure 5.8 Radial convergence and tangential stress in vicinity of tunnel face 137 Figure 5.9 Modelling sequence flow chart in the two-dimensional models 138 Figure 5.10 Shaft lining closure vs. the properties of the Marl 139 Figure 5.11 Max. 1 in shaft lining vs. the properties of the Marl 140 Figure 5.12 Shaft lining closure vs. the thickness of the weathered Marl 142 Figure 5.13 Max. 1 in shaft lining vs. the thickness of the weathered Marl 142 Figure 5.14 Shaft lining closure vs. background stress ratio 144 Figure 5.15 Max. 1 in lining vs. background stress ratio 144 Figure 5.16 Failure state of the original shaft lining under background stress ratio = Figure 5.17 FLAC 2D mesh for possible point loading model (not full window) 147 Figure 5.18 Failure state and schematic shape change of the original shaft lining under possible point loading 148 Figure 5.19 Lateral movement of the original lining 148 Figure 5.20 Detailed finite difference mesh of the shaft linings 152 Figure 5.21 Shaft linings closure from the two-dimensional models 153 Figure 5.22 Ratio of lining s closure with inner radius of each lining 153 Figure 5.23 Principal stress tensors in the first relining 155 Figure 5.24 Mohr circles and strength envelop in the Mohr-Coulomb failure criteria 156 x

14 List of Figures Figure 5.25 Maximum major principal stress and maximum deviator stress in shaft linings 156 Figure 5.26 The ratio of the max. deviator stress in shaft linings with the corresponding HSC strength 157 Figure 5.27 Major principal stress contour and direction of displacement in the first relining 158 Figure 6.1 Schematic inset of the shaft and the roadway 162 Figure 6.2 Mesh in the dimensions of the first relining system 165 Figure 6.3 Curves obtained in the process of calculating equivalent properties for the shaft s first HSC relining system 166 Figure 6.4 Mesh in the dimensions of the original shaft lining 167 Figure 6.5 Consistent mesh for the original lining part of vertical section 169 Figure 6.6 Non-consistent mesh for the first relining part of vertical section 169 Figure 6.7 Interfaces in the relining systems in the numerical models 170 Figure 6.8 Excavation steps flow chart in numerical modelling 172 Figure 6.9 Schematic shaft relining sequences in the continuous model 173 Figure 6.10 Geological stratigraphy in the study 175 Figure 6.11 Numerical model domain and mesh in the study 176 Figure 6.12 Foundation of the intermediate tower - vertical section 179 Figure 6.13 Foundation of the Manshaft - vertical section 180 Figure 6.14 Vertical section of the whole model mesh for this study (through X-Z plane) 181 Figure 6.15 Plan of shaft inset level at m below shaft collar (BSC), the inset of the roadway and the shaft 182 Figure 6.16 Plan view of wing walls modelled in this study (through X-Y plane) 183 Figure 6.17 Boundary conditions in the three-dimensional models in this study 184 xi

15 List of Figures Figure 6.18 Conceptual graded plastic zone around the shaft 186 Figure 6.19 Plan view of graded weathered Marl simulated in the three-dimensional models 187 Figure 6.20 Mohr-Coulomb strength envelopes for the Marl in the three-dimensional models 189 Figure 6.21 Displacement measure points in the three-dimensional models (not to scale) 193 Figure 6.22 Horizontal displacements of the original lining s inner surface 194 Figure 6.23 Horizontal displacement contour of the original shaft lining before the roadway excavation (Roadway direction: Y) 194 Figure 6.24 Horizontal displacement contour of the original shaft lining after the roadway excavation (Roadway direction: Y) 195 Figure 6.25 Horizontal displacement vectors of the original shaft lining before the roadway excavation 196 Figure 6.26 Horizontal displacement vectors of the original shaft lining after the roadway excavation 197 Figure 6.27 Horizontal displacements of the shaft relinings inner surface 197 Figure 6.28 Horizontal displacement contour of the first relining (Roadway direction: Y) 198 Figure 6.29 Horizontal displacement contour of the second relining (Roadway direction: Y) 199 Figure 6.30 Horizontal displacement contour of the third relining (Roadway direction: Y) 199 Figure 6.31 Vertical stress z in the original lining after the shaft excavation 202 Figure 6.32 Vertical stress z in the original lining after the roadway excavation 203 Figure 6.33 Vertical stress z in the first relining 204 Figure 6.34 Vertical stress z in the second relining 205 xii

16 List of Figures Figure 6.35 Vertical stress z in the third relining 206 Figure 6.36 Principal stress contours for the original lining: 9.8 m above the roadway roof in the Marl stratum, before the roadway excavation 208 Figure 6.37 Minor principal stresses contour of the shaft linings: 9.8 m above the roadway roof in the Marl stratum 210 Figure 6.38 Schematic horizontal closure of the shaft lining through the Marl and Potash strata in the model 212 Figure 6.39 Plastic states of the shaft linings at 7 m above the roadway roof in the Potash stratum (the inside two rings are the shaft linings) 213 Figure 6.40 Displacement vectors of the first relining in the independent model (Roadway direction: Y) 214 Figure 6.41 Interface normal stress in the second relining in the independent model (Roadway direction: Y) 215 Figure 6.42 Interface shear stress in the second relining in the independent model (Roadway direction: Y) 216 Figure 6.43 Interface shear failure in the first relining in the independent model (Roadway direction: Y) 217 Figure 6.44 Interface shear failure in the second relining in the independent model (Roadway direction: Y) 218 Figure 6.45 Interface shear failure in the third relining in the independent model (Roadway direction: Y) 218 Figure 6.46 Vertical stress z in the first relining in the independent model 220 Figure 6.47 Vertical stress z in the second relining in the independent model 221 Figure 6.48 Vertical stress z in the third relining in the independent model 222 xiii

17 List of Tables LI ST OF TABLES Table 2.1 Maj or engineering rock m ass classifications 24 Table 2.2 Rock Mass Rating System 28 Table 2.3 Classification of individual param eters used in the Tunnelling Quality I ndex Q 33 Table 2.4 ESR values suggest ed by Bart on et al 36 Table 2.5 Boulby m ine shaft lining sequence and inform ation (through the Marl zone) 62 Table 2.6 Actual support load capacity of the concrete lining syst em s at Boulby m ine 63 Table 3.1 Charact erisation of rock m asses on the basis of interlocking and joint alteration 73 Table 3.2 Estim ate of Geological Strength I ndex GSI based on geological descriptions 74 Table 3.3 Guidelines for estim ating disturbance fact or D 79 Table 3.4 Average UCS and Young s m odulus of HSC used at Boulby m ine 88 Table 3.5 Average t ensile strengt h of HSC used at Boulby m ine 88 Table 3.6 Mohr- Coulom b properties for HSC used at Boulby m ine 89 Table 3.7 Young s m odulus of NSC 91 Table 3.8 Poisson s ratio of NSC 91 Table 3.9 Tensile strength of NSC 92 Table 3.10 I nput properties for all concrete m aterials in the num erical m odelling 92 Table 3.11 Physical properties a com parison of typical products 97 Table 3.12 I nput properties for the interfaces elem ents representing the epoxy resin between concret e blocks 98 Table 3.13 Com pressive st rength requirem ents given as charact eristic values for m asonry cem ent 98 Table 3.14 I nput properties for the interfaces elem ents representing the cem ent m ortar between concrete blocks 100 Table 3.15 Mohr- Coulom b properties obtained from the plywood-concrete direct shear t est 104 Table 3.16 Com pression test data on plywood sam ple 105 xiv

18 List of Tables Table 3.17 Table 3.18 Table 3.19 Table 3.20 I nput properties for the interfaces elem ents representing the plywood pack between concret e blocks 106 The stiffness m easured in the com pression and nano- indentation tests 107 I nput properties for polyurethane and verm iculite in the num erical m odelling 108 I nput properties of the cem ent grout used in the num erical m odelling 109 Table 4.1 FLAC 2D / FLAC 3D constitutive m odels 121 Table 5.1 Background st ress ratio used in the m odels 131 Table 5.2 Table 5.3 Table 5.4 Table 5.5 Table 6.1 I nput properties for the Marl in param etric studies on the effect of its properties on the stability of the linings 132 I nput properties for the weathered and un- weat hered Marl in param etric studies on the effect of the extent of weathered Marl on the stability of the original shaft lining 134 Dim ensions of shaft linings through the Marl zone at Boulby m ine 150 Dim ensions used for the weathered Marl zone in the two- dim ensional m odels 151 Equivalent input properties for the HSC used in shaft s relining system s at Boulby m ine 168 Table 6.2 Shaft excavation sequences used in the m odels 171 Table 6.3 Dim ensions used for the weathered Marl zone in the three- dim ensional m odels 188 Table 6.4 I nput properties for the Marl used in the m odels 188 Table 6.5 Stiffness com parison between rocks and backfill m aterials 190 Table 6.6 Maj or principal stress 1 of the shaft linings inner surface 207 Table 6.7 Minor principal stress 3 of the shaft linings inner surface 207 Table 6.8 Maj or principal stress 1 of the first relining s inner surface 223 Table 6.9 Minor principal stress 3 of the first relining s inner surface 223 xv

19 Notation NOTATI ON σ Norm al stress σ Norm al stress difference σ θ Tangent ial st ress σ r Radial stress σ c Uniaxial com pressive strength of rock m ass σ ci Uniaxial com pressive strength of intact rock σ h The horizontal com ponent of ground st ress σ h av The average horizontal com ponent of ground st ress σ t Tensile strength σ x The horizontal ground stress in x direction σ y The horizontal ground stress in y direction σ z The vertical com ponent of ground st ress σ 1 Maj or principal st ress σ 2 I nterm ediate principal stress σ 3 Minor principal stress ' σ 1 Maxim um effective st ress at failure ' σ 3 Minim um effective stress at failure ' σ 3 m ax The upper lim it of confining stress over which the relationship between the Hoek- Brown and the Mohr- Coulom b criteria is considered τ Shear stress τ r θ Shear stress in polar coordinates syst em τ c Shear stress difference caused by c xvi

20 Notation τ ϕ Shear stress difference caused by ϕ ϕ Friction angle ϕ Friction angle difference ε Strain difference The background stress ratio, σ x / σ y ν a 1 B c c CMC D De Poisson s ratio Excavation radius Bulk m odulus Cohesion Cohesion difference The Coal Mine Classification The disturbance fact or The equivalent dim ension of the excavation E Ei Young s m odulus Young s m odulus of the intact rock Erm Young s m odulus of the rock m ass ESR Excavation support ratio f c Concret e cube com pressive strength fck Charact eristic cylinder com pressive st rength f cm Mean value of concret e cylinder com pressive st rength f, t f sp GSI h HSC Ja Tensile strength of concret e Geological Strength I ndex The depth High strength concrete The joint alteration num ber Jn The joint set num ber xvii

21 Notation Jr The j oint roughness num ber Jw The joint water reduction factor K n Norm al stiffness K s Shear stiffness k 0 The ratio of the average horizontal com ponent of ground st ress to the vertical com ponent of ground st ress m i The intact rock param eter (constant) m b, s and a The Generalized Hoek- Brown strength param eters NSC P Q r RQD RMR r/r S SRF T UCS UTS Norm al strength concret e Norm al force The Rock Tunnelling Quality I ndex The distance from the excavation face The Rock Quality Designation I ndex The Rock Mass Rating Concret e lining s inner radius decreasing ratio Shear m odulus A stress reduction fact or Shear force Uniaxial com pressive strength Uniaxial tensile strength z m in The sm allest width of an adjoining zone in the norm al direction in FLAC 2D / FLAC 3D m esh xviii

22 Chapter 1 I ntroduction CHAPTER 1 I NTRODUCTI ON 1.1 I ntroduction Geotechnical engineers always face a dilem m a when a structure, e.g. an underground excavation, is required t o be designed and construct ed in a rock m ass in m ining, petroleum or civil engineering. I t is well known that a rock m ass with its heterogeneous nature is inherently very com plex in it s structure and m echanical behaviour. This m eans that m any influential param et ers cannot be precisely det erm ined and this factor alone m akes design very difficult. Before the advent of com puters, structures in rock m asses were designed m ainly based on rules of thum b and experience. They usually tended t o be over- designed with excessive safety fact ors and the design was based on situations sim ilar to the one for which the new design was being developed. This raises the question however, what should the geot echnical engineers do with problem s for which no past experience is available? They have to seek m ore rational solutions for these rock m echanics problem s, t aking both the safety factor and econom ic cost of the design into account. A wide variety of t echniques have been developed t o deal with com plex rock m echanics problem s, such as lim it equilibrium m ethods, photo- elastic techniques and the use of physical m odels. At present, com put er based num erical m odelling m ethods are very popular for solving rock m echanics problem s due to rapid advancem ents in com puter t echnology and its availability to engineers. A num ber of num erical m ethods of analysis have been developed over the past thirty years, for exam ple the Finite Elem ent 1

23 Chapter 1 I ntroduction Method (FEM), the Boundary Elem ent Method ( BEM), the Discret e Elem ent Method (DEM), the Finite Difference Method (FDM) and so on. This thesis is based on research into num erical m odelling application of FDM to a particular rock m echanics problem, com bining theoretical, experim ental and num erical m odelling works. I n this research, the shaft lining stability at Boulby m ine has been investigated as a practical engineering exam ple using com m ercial FDM codes - FLAC 2D / FLAC 3D. There are m any advantages to using a practical engineering exam ple for this research. The m ost im portant one is that the in situ observations, the rock engineers experience at Boulby m ine, and the available in situ m easurem ents provide validation of the num erical m odelling. However, m any factors at the Boulby m ine site have m ade this num erical m odelling research challenging, including low strength rock strata, a high ground st ress field, com plicated shaft lining structures, com plex failure and yield conditions of the shaft lining and the scarcity of laborat ory test data for the weakest rock m aterial. I t is recognised that the usefulness of powerful num erical analysis program s is greatly limited if the analyst does not have reliable input data for rock m ass properties. Therefore, the m ethodology of obtaining appropriate m aterial properties for rock m ass in num erical m odelling from laboratory tests data has also been studied. 1.2 Problem Definit ion Boulby m ine (Cleveland Potash Ltd.) is located on the North- East coast of England in the county of Cleveland and lies within the North Yorkshire Moors National Park (Figure 1.1). The m ine produces a m illion tonnes of potash product in various grades annually, prim arily to be used as a fertilizer. I n addition, about 750,000 tonnes of rock salt is produced for 2

24 Chapter 1 I ntroduction road de- icing (William s and Auld 2002). The potash seam m ined is about 7 m thick on average and approxim ately in a horizontal plane however with a shallow dip from nort hwest to southeast (average gradient is 1: 33). The com plete workings of the Boulby m ine lie approxim ately 800~ 1150 m below sea- level. The potash is generally m ined where the seam is m ore than 4 m thick (William s and Auld 2002). Redcar Middlesbrough North York Moors National Park Whitby Scarborough Figure 1.1 Location of Boulby m ine (William s and Auld 2002) There are two shafts at Boulby m ine, No. 1 shaft (rock shaft) and No. 2 shaft (m an shaft), bot h of which were sunk during the period 1968 to Both shafts are around 5.5 m finished diam eter and approxim ately 1150 m in depth, m aking them the deepest in the United Kingdom at that tim e. The upcast of rock shaft is used prim arily for m ineral winding and the m anwinding- shaft is the downcast situated 91 m away, in which m en 3

25 Chapter 1 I ntroduction and m aterials are wound in two cages that use rope guides (William s and Auld 2002). The geological strata, through which the Boulby twin shafts are sunk is shown in Figure 1.2. At a depth of approxim ately 1100 m, close to the bottom of the shafts, a layer of Carnallitic Marl (about 9 m thick, Marl for short in later chapters) overlies the potash seam. The Marl, a reddishbrown saliferous clay, is often wet and poorly consolidated with frequent slicken sides and veins of halite and sylvinite (William s and Auld 2002). The perm anent support of the twin shafts through the zone of Marl stratum has proven difficult and now consists of a segm ental concrete lining. Both shaft linings have suffered considerable radial pressure from the Marl stratum together with vertical com pression from the upper part of the shafts resulting from subsidence of the host surrounding rock. This subsidence likely resulted from large num bers of roadway excavation in shafts pillar area. These pressures caused gradual failure of the concret e lining of the shafts in the Marl zone and failure of the relatively weak unsupported wing walls at the bott om of the shafts at the inset level (Chilton and Maxwell 1989). 4

26 Chapter 1 I ntroduction Figure 1.2 Stratigraphic section (William s and Auld 2002) After several years, the deterioration of the shaft s concrete lining walls was so extensive that replacem ent of the lining becam e necessary through this zone. Repair work on two shafts has been carried out twice so far. The first relining of both shafts through the Marl zone took place during 5

27 Chapter 1 I ntroduction 1983~ 1986, and they were again relined (second relining) through the sam e zone during 1997~ At present, dam age to the shaft s concrete lining (second relining) is again becom ing severe, and a further repair (third relining) is now required and being planned. The shaft relinings through the Marl zone have always been start ed with the m an shaft each tim e. To date, the design of the third relining and som e preparation work for reconst ruction has been com pleted for the m an shaft. 1.3 Aim s and Objectives The m ain aim of this research project was the application of num erical m odelling m ethods to rock m echanics problem s in com plicated rock st rata under high stress field, com bining theoretical, experim ental and num erical m odelling work. Specifically, a practical finite difference m odelling approach for sim ulating the shaft lining stability in the shaft bottom area of the m ine has been developed using the com m ercial software FLAC 2D / FLAC 3D ( I tasca, 2008). The specific aim s and obj ectives can be sum m arized as follows: 1) To develop the m ethodology of obtaining appropriate rock m ass input m aterial properties t o use in num erical m odelling based on laborat ory test data, to m ake the num erical m odels m ore reliable. 2) To undertake param et ric studies of different rock m at erials properties to det erm ine their potential effects on the shaft lining stability. 3) To num erically sim ulate all the Boulby historical cases of shaft concret e linings, and t o analyze the m odelling results and com pare them with the available m easured data t o det erm ine the shaft lining probable failure m echanism. 4) To predict, using the num erical m odels, the long- term stress and deform ation conditions for the latest newly designed shaft lining 6

28 Chapter 1 I ntroduction syst em under the severe ground loading in particular strata zones. This will supply im portant reference data for Boulby m ine shaft engineers (especially for the design and construction of the third relining of the rock shaft). 1.4 Technical Challenges The st ructures of shaft lining system s at Boulby m ine are very com plex and the behaviour of the Marl is not well understood. The m ain com ponents of the shaft lining system s are in situ cast concrete or concret e blocks. I n addition, som e special yielding designs have been introduced and im plem ented to obtain ideal shaft lining system s at Boulby m ine, which were expect ed to resist severe ground stress effectively over tim e. I n this research, an attem pt has been m ade to develop num erical m odels as close t o the actual engineering structure as possible although there were som e sim plifications that had to be m ade. There were m any t echnical difficulties encountered during this study, the m ost problem atic of which are discussed as follows: 1) I t has been difficult to det erm ine the final strength and stiffness properties for the Marl used in the num erical m odels. The Marl is a weak rock and has a tendency t o squeeze, which has been dem onst rated by the gripping of the drill rods during boring (Squirrell 1992). This weak rock easily weathers on exposure. I t is not norm ally exposed during m ining operations, except during shaft lining restoration work. Therefore it is difficult to obtain and preserve the sam ples of this rock for laborat ory t est s, which are a significant and reliable data source for det erm ining the m aterial properties. Only two lim ited sets of t est dat a have been available and utilised for the Marl in this research. 7

29 Chapter 1 I ntroduction 2) There has also been som e difficult problem in num erical m odelling of the original shaft lining syst em. I n the original lining system at Boulby m ine, verm iculite and polyurethane foam s were used to backfill the gap (around 0.4 m thick) between the concret e lining and excavation face through the Marl stratum and the stratum above it. These m aterials are very soft com pared with the surrounding rock and concret e used in the original shaft lining at Boulby m ine, and their stiffnesses are several thousandths of those of the lining and the rock. When these m aterials were included in the num erical m odels, it resulted in m any problem s, especially in three dim ensional m odelling, such as unrealistic deform ation of the original concret e lining and a dram atic increase in the program run tim e. The solutions adopted to deal with this problem are discussed in detail in a later chapter. 3) The problem of m odelling of j oints between concret e blocks also caused difficulties. For all the shaft relining system s at Boulby m ine, high strength concret e (HSC) blocks were em ployed, with different m aterials filled between the concret e blocks each tim e, including epoxy resin, cem ent m ortar and plywood packs. All these j oints are very thin (12~ 18 m m ) com pared t o the concrete blocks (around 0.5 m 0.5 m ) but are im portant to the m echanical behaviour of the whole concrete lining syst em s. Therefore interface elem ents have been built in FLAC 2D / FLAC 3D to be used to represent their behaviour in num erical m odels. However, it is very difficult to determ ine the appropriate m echanical properties for the interface elem ents for each relining m odel in the absence of laboratory test data. I n order to solve this problem, som e laborat ory tests have been conducted, but m ost properties for the interface elem ents have been assum ed based on 8

30 Chapter 1 I ntroduction som e reference papers, British Standards and available test data from Boulby m ine. 4) The dim ensions of the shaft concrete lining through the Marl stratum changed every tim e it was replaced. The expected ideal num erical m odelling in this research is to try to sim ulate all the historical cases of the shaft lining system s in their real dim ensions continuously in a single m odel. In this way, the effect of the historic changes in the stress field on each shaft lining stability could be investigated from the shaft s initial construction, original lining installation, the construction of the inset and the roadway leading from the shaft, and subsequent relining phases. However, the changing dim ensions of the restored shaft lining m akes this im possible since the finite difference m esh cannot be changed once the m odelling of the original shaft excavation is started. Equivalent m aterial properties for the shaft relining system s have been developed in this research to solve t his problem. 1.5 Research Out line The first stage of the study was a com prehensive literature review which concentrated on the following fields and is described in Chapter 2: 1) The virgin ground st ress stat e and its influence on underground excavations 2) Rock m ass classification system s and m ethods t o determ ine rock m ass strength and stiffness for num erical m odels 3) Rock m echanics influences on general shaft stability problem s 4) Previous rock m echanics research at Boulby m ine 5) The history of shafts at Boulby m ine, including const ruction and restorations and available in situ m easurem ents of stress and displacem ents of shaft linings 9

31 Chapter 1 I ntroduction Following the literature review, a m ethodology for the laboratory determ ination of geot echnical param eters for the rock and other support m aterials used in this research is described in Chapter 3. This allowed a database of reliable rock and m at erial properties for this research to be developed. New laboratory test s have been conducted and previously conducted t esting data integrated into the database. Additionally, tim e- dependent ( creep) t ests on som e rock m at erials and laboratory tests (uniaxial and triaxial com pression tests and Brazilian Disc tests) on sam ples of the concrete from the shaft linings at Boulby mine were conducted in the Nottingham Centre for Geom echanics ( NCG). For the second and third shaft relining, HSC concret e blocks were em ployed and squeezable plywood packs were inserted between the blocks. To m ake the num erical m odelling closer to the real situation, the properties of the interfaces between the concret e block and the plywood pack were needed. Therefore, shear box t est s between the concrete and the plywood packs were also carried out in the laborat ory at the NCG. The database of m at erial properties from Boulby m ine com prises all the above laboratory tests data and the laborat ory tests data from previous rock m echanics research at Boulby m ine, including Patchet s t ests (1970), Cook s t ests ( 1974) ( both from the University of Newcastle upon Tyne) and tests conducted at the Royal School of Mine I m perial College ( 2000). The m aterials m echanical properties used in later num erical m odelling were based on this database. I n addition, several field visits to the Boulby m ine were arranged, which were helpful to prom ot e num erical m odelling, m odelling results analysis and com parison with in situ m easurem ents. Num erical m odelling has then been conducted following these preparatory works, including an analysis of all the historical cases of the shaft concrete 10

32 Chapter 1 I ntroduction relining syst em s. The content of this part of t he research is produced in Chapters 5 and 6 aft er a brief overview of the num erical software used in Chapter 4. The potential effect of uneven loading on the original concrete lining and the effect of weathering on the surrounding rock ( Marl) were also taken into account. Num erical m odelling results were analyzed and com pared with in situ m easurem ents and an att em pt was m ade t o find the probable failure m echanism s of the concret e linings. Based on all the num erical m odelling results and available in situ m easurem ents, the long- term st ress and deform ation conditions of the third shaft relining system under severe ground loading was predicted. Additionally, the effect of tim e dependent ( creep) behaviour of related rocks on the shaft lining syst em s at Boulby m ine is discussed. This thesis ends with conclusions and recom m endation in Chapter 7 and four appendix files: 1) Sum m ary of Boulby Mine Rock Mat erials Laboratory Tests Data, which were collected from several PhD theses and test reports, which supplied im portant raw data of the rock m aterials properties for this research. 2) Mohr- Coulom b/ Hoek- Brown Properties of the Rock Materials at Boulby Mine, which were based on the appendix above and were used with m ass reductions in all the num erical m odels presented in this research. 3) Laboratory Uniaxial and Triaxial Strength Test and Brazilian Disc Test Data of the Concrete Segm ental Linings from Boulby Mine. 11

33 Chapter 2 General Literature Review CHAPTER 2 GENERAL LI TERATURE REVI EW 2.1 I n situ St ate of Ground St ress I n situ pre- existing ground stresses in the rock m ass prior to any artificial disturbance ( such as an excavation or construction work) are referred to as the initial stresses. The initial stresses are disturbed and re- distributed due to m an- m ade excavations especially in the dom ain im m ediately surrounding the excavation. The new ground stresses after the disturbance are called induced stresses. The in situ state of ground st ress is a fundam ental concern not only for the design and construction of civil and m ining engineering structures in rock, but also for num erical sim ulations of any geom echanics problem s. I t is an essential com ponent to be considered in setting up num erical m odels. The initial in situ stresses are highly variable natural phenom ena which are related to the weight of the overlying m aterials, the geological history, tectonic m ovem ents and structural geological features ( Whittaker and Frith, 1990). Usually, ground st resses represent three-dim ensional quantities which are m athem atically described as tensors. I n m any cases the principal directions of the ground st ress tensors are parallel and perpendicular to the earth s surface. These are called horizontal and vertical stresses. The vertical and horizontal stresses can be treated separately to describe the change of stress m agnitudes with depth ( Herget, 1988). I n the stress field close to the surface in the depth range, the horizontal stresses are generally governed by the Poisson s effect in conjunction with 12

34 Chapter 2 General Literature Review the vertical stress, which is com m only calculated from the gravity loads due to the weight of the overlying m aterials (Whittaker and Frith, 1990). The ratio of σ : σ is given as 0 h z k, whereby: σ h σ z = k 0 = ν 1 ν (2.1) Wher e, σ h, the horizontal com ponent of ground st ress σ z, the vertical com ponent of ground stress k 0, the Earth Pressure Coefficient ν, Poisson s ratio Terzaghi and Richart (1952) also suggested that in the case of sedim entary rocks in geologically undisturbed regions where the strata were built up in horizontal layers in such a way that there was no lateral strain, the horizontal stresses are equal and are given by the Equation (2.1). This equation derives from the sym m etry of one- dim ensional loading of an elastic m aterial over a continuous plane surface which infers a condition of no horizontal strain ( Goodm an, 1980). However, the basic assum ptions used in Equation (2.1) do not apply to the real geological situations where the rock m ass has experienced a com plex geological history and contains m any discontinuities ( j oints, cracks, bedding planes and so on). To understand the ground stress condition or st ress fields around m ine sites and in different geological environm ents, in situ stress m easurem ents will supply significant inform ation. Figures 2.1 and 2.2 show vertical stress and average horizontal stress with depth based on world stress m easurem ents data ( Herget, 1973). 13

35 Chapter 2 General Literature Review Vertical stress σ z, MPa Depth below surface h, m σ z = h Scandinavia Wawa Elliot Lake Mount I sa Snowy Mountains Tasm ania South Africa Zam bia Figure 2.1 Results of st ress m easurem ents: vert ical stress ( Herget, 1973) 14

36 Chapter 2 General Literature Review Average horizont al st ress σ h av, MPa σ h = h Depth below surface h, m σ h < σ z USA-Average of 14 Scandinavia Wawa Elliot Lake Ottawa North Bay Mount I sa Snowy Mountains Tasm ania South Africa Zam bia British Colum bia East I celand I reland Spitzbergen σ h > σ z σ h = σ z Figure 2.2 Results of st ress m easurem ents: average horizontal stress (Herget, 1973) Based on the st ress m easurem ent results shown in Figure 2.1, Herget (1973) suggested the average relationship between the vertical stress and the depth follows the equation: σ = h (2.2) z Wher e, σ z, the vertical ground stress, MPa h, depth, m 15

37 Chapter 2 General Literature Review At the sam e tim e, the horizontal stress m easurem ents in Figure 2.2 have been separated into various populations using their relationships with the vertical stress: σ < σ 1) h v, σ = σ 2) h v, σ > σ 3) h v, e.g. Scandinavia (2.3) e.g. South Africa (2.4) prevailing (2.5) σ = h (2.6) h Wher e, σ h, the horizontal ground st ress, MPa σ z, the vertical ground stress, MPa h, depth, m I t can be seen from Figure 2.2 that the horizontal stresses were higher than the vertical stress in m ost cases of Herget s in situ stress m easurem ents collection where the depth was between 0 m and 1000 m ( Herget 1973). Brown and Hoek (1978) also collated the published results of st ress m easurem ents m ade around the world and select ed the data presented in Figures 2.3 and

38 Chapter 2 General Literature Review Vertical stress σ z, MPa Depth below surface h, m Australia U.S.A Canada Scandinavia Southern Africa Other Regions σ z = h 3000 Figure 2.3 Results of st ress m easurem ents: vert ical stress ( Brown and Hoek, 1978) 17

39 Chapter 2 General Literature Review k σ = σ h av z Depth below surface h, m Australia U.S.A Canada Scandinavia 1500 k = h Southern Africa Other Regions 100 k = h 3000 Figure 2.4 Variation of ratio of average horizontal stresses to vertical stress (Brown and Hoek, 1978) They found that the m easured vertical stresses were in fair agreem ent with the prediction that the vertical com ponent of st ress was sim ply a function of depth and cover rock density (usually in the range of 20 t o 30 kn/ m 3 ). Based on those m easured results, they obtained the following Equation (2.7) which gives the average relationship for the vertical stress in relation to depth: 18

40 Chapter 2 General Literature Review σ z = h (2.7) Wher e, σ z, the vertical ground stress, MPa and h, depth, m I t can be seen that the Equation ( 2.2) gives higher vertical stress predictions com pared with the Equation (2.7) when the depth is lower than 1870 m. Stress m easurem ent results collected by Brown and Hoek (1978) also show that the average horizontal stress ( σ h av )and the vert ical st ress ( σ ) tend to equalise (i.e. hydrostatic stress conditions) z when the depth increases towards and beyond 1000 m as shown in Figures 2.2 and 2.4. As report ed by Hoek and Brown (1980), this phenom enon confirm s t he suggestion by Heim (1912) and Talobre (1957): the inability of rock t o support high stresses with large m agnitudes differences together with the effect s of tim e- dependent deform ation of the rock m ass can cause lateral and vertical stresses to equalise over periods of geological tim e. Heim s rule (1912) is widely used in weak rocks ( e.g. coal m easures and evaporites) and it has been found to give a good approxim ation of the in situ stress field in these m aterials ( Hoek and Brown, 1980). I t should be rem em bered that only the average horizontal stress is plotted in Figure 2.4 and in m any cases there is a significant difference bet ween the horizontal stresses in different directions. For practical engineering problem s, it m ay be useful to consider the significance of the individual stresses rather than the average (Hoek and Brown, 1980). However, in both Mohr- Coulom b and Hoek- Brown failure criteria, the influence of the interm ediate principal stress σ 2 is not taken into account. This assum ption appears t o be justified by both the results of t est s by 19

41 Chapter 2 General Literature Review Hoj em and Cook (1968) and the investigations by Brace (1964). Hoj em and Cook (1968) investigated intact rock sam ples in triaxial tests with states of stress σ 1 σ 2 σ 3. They concluded that the strength of rock increases with increasing interm ediate principal stress σ 2 level but that increase is sm all enough to ignore for m ost practical application. Brace (1964) carried out so- called triaxial extension t ests with σ 1 = σ 2 > σ 3 ( where σ 3 is the axial stress in the specim en) as well as the usual triaxial tests with σ 1 > σ 2 = σ 3. Brace found no significant variation between the results obtained when σ 1 = σ 2 > σ 3 and when σ 1 > σ 2 = σ 3. He concluded that the interm ediate principal stress σ 2 has a negligible influence upon the failure of the rocks which he tested. Based on these available evidences, Hoek and Brown (1980) suggest ed that it is adm issible to ignore the influence of the interm ediate principal st ress σ 2 upon the failure of brittle rock. This assum ption is im portant in keeping the failure criterion as sim ple as possible in order that it can be extended to include the effects of joints and pre- existing fractures ( Hoek and Brown, 1980). 2.2 Stress Distribution around Excavations The creation of an underground excavation will alter the in situ stress field in close proxim ity according to the size and shape of the excavation and the nature of the rock m ass in term s of its failure charact eristics. The rock left standing has to take m ore loading because the original support provided by the rock within the excavation has been rem oved. I n som e cases, the induced stresses by the disturbance are high enough to exceed the strength of the rock, leading to failure of the rock adjacent t o the 20

42 Chapter 2 General Literature Review excavation boundary. This instability m ay be in the form of gradual closure of the excavation, roof falls and slabbing of sidewalls or even rock bursts. One of the earliest solutions for the two- dim ensional distribution of stresses around an opening in an elastic body was published by Kirsch (1898) for the sim plest cross- sectional shape, the circular hole, using m athem atical theory of linear elasticity, illustrated in Figure 2.5. Vertical applied stress z Horizontal applied stress h= k0 z Stress com ponents at point (, ) Radial: = [(1 + ) 1 + (1 ) ](2.8) Tangential: = [(1 + ) 1 + (1 ) ] (2.9) Shear: = [ (1 ) ] (2.10) Figure 2.5 Equations for the st resses in the m at erial surrounding a circular hole in a stressed elastic body ( Hoek and Brown, 1980) 21

43 Chapter 2 General Literature Review As the distance r from the excavation increases, the influence of the excavation on the stresses in the rock decreases. Based on Kirsch s equations, a plot of the ratio of / z against the distance r along the horizontal axis of the stressed m odel is given in Figure 2.6. Sidewall stress / vertical applied stress z a Ratio: radial distance r / hole radius a 1 Figure 2.6 Variation in ratio of tangential stress to vertical applied stress z with radial distance r along horizontal axis for k 0 = 0 ( Hoek and Brown, 1980) Figure 2.6 shows that the stress concentration effect of the hole dies away fairly rapidly and that, at r= 3a 1, the ratio of induced to applied stress is very close to unity, which m eans the excavation only creat es a local disturbance. According to this fact, the general rule in m odel studies of stresses around underground excavations is that the m inim um size of the m odel should be 3 to 4 tim es the m axim um dim ension of the excavation in the m odel (Hoek and Brown, 1980). However, it should be noted that the m odel in Figure 2.5 is an elastic m odel under com pressive stress. The m odel size suggestion above m ay be only suitable for hard rock, but t ends 22

44 Chapter 2 General Literature Review to underestim ate the m odel size for the problem s in soft ( weak) rock in a high hydrostatic ground stress field. Stress distribution around different shape excavations or m ultiple underground excavations is m ore com plicated as it is influenced by several other factors. For exam ple, the orientation of the rectangular excavation plays an im portant role in the induced stresses distribution in surrounding rock. Furtherm ore, for m ultiple excavations, the distance between excavations will significantly influence the induced stresses distribution in surrounding rock. 2.3 Rock Mass Classification Syst em s I nt roduct ion Creating underground excavations and installing support are extrem ely com plex engineering activities. Prediction of virgin rock m ass behaviour, support pressure and t unnel closure is always one of the m ost difficult problem s in rock engineering although m uch research has been focused on this area over m any years. At the sam e tim e, large am ounts of num erical m odelling software has been developed t o sim ulate and help solve geological and geotechnical problem s. I n order t o obtain a good sim ulation, the input data m ust be of high quality, which m ainly com prises of m echanical and physical properties of the rock m ass. The rock m ass usually contains a lot of irregular discontinuities, e.g. joints, bedding planes and faults. I t is practically im possible to obtain all the properties of the rock m ass by direct tests or m easurem ents. I t has been recognized for a long tim e that a system was needed to classify the strength of a rock m ass including its discontinuities as a whole 23

45 Chapter 2 General Literature Review rather than just the strength of a piece of the intact rock. This classification syst em should be based on a sufficient num ber of in situ experiences ( geological surveys, observations or m easurem ents in the rock m ass). Such a classification system acts as a vehicle which enables a designer t o relate the experience of rock conditions and support requirem ents gained on other sites to the conditions anticipated on his own site ( Hoek and Brown, 1980). This is m ore realistic and useful for the practical mining or civil engineering situation. Bieniawski ( 1989) reviewed the developm ent of rock m ass classification syst em s, the m ost com m on of which are sum m arized in Table 2.1. The following section after Table 2.1 briefly sum m arizes som e of the m ore im portant classification syst em s. N am e of Classifications Originator and date Country of origin Applications Rock load Terzaghi, 1946 USA Tunnels with steel support Stand-up tim e Lauffer, 1958 Austria Tunnelling New Austrian Tunnelling Method (NATM) Rabcewicz, 1964 Austria Tunnelling Rock quality designation Deere et al., 1964 USA Core logging, t unnelling RSR concept Wickham et al., 1972 USA Tunnelling RMR system (Modified) Bieniawski, 1973 Bieniawski, 1989 South Africa Tunnels, m ines, slopes, foundations Q-system Barton et al., 1974 Norway Tunnels, Cham bers Strength-size Franklin, 1975 Canada Tunnelling Basic geotechnical description I SRM, 1981 General, com m unication Unified classification William son, 1984 USA General, com m unication Table 2.1 Maj or engineering rock m ass classifications ( Bieniawski, 1989) 24

46 Chapter 2 General Literature Review Rock Qualit y Designation ( RQD) The Rock Quality Designation index (RQD), which has played an im portant role in the developm ent of rock m ass classification schem es, was proposed based on core recovery by diam ond drilling by Deere in This index provides the first m ethod to quantitatively classify rock m asses. RQD is defined as the percent age of intact rock pieces (longer than 100 m m ) within a total length of borehole, as follows: Length of I ntact Rock Pieces ( > 100 m m) RQD(% ) = 100 (2.11) Total Length of Borehole To accurately present t he quality of the rock m ass, only the core broken by j oints or other naturally occurring discontinuities are considered. Drill induced breaks m ust be ignored. Deere proposed the following relationship between the RQD values and the engineering quality of the rock m ass: RQD Rock Quality < 25% Very poor 25 50% Poor 50 75% Fair 75 90% Good % Very good RQD can also be obtained from m easurem ents of fracture spacings in excavation walls (Priest and Hudson, 1976). Obviously, RQD is a sim ple and quick practical index used to describe rock quality. However, the value of RQD is very sensitive to a change of borehole orientation. At the sam e tim e, RQD s definition shows that som e im portant factors were not taken into account, such as rock st rength, discontinuities character, discontinuities orientation and environm ent factors, which have great 25

47 Chapter 2 General Literature Review influence on the behaviour of a rock m ass surrounding an underground opening. Therefore, RQD on its own is not com prehensive enough as a m ethod t o classify rock m asses. But as a com ponent in other system s, e.g. RMR (Bieniawski 1974), it can be a very valuable single param et er to help classify rock m asses Rock Mass Rating ( RMR) Syst em The rock m ass is com posed of intact rock blocks with various geological discontinuities between them and therefore the properties of both intact rock and the discontinuities should be taken into account. The Rock Mass Rating (RMR) system is this kind of rock m ass classification system, com bining several factors such as RQD, uniaxial com pressive st rengt h of intact rock and the condition of discontinuities. I t was proposed by Bieniawski (1974) of the South African Council for Scientific and I ndustrial Research ( CSI R). This syst em is called the CSIR Geom echanics Classification or the Rock Mass Rating (RMR) syst em, and is based upon case histories drawn from civil engineering. Over the years, this system has been successively refined as m ore case records have been exam ined. After m odification based on its application experience by Bieniawski (1989), this system has six param eters listed below: Uniaxial com pressive strength of rock m aterial Rock Quality Designation (RQD) Spacing of discontinuities Condition of discontinuities Groundwater conditions Orientation of discontinuities 26

48 Chapter 2 General Literature Review The RMR syst em is presented in Table 2.2, giving the ratings for each of the six param et ers listed above. Different rat ings are assigned to each param et er according to its degree of im port ance and a higher overall rating indicates a better rock m ass condition (Part A in Table 2.2). The RMR rating is adjusted according to the specific engineering application (Part B in Table 2.2). The final RMR rating is divided into five groups indicating the rock m ass conditions (Part C in Table 2.2) and the practical m eaning of each group is described in Part D in Table 2.2. This classification is one of the two classifications recom m ended by Hoek and Brown ( 1980) for general use in the prelim inary design of underground excavations. 27

49 Chapter 2 General Literature Review * Som e conditions are m utually exclusive. For exam ple, if infilling is present, the roughness of the surface will be overshadowed by the influence of the gouge. I n such cases use A.4 directly. * * Modified after Wickham et al (1972). Table 2.2 Rock Mass Rating System (Bieniawski 1989) 28

50 Chapter 2 General Literature Review So far, several m odifications have been proposed in the worldwide based upon Bieniawski s RMR system in order to m ake the classification m ore relevant to m ining and civil engineering applications (Whittles 1999). Em pirical relationships have been established between the RMR value and design param et ers such as rock m ass strength and stiffness, tunnel support requirem ents, factors of safety, stand- up tim es and support loads (Whittles 1999). I n this way, the RMR system can be used in the design of a structure. Laubscher (1977, 1984), Laubscher and Taylor (1976) and Laubscher and Page (1990) have described a Modified Rock Mass Rating (MRMR) system for m ining. This system took the basic RMR value, and adjusted it to account for the in situ and induced st resses, stress changes and the effect s of blasting and weathering. I t should be not ed that Laubscher's MRMR system was m ainly based upon cases from caving operations. The structure of the RMR system has been successfully used as a basis for m ost of the rock m ass classifications in use today ( Whittles 1999). A rock m ass classification system specifically for UK Coal Measure strata was proposed and developed by Whittles (1999), which is sim ilar in structure to Bieniawski s RMR system. I t is called the Coal Mine Classification rating (CMC) and is introduced in the following section Coal M ine Classificat ion ( CMC) I n m ost em pirical equations proposed for estim ating the strength and stiffness properties, the rock m ass is assum ed isotropic (Whittles et al 2007). Within UK coal m ines, the geological strata conditions are usually weak st ratified rock m asses in a high stress environm ent. I t is known that the st rength and deform ation of a stratified rock m ass varies depending on 29

51 Chapter 2 General Literature Review the loading direction in relation to the orientation of the lam ination planes. I t was thought by Whittles (1999) that the existing rock m ass classifications have lim ited applicability for the anisotropy within UK coal m ines. Therefore, a rock m ass classification system specifically for UK coal m ines, nam ed the Coal Mine Classification (CMC), was proposed and developed (Whittles 1999), based on the existing established classifications and the unique properties to the UK coal m ining environm ent. By this specific classification, the strength and stiffness properties of rock st rata encountered within UK coal m ines can be predicted. CMC s output can be useful in determ ining representative engineering properties of rock st rata used in num erical m odelling techniques for underground roadway design in retreat face longwall m ining. Based on a database of inform ation obtained from 118 different rock m ass classifications, the CMC s param et ers have been identified, which was thought by Whittles to have the great est influence on the typical strata deform ation m echanism s that occur within UK coal m ines. The identified param et ers were synthesized and listed as follows: Unconfined Com pressive Strength Bedding/ Lam ination Properties Spacing Strength Joint Properties Set Num ber Spacing Orientation Strength Fissility 30

52 Chapter 2 General Literature Review Water Flow Moisture Sensitivity The selected param eters do not all have the sam e degree of influence on the st rength and stiffness properties of the rock st rata. Therefore, a relative im portance weighting and rating scale for each individual param et er on the m echanism of strata deform ation has been proposed. The basic CMC for a stratum unit is derived as a sum m ation of the ratings attributed to each m easured param eter. The rating can vary between 0 with extrem ely poor rock m ass conditions and 100 suggesting a very strong rock m ass with no weakness planes. When applying the CMC, adj ustm ents can be m ade where required to t he basic rating to account for the effect of joint/ cleat orientation relative to the orientation of the rib sides or coal face. The anisotropic nature of the UK coal m easures strata was charact erized within the CMC by the calculation of separat e ratings for directions parallel to and perpendicular to bedding. The lithological and structural characteristics of the rock st rata were also taken into consideration which m ay be significant to the engineering properties of the st rata but not previously identified. To validate the CMC system as a m eans of predicting the strength and stiffness properties of t he rock m ass, the CMC was applied to the st rat a at case study localities within rock bolted roadways within three UK m ine sites. At the sam e tim e, num erical m odelling of the case study localities were developed using the finite difference code FLAC 2D to sim ulate strata behaviour. The input m echanical properties of the rock st rata were determ ined from the CMC. The results of the num erical m odelling indicated that the predictions produced by the num erical m odels reflected the pattern and scale of deform ations actually m easured in- sit u within the 31

53 Chapter 2 General Literature Review coal m ine roadways, t hus indicating that the CMC system provides a m eans of predicat ively det erm ining t he engineering propert ies of t he insitu UK Coal Measure st rata Rock Tunnelling Qualit y I ndex, Q This classification was proposed in 1974 by Barton et al of the Norwegian Geotechnical I nstitute ( NGI ) on the basis of evaluating a large num ber of case histories of underground excavation stability. The value of this index Q is defined by: RQD Jr Jw Q = (2.12) J J SRF n a Where RQD is Deere s Rock Quality Designation defined by Equation 2.11, J n is the joint set num ber, J r is the joint roughness num ber, J a is the j oint alteration num ber, J w is the joint water reduction factor, and SRF is a stress reduction factor. The first quotient (RQD/ J n ) represents the structure of the rock m ass, a crude m easure of the block or particle size. The second quotient ( J r / J a ) represents the shear strength of the inter- block. The third quotient (J w / SRF) is a com plicated em pirical factor describing the 'active stress'. SRF can be regarded as a t otal stress param eter. The param et er J w is a m easure of water pressure, which has an adverse effect on the shear strength of joints due t o a reduction in effective norm al st ress. The values for single param eter are obtained from the very com prehensive Table

54 Chapter 2 General Literature Review Table 2.3 Classification of individual param eters used in the Tunnelling Quality I ndex Q (Bart on et al 1974) 33

55 Chapter 2 General Literature Review Table 2.3 (cont d) Classification of individual param eters used in the Tunnelling Quality I ndex Q (Bart on et al 1974) 34

56 Chapter 2 General Literature Review Table 2.3 (cont d) Classification of individual param eters used in the Tunnelling Quality I ndex Q (Bart on et al 1974) I n order to relate the Q value to the stability and support requirem ent s of underground excavations, Barton et al (1974) defined an additional param et er called the Equivalent Dim ension, D e, of the excavation. This dim ension is defined as: 35

57 Chapter 2 General Literature Review Excavat ion Span, Diam eter or Height ( m) D e = ( 2.13) Excavat ion Support Ratio ( ESR) The value of ESR is a quantity, related to the use of the excavation and to the degree of safety which is dem anded of the support system installed t o m aintain the stability of the excavation. Barton et al (1974) suggested the following values in Table 2.4: Excavation Category ESR Tem porary m ine openings. 3-5 Perm anent m ine openings, water tunnels for hydro power (excluding high pressure penstocks), pilot tunnels, drifts and headings for large excavations. 1.6 Storage room s, water treatm ent plants, m inor road and railway tunnels, surge cham bers, access tunnels. 1.3 Power stations, m ajor road and railway tunnels, civil defence cham bers, portal intersections. 1.0 Underground nuclear power stations, railway stations, sports and public facilities, factories. 0.8 Table 2.4 ESR values suggest ed by Bart on et al ( 1974) Figure 2.7 shows the relationship between the Tunnelling Quality I ndex Q and the Equivalent Dim ension D e of an excavation which will stand unsupported. Figure 2.7 can also be utilized to determ ine the support categories required t o m aintain excavation stability. 36

58 Chapter 2 General Literature Review Figure 2.7 Estim ated support categories based on the Tunnelling Quality I ndex Q (Grim stad and Barton 1993) Conclusions Prediction of virgin rock m ass behaviour, support pressure and underground excavation closure requires an estim ation of the m echanical properties of the rock m ass. The m echanical properties of the in situ rock m ass are influenced by m any fact ors, such as intact rock strength, t he nature and orientation of planes of discontinuities, weathering and ground water conditions. Laboratory tests can provide m echanical properties for intact rock, which can supply som e inform ation for the upper lim it of the rock m ass m echanical properties, but cannot provide those for the in situ rock m ass. However, by m eans of the rock m ass classification, the m echanical properties of the rock m ass m ay be estim ated. Many rock m ass classifications have been developed over t he last sixty years. 37

59 Chapter 2 General Literature Review Most of the m ulti- param eter rock m ass classifications ( RQD, RMR and Q syst em s) were developed from civil engineering case histories and have been widely utilized in the civil engineering industry to assist with the assessm ent of rock support requirem ents. However, there are obvious differences between m ining and civil engineering design approaches to rock m ass classification. One of the fundam ental differences is higher ground stress condition (at deeper position) and bigger opening s dim ension (som e m ine roadways) in m ining industry. As there are often m any kinds of discontinuities surrounding a m ine roadway, such as bedding planes, joints and faults. These classifications are som ewhat conservative if used directly in the m ining industry. 2.4 Shaft St abilit y Problem s I n a m ine environm ent, m any fact ors will influence the stability of underground excavations. These factors include the size and shape of the excavations, the m agnitude of the existing stress regim e, geological structures, such as faults, folds and altered zones occurring in the strata. Failure frequency also is increased by the presence of ground water ( Bruneau et al 2003). Shafts are exam ples of perm anent m ining excavations. Because of the frequent use of such excavations by m ine personnel, a significantly higher degree of security is required than for other m ine openings (Vandewalle 1998). I t is report ed by Beus and Board (1984) that secondary excavat ion, such as inset and roadway construction leading from the shaft, stat ion, etc., can be expected to influence rock m ovem ent and shaft lining pressure at least as m uch as does shaft sinking. I n m ature m ines, the influence of geological structural features and t he m odified stress regim es, 38

60 Chapter 2 General Literature Review which m ay be caused by som e underground excavation very close to the shafts, on the stability of shafts is even m ore dom inant ( Bruneau et al 2003). Groundwater inflow is also a serious problem for shaft s stability. Two exam ples are presented in this section. I n October 1998, consultants were called in, after a serious water ingress, t o investigate the feasibility of precem entation to control groundwater inflow into the proposed ventilation shaft No.1A at I m pala Platinum m ine (Bothm a 2001). South Deep s m ain shaft at Western Areas Gold m ine was flooded by an inrush of water at about 450 m below collar ( the upperm ost portion of the shaft and acting as a protective barrier to prevent water and soil from ent ering the shaft) in May 1996, leading to a tactical withdrawal up the shaft. A survey on shaft wall failures showed that 90% of all the shaft walls that failed were in shale, coal and m arls ( Herget 1988). Most shaft s in m edium strength rock without geological failure surfaces are self supporting. I n these cases linings are often installed for other than structural reason, e.g. control of wat er and weathering. However, if shafts reach great depths, in situ stresses m ight exceed in situ m aterial strength. I f the m at erial is weak, this critical depth is reached sooner (Herget 1988). I n unfavourable ground conditions, the const ruction of circular shafts is required. The m ost com m only used shaft design in m odern day m ining is actually of circular or elliptical shape which in itself is self- supporting and accom m odating if a concret e lining is being utilized. The circular shafts avoid stress concentrations in corners and benefit from arching action in the supported m at erial. Based on a field experim ent involving the sinking of two full- size test shafts to directly com pare t he deform ational behaviour of circular and rectangular shapes, Beus and Chan (1985) concluded that: 39

61 Chapter 2 General Literature Review 1) The circular shape is less sensitive to geologic discontinuities and applied stress field. 2) The rectangular shape is subj ect to a variety of behavioural m odes, including beam bending and buckling. 3) Regardless of shaft shape and in situ stress field, shaft wall displacem ent is significantly affected by rock m ass anisotropy and geologic discontinuities. Design and construction of perm anent m ine workings, especially their shafts, faces the task of their reliable support for the whole service life period of the m ine ( Olovyanny and Kozel 2005). Shafts, which are heavily trafficked openings, should have rockbolts and/ or reinforced shotcret e installed to prot ect personnel and equipm ent from rockfalls (Vandewalle 1998). The experience gained in operation of shafts indicates that when the shaft s intersect the salt layers at a depth m ore than 300 m, dam ages of a concrete or ferroconcret e support sharply intensify (Kozel 2001). For supporting shafts, rockbolts, st eel- fibre reinforced shotcret e lining and m esh reinforced shotcret e lining are oft en utilized ( Vandewalle 1998, Bothm a 2001 and Erasm us et al 2001). I n Nikolaichuk s paper (1978), a two- layer support with a yielding external layer was offered for the use in salt rocks for m aking perm anent workings, vertical shaft in particular, safe. When this support was applied, the radial displacem ents of the rock surrounding the vertical shaft com pact the yielding layer of the support, and the pressure on its rigid (internal) concrete layer was zero until a certain tim e when the rigid layer intervened in the joint action with the salt rocks. The radial displacem ents of the unsupported rock intensified with tim e due to continuous creep of rocks so that pressure on the concret e support grew as well. 40

62 Chapter 2 General Literature Review Com bining m ature num erical sim ulation techniques and field observat ion is a very popular, helpful and rational option for researchers of rock m echanics problem s at present. Two practical exam ples relating to shafts are briefly discussed in this section. One is that there has been observed evidence of degradation of the shaft concrete lining in the early 1990s at the Copper Mine, at Mount I sa, Aust ralia. The shaft degradation has been attributed to the presence of two m ajor geological structures (two faults), which intersect the shaft in two distinct locations. To gain a better understanding of the m echanism s inducing dam age t o the shaft, the influence of faulting and m ining sequence on the stability of the m ain m ine shaft were investigated by m eans of field investigations and num erical m odelling. The num erical m odelling results have a fairly good agreem ent with the recorded field observation (Bruneau et al 2003). The other exam ple is from a large gold m ine in South Africa, East Rand Proprietary Mines Ltd. The lower levels of this m ine were exploited by m eans of inclined shafts. Below 3000 m, failure of the m onolithic concret e linings charact eristically occurred when m ining work cam e near t o the shaft. I t appeared that failure did not occur as a result of an increasing stress field but from a general reduction in stress. The m arked relaxation of the high stress in the rock sidewall induced a high tensile stress in the adjacent lining. This som ewhat paradoxical suggestion was confirm ed quantitatively by finite elem ent analysis and qualitatively by in situ deform ation m easurem ents. The m ethod of support has consequently been changed com pletely to one using reinforced shot crete and rockbolts (Ortlepp 1974). 41

63 Chapter 2 General Literature Review 2.5 Previous Rock Mechanics Research at Boulby Mine The geology overlying the Potash seam at Boulby is a m ixture of m arine sedim ents and evaporites. Figure 2.8 shows the general sequence of strata based on the inform ation obtained by Boulby m ine. The detailed geology near the working seam (Potash) is shown in Figure 2.9. The st rata are generally flat while the thickness of various beds varies considerably within the area of Boulby m ine. Details of the whole geology have been described previously by Patchet ( 1970) and Cook ( 1974). The laboratory test data have been collected from these two PhD theses and som e ot her laboratory test reports are shown in the Appendix I of this thesis for all the rock types in this geology. However, only part of the geology has been included in the num erical m odelling in this thesis to save on the m odels size and num erical calculation tim e. This is m ainly the Middle Evaporites in the Perm ian strata shown in Figure

64 Chapter 2 General Literature Review SURFACE SEA LEVEL JURASSI C TRI ASSI C LI AS SHALES RHAETI C MERCI A MUDSTONES (KEUPER MARL) SHERWOOD SANDSTONE (BUNTER SANDSTONE) DEPTH BELOW SURFACE I N METERS MI NE LEVEL PERMI AN CARBON I FEROUS PERMI AN EVAPORI TES Figure 2.8 Strata sequence of Boulby potash m ine (Boulby m ine) 43

65 Chapter 2 General Literature Review Halite with Mudst one interbeds Upper Halite UPPER EVAPORI TES MI NE LEVEL Upper Anhydrite Carnallitic Marl Middle Potash Middle Halite Middle Anhydrite Middle Dolom ite MI DDLE EVAPORI TES Lower Anhydrite PERMI AN STRATA Lower Halite Polyhalite Polyhalite Floor (Anhydrite) LOW ER EVAPORI TES Dolom ite Figure 2.9 Detailed geology of the Perm ian strat a at Boulby m ine 44

66 Chapter 2 General Literature Review During the past forty years, m uch rock m echanics research has been carried out at Boulby m ine, som e of which supplied im portant reference for this research and is briefly sum m arized as follows: 1) The laboratory tests initiated by Buzdar (1968) and carried out by Patchet (1970) I n Patchet s thesis, t he m echanical propert ies and st rengths of the com plete geological succession at Boulby were studied. Patchet defined all strata from surface to Upper Halite shown in Figure 2.9 as Upper Strata, and strata from Upper Anhydrite to Middle Halite shown in Figure 2.9 as Near-seam Strata. His laboratory tests of the near- seam rocks included the uniaxial and triaxial com pressive tests, t ensile tests and uniaxial tim e- dependent ( creep) test s. Som e of the basic conclusions from Patchet s work were as follows: Neither all the upper strata nor the stratum of Middle Potash nor the other near-seam st rata should offer any problem s t o the underground stability. Near-seam beds dip gently and this factor can be neglected as influencing underground stability. Ext ensive shaft stability problem s will occur in the weakest near- seam rock the Marl. Except for the Upper Anhydrite shown in Figure 2.9, all other nearseam rock m at erials have low com pressive and tensile strength, failures of which were very slow and explosive failures were rarely found. The Marl can be considered as plastic under m ost conditions and as a stratum, it probably has no tensile strength. With regard t o the possible effect of the tim e dependent behaviour of the Middle Potash: for long term stability of pillared m ine workings it was essential for a triaxially confined core of rock to exist within the pillar and rem ain confined, even though slightly diminished with tim e. 45

67 Chapter 2 General Literature Review 2) The research by Cook ( 1974) Cook continued Patchet s research project and focused on the stability of the shaft excavations through the Upper Evaporites strata in Figure 2.9. Cook ext ended the laborat ory t esting program m e t o t riaxial tim e dependent ( creep) testing in order to analyse the tim e dependent properties of the evaporites, both in the laboratory and in the field. Model work had been undertaken in the laboratory in order to dem onstrate the deform ation of openings in tim e dependent m aterial and dim ensional analysis has been used to relate this behaviour to the deform ation of large underground excavations. The m an shaft at Boulby m ine was instrum ented in order to m onitor the in situ behaviour and com pare the obtained m ovem ents with these predicted from laborat ory experim ents when it was sunk through the Upper Halite stratum, which possesses t im e dependent properties. Based on Cook s t est s, a gap (0.46 m ) was left between the surrounding rock and the shaft lining through the Upper Halite to allow for tim e- dependent radial closure of the excavation. 3) Hebblewhite s work (1977) Hebblewhite put em phasis on establishing the design criteria for underground Potash workings based on rock m echanics principles and m easurem ents taken in the field. Hebblewhite agreed with Patchet and also stated in his PhD thesis that the Marl was the weakest rock in the sequence and provided a m ajor problem of stability both in the underground workings and in the shaft. Hebblewhite analyzed the possible water problem during the m ining in the Potash seam which could have very serious consequences. The only waterbearing stratum in the sequence was the m assive Bunter Sandstone 46

68 Chapter 2 General Literature Review ( Figure 2.8), which consists of fine grained, red sandstones grading into m udstones. The sandstone stratum has low perm eability under high hydrostatic pressure. During shaft - sinking there was evidence of fissures containing water from t he sandst one occurring in the stratum between the Bunter Sandst one (Figure 2.8) and the Upper Evaporites (Figure 2.9). This stratum can approach t o within 70m above the Potash seam and form the only low perm eability bed of significant thickness between the saturated Bunter Sandstone beds ( Figure 2.8) and the evaporites below (Figure 2.9). A thin band of Anhydrite occurs above the Upper Evaporites (Figure 2.9) and is also relatively imperm eable. This com bination of beds com poses the m ain barrier preventing possible inflow of wat er into t he m ine workings in the Potash. 4) Research by Golder Associates (1997) Golder Associates have undertaken research for Boulby m ine to optim ise the extraction ratio across the m ine, particularly at the south end of the m ine and revise the prim ary panel and pillar layouts using num erical m odelling. FLAC 2D was utilized in the m odelling for the ext raction ratio and panel layout review. Meanwhile, the stresses and displacem ents around m ine openings were sim ulated using VNFOLD (3D), a displacem ent discontinuity program. Tim e- dependent ( creep) curves and param eters of Middle Halite and Middle Potash were discussed in this research. 5) Laboratory t ests at the Royal School of Mines, I m perial College (2000) A series of laboratory tests on several rock m aterials ( som e near- seam rocks and Polyhalite) were conducted by the Royal School of Mines, I m perial College (RSM) in July The test s included uniaxial com pression test s, single stage and 5- stage triaxial com pression tests and 47

69 Chapter 2 General Literature Review Brazilian Disc tensile strength tests. The following data were obtained from these test s and have been included in Appendix I in this thesis: Dynam ic and static Young s m odulus ( E) Poisson s ratio ( ) Mohr- Coulomb strength properties (cohesion c and friction angle ) Tensile strength Uniaxial com pressive strength ( UCS) 6) Laboratory test s at the Nottingham Centre for Geom echanics in the University of Nottingham (2007~ 2009) During 2007 and 2009, a series of laboratory tests on the rock m at erials from Boulby m ine, m ainly from Middle Evaporites and Lower Evaporites in the Perm ian Strata ( Figure 2.9), were carried out at the Nottingham Centre for Geom echanics ( NCG) in the University of Nottingham. The t ests included uniaxial com pression tests, single stage and 5- stage triaxial com pression tests, and Brazilian Disc tensile strength test s, following the m ethodology outlined in Rock Characterisation Testing and Monitoring I SRM suggested m ethods" ( Pergam on Press 1981). All the data have been collected from these tests and shown in Appendix I in this thesis. Uniaxial tim e- dependent (creep) tests under different t em peratures on som e rock types from Boulby m ine have also been conducted at the NCG. 2.6 Hist ory of the Shafts at Boulby Mine The Design for t he Original Lining of the Shafts The two shafts at Boulby m ine were originally constructed during 1968~ They were approxim ately 5.5 m finished internal diam eter and approxim ately 1150 m deep. Figure 2.10 is an indicative longitudinal 48

70 Chapter 2 General Literature Review section through the rock shaft as originally constructed (William s and Auld 2002). Surface Upper Tower m 1 6 Gap Upper Halite Verm iculite Fill I nterm ediate Tower 36.9 m Upper Anhydrite Marl Halite Parting Potash Seam Macalloy Bars Polyuret hane Foam Vent I nset Lower Tower 25.3 m Wing Wall Station Level Halite Foundation Figure 2.10 I ndicative longitudinal section through original rock- shaft lining (William s and Auld 2002) As shown in Figure 2.10, both of the shafts were com posed of three sections: the upper t owers, the interm ediate towers and the lower towers. 49

71 Chapter 2 General Literature Review The upper t ower is by far the longest, approxim ately 1040 m down from the surface. They were m ostly lined in unreinforced concret e that was cast in situ directly against the host rock. The section in the rock shaft through the Bunter Sandstone zone ( 610~ 914 m ) was sunk using ground freezing as a tem porary support and then a com bined concret e and st eel lining as a perm anent support. For the sam e section in the m an shaft, sinking was carried out using grouting for groundwater control and a perm anent lining of cast-iron tubbing was installed. Below the upper towers, the interm ediate towers are about 37 m long with their foundations in the Upper Anhydrite. The lower towers are beneath the interm ediate towers and 25.3 m in height. They are suspended by Macalloy bars em bedded in the lining and also attachm ents t o the thrust rings associated with the foundations of the interm ediate towers. Bot h interm ediate and lower towers are lined with reinforced concret e. A gap of 0.46 m (Figure 2.10, 1 6 gap) was left between the interm ediate and upper t owers t o absorb any relative m ovem ent (Chilton and Maxwell 1989). Cleasby et al. ( 1975) referred to ext ensive rock m echanics studies at the University of Newcastle upon Tyne that showed that the Halite would exhibit creep properties and it was expect ed that the shaft walls would converge som e 150 m m in diam eter within two m onths of excavation. So, the com pressible m aterials, verm iculite fill for interm ediate towers and polyurethane fill for lower towers, were placed in the 0.46 m gaps between the reinforced concret e shaft lining and the surrounding rock intending to absorb ground radial m ovem ent due t o the creep of the Halite and Potash beds and relieve the pressure on the lining. I t was considered that several years would elapse before the Marl would m ove far enough to exert high pressure upon the shaft walls. However, cracks appeared in the walls of both shafts aft er only two years (Chilton and Maxwell 1989) and within a 50

72 Chapter 2 General Literature Review decade of their com pletion the lower towers in the shafts were so severely distressed that they bot h had to be replaced. Because of different construction m ethods for the interm ediate and lower towers, different com pressible m aterials were chosen for them. The interm ediate t owers were construct ed from the bottom foundation upwards and the concret e was cast against bags of verm iculite placed against the excavation face. However, the lower t owers were lined from the top downwards in stages, suspended on hanging rods. The polyurethane foam, with its poorer squeezable properties, had to be sprayed on to the excavation face first as the backing to the concrete lining in the lower towers through the Marl (William s and Auld 2002) The Design for t he First Relining of t he Shaft s Rock bolts, weld m esh, shotcrete and com binations of these had been used in an attem pt to m aintain the shafts in a reasonable stat e of repair (Chilton and Maxwell 1989), but by 1983 it was obvious that the shaft lining was too badly dam aged to offer resistance to the m ovem ents of the Marl. The shaft lining throughout the Marl zone had to be rem oved and replaced. The first relining design was based on uniform geostatic pressure in the order of N/ m m 2 acting on a circular shaft (Chilton and Maxwell 1989). The first relining design for the m an shaft is illustrated in section and plan in Figures 2.11 and The design for the rock shaft s lining was sim ilar. I t com prised rings of precast high strength concrete (HSC) blocks, with a guaranteed com pressive strength of over 100 N/ m m 2, support ed on steel decks suspended by Macalloy-bar hanging rods. The blocks were 610 m m high and 1067 m m thick. Each block weighed 51

73 Chapter 2 General Literature Review approxim ately 1 tonne, which was considered the limit for safe handling in the shaft (William s and Auld 2002) m I D Reinforced Foundation m LVL Manshaft Lower Bracket Supporting Middle Tower 16 No Bars Extended to Support Circular Channel Fram e Upper Anhydrite Grout Backfill Circular Support Channel Fram e Existing 40 m m Macalloy Bars To I nner & Outer Positions 5.79 m Dia. I nside Steel Decks Marl A Deck 36 No 100 N/ m m 2 Concrete Blocks 1067 Deep, 610 High Per Ring m LVL Halite Parting m LVL Potash B Deck Relief Excavation Halite C Deck Figure 2.11 First relining for the m an shaft, section (William s and Auld 2002) 52

74 Chapter 2 General Literature Review 36 Blocks per row, m an shaft 32 blocks per row, rock shaft Block thickness (Radial) 1067 m m 5791 m m Diam eter (Man shaft) Figure 2.12 First relining, plan (William s and Auld 2002) Because of the failure of the original concret e lining with the com pressible backfill, a rigid lining system was adopted for t he first relining to resist full geostatic pressure from the Marl. Epoxy resin was placed between the vertical joints and cem ent m ortar was em ployed in the horizontal joints to achieve a bond between concret e blocks. Cem ent was pum ped into the gap between the back of the blocks and the excavation face to form an incom pressible fill, so that any horizontal pressure would be transferred via the blocks around the shaft in the form of hoop stress. The gap between each deck and the row of blocks im m ediately below was about 0.23 m. This gap was filled with cem ent (Chilton and Maxwell 1989). I n addition, the new lining would have to cope with vertical m ovem ent of the shafts. This new lining, although regarded as t em porary, was expect ed to last for 5~ 10 years before a m ore effective lining would be installed based on a better understanding of the behaviour of the surrounding strata. However, 53

75 Chapter 2 General Literature Review m inor deterioration had taken place in both shaft linings after nearly three years in the rock shaft and only approxim ately two years in the m an shaft The Design for t he Second Relining of t he Shaft s At the beginning of 1996, det erioration of the first relining through the Marl zone in both shaft s was so severe (Figure 2.13) that replacem ents were once again necessary. Figure 2.13 Dam aged m anshaft before the second relining (William s and Auld 2002) I n fact, work had com m enced on the m an shaft several years before to relieve the distress in its lining by partial excavation (left bottom in Figure 2.11) behind the lining to reduce ground pressure. Contrary to the original aim, this exercise exacerbated the lining s dam age by t ranslating and accelerating deterioration further up the lining. New linings ( second relining) were again designed and installed through the Marl zone in the twin shafts during 1998~

76 Chapter 2 General Literature Review The second relining design shown in Figures 2.14 and 2.15 was similar t o that for the first relining, but based on the consideration of com patibility of deform ations between the surrounding Marl and the shaft lining. The m aj or difference was that the second relining system included a flexibility which was introduced into the rigid concret e lining to allow the surrounding host rock tim e- dependent ( creep) inward m ovem ents. This was achieved by using double rings of blocks with squeezable plywood packs in all horizontal and vertical joints between blocks and rings. At the sam e tim e, it can be seen from Figure 2.15 that gaps left between the top rows of blocks and t he deck im m ediately above severed the lining s continuity. These gaps also acted as a flexible coupling between adjacent deck and block sections in addition to facilitating the construction process m m Diam eter (Man shaft) 5862 m m Diam eter (Man shaft) Figure 2.14 Second relining, plan (William s and Auld 2002) 55

77 Chapter 2 General Literature Review 5.51 m I D I nterm ediate Tower Foundation m LVL Upper Anhydrite Marl Halite Parting Potash Top of Wing Wall Halite m Onset LVL Figure 2.15 Second relining, section (William s and Auld 2002) 56

78 Chapter 2 General Literature Review Chilton and Maxwell (1989) recorded that t he original shaft lining had failed in an elliptical m anner, with tensile cracking on the m inor axis and spalling on the m aj or axis. The first relining failed in exactly the sam e m anner. This failure condition should be kept in m ind when any relining design is carried out. During the second relining design, som e errors t hat had been m ade in the first design were realized and correct ed for in the second relining design (William s and Auld 2002), including: Higher assum ed lining factor of safet y. A value of full geostatic pressure of N/ m m 2 was adopted for the second relining design. The first relining was designed for a lower geostatic pressure ( N/ m m 2 ). The first relining design was only based on uniform geostatic pressure with the concept of the 1: 2 horizontal to vertical stress ratio. The new design included a non-uniform loading condition due to the observed ovality failure and a horizontal to vertical stress ratio approaching 1: 1 as full geostatic pressure was expected to be subsequently im posed on the lining with time because of tim e- dependent ( creep) behaviour of Middle Halite and Potash. The lining design for t he second shaft relining was based on the com patibility of deform ations between the surrounding rock and the shaft lining, which had not been taken into account for the first relining design. Precast m icrosilica HSC with a 28- day cube test com pressive st rengt h of 120 N/ m m 2 was utilized in the form of 16 double rings of 40 blocks (William s et al. 2001) shown in Figure The blocks were 0.6 m high with a thickness of 0.55 m and the weight of each single block was approxim ately half tonne. Macalloy- bar hanging rods, attached t o spile 57

79 Chapter 2 General Literature Review beam s located below the thrust rings associated with the foundations of the interm ediate towers, support ed the steel decks carrying the rings of precast concrete blocks. Marine grade plywood squeeze packs (BS 1088: 1966), 18 m m t hick, separated the blocks vertically, both in the radial direction between each block and circum ferentially in the gap between the double rings. Horizontally, between each double ring, 12-m m m arine- grade plywood was used as a levelling layer. Pozam ent GP2.5 ( ordinary Portland cem ent pulverized fuel ash) grout with a characteristic strength of 15 N/ m m 2 (based on cubes t est ed at 28 days) was pum ped into the gap between the back of the blocks and the excavation face to form a fill of a sim ilar strength to the Marl (William s and Auld 2002). Theoretically, this new second relining had a factor of safet y of 1.47 after 30 years t o the lining failure stress of N/ m m 2 with a deform ation capability of 33 m m, which was det erm ined by finite- elem ent analysis (William s and Auld 2002) The Design for t he Third Relining of t he Shaft s During recent years, dam age t o the shaft lining was increasing ( Figure 2.16) and a further third relining is required. Plywood pack j oints highlighted in red in Figure 2.16 show m assive shear failure in the concret e lining system. 58

80 Chapter 2 General Literature Review Figure 2.16 Dam aged m anshaft before the third relining (Boulby m ine 2009) The Boulby m ine has been working on the third relining design in recent years, which com bines features of the design for the first relining with those for the second relining. The third relining will be firstly started in the m an shaft again in the bottom - up direction. The new third relining syst em m ainly com prises of a single ring of HSC blocks (shown in Figure 2.17) with 12 m m thick plywood packs (BS 1088: 1966) located vertically (radially) and horizontally between blocks. There will be 18 rows vertically and no construction gaps will be required, as were adopted in the first and second relining. 59

81 Chapter 2 General Literature Review Block thickness (Radial) 1214 m m 6168 m m Diam eter (Man shaft) Figure 2.17 Third relining, plan (Boulby m ine 2009) Precast HSC with a 28- day cube t est com pressive strength of 120 N/ m m 2 will be used. The blocks are 600 m m high with a thickness of 1214 m m. Each block weighs approxim ately 1.3 t onnes. For the backfill m aterial in the gap between the back of the blocks and the excavation face, the cem ent grout used in the second relining will again be adopted. This is Pozam ent GP2.5 ( ordinary Portland cem ent pulverized fuel ash) grout with a charact eristic strength of 15 N/ m m 2 ( based on cubes t est ed at 28 days) Conclusions The collected detailed data about the original shaft const ruction and all relinings are shown in Table 2.5. I n the last four decades, the shaft linings at Boulby m ine have experienced two relinings through the Marl zone and each relining has lasted less than 15 years. I t has been hypothesized by the author that there was a plastic zone at the shaft periphery due t o the 60

82 Chapter 2 General Literature Review shaft excavation disturbance to the confined surrounding rock m ass and this zone would becom e bigger (Figure 2.18) as the relinings were carried out. So a stronger support was required. The characteristic com pressive strength of concrete used in the original shaft lining system, and the first and second shaft relinings through the Marl zone were 34.5 MPa, 100 MPa and 120 MPa, respectively. But actually the strength of the whole shaft lining system had not achieved those high values since they were not intact concrete but were discontinuous with som e j oints (described in section 2.6) between the concret e blocks. Plastic zone Original shaft Shaft after relining Figure 2.18 Plastic zone becom ing bigger with relining (not to scale) 61

83 Chapter 2 General Literature Review Concrete lining Backfill betw een the liner and excavation face Excavation diam eter Lining inner diam eter Original lining I n situ cast concrete, 34.5 MPa; 0.75 m thick, continuous in vertical direction. Polyurethane fill; 457 m m thick m 5.49 m 1 st relining Precast HSC blocks; 28 days cube com pressive strength, 100 MPa; 24 levels, 36 rings in rock shaft, 32 rings in m an shaft, discontinuous in vertical direction; Blocks 610 m m high, 1067 m m thick; Rigid lining system, epoxy resin between the vertical joints and cem ent m ortar in the horizontal joints. Cem ent Rock shaft: 7.80 m + backfill thickness Man shaft: 7.93 m + backfill thickness Rock shaft: 5.66 m Man shaft: 5.79 m 2 nd relining Precast HSC blocks, m icrosilica concrete CRC; 28 days cube com pressive strength, 120 MPa; 16 levels, double rings, 40 blocks in each ring, discontinuous in vertical direction; Blocks 600 m m high, 577 m m thick; Flexible lining system, squeezable plywood packs in all joints between concrete blocks, 12 ~ 18 m m thick. Pozam ent GP2.5 (OPC/ PFA) grout; 28 days cube com pressive strength 15MPa. Rock shaft: sim ilar design as m an shaft Man shaft: 8.21 m + backfill thickness Rock shaft: sim ilar design as m an shaft Man shaft: 5.86 m 3 rd relining Precast HSC blocks, m icrosilica concrete CRC; 28 days cube com pressive strength, 120 MPa; 18 levels, single ring, 32 blocks in each ring, continuous in vertical direction; Blocks 600 m m high, 1214 m m thick; Flexible lining system, squeezable plywood packs in all joints between concrete blocks, 12 ~ 18 m m thick. Pozam ent GP2.5 (OPC/ PFA) grout; 28 days cube com pressive strength 15MPa. Man shaft: 8.60 m + backfill thickness Man shaft: 6.17m Table 2.5 Boulby m ine shaft lining sequence and inform ation (through the Marl zone) 62

84 Chapter 2 General Literature Review Based on the literature review of shaft lining and relining history at Boulby m ine, aother assum ption has been postulated by the author in this research, with regard t o the passive support load capacity of the concrete lining system involved in the shaft relining through the Marl zone. I n this assum ption, the actual support load capacity of each concret e lining syst em is supposed t o be given by the thickness of concrete lining m ultiplied by the characteristic com pressive strength of concret e, shown in Table 2.6. Concrete lining system Thickness of concrete lining characteristic com pressive strength of concrete (MN/ m ) Original one = st relining = nd relining = rd relining = Table 2.6 Actual support load capacity of the concret e lining system s at Boulby m ine This conceptual assum ption is illustrated in Figure Although the actual support load capacity of the concret e lining system in history (black line in Figure 2.19) has been im proved, it was still not big enough to resist increasing severe ground stress from surrounding strata ( in Figure 2.19, the black line is lower than the other three lines, which represents trends of the required support load capacity of the lining syst em ). 63

85 Chapter 2 General Literature Review Passive support load capacity (MN/ m ) Stages Actual capacity Required capacity- Possible 1 Required capacity- Possible 2 Required capacity- Possible 3 Figure 2.19 Conceptual relationship between strength of lining required and actual strength of lining Theoretically, there are three possible trends of the required support load capacity of the concret e lining system with tim e (relining stages): I n the first possible trend ( green line in Figure 2.19), there is a linear relationship between the required support load capacity of the shaft lining system and tim e. I n t he second possible trend ( blue line in Figure 2.19), the required support load capacity of the shaft lining system increases with tim e linearly after the shaft excavation and lining s installation. However, after som e period of work tim e, the required capacit y increases with tim e dram atically. I n the third possible trend ( red line in Figure 2.19), the required support load capacity of the shaft lining system increases with tim e 64

86 Chapter 2 General Literature Review linearly after the shaft excavation and lining s installation. After som e period of work tim e, the trend of the required capacity tends to be steady, and no big enhancem ent is needed for the support load capacity of the further relining system. I n the first and second trends ( especially in the second t rend), the lining syst em with ultra high support load capacity is required for the further relining system, which m ay be im possible to achieve in term s of design and cost in practice. On the other hand, it is thought by the author that the third trend is m ore likely to occur in reality because the ground stress condition in the surrounding strata will finally achieve a st eady stat e. For the actual support load capacity of the further third shaft relining system at Boulby m ine, it should be big enough to exceed the required support load capacity of the lining system t o resist increasing severe pressure from surrounding strata for a m uch longer tim e. 2.7 I n situ St ress Measurem ents at Boulby Mine Som e in situ stress m easurem ent data of the Potash and Marl strat a at Boulby m ine were presented in a previous report by Potts et al (1976). Som e conclusions in this report follow: The vertical stress in the Potash seam was N/ m m 2 ± 18% (25.43~ N/ m m 2 ); The horizontal stresses were N/ m m 2 ± 18% ( 11.68~ N/ m m 2 ) and N/ m m 2 ± 18% ( 13.54~ N/ m m 2 ); Within the tolerance of 18% the horizontal stress field in the Potash seam was uniform in all directions; The horizontal to vertical stress ratio, k 0, m easured in the Potash seam was approxim ately 1: 2; 65

87 Chapter 2 General Literature Review The horizontal- to- vertical stress ratio as m easured in the Potash seam was approxim ately 1: 2 ( Potts et al 1976), and this led to the adoption of the design pressure of N/ m m 2 for the first relining design (Clifton and Maxwell 1989). However, this is only suitable for undisturbed ground conditions. For the weak rock aft er the disturbance due t o excavation and installation of lining, hydrostatic stresses are expected t o subsequently act on the lining with tim e. I n other words, the horizontal ground stress tends t o be equal to the vertical ground stress in a weak rock m ass with tim e. This agrees with the phenom enon and the suggestion (Heim 1912, Talobre 1957) about the in situ ground stresses described in Section 2.1: the inability of rock to support high stresses with large m agnitudes differences together with the effect s of tim e- dependent deform ation of the rock m ass can cause lateral and vertical stresses t o equalise over periods of geological tim e. The first shaft relining at Boulby m ine was instrum ented. Readings taken up to 750 days from installation showed a steadily increasing, uniform, horizontal stress field in the Marl section. Unfortunately, the instrum ents failed through corrosion (William s and Auld 2002). During the second shaft relining, m onitoring was also included in the form of 48 vibrating wire flat j acks cast into and affixed to certain blocks (in rows 2, 7,11 and 15 only in Figure 2.14). Three years after the m an shaft was relined, the recorded highest tangential stress (hoop st ress) was som e 34 N/ m m 2 (Figure 2.20) in the inner course of blocks in row 7 (William s and Auld 2002) in Figure

88 Chapter 2 General Literature Review Stress ( MPa) Tangential stress in inner course of blocks Tangential stress in outer course of blocks Radial stress on the back of the relining Figure 2.20 Recorded st ress in row 7 in the second relining (m an shaft, William s and Auld 2002) The ext ent of m ovem ent occurring in the lining exceeded that of the design and ultim ately caused breaks in the cable- runs that rendered the instrum ents unreadable. However, up to six years of data has been collected (Boulby m ine). Aft er that, the m ovem ent occurring in the lining was too big and caused the m onitoring instrum ents to becom e unreadable. 2.8 I n situ Deform at ion Measurem ents at Boulby Mine When the m an shaft at Boulby m ine was sunk through the Upper Halite stratum (Figure 2.9), it was instrum ented in order to m onitor the in situ behaviour of the rock m ass around the shaft, which has been described in Cook s thesis (1974). The instrum entation consisted of four radial borehole extensom eter syst em s installed at various orientations about the circular shaft excavation (Figure 2.21). Within each borehole, m echanical anchors 67

89 Chapter 2 General Literature Review were established at distances of 0.6 m, 1.5 m, 3.0 m and 4.5 m respectively and m ovem ents were transferred to a m outh station located within the perm anent concrete lining. N 4.5 m 3.0 m 1.5 m 0.6 m Excavation face Shaft Gap Concret e Borehole ext ensom eter syst em Figure 2.21 I nstrum entation layouts at m an shaft through Upper Halite stratum (Cook 1983) The m easured radial creep of the surrounding rock m ass in the instrum ented level in the Upper Halite stratum was approxim ately 70 m m (Cook 1983). This value included an estim ate of creep during the initial 24 hours period before m easurem ents were started, based on the initial m easured rate of creep. The in situ investigation results show that: The m ovem ent of the surrounding rock m ass was tim e dependent towards the shaft axis, and occurred at a distance of 4.5 m from the excavation face, which is approxim ately equal to one radius into the solid. 68

90 Chapter 2 General Literature Review The rock displacem ents at any particular radius were uniform for different orientations around the shaft which indicated that the excavation was subj ect ed to a uniform com pressive stress field and that the rock was acting as an isotropic and hom ogeneous m aterial. Lateral m ovem ent of the perm anent shaft lining through the evaporites has occurred at the instrum ented level. This was probably caused by a differential settlem ent of the foundation crib form ed in the Upper Anhydrite. The rat e of the lateral m ovem ent of the lining decreased with tim e and after 300 days becam e negligible. All these in situ stress and deform ation m easurem ents supply significant reference data for validation of num erical m odelling and back- analysis research. 2.9 Chapt er Sum m ary This chapter com prises the general literature review required for this research. The in situ ground stress stat e and induced stress distribution around excavations were firstly reviewed. Then, the developm ent history of rock m ass classification system s was introduced, followed by a brief sum m ary of som e of t he m ore im portant classification system s. Som e possible factors influencing shaft stability and two brief practical exam ples were then described. At the end of this chapter, all the designs for the original shaft lining and the historical relinings at Boulby m ine were described in detail. This is the data on which all num erical m odelling in this research were based. Som e available in situ stress and deform ation m easurem ents at Boulby m ine were also included. Chapter 3 focuses on the m ethodology of laboratory determ ination of input m aterial geot echnical properties for the later num erical m odelling. 69

91 Chapter 3 Determ ining I nput Parameters in Num erical Models CHAPTER 3 LABORATORY DETERMI NATI ON OF GEOTECHNI CAL PARAMETERS 3.1 Determ ination of Rock Mass Strength I nt roduct ion Reliable estim ates of the strength and deform ation characteristics of rock m asses are required for alm ost any form of analysis used for the design of slopes, foundations and underground excavations. One of the m ajor obstacles which are encountered in num erical m odelling for rock m echanics problem s is how to choose the appropriate input data for rock m ass properties. The usefulness of elaborat e constitutive m odels, and powerful num erical analysis program s, is greatly limited, if the analyst does not have reliable input data for rock m ass properties. As is well known, there are usually som e j oints and weakness planes in rock m asses which act in reducing the strength of the rock m ass t o som e value less than that of the intact rock. I t is im possible in m ost cases to charact erize the deform ability and strength of rock m asses using laboratory t ests, because to be representative of the discontinuity and heterogeneity usually occurring in rock m asses, the specim ens would have to be excessively large. Even the usual in situ tests cannot supply satisfactory results in m ost cases, because the rock m ass zone under t est has been already disturbed by the excavation and the test ed volum es are not yet representative of the rock m ass. 70

92 Chapter 3 Determ ining I nput Parameters in Num erical Models However, the laborat ory test s results based on sm all scale rock specim ens are very helpful for estim ating the deform ability and strength charact eristics of the rock m asses. The deform ability and strength charact eristics of the rock specim ens can be obtained from the laborat ory tests, the results of which are usually higher in m agnitude than those of the rock m asses because of fewer discontinuities in sm all scale rock specim ens and the scale effect of t ests. After that, som e em pirical m ethods, which are based on rock m ass classifications (described in Chapter 2) and abundant in situ engineering experience, can be used to reduce the deform ability and strength characteristics of the intact rock specim ens t o get those of the rock m asses, which can be used in num erical m odelling for rock m echanics problem s. The software program RocLab, produced by Rocscience I nc., goes a long way toward obtaining rock m asses m echanical properties from the laboratory test results of the intact rock sam ples. This software has been used in this research project t o obtain the input data for num erical m odelling. This section presents the im portant rock strength indices used in this software, what t his software can do and how this software works Geological St rengt h I ndex ( GSI ) Bieniawski s RMR had been published in 1974 and has gained popularity within the rock m echanics field. However, by 1995 it had becom e increasingly obvious that Bieniawski s RMR was difficult to apply to very poor quality rock m asses ( Hoek and Marinos, 2006). A system based m ore heavily on fundam ental geological observations and less on num bers was needed. This resulted in the developm ent of the Geological Strength I ndex ( GSI ). 71

93 Chapter 3 Determ ining I nput Parameters in Num erical Models GSI was proposed and developed by m any researchers and geologists: Hoek et al 1995, Hoek 1994, Hoek and Brown 1997, Hoek et al 1998, Marinos and Hoek, I t provides a num ber which is used t o estim ate the reduction in rock m ass strength, when com bined with the intact rock properties, for different geological conditions as identified by fundam ental geological field observations. This system is present ed in Table 3.1 and Table 3.2. Experience has shown that Table 3.1 is sufficient for field observations since the letter code that identifies each rock m ass cat egory can be entered into a field log ( Hoek 2000, 2007). Lat er, these codes can be used to estim ate the GSI value from Table 3.2. Generally, controlled blasting and bulk blasting lead to a great difference in the appearance of a rock face. Wherever possible, the undam aged face should be used to estim ate the value of GSI since the overall aim is to determ ine the properties of the undisturbed rock m ass (Hoek 2000, 2007). 72

94 Chapter 3 Determ ining I nput Parameters in Num erical Models I n earlier versions of this table the term s BLOCKY/ SEAMY and CRUSHED were used, following the term inology used by Terzaghi (1946). However, these term s proved to be misleading and they have been replaced, in this table by BLOCKY/ DI STURBED, which m ore accurately reflects the increased m obility of a rock m ass which has undergone som e folding and/ or faulting, and DI SI NTEGRATED which encom passes a wider range of particle shapes. Table 3.1 Characterisation of rock m asses on the basis of interlocking and j oint alteration (Hoek and Brown, 1997) 73

95 Chapter 3 Determ ining I nput Parameters in Num erical Models Table 3.2 Estim ate of Geological Strength I ndex GSI based on geological descriptions (Hoek and Brown, 1997) For generally com pet ent rock m asses (GSI > 25), the 1989 version of Bieniawski s RMR classification (described in Chapter 2, section 2.3) can be 74

96 Chapter 3 Determ ining I nput Parameters in Num erical Models used to estim ate GSI (Hoek and Brown, 1997) using the following Equation (3.1), GSI = RMR 89 5 (3.1) RMR is the basic RMR value by setting the groundwater rating at 15 ( dry) and without adjustm ent for joint orientation. For very poor quality rock m asses ( GSI < 25), the value of RMR is very difficult to estim ate and the correlation between RMR and GSI is no longer reliable. Consequently, RMR classification should not be used for estim ating the GSI values for poor quality rock m asses Hoek- Brow n Failure Crit erion I t is usually not practical to det erm ine directly the strength properties of the rock m ass as described in section Therefore rock m ass failure criteria have been developed that allow est im ation of the rock m ass strength by reducing that of the intact rock by an am ount related to the degree of discontinuity. One of the m ost popular and widely used rock m ass failure criteria is t he Hoek- Brown failure criterion ( Cart er et al 1991), which was first proposed in I t is an em pirical relation that charact erizes the st ress conditions that lead to failure in rock m asses. The significant contribution of Hoek-Brown failure criterion was to link the m athem atical equation to geological observations. At the beginning, the basic tool for geological input in this failure criterion was Bieniawski s RMR, then turned to a m ore sophisticated index - GSI. One of the issues that had been troublesom e t hroughout the developm ent of the Hoek- Brown failure criterion has been the relationship between it (with the non-linear param et ers m and s described later in this section) 75

97 Chapter 3 Determ ining I nput Parameters in Num erical Models and the Mohr- Coulom b criterion ( with the param et ers cohesion c and friction angle ) (Hoek and Marinos, 2006). Since many geotechnical software program s for soil and rock m echanics are written in term s of the Mohr- Coulom b failure criterion, which is used t o define the shear strength of soils and intact rocks at different applied norm al stress, it is necessary to define the relationship between (m, s) and (c, ). In this way, the Hoek- Brown failure crit erion can be used t o det erm ine equivalent Mohr- Coulom b param eters ( cohesion c and friction angle ) for each rock m ass and stress range to be input into the geotechnical software. A m aj or revision of the Hoek- Brown criteria was carried out in order t o sm ooth out the curves, necessary for the application of the Hoek- Brown criterion in num erical m odels, and to update the m ethods for estim ating Mohr- Coulom b param eters ( Hoek et al 2002). The final relationships between the Mohr-Coulom b and the Hoek- Brown criteria were derived by com paring hundreds of tunnel and slope stability analyses in which both criteria were used and t he best m atch was found by iteration ( Hoek et. al 2002). A set of equations linking the two are presented later in section The Hoek-Brown criterion (2002) has been found practical in the field and appears to provide the m ost reliable results for use as input for m ethods of analysis in current use in rock engineering. A related m odification for estim ating the deform ation m odulus of rock m asses was m ade by Hoek and Diederichs (2006) RocLab Soft w are RocLab, produced by Rocscience I nc., is a free soft ware program for determ ining rock m ass strength param et ers, in which the calculations are based on the latest version of the Generalized Hoek- Brown failure criterion 76

98 Chapter 3 Determ ining I nput Parameters in Num erical Models ( Hoek et. al 2002, Hoek and Diederichs 2006). Figure 3.1 shows the RocLab software s user interface. Figure 3.1 RocLab software user interface The program RocLab provides a sim ple and intuitive im plem entation of the Hoek- Brown failure criterion, allowing users to easily obtain reliable estim ates of rock m ass properties including equivalent Mohr- Coulom b parameters (c, ). This software also visualizes the effects of changing rock m ass param eters, on the failure envelopes. Several param et ers are needed for using this software, which are listed and briefly introduced as follows: The geological strength index, GSI, as described in section The disturbance fact or, D 77

99 Chapter 3 Determ ining I nput Parameters in Num erical Models D depends upon the degree of disturbance to which the rock m ass has been subject ed by blast dam age and stress relaxation. I t varies from 0 for undisturbed in situ rock m asses t o 1 for very disturbed rock m asses. The guidelines for estim ating disturbance factor D are shown in Table 3.3. The intact rock param eter (constant), m i m can also be det erm ined by using triaxial lab tests data on intact i rock in the RocLab software. Unconfined com pressive strength of intact rock, σ ci σ ci can be also det erm ined by using triaxial lab tests data on intact rock in the RocLab software. The intact rock deform ation m odulus, E i ' σ 3 m ax The upper lim it of confining stress over which t he relationship between the Hoek- Brown and the Mohr- Coulom b criteria is considered, has to be det erm ined for each individual case. 78

100 Chapter 3 Determ ining I nput Parameters in Num erical Models Table 3.3 Guidelines for estim ating disturbance factor D (Hoek 2007) The following are som e of the tasks that can be accom plished with RocLab. Det erm ine rock m ass deform at ion m odulus Initially, the rock m ass deform ation m odulus Equation (3.2) (Hoek and Brown 1988) E was estim ated using rm 79

101 Chapter 3 Determ ining I nput Parameters in Num erical Models (( RMR 10) / 40) E rm = 10 (3.2) This equation was m odified over the years. The GSI was introduced to overcom e the deficiencies in Bieniawski s RMR for very poor quality rock m asses (Hoek 1994, Hoek et. al 1995). A disturbance fact or D t o account for stress relaxation and blast dam age was also introduced ( Hoek et. al 2002). Based on data from a large num ber of in situ m easurem ents from China and China Taiwan, the equation was again updated (Hoek and Diederichs 2006) to be Equation (3.3), which is used in Roclab to obtain E by inputting rm E i, GSI and D. E rm ( 1 D = E i + ) (3.3) (( D GSI ) / e ) Det erm ine Generalized Hoek- Brow n st rengt h param et ers Initially, RMR and m i were required for estim ating Hoek- Brown strength param et er m, and only RMR were required for estim ating s b ( Hoek and Brown 1988). Then the Generalised Hoek- Brown criterion was introduced with the application of GSI replacing RMR (Hoek 1994, Hoek et. al 1995). Hoek et. al (2002) proposed a new set of relat ionships bet ween GSI, m b, s and a to give a sm oother transition between very poor quality rock m asses ( GSI < 25) and st ronger rocks. A disturbance factor D to account for stress relaxation and blast dam age was also introduced. This new set of relationships, Equations (3.4~ 3.6), are used in the RocLab software: m b GSI 100 = m exp( ) (3.4) i 28 14D GSI 100 s = exp( ) (3.5) 9 3D 80

102 Chapter 3 Determ ining I nput Parameters in Num erical Models a 1 GSI 15 = + ( e e ) (3.6) Det erm ine equivalent Mohr- Coulom b param et ers There is no direct correlation between the Mohr- Coulom b criterion and the non- linear Hoek-Brown criterion. I n the Generalized Hoek- Brown failure criterion ( Hoek et. al 2002, Hoek and Diederichs 2006), Equation (3.7) is used to generat e a series of triaxial test values, sim ulating full scale field tests, and a statistical curve fitting process by a linear regression analysis is used to derive an equivalent Mohr envelope. σ ' ' ' 3 a σ 1 = σ 3 + σ ci (m b + s) (3.7) σ ci Wher e ' σ and 1 ' σ 3 are the m axim um and m inim um effective st resses at failure, m b, s and a are Generalized Hoek- Brown param eters. I n Roclab, t he best-fit Mohr- Coulom b strength envelope is determ ined over a st ress range that can be defined based on user application (i.e. tunneling or slope stability), in principal stress space i.e. σ 1 vs. σ 3 and/ or norm al shear stress space i.e. σ vs. τ. Equivalent Mohr- Coulom b strength param eters (cohesion c and friction angle ) can be ' calculated autom atically using σ, ci σ and Generalized Hoek- Brown 3 m ax strength param et ers m b, s and a. The following Equations are used in the RocLab software: ' a 1 ' 1 6am b ( s + m bσ 3n ) ϕ = sin [ ] ) (3.8) ' a 1 2(1 + a)(2 + a) + 6am ( s + m σ ) b b 3n 81

103 Chapter 3 Determ ining I nput Parameters in Num erical Models c ' ' ' a 1 σ ci [ (1 + 2a) s + (1 a) m bσ 3n ] ( s + m bσ 3n ) = (3.9) ' a 1 (1 + a)(2 + a) 1 + (6am ( s + m σ ) ) / ((1 + a)(2 + a)) b b 3n Where σ ' 3 n = ' σ 3 m ax σ ci Det erm ine t he uniaxial com pressive strength ( UCS) of t he rock m ass, σ c The UCS of the rock m ass ' σ can be obtained by setting σ 0 in c 3 = Equation (3.7), giving Equation (3.10), which is used in the RocLab software: = σ s a σ c ci (3.10) Det erm ine t he t ensile st rengt h of t he rock m ass, σ t The t ensile strength of the rock m ass σ t can be obtained by setting ' ' σ 1 = σ 3 = in Equation (3.7), which represents a condition of biaxial σ t tension. Hoek (1983) showed that, for brittle m aterials, the uniaxial tensile strength is equal to the biaxial tensile st rength. This gives Equation (3.11), which is used in the RocLab software: σ t = s σ / m (3.11) ci b 3.2 Rock Mat erials from Boulby Mine Laborat ory Test s Dat a Collect ion I n the early 1970 s, m uch of the research work on Boulby m ine shafts sinking and concret e liner installation were undertaken by the University of Newcastle upon Tyne. Two PhD theses ( Patchet 1970 and Cook 1974) are 82

104 Chapter 3 Determ ining I nput Parameters in Num erical Models often referred t o by this author on the topic of tests to obtain the properties of the rock m aterials. Proj ect and test reports by consultants engaged by Boulby m ine in recent years, such as the RSM (2000) and the NCG (Stace et al 2007 and 2008, Jia et al 2009) have also been helpful to this research proj ect. The lab testing of the Boulby m ine rock m at erials is restricted by the lack of available m aterial. Most of the specim ens were obtained from the cores of the explorat ory boreholes sunk from the surface to the Potash seam. Considerable quantities of the Middle Potash, t he ore body were required for chem ical analysis and ore t reatm ent investigations and this restricted the am ount available for the t esting program m e. The laborat ory testing of the borehole cores of the North Yorkshire rocks was carried out by Patchet (1970) and Cook (1974). Their test results, particularly those relating to the strength and deform ation properties of t he evaporite deposits, are collected together in this thesis with recent test s results ( NCG test reports 09/ 2007 and 06/ 2008) on Boulby m ine rock sam ples conducted at the NCG, as a database for obtaining the input rock properties for num erical m odelling. The detailed strata sequence is shown in Figures 2.8~ 2.9 and the collected t ests data is seen in Appendix I. Patchet (1970) pointed out in his thesis that all the rock m aterials from Perm ian Strata ( Figure 2.8) are com petent, especially the Anhydrite and Polyhalite, but the Marl, nearly 10m thick j ust overlying the Potash seam, is the weakest rock m aterial in the geological sequence ( Figure 2.8). As a rock m at erial, it has a very low tensile strength and as a st ratum it probably has no tensile st rength. I t can be considered as plastic under m ost conditions. The Marl s position in the im m ediate roof is closely associated with the instability of the shaft linings. 83

105 Chapter 3 Determ ining I nput Parameters in Num erical Models The Marl is a weak rock and has a tendency to squeeze. This has been dem onst rated by the gripping of the drill rods during boring (Squirrell 1992). This weak rock easily weathers on exposure. I t is not norm ally exposed during m ining operations, except during shaft lining rest oration work. Therefore it is difficult to obtain and preserve the sam ples of this rock for laborat ory t est s, which are the m ost significant and reliable data source for determ ining the m at erial properties. I n recent tests conducted in the NCG, the Marl was not available. Only two limited sets of t est data have been available and utilised for the Marl in this research: Patchet s tests (1970) and test s of the RSM ( 2000). The results of these two sets of tests are shown in Appendix I. Mohr-Coulom b strength envelopes have been drawn from the t riaxial com pression test data of these two sets of tests ( shown in Figure 3.2). Figure 3.2 Mohr- Coulom b strength envelopes for the Marl obtained from tests data I t can be seen that the two sets of t ests data show very different m echanical properties for the Marl. I t is thought by the author that the 84

106 Chapter 3 Determ ining I nput Parameters in Num erical Models Marl sam ples going to the RSM were from t he position near the shaft excavation face and were already heavily weathered while the sam ples in Patchet s tests were obt ained from a m ore prot ect ed position and were not weathered as m uch Mat erials Propert ies Used in Modelling Mohr- Coulom b failure criteria have been chosen for all rock m at erials from the Boulby m ine. To account for the influence of scale and the presence of discontinuities in the larger rock m ass, input properties (strength and stiffness) of the rock m aterials used in num erical m odels were obt ained from reducing various tests results shown in the database in Appendix I. As introduced in section 3.1, the RocLab software has been utilized in this research t o calculate the input properties for all rock m aterials in num erical m odels. Based on the database in Appendix I, Mohr- Coulom b properties of m ost of the rock m aterials from Perm ian Strata ( Figure 2.9) were calculated and are listed in Appendix I I. 3.3 Laboratory Tests on Concrete Used at Boulby Mine I nt roduct ion I n order t o obtain the input data for the concrete m at erial in the num erical m odels in this research, laboratory tests on high strength concrete ( HSC) from the Boulby m ine have been carried out at the NCG. Four HSC blocks, one for the first relining, one for the second relining and two for the t hird relining of the shafts, have been supplied by the Boulby m ine. Sam ples of HSC prepared at the NCG are shown in Figure

107 Chapter 3 Determ ining I nput Parameters in Num erical Models Figure 3.3 Sam ples of concrete from Boulby m ine (L: 100 m m, D: 50 m m ) I t can be seen from Figure 3.3 that the coarse aggregat es in the HSC used in the third relining are sm ooth and round- shaped, and the coarse aggregat es in the HSC used in the second relining are sm aller than those in the HSC used in the first and third relining. The concret e used in the second relining was m ost com pact in structure and the concrete used in the first relining was the least com pact one with sharp- shaped coarse aggregat es in it. The laborat ory tests, following the m ethodology outlined in Rock Charact erisation Testing and Monitoring I SRM suggested m ethods" (Pergam on Press 1981), on concret e from the Boulby m ine included: UCS and Young s m odulus tests on 44 sam ples from 3 concret e types, tests conduct ed on the RDP 1000 kn press (Figure 3.4). I n obtained stress- strain curves for each type concrete, the average gradient at 50% of the elastic region (between the origin and yield point) was calculated as the Young s m odulus of this type concrete. Tensile tests ( Brazilian disc tensile tests) on 15 sam ples from 3 concret e types, tests conducted on the 200 kn Denison press. 86

108 Chapter 3 Determ ining I nput Parameters in Num erical Models Single stage triaxial tests on 37 sam ples from 3 concret e types t est ed on the RDP 1000 kn press (Figure 3.5). Figure 3.4 Test set up for UCS and Young s m odulus Figure 3.5 Test set up for t riaxial com pressive t ests 87

109 Chapter 3 Determ ining I nput Parameters in Num erical Models Laborat ory Test s Result s and Analysis The detailed laboratory t ests data on the concrete used in the shaft relinings at Boulby mine are shown in Appendix I I I. Tables 3.4~ 3.5 sum m arize the average UCS tests and tensile tests results of three concret e types used at Boulby m ine. Concrete used in Sam ple No. Density (g/ cm 3 ) UCS (MPa) E (GPa) E/ 1000UCS (% ) 1 st relining nd relining rd relining Mean: Table 3.4 Average UCS and Young s m odulus of HSC used at Boulby m ine Concrete used in Sam ple No. Tensile Strength (MPa) Tensile/ UCS (% ) 1 st reline nd reline rd reline Mean: 6.13 Table 3.5 Average t ensile st rength of HSC used at Boulby m ine I n this research, the Mohr- Coulom b m odel, the conventional m odel used to represent shear failure in soils and rocks, has been chosen for the concret e m aterial in the num erical m odelling. Verm eer and deborst ( 1984) report ed that laborat ory test results for sand and concrete m atched well with the Mohr- Coulom b criterion. The Mohr- Coulom b m aterial propert ies 88

110 Chapter 3 Determ ining I nput Parameters in Num erical Models for the concret e obtained from the single state t riaxial com pressive strength tests are sum m arized in Table 3.6. Concrete used in Sam ple Diam eter (m m ) Sam ple No. Cohesion (MPa) Friction Angle ( ) 1 st reline 2 nd reline rd reline Mean: 0.23 UCS Table 3.6 Mohr- Coulom b properties for HSC used at Boulby m ine I t can be seen that there are also conclusions on the approxim ate relationships of the Young s m odulus-ucs, tensile st rength- UCS and cohesion- UCS of these concret es in Tables 3.4~ 3.6. These conclusions were helpful for det erm ining som e input properties for num erical m odelling in this research, which will be described later in sections 3.3.3, 3.4 and 3.5. The concrete blocks for the 1 st and 2 nd relinings were m ore than 10 years old whereas the concrete blocks for the 3 rd relining were recently fresh m ade. There is years gained strength for the concrete used in the 1 st and 2 nd relining. At the sam e tim e, it should be noted that the sam ples t ested in UCS tests are cylindrical and tall ( Diam eter near 50 m m ); therefore the strengths obtained from these test s were lower than their expected charact eristic strength values which are norm ally obtained from t est ing cubic sam ples (100 m m ). 89

111 Chapter 3 Determ ining I nput Parameters in Num erical Models For the single stage t riaxial com pressive strength tests, under the sam e confinem ent, sam ples with sm aller diam eter ( 42 m m ) gave st ronger strength com pared with those with bigger diam eter (49 m m ). Com parisons between individual test result s do not take into account condition of sam ple flaw, e.g. air hole, aggregates size etc Mat erial Propert ies Used in Modelling Since laboratory test data of in situ cast concrete used in the original shaft lining at Boulby m ine, with the exception of its UCS value (34.5 MPa) was not available, m any papers, British Standards and Eurocode were referred to, to find param eters for the Young s m odulus, Poisson s ratio and tensile strength of norm al strength concrete ( NSC). A brief conclusion of t hese references results is shown in Tables 3.7~ 3.9. The Mohr- Coulom b properties ( cohesion and friction angle ) of the in situ cast concrete used in the original shaft lining were estim ated based on experiences and the approxim ate relationship between the cohesion and UCS of the concret e ( shown in Table 3.6). Based on the above laborat ory test s in section and references in 3.3.3, input properties for all concret e m aterials used in the num erical m odellings for the original shaft lining and relining system s at Boulby m ine are sum m arised in the Table

112 Chapter 3 Determ ining I nput Parameters in Num erical Models Reference Structural Eurocode PP1990: 2007 Eurocode: Design of Concrete Structures Part 1 Young s m odulus (GPa) E Note f = 22 ( GPa 10 f = 0. 8f, 15 ~ 105) cm 0.3 c ), ( c cm 1 / 3 Ec = 9.5 ( f ck + 8), GPa f = 0. 8f, 10 ~ 60) ( c ck Koksal, H. O. et al E = 1000 f c Arslan, G Hughs et al BS 8110 Part Average 26 E 0.5 E = 4750f c 0.5 c 4 = 4 10 f ( f < 80 MPa) c 0.33 Ec = 9.1 fc, MPa ( f 30 ~ 60) c 6 psi Note: f - Mean value of concrete cylinder com pressive st rength cm f - Concrete cube com pressive strength c f - Charact eristic cylinder com pressive strength ck Table 3.7 Young s m odulus of NSC ( GPa) Reference Poisson s ratio Note Dahl v = ( f c ) f c ( f c 40 ~ 100) Hussein & Marzouk ~ 0.28 Koksal, H. O. et al f 10 ~ 30 c Eurocode: Design of Concrete Structures Part Average 0.2 Not e: f - Concret e cube com pressive strength c ν - Poisson s Ratio Table 3.8 Poisson s ratio of NSC 91

113 Chapter 3 Determ ining I nput Parameters in Num erical Models Reference Structural Eurocode PP1990: 2007 Eurocode: Design of Concrete Structures Part 1 Tensile Strength (MPa) Note 2.6 for C30, 2.9 for C for C30, 2.9 for C37 Hussein & Marzouk (cube, 40) Test value Koksal, H. O. et al f sp = 0. 1f c Ansar & Li (cylinder,47) Test value Zheng et al f t = 0.42( f c ) 0.5 Average 2.86 Note: C30 Concret e with com pressive st rengt h of 30 MPa ( cubes tested at 28 days). f - Mean value of concret e cylinder com pressive strength cm f - Concrete cube com pressive strength c f, t f sp - Tensile strength of concret e Table 3.9 Tensile strength of NSC ( MPa) Concrete used in Young s m odulus (GPa) Poisson s ratio Cohesion (MPa) Friction angle ( ) Tensile st rengt h (MPa) Original lining st relining nd relining rd relining Table 3.10 I nput properties for all concret e m at erials in the num erical m odelling 92

114 Chapter 3 Determ ining I nput Parameters in Num erical Models 3.4 I nt erface Problem s in the Shaft Lining Modelling I nt roduct ion For all the shaft relining system s at Boulby m ine, HSC blocks were em ployed, with different m aterials filled between the concret e blocks each tim e. Adhesive m aterials, epoxy resin and cem ent m ortar, were em ployed between the concrete blocks in the first shaft relining and squeezable plywood packs were used in the second and third shaft relinings. All these m aterials com pose m any j oints in the concrete relining syst em s. These j oints were actually very thin, 12~ 18 m m in thickness, com pared to the concrete blocks dim ensions ( around 0.5 m 0.5 m ). However, these j oints are im portant t o the m echanical behaviour of the whole concrete lining system s. Because of finite difference m esh generation limitation described later in Chapter 4, solid elem ents with som e thickness cannot be used to represent these m aterials in the num erical m odels. To solve this problem, interface elem ents with appropriate properties have been built into m odels to be used to represent epoxy resin/ cem ent m ortar/ plywood packs between concrete blocks in the num erical m odelling in this research. An interface is represented as a norm al and shear stiffness ( K and n K s ) between two planes which m ay contact each other in num erical m odels. The following m aterial properties are needed for the interface elem ents used in the Boulby m ine shaft lining m odelling: K, Norm al stiffness n K, Shear stiffness s C, Cohesion, Friction angle 93

115 Chapter 3 Determ ining I nput Parameters in Num erical Models t, Tensile strength The bonding at interfaces in concrete structures is im portant for safety and durability (Kunieda et al 2000). Therefore, t he perform ance of the whole restored concret e lining is strongly dependent on the perform ance of the interfaces. The chances of failure by cracking along the interface are higher because of stress concentrations and rapid change of stress levels along them (Lim et. al 2001). Furherm ore, Santosh and Kishen s experim ental ( 2010) results im plied that the greater the difference in com pressive strength or elastic m oduli m ism atch between the m at erials on both sides of the interface, the great er is the vulnerability to cracking and failure for the sam e loading configuration. The interfaces used in this num erical m odelling proj ect allow slip and separation. For this type of interface, the st rength properties (friction angle, cohesion c and tensile strength t ) are im portant, but the stiffness properties are not ( I tasca 2008). A good rule- of- thum b is that K n and K be set to ten tim es the equivalent stiffness of the stiffest s neighbouring zone (Itasca 2008). I n this research, the results of the early three dim ensional numerical m odels im plied that setting different values for K with K m ade no difference to the m odelling results. Therefore, the n S sam e value was assigned to both K and n K for sim plification in this S research. K, n K and the apparent stiffness ( expressed in stress per- S distance units) of a zone in the norm al direction are calculated using the Equations (3.12~ 3.14) : K n 4 B + S = K 10 m ax[ 3 s = ] (3.12) z m in 94

116 Chapter 3 Determ ining I nput Parameters in Num erical Models E B = 3(1 2ν ) ( 3.13) E S = 2(1 + ν ) ( 3.14) Where E, B and S are the Young s m odulus, bulk and shear m oduli, respectively; ν is the Poisson s ratio; and zm in is the sm allest width of an adj oining zone in the norm al direction (Figure 3.6). The m ax not ation indicates that the m axim um value over all zones adj acent t o the interface is to be used ( e.g., there m ay be several m aterials adj oining the interface). Figure 3.6 Zone dim ension used in stiffness calculation (Itasca 2008) I n the following sections, the input stiffness properties for the interface elem ents used in the num erical m odels in this research have been calculated using Equations (3.12~ 3.14), and t he strength properties have been estim ated from t he laboratory tests dat a and som e standards on strength properties of t he related m aterials. 95

117 Chapter 3 Determ ining I nput Parameters in Num erical Models I nt erfaces bet w een Epoxy Resin and Concret e Epoxy resin was used as an adhesive between concret e blocks in each single layer in the first relining of the Boulby m ine shaft lining. Epoxy resins are the m ost im portant class of therm osetting resins for m any engineering applications because of their outstanding adhesion to m ost surfaces, superior m echanical properties ( strength and stiffness), low shrinkage and good therm al characteristics (Vabrik et. al 1998, Denq et. al 1999, Kaj i et. al 1999, Yang et. al 2007). The use of epoxy resin in civil engineering has been established for over half of a century. For exam ple, use as const ruction adhesives between pre- cast elem ents, use as structural m ortars and application in concrete repairs works. Being liquid tight and fast curing m ake them popular as concrete repairing adhesives and joint fillers having a tough and solid network (Spee et. al 2006). In civil engineering applications, epoxy resins are alm ost invariably used directly bonded to concrete or other cem entitious m aterial. Table 3.11 shows the com parison of the m echanical and other properties of the epoxy resin system with those of cem entitious grout ( Tabor 1978). I t can be seen from Table 3.11 that the epoxy resin system has a lower Young s m odulus than the cem entitious grout syst em and this has to be taken into account when choosing input properties for t he interfaces between the epoxy resin and concrete in num erical m odelling. The data in Table 3.11 also im plies that the bond, tensile and shear st rengths of correctly form ulated epoxy resin based adhesives are considerably higher than those of good quality traditional cem entitous m ortar jointing techniques. Epoxy resin m akes the j oined sections as strong as m onolithic concret e and allows them to rem ain waterproof ( long- term ), even when the j oints are less than 1 m m thick (Shaw 1982). 96

118 Chapter 3 Determ ining I nput Parameters in Num erical Models Grouts, m ortars and concretes Epoxy resin Cem entitious Com pressive strength (MPa) Young s m odulus (GPa) Flexural strength (MPa) Tensile strength (MPa) Elongation at break (% ) Water absorption, 7 days at 25 (% ) Table 3.11 Physical properties a com parison of typical products ( Tabor 1978) According to British Standard BS : 2007, the polyest er resin used to achieve a bond between a rockbolt and the strata in coal m ines should have the Young s m odulus greater than 11 GPa and the UCS great er t han 80 MPa, which is m uch higher than that of NSC. Based on the reference data above, for the interfaces between the epoxy resin and concrete blocks in the first relining system, the cohesion c and friction angle of the first relining concrete (bigger sam ples results, shown in Table 3.6) was chosen as those of the interfaces; the m iddle value of the tensile strengths shown in Table 3.11 was chosen as the tensile strength. For calculating the stiffness properties of the interface in the first relining syst em, the stiffest neighbouring m aterial for the interface is the HSC concret e with Young s m odulus of 32.8 GPa and Poisson s ratio 0.2 ( Table 3.10). The m inim um zone size adj acent to the interface is designed to be 1.34 m for the first shaft relining m odel in this research. Therefore, according to the Equat ions (3.12~ 3.14), for t he interfaces between the 97

119 Chapter 3 Determ ining I nput Parameters in Num erical Models epoxy resin and concret e blocks in the first relining system, the stiffness is 272 GPa/ m. The final chosen input properties for the interfaces between the epoxy resin and concrete blocks in the num erical m odelling of the first relining in this research are shown in Table K n (GPa/ m ) K s (GPa/ m ) Cohesion (MPa) Friction angle ( ) Tensile strength (MPa) I nterfaces Table 3.12 I nput properties for the interfaces elem ents representing the epoxy resin between concret e blocks I nt erfaces bet w een Cem ent Mort ar and Concret e I n the first relining of the m ine shafts, epoxy resin was used to bond precast concrete blocks t ogether to form rings, then cem ent m ortar was used to bond several concret e- block rings together t o form a section. I t can be seen as a m asonry st ructure. I n order to obtain the m echanical properties of the cem ent m ortar used in the m asonry structure, the European Standard for m asonry cem ent BS EN 413-1: 2004 has been referred to. Table 3.13 shows the 28 days com pressive st rength requirem ents given as charact eristic values for different types of m asonry cem ent. Type 28 day (standard) strength (MPa) MC MC 12.5 MC 12.5 X MC 22.5 X Table 3.13 Com pressive strength requirem ents given as characteristic values for m asonry cem ent ( BS EN 413-1: 2004) 98

120 Chapter 3 Determ ining I nput Parameters in Num erical Models British Cem ent Association (BCA) points out that its m em ber com panies will m anufacture m asonry cem ent t o class MC 12.5 of BS EN 413-1: Therefore, it was assum ed that MC 12.5 has been used in the first relining of the Boulby m ine shafts, with 28 days com pressive strength of 12.5 MPa. For the Young s m odulus and tensile strength of the m asonry cem ent, the following assum ptions based on generalised test data are adopted (Wilson 1980, Reddish 1989), which also approxim ately agree with the laboratory tests data shown in Tables 3.4 and 3.5: E = 300 UCS = GPa (3.15) 1 UTS = UCS = MPa ( 3.16) 10 Where E is Young s m odulus, UCS is uniaxial com pressive strength and UTS is tensile strength. Usually the interface between the cem ent m ort ar and concret e is relatively weaker than the m aterial on either side of it. Based on reference data and analysis above, 80% of the cem ent m ortar s t ensile strength 1 MPa was chosen as the tensile strength. Table 3.6 shows that in Mohr-Coulom b properties for concrete tested in this research, cohesion is approxim ately 23% of the UCS. This guideline has been utilised to estim ate the cohesion of the interfaces between the cem ent m ortar and concrete blocks in the first relining system. Therefore a slightly lower value, 20% of the m asonry cem ent s UCS, 2.5 MPa, was chosen as the cohesion of the interfaces between the cem ent m ortar and concrete blocks in the first relining syst em. The stiffest neighbouring m aterial for the interface is still the HSC concret e. However, for the interfaces between the cem ent m ortar and concret e 99

121 Chapter 3 Determ ining I nput Parameters in Num erical Models blocks in the first relining system, the m inim um zone size adj acent to the interface is designed to be 0.6 m in the num erical m odel in this research. Therefore, according to the Equations (3.12~ 3.14), for the interfaces between the cem ent m ortar and concrete blocks in the first relining syst em, the stiffness is 607 GPa/ m. The final chosen input properties for the interfaces between the cem ent m ortar and concrete blocks in num erical m odelling of the first relining in this research are sum m arised in Table K n (GPa/ m ) K s (GPa/ m ) Cohesion (MPa) Friction angle ( ) Tensile strength (MPa) I nterfaces Table 3.14 I nput properties for the interfaces elem ents representing the cem ent m ortar between concrete blocks I nt erfaces bet w een Plyw ood Pack and Concret e The m arine grade plywood packs (BS 1088: 1966) were em ployed between the concrete blocks in the second and third relinings of the Boulby m ine shaft lining. The interface elem ents em ployed in num erical m odelling to represent the plywood packs were without tensile strength since plywood packs were not glued to the concrete blocks in the relining syst em s. The m echanical properties of the interface between the plywood pack and the concrete blocks were taken from an analysis of com pression tests results supplied by Boulby m ine and direct shear t est ( shear box tests) conduct ed at the NCG. For the direct shear test (shear box tests) bet ween the plywood pack and concret e block, the auto- shear direct and residual autom atic shear 100

122 Chapter 3 Determ ining I nput Parameters in Num erical Models apparatus (Mod: 27 WF2160, produced by Wykeham Farrance) was utilized. The test equipm ent consist of a m et al shear box in which the sam ple is placed as shown in diagram Figures 3.7. The box is split horizontally into two halves. Norm al force on the sam ple is applied from the top of the shear box by dead weight. Shear force is applied to the side of the top half of the box to cause failure in the sam ple. Loading plate Norm al force P Shear box Fixed Plywood sam ple Concret e sam ple Fixed Velocity Figure 3.7 Diagram of direct shear t est For the given t est, the norm al st ress and shear stress can be calculated using Equations (3.17~ 3.18) : σ = area of norm al force cross sec tion of sam ple = P A (3.17) τ = area of shear force cross sec tion of sam ple = T A (3.18) The test was repeated m ore than three tim es with different value for force P ( norm al force) and difference value for force T ( shear force). Mohr- Coulom b properties ( cohesion c and friction angle ) then could be obtained from theσ τ curve. 101

123 Chapter 3 Determ ining I nput Parameters in Num erical Models I n this research, the dim ension of the m arine plywood (BS: 1088) sam ples was 100 m m 100 m m 18 m m, and the dim ension of the concrete blocks was 97 m m 97 m m 20 m m (Figure 3.8), which is NSC ( when the direct shear tests were carried out, the HSC blocks used at Boulby m ine were not available. So NSC sam ples were utilised and it was assum ed that it would not influence the results m uch). a. Plywood b. Concrete Figure 3.8 Marine plywood and concret e sam ples used in direct shear test The surface of the plywood sam ple used in this test was not sm ooth but with parallel texture shown in Figure 3.8, which would influence the test results. Therefore, two groups of direct shear t ests between the concrete sam ple and the plywood sam ple have been carried out. I n one group test, the shear force direction was parallel to the texture of the plywood surface and in the other group test, the shear force direction was perpendicular to the texture of the plywood surface. For each group t ests, the applied shearing rate was 1 m m / m in and the applied norm al force were 30, 50, 100, 150 kn. The obtained σ τ curves linearly fitted from the t est points are shown in following Figures 3.9 and

124 Chapter 3 Determ ining I nput Parameters in Num erical Models Figure 3.9 σ τ curves obtained from the direct shear tests: shear force perpendicular to the t exture of the plywood surface Figure σ τ curves obt ained from the direct shear test s: shear force parallel to the texture of the plywood surface 103

125 Chapter 3 Determ ining I nput Parameters in Num erical Models I t can be seen from Figures 3.9~ 3.10 that two groups of Mohr- Coulom b properties ( cohesion c and friction angle ) had been gained, and are shown in Table For sim plification, the m ean values of the two groups Mohr-Coulom b properties ( cohesion c and friction angle ) were utilised for the interface elem ents representing the plywood packs between the concret e blocks in the second and third relining m odelling in this research. When the shear force direction is: Cohesion (kpa) Friction angle ( ) Perpendicular to the texture of the plywood surface Parallel to the texture of the plywood surface Mean value Table 3.15 Mohr- Coulom b properties obtained from the plywood- concrete direct shear t est Boulby m ine (2009) had a series of com pression test data on the plywood packs (BS 1088: 1966), in which a com pressive stress of 75 MPa was applied to plywood sam ples. Only one typical group test data has been supplied to this research shown in Table 3.16, in which the original thickness of the sam ple was 17.1 m m. The com plete stress- strain curve is shown in Figure

126 Chapter 3 Determ ining I nput Parameters in Num erical Models Stress Strain Com pression rate in t hickness MPa % % % % % % % % % % Table 3.16 Com pression test data on plywood sam ple (Boulby m ine 2009) Stress ( MPa) St rain Figure 3.11 Stress- strain curve for the plywood pack used in relining syst em s (Boulby m ine 2009) I t was thought that the residual behaviour of the plywood pack in the com pression test was a key fact or to the Young s m odulus of the plywood pack. Based on the typical group test data supplied by Boulby m ine, the 105

127 Chapter 3 Determ ining I nput Parameters in Num erical Models Young s m odulus of the plywood packs was calculated from the steeper part of the st ress- strain curve in Table 3.16 and Figure 3.11 ( strain from to 0.708), using the following Equation ( 3.19) : E = σ ( 3.19) ε Wher e E is t he Young s m odulus, ε is the strain difference. σ is the norm al stress difference and According to the Equation 3.19, the Young s m odulus of the plywood packs is 0.7 GPa. Therefore, in the second and third relining system s, the stiffest neighbouring m aterial for the interface is st ill the HSC concret e, the stiffness properties of which are shown in Table The m inim um zone size adjacent to the interface is designed to be 0.6 m for the second and third shaft relinings m odel in this research. Therefore, according to the Equations (3.12~ 3.14), for the interfaces between the plywood pack and concret e blocks in the second relining system, the stiffness is 667 GPa/ m. For the interfaces between the plywood pack and concrete blocks in the third relining system, the stiffness is 606 GPa/ m. All the properties for the interface elem ents representing the plywood pack bet ween the concret e blocks in second and third relining m odelling in this research are sum m arised in Table I nterface in K n (GPa/ m ) K s (GPa/ m ) Cohesion (kpa) Friction angle ( ) 2 nd relining rd relining Table 3.17 I nput properties for the interfaces elem ents representing the plywood pack between concret e blocks 106

128 Chapter 3 Determ ining I nput Parameters in Num erical Models 3.5 Ot her Param eters used in the Shaft Lining Modelling Mat erial Propert ies of Polyuret hane and Verm iculit e Polyurethane and verm iculite were utilised as backfill m aterials in the gap between the concrete liner and the shaft excavation face in the original shaft lining system at Boulby m ine. I n the num erical m odelling in this research, both of these two backfill m aterials were set t o be elastic at all positions to m ake the num erical calculation faster. Goodall et al (2002) in University of Cam bridge have carried out experim ents t o m easure the stiffness of verm iculite and the results ( Table 3.18) show the highly anisotropic nature of verm iculite particles, which exhibit a stiffness nearly 20 tim es greater in-plane than in the throughthickness direction. Moreover, the stiffnesses in both directions are very low, due to the open exfoliated structure of verm iculite. A low value, 1 MPa was chosen as Young s m odulus of the verm iculite in this study. Material Young s m odulus (MPa) Verm iculite through thickness 1.0 Verm iculite in-plane 19.9 Table 3.18 The stiffness m easured in the com pression and nanoindentation tests (Goodall et al. 2002) With regard to the Poisson s ratio of the polyurethane, it was report ed by Cam pbell (2007) that the polyurethane foam norm ally has a positive Poisson s ratio when it is stretched. However, when the foam is com pressed, it has a negative Poisson s ratio. Gercek ( 2007) also m ade a conclusion from previous researchers study that polym er foam with an inverted or re- entrant cell structure has a negative Poisson s ratio. 107

129 Chapter 3 Determ ining I nput Parameters in Num erical Models However, no value has been found as a reference for the Poissons ratio of the polyurethane. Therefore, it has been hypothesised that the Poisson s ratio for the polyurethane was zero because of lack of any inform at ion. The densities and the Young s m odulus of the polyurethane (Table 3.19) were chosen referring to aninc.com / foam.htm l. The verm iculite was thought to have a higher density than the polyurethane and for its Poisson s ratio, it was also assigned zero due to lack of any inform ation. The input m aterial properties for the polyurethane and verm iculite used in this study are sum m arized in the Table Materials Density (kg/ m 3 ) Young s m odulus (MPa) Poisson s ratio Polyurethane Verm iculite Table 3.19 I nput properties for polyurethane and verm iculite in the num erical m odelling Mat erial Propert ies of Cem ent Grout A cem ent grout, Pozam ent GP2.5 ( ordinary Portland cem ent pulverized fuel ash) grout with a characteristic strength of 15 N/ m m 2 (based on cubes test ed at 28 days) was pum ped into the gap between the back of the blocks and the excavation face in the second and third relinings of the Boulby m ine shaft lining. It aim ed to form a fill of a sim ilar st rength to the Marl (William s & Auld 2002). For sim plification, it was assum ed in this research that this kind of cem ent grout had the sam e m at erial properties as the cem ent m ortar described in the section 3.4.3, which are also sim ilar to those of the Marl. The input properties of the cem ent grout used in the num erical m odelling are shown in Table

130 Chapter 3 Determ ining I nput Parameters in Num erical Models Young s m odulus (GPa) Poisson s ratio Cohesion (MPa) Friction angle ( ) Tensile strength (MPa) Cem ent grout Table 3.20 I nput properties of the cem ent grout used in the num erical m odelling 3.6 Chapt er Sum m ary Chapter 3 concentrates on the m ethodology of laborat ory determ ination of input geotechnical param eters for all the m aterials used in the later num erical m odellings. Firstly, the RocLab software was introduced, which was used t o obtain the input properties for rock m at erials from Boulby m ine used in the num erical m odelling. After that, all the related laboratory tests data from previous rock m echanics research at Boulby m ine were collected com prising a database, including Patchet s tests (1970), Cook s tests (1974) (both from the University of Newcastle upon Tyne), test s conducted in the RSM (2000) and the NCG ( 2007~ 2009). Based on this database, the input properties for the rock m at erials and concrete used in the num erical m odellings were obtained. I nput properties for other support m aterials used in the num erical m odellings were also obtained ( by referring to papers, British standards or analysing tests data) and listed in this chapter, such as interfaces between different backfill m aterials and concrete blocks, backfill m aterials in the gap between the concrete lining and the excavation face. The com m ercial finite difference code FLAC 2D / FLAC 3D will be briefly introduced in the following Chapter

131 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D CHAPTER 4 I NTRODUCTI ON OF FLAC 2 D / FLAC 3 D 4.1 I ntroduction Fast Lagrangian Analysis of Continua ( FLAC 2D, I tasca) is a two- dim ensional explicit finite difference program and has been specially developed for geot echnical and m ining engineering m echanics com putation. This program can sim ulate nonlinear behaviour of structures built of soil, rock or other m at erials that m ay undergo plastic collapse and flow when t heir yield limits in shear or tension are reached. This kind of m odelling can be treat ed very effectively and accurately with Mohr- Coulom b and other elasto- plastic constitutive m odels, as can nonlinear response associated with large strains and deform ations. A variety of functions allow supports such as roof bolts, st eel arches and liners t o be incorporat ed into the m odel. FLAC 3D is developed based on the well- established two-dim ensional program and has essentially the sam e capabilities as FLAC 2D at present. Therefore, m any of the two- dim ensional applications can now be extended into three dim ensions with FLAC 3D. The m ain difference between them is that three- dim ensional analyses generally need m uch m ore random access m em ory ( RAM) and CPU tim e than a sim ilar two- dim ensional m odel does. 4.2 Fields of Application FLAC 2D / FLAC 3D has been used ext ensively, prim arily for analysis and design in mining engineering and underground construction. The explicit, tim e- m arching solution of the full equations of m otion (including inertial 110

132 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D term s) perm its the analysis of progressive failure and collapse, which are im portant phenom ena in studies related to m ine design. Som e possible applications of these softewares are noted below. Mechanical loading capacity and deform ations in slope stability and foundation design; Evolution of progressive failure and collapse in hard rock m ine and tunnel design; Factor- of- safet y calculation in stability analyses for earth structures, em bankm ents and slopes; Evaluation of the influence of fault structures in m ine design; Restraint provided by cable support on geologic m aterials in rock bolting, tiebacks and soil nailing; Fully and partially saturated fluid flow, and pore- pressure build- up and dissipation for undrained and drained loading in groundwater flow and consolidation studies of earth- retaining structures; Tim e- dependent creep behaviour of viscous m aterials in salt and potash m ine design; Dynam ic loading on slip- prone geologic struct ures in earthquake engineering and m ine rock- burst studies; Dynam ic effects of explosive loading and vibrations in tunnel driving or in m ining operations; Seism ic excitation of structures in earth dam design; Deform ation and m echanical instability resulting from therm al-induced loads in perform ance assessm ent of underground repositories of high-level radioactive waste; and Analysis of highly deform able m aterials in bulk flow of m at erials in bins and m ine caving. 111

133 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D 4.3 Fundam ent al Com ponent s of a Problem FLAC 2D / FLAC 3D offers a wide range of capabilities to solve com plex problem s in m echanics, and especially in geom echanics. I n order to set up a m odel to run a sim ulation, five fundam ental com ponents of a problem m ust be specified: A finite difference grid Boundary conditions Initial stress conditions Constitutive m odel Material properties After these conditions are defined in num erical m odels, the initial equilibrium state is calculated for the m odel. An alteration is then m ade (e.g., excavate m aterial or change boundary conditions), and the resulting response of the m odel is calculated. The general solution procedure, illustrated in Figure 4.1, is convenient because it represents the sequence of processes that occurs in the physical environm ent. 112

134 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D Start MODEL SETUP 1. Generate grid, deform to desired shape 2. Define constitutive behaviour and m aterial properties 3. Specify boundary and initial conditions Set to equilibrium state Results unsatisfactory Exam ine t he m odel response Model m akes sense PERFORM ALTERATI ONS For exam ple, Excavate m aterial Change boundary condit ions Step to solution More tests needed Exam ine t he m odel response Acceptable result Yes Param eter study needed No End Figure 4.1 General solution procedure ( I tasca, 2008) Finit e Difference Grid The finite difference grid, organised in a row and colum n fashion, defines the physical geom et ry of the problem under study. I n two- dim ensional 113

135 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D m odels, grids are com posed of convex quadrilateral elem ents. I n threedim ensional m odels, discretization of the volum e under study is done into hexahedral zones by default. The user also has the capability to im port a tetrahedral m esh into three- dim ensional m odels. The finite difference grid size and zone num bers m ust be decided on a balance between the accuracy of results required and the com putational tim e (the solution speed). I n general, the finer the m eshes are, the m ore accurat e the results should be. However, the increase of the zone num bers m ay lead to a decrease in com putation speed and an increase in com puter m em ory requirem ents. So relatively fine m eshes are defined where the stress or strain gradients are high (e.g., in the vicinity of excavations) and other part s of the m odel are represented by a coarse grid to obtain the balance, which is illustrated in Figure 4.2. Excavation Zone Figure 4.2 Gradually changed m esh: fine m esh in the vicinity of excavation (inside red dashed line), coarse m esh in other parts of the m odel 114

136 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D For the m axim um accuracy, the zone size should increase or decrease gradually ( Figure 4.2) with a specific ratio to prevent a sudden change in neighbour zone size (Figure 4.3). Excavation Zone Figure 4.3 Sudden changes in neighbour zone size (inside red dashed line) The aspect ratio of zone dim ensions should also be as near unity as possible; anything above 5: 1 is pot entially inaccurate. However, high aspect- ratio zones are quite acceptable in regions of low strain gradient, such as rem ot e boundary regions. I f a large and com plex problem is under sim ulation, in which the geom etry and loading are sym m etrical about one or m ore planes, a sym m etric m odel is a good choice to decrease the zone num bers and so to speed up the num erical calculation. For exam ple, a problem of stress analysis of a water tunnel (shown in Figure 4.4) is t o be solved, which is excavated in rock, subsequently lined, and then pressurized. The layout and geom etry 115

137 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D of the tunnel shown in Figure 4.4 are axisym m etric about the center of the tunnel, perm itting only half of the problem t o be sim ulated along the line of sym m etry. CL Rock X= 0 Figure 4.4 Geom etry for an exam ple wat er tunnel For a specific problem, there are m ainly three steps t o build up a finite difference grid to fit the physical region under study: Firstly, to decide on t he geom et ric extent of the grid, i.e. m odel boundary described in later section Secondly, to specify the num ber and distribution of zones within the grid based on a balance between the accuracy of results required and the com putational tim e (the solution speed), which has been discussed in the beginning part of section Finally, to arrange the position of object under study, such as the excavation and supporting structure I t is helpful to m ake a rough drawing as a grid draft before building up a finite difference grid in num erical m odels. 116

138 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D Boundary Condit ions Boundary and initial stress conditions define the in- situ state (i.e., the boundary and st ress condition before a change or disturbance in the problem state is introduced) of the geom echanical problem. Boundaries are of two categories: real and artificial. Real boundaries exist in the physical object being m odelled, such as the ground surface, the excavation surface, et c. However, artificial boundaries do not exist in reality. Due to const raints on m em ory and analysis tim e, it m ay not be possible to cover the whole body with zones when m odelling very large bodies (e.g., tunnels and very deep shafts). Then, artificial boundaries are placed sufficiently far away from the problem dom ain of interest ( area of high stress and strains) so that the behaviour in that area is not affected greatly. To obtain the balance between m odelling results as accurat e as possible and run tim e considerations, one m ust be very careful to define the position of the artificial boundary. I n general, for the analysis of a single underground excavation, boundaries should be located roughly ten excavation diam eters from the excavation periphery. This distance, however, can vary depending on the purpose of the analysis. I f failure is of prim ary concern, then the m odel boundaries m ay be closer; if displacem ents are im portant, then the distance to the boundaries m ay need t o be increased ( I t asca, 2008). Mechanical boundaries are of two m ain types in a num erical m odel: prescribed- displacem ent or prescribed- stress. A free surface is a special case of the prescribed- stress boundary. Stress boundaries can be determ ined by applying forces or stresses to the boundary. I n order to 117

139 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D apply a given displacem ent to a boundary, the boundary s velocity is prescribed first and then the desired displacem ent will occur in the boundary after a given num ber of tim e steps. A fixed boundary causes both stress and displacem ent to be underestim ated, while a stress boundary does the opposite. The two types of boundary condition bracket the true solution. There is a third type, the infinite elastic boundary ( I EB), which covers artificial boundaries. Boundary conditions (shown in Figure 4.5) allow the m odel to be loaded on different specified boundaries, whilst allowing others to rem ain fixed, thereby facilitating stress regeneration within the m odel. I nitially, this m odel was loaded under gravity conditions representing overburden load applied vertically. I nternal stresses m ust also be applied, both horizontal and vertical. However, a lim ited num ber of reliable in situ stress m easurem ents were carried out prior to the com m encem ent of m ining, therefore only post- m ining stress configurations are known. Free surface Model boundary Excavation Horizontal boundary stress Zone Fixed bottom boundary Figure 4.5 Exam ple of boundary conditions 118

140 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D I nit ial St ress Condit ions There are in- situ virgin stresses in the ground in all civil or m ining engineering projects before any excavation or construction is started. These in- situ stresses will be redistributed after excavation or construct ion especially in the dom ain surrounding the excavation and construction. The virgin stresses can greatly influence the subsequent behaviour of the m odel. So it is im portant to reproduce this in-situ state in num erical m odel grids by setting initial stress conditions. I deally, inform ation about the initial stress state com es from field m easurem ents but, when these are not available, the m odel can be run for a range of possible conditions. Although the range is pot entially infinite, there are a num ber of const raining factors ( e.g., the system m ust be in equilibrium, and the chosen yield criteria m ust not be violated anywhere) Const it ut ive Models The constitutive m odel in num erical m odels dictates the type of response the m odel will display upon disturbance ( e.g., deform ation response due to excavation). There are t welve basic constitutive m odels provided in FLAC 2D Version 6.0 and FLAC 3D Version 3.1, respectively, arranged into null, elastic and plastic m odel groups. The null m aterial m odel in num erical m odels represents m at erial that is rem oved or excavat ed. The stresses within a null zone are set to zero and no body forces ( e.g., gravity) act on these zones. The null m odel is useful to m odel the excavation and backfilling of the excavation. Models in the elastic group are utilized to represent m aterials which are characterized by reversible deform ation upon unloading and the st ress- strain laws are linear and path- independent. No failure happens to the elastic m aterial 119

141 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D since the strength is infinite in the elastic m odel. The plastic m odels are used to describe alm ost all m aterials with a property that includes som e degree of perm anent, path- dependent deform ation (failure) and the consequence of the nonlinearity of the st ress- strain relations. Table 4.1 presents a sum m ary of all the m odels with exam ples of representative m at erials and possible applications of the m odels. It should be noted that orthotropic elastic m odel is only supplied in t hreedim ensional m odels and the Cap- Yield (Cysoil) m odel only exists in twodim ensional m odels. The Mohr-Coulom b m odel in the plastic m odel group is applicable for m ost general engineering studies and utilized widely. Also, Mohr- Coulom b param eters for cohesion and friction angle are usually m ore- readily- available than other properties for geo- engineering m aterials. Except for these basic m odels, several optional features are available as separate m odules that can be included in num erical m odels at an additional cost per m odule, such as m odels for dynam ic analysis, therm al analysis, m odelling creep- m aterial behaviour, and two- phase flow analysis. With the powerful built-in program m ing language, FI SH, the user can also define new variables, functions and their own constitutive m odels. 120

142 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D Group Model Representative Material Exam ple Application Null Null Void Holes, excavations, regions in which m aterial will be added at later stage I sotropic Elastic Hom ogeneous, isotropic continuum ; linear stressstrain behavior Manufactured m aterials (e.g., steel) loaded below strength lim it; factor-ofsafety calculation Elastic group Orthotropic Elastic Materials with three m utually perpendicular planes of elastic sym m etry Colum nar basalt loaded below strength lim it Transversely I sotropic Elastic Thinly lam inated m aterial exhibiting elastic anisotropy (e.g., slate) Lam inated m aterials loaded below strength lim it Drucker-Prager Plasticity Lim ited application; soft clays with low friction Com m on m odel for com parison to im plicit finite-elem ent program s Mohr-Coulom b Plasticity Loose and cem ented granular m aterials; soils, rock, concrete General soil or rock m echanics (e.g., slope stability and underground excavation) Strain-Hardening / Softening Mohr- Coulom b Plasticity Granular m aterials that exhibit nonlinear m aterial hardening or soft ening Studies in post-failure (e.g., progressive collapse, yielding pillar, caving) Ubiquitous-Joint Plasticity Thinly lam inated m aterial exhibiting strength anisotropy (e.g., slate) Excavation in closely bedded strata Plastic group Bilinear Strain- Hardening/ Softening Ubiquitous-Joint Plasticity Lam inated m aterials that exhibit nonlinear m aterial hardening or soft ening Studies in post-failure of lam inated m aterials Double-Yield Plasticity Lightly cem ented granular m aterial in which pressure causes perm anent volum e decrease Hydraulically placed backfill Modified Cam -Clay Plasticity Materials for which deform ability and shear strength are a function of volum e change Geotechnical construction on clay Hoek-Brown Plasticity I sotropic rock m aterials Geotechnical construction in rock Cap-Yield (Cysoil) Plasticity Soils that exhibit decreasing stiffness as plastic strains develop Geotechnical construction in soft soils Table 4.1 FLAC 2D / FLAC 3D constitutive m odels (Itasca, 2008) 121

143 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D Mat erial Propert ies The m aterial properties required in num erical m odels are generally categorized in two groups: elastic deform ability properties and st rength properties. Additionally, there are special considerations such as the definit ion of post - failure propert ies, t he ex t rapolat ion of laborat orym easured properties to the field scale and so on. The selection of propert ies is often the m ost difficult part in the generation of a m odel because of t he high uncertainty in the property database. The field data will never be known com pletely, especially in geom echanics. However, with the appropriate selection of properties based upon the available lim ited database, an im portant insight into the physical problem can still be gained. Material properties are conventionally derived from laboratory testing program s. As for the intact rock, the Young s m odulus can be det erm ined in the laboratory tests and the deform ation m odulus required for a Mohr- Coulom b m odel can be derived: E B = ( 4.1) 3(1 2ν ) S = E 2(1 + ν ) ( 4.2) Where E, Young s m odulus; ν, Poisson s ratio; B and S, bulk and shear m odulus. Determ ining the cohesion c and friction angle of the rock m aterial requires a series of t riaxial tests of which the results for various confining stresses are plotted as Mohr s circles. With Mohr s circles plotted, a failure envelope can be drawn and the cohesion c and friction angle can be determ ined from this envelope (Figure 4.6). The rocks around an underground tunnel are generally under com pressive stress and thus generally fail in shear. 122

144 Chapter 4 I ntroduction of FLAC 2D / FLAC 3D C = Cohesion = Friction angle C Figure 4.6 Det erm ination of m at erial properties for Mohr- Coulom b m odel 4.4 Chapt er Sum m ary The com m ercial finit e difference codes FLAC 2D / FLAC 3D were briefly introduced in this chapter, including their fields of application and fundam ental com ponents of num erical m odelling. The num erical m odelling of shafts lining system s will be described and discussed in detail in the following Chapters 5~ 6. The r eader is rem inded t hat t he running t im e in t he num erical Mohr- Coulom b m odel in this research is a series of tim e-steps, totally different from the shaft linings total work tim e, which is around 10 years, or m ore. The deform ation and stress results shown in this thesis were the final state of the num erical m odels when m echanical equilibrium was reached and do not represent fully the ongoing situation experienced over the lining life. They are however, useful when drawing com parisons between the perform ances of the four different lining types. Any further additional loading or creep properties put into the m odel would lead to additional deform ations and stresses, which represent continuous deform ing conditions in the shaft concrete lining system s during their working life. 123

145 Chapter 5 Two-Dim ensional Models CHAPTER 5 TW O- DI MENSI ONAL NUMERI CAL MODELLI NG OF SHAFT LI NI NG SYSTEMS 5.1 I ntroduction The FLAC 2D num erical code has been used t o set up two- dim ensional m odels for the stability analysis of the shaft linings through the Marl stratum at Boulby m ine. A plane- strain 2D analysis has been perform ed in this research because of sm all deform ation along the shafts vertical axis com pared with their lengths, which can be neglected. The investigation presented in this chapter focuses on the following aspect s: Param etric studies on t he effect of rock properties of the Marl, and the effect of the extent of weathered Marl on the stress and deform ation conditions of the shaft linings, A param et ric study on t he effect of the ground stress field (hydrostatic or not) on the st ress and deform ation conditions of the shaft linings, The effect of possible point loading on the shaft linings on the stress and deform ation conditions of the shaft linings, Modelling for the st ress and deform ation conditions of the original shaft lining and relinings. I n this research, the m ost detailed inform ation available for the original shaft lining and relining syst em s was obtained from several CAD drawings of the m an shaft. Additionally, it has already been stat ed in Chapters 1~ 2 ( sections 1.2 and 2.6) t hat the shaft relinings through the Marl zone have always been start ed with the m an shaft and the rock shaft relining has 124

146 Chapter 5 Two-Dim ensional Models adopted a sim ilar design as that for the m an shaft although internal dim ensions have differed slightly between shafts. All num erical m odels in Chapters 5~ 6 in this research have been based on the m an shaft at Boulby m ine. As already briefly introduced in Chapter 4, a variety of functions in FLAC 2D / FLAC 3D codes allow supports such as rock bolts, steel arches and liners ( called structural elem ents) t o be incorporat ed into the num erical m odels. Therefore, the liner elem ents in FLAC 2D / FLAC 3D codes can be used to m odel the shaft linings in this research. However, these st ructural elem ents are in the form at of line ( 2D) or plane ( 3D) without thicknesses shown in Figure 5.1. The liner elem ents in the form at of line (2D) or plane (3D) m ake it im possible in this research to analyze the detailed stress conditions (e.g. stress contours) within the shaft concrete linings, which have a significant physical thickness (0.75~ 1.2 m ). FLAC 2D m esh Rockbolt Figure 5.1 Deform ed shape of 25 m m diam eter rockbolt following rupture at end of shear test ( I tasca, 2008) 125

147 Chapter 5 Two-Dim ensional Models Additionally, for the shaft HSC relinings with various joint fillings (epoxy resin, cem ent m ortar and plywood packs), it is im practicable to m odel these im portant struct ural joints interacted with the line/ plane liner elem ents in num erical m odels. The solid two/ three dim ensional elem ents have been utilised to m odel the shaft linings in all num erical m odels in this research t o solve these problem s. 5.2 Param etric St udy The Marl zone is the weakest near- seam zone in the rock sequence and the shaft lining repair work always occurred within this over- 9m - t hick weak zone. Therefore, the first m odelling task focuses on sim ulating the shaft linings stress and displacem ent conditions through this zone. The effect s of the properties of the Marl and the ground st ress field (hydrostatic or not) on the st ress and deform ation conditions of the shaft linings have been studied in the m odels, using the original shaft lining as an exam ple. Additionally, the concept of a plastic zone of the weathered Marl has been introduced into this research. The effect of the ext ent of weathered Marl on the stress and deform ation conditions of the original shaft lining has also been studied in the m odels Geom et ry of t he Model and Mesh Definition Due to the num erical m odelling constraints on com put er m em ory and analysis tim e, it is not possible to cover the whole structure with zones when m odelling very large st ructures ( e.g., deep shafts). I n that case, artificial boundaries are placed around the m odel dom ain, which are sufficiently far away from the problem dom ain of interest ( the area of high 126

148 Chapter 5 Two-Dim ensional Models stresses and strains), so that the behaviour in that area is not greatly affected. The guidelines for defining the position of the artificial boundary in the num erical m odels have been discussed in Chapter 4. Figure 5.2 shows the conceptual layout of the m odel dom ain for a circular shaft of 7.9 m in diam eter support ed by a 0.75 m thick concret e lining, with a 0.45 m thick com pressible m aterial between the concret e lining and the excavation face (dim ensions can be found in Table 2.5 in Chapter 2). Shaft Marl Figure 5.2 A horizontal slice in Marl in two- dim ensional m odel (not to scale) The geom et ry of the problem area and the finite difference grid used in m odels are shown in Figure 5.3. Laterally, the m odel was approxim ately ten tim es the shaft excavation radius. Because this is a sym m etrical problem, only a quart er shaft has been m odelled to save the program m e running tim e and m em ory. 127

149 Chapter 5 Two-Dim ensional Models 40 m 40 m Shaft Figure 5.3 Finite difference grid used in the two- dim ensional m odels Boundary and I nit ial St ress Condit ions The boundary and initial in situ stress conditions have a significant influence on the behaviour of a geot echnical engineering m odel. I t is very im portant to accurat ely reproduce these conditions before any 128

150 Chapter 5 Two-Dim ensional Models const ruction or excavation process is start ed. I n order t o estim ate the initial stress stat e existing near the shaft, the vertical and horizontal stresses m ust be input into the m odels. I n Chapter 2 of this thesis, the in situ state of ground stress and the available results of stress m easurem ents m ade around the world have been reviewed and discussed in detail. Based on those m easured results, Brown and Hoek (1978) obtained the Equation (2.7) giving the average relationship for the vertical com ponent of stress in relation to depth. St ress m easurem ent result s also show t hat σ ( the average horizontal h av stress and σ z (the vertical stress) t end to equalise (i.e. hydrostatic stress conditions) when the depth increases towards and beyond 1000 m. This rule is widely used in weak rocks ( e.g. coal m easures and evaporites) and it has been found to give a good approxim ation of the in situ stress field in these m at erials ( Hoek and Brown, 1980). This rule is also used in this m odelling proj ect. The initial background stress was reconstruct ed based on hydrostatical in situ stresses in the whole m odel dom ain, calculated from the following Equation (5.1): σ = σ = σ = h MPa (5.1) x y z Where h is the stratum depth. Based on Figures 2.9 and 2.11 in Chapter 2, h = 1090 m has been chosen for the Marl stratum and Figure 5.4 shows the boundary and hydrostatic ( horizontally) initial stress conditions used in m ost of the twodim ensional m odels. 129

151 Chapter 5 Two-Dim ensional Models y = MPa x = MPa x = y = MPa Figure 5.4 Boundary and initial stress conditions of the two- dim ensional num erical m odel Except for the param et ric study on the influence of the ground stress field on the stability of the original shaft lining, all other m odels for param etric studies and the possible point loading on shaft lining have been done under a hydrostatic stress field in the m odels. When the effect of the ground stress field (hydrostatic or not) on the stress and deform ation conditions of the original shaft lining was studied, the initial background stress state was reconstructed in the num erical m odels based on the following Equation (5.2): σ x = λσ y = λσ z = λ (5.2) Where is the background stress ratio σ / σ, with a range from 0.5 to x y 1.0 in this research which is shown in Table

152 Chapter 5 Two-Dim ensional Models σ (MPa) σ (MPa) λ x y Table 5.1 Background st ress ratio used in the m odels Mat erial Propert ies Various m aterials are involved in the m odels in this research, such as the surrounding rock types, concretes used as shaft linings, cem ent grout backfilled in the gap bet ween the linings and excavation face and so on. As described in Chapter 3 (section 3.3), Mohr- Coulom b failure criteria has been chosen for all rock, concret e and cem ent grout m aterials in this research. The m ethodology for obtaining the input m aterial properties and the final version of them used in the num erical m odels has been presented and discussed in Chapter 3 in this thesis. I n this section, only the final input m aterial properties used in the m odels are briefly introduced Marl Patchet s t est results (1970) after reduction using the RocLab soft ware (introduced in Chapter 3) were chosen as the base m aterial properties of the Marl in the param etric studies. The GSI used in the RocLab software was estim ated to be a lower value (30) for the Marl according to previously reported in situ experience. The Young s m odulus, cohesion c 131

153 Chapter 5 Two-Dim ensional Models and friction angle of the Marl have been decreased (Table 5.2) to investigate their effect s on stress and deform ation conditions of the shaft linings (using the original lining as an exam ple). Materials Young s m odulus ( GPa) Poisson's ratio Cohesion ( MPa) Friction angle ( ) Tension ( MPa) Marl Note: The properties underlined are Patchet s ( 1970) test results after reduction using GSI = 30, and are the base properties. Table 5.2 I nput properties for the Marl in param etric studies on the effect of its properties on the stability of the linings I t has been m entioned by Pat chet (1970) that the Marl can be considered as plastic under m ost conditions and as a stratum, it probably has no tensile strength (Chapter 2, section 2.5). Therefore, no param et ric study on the tensile strength of the Marl will be carried out although som e low values have been assigned to the Marl in this part of the research. When the effect of the ground st ress field (hydrostatic or not) on the stress and deform ation conditions of the original shaft lining was studied, Patchet s (1970) t ests results after the reduction shown in Table 5.2 were used as the properties of the Marl and kept unchanged. I n Chapt er 2 it was stated that the Marl is a weak rock and m ore easily weathers on exposure when com pared with ot her surrounding rock types at Boubly m ine. I t has been assum ed by the author in this research that, 132

154 Chapter 5 Two-Dim ensional Models in the real engineering situation, a plastic zone of weathered Marl was m odified away from the shaft excavation face because of its exposure in the shaft excavation process and its subsequent relinings. This plastic zone of weathered Marl is schem atically shown in the Figure 5.5. Figure 5.6 shows how this concept has been sim ulated in the m odels Shaft 1 Weathered Marl 2 Un- weathered Marl (not to scale) Figure 5.5 Conceptual plastic zone around the shaft Un- weathered Marl Weathered Marl Polyurethane Shaft Lining Figure 5.6 Weathered Marl sim ulated in the two- dim ensional m odels The extent of weathered Marl into the shaft wall refers to the thickness of weathered zone that is the distance between the out er boundaries of 133

155 Chapter 5 Two-Dim ensional Models weathered zone and the polyurethane layer. Distances of 1, 2, 3, 4, 6 m have been adopted in this part of the research, which were approxim ately 0.25, 0.5, 0.75, 1 and 1.5 tim es the shaft initial excavation radius (nearly 4 m ), respectively. When the effect of the extent of weathered Marl on the stress and deform ation conditions of the original shaft lining were studied, the RSM tests (2000) results after reduction using the RocLab software were chosen as the m aterial properties of the weathered Marl. Table 5.3 shows the input properties for the weathered and un- weathered Marl in the m odels for the param etric study on the effect of the extent of weathered Marl on the st ress and deform ation conditions of the original shaft lining. Figure 5.7 shows the Mohr- Coulom b strength envelopes for the laborat ory test data and input properties used in this part of param et ric study for t he un- weathered and weat hered Marl. Materials Young s m odulus ( GPa) Poisson's ratio Cohesion ( MPa) Friction angle ( ) Tension ( MPa) Un- weathered Marl Weathered Marl Table 5.3 I nput properties for the weathered and un- weathered Marl in param et ric studies on t he effect of the extent of weathered Marl on the stability of the original shaft lining 134

156 Chapter 5 Two-Dim ensional Models Drawn from Patchet s tests (1970) Drawn from RSM s tests (2000) Un- weathered Marl Weathered Marl Figure 5.7 Mohr- Coulom b strength envelopes for the Marl I n Situ Cast Concrete and Polyurethane Since laboratory test data of the in situ cast concrete used in the original shaft lining at Boulby m ine, with the exception of its UCS value (34.5 MPa) was not available, the input properties for this concret e used in the m odels have been estim ated based on experiences and references as described in section in Chapter 3. The final input properties for the in situ cast concret e can be found in Table The input properties for the polyurethane, which has been set as pure elastic in the m odels for the original shaft lining syst em, can be found in Table St ress Relaxat ion and Modelling Sequence After the grid was generated and the input m aterial properties were assigned for rock m at erials, in situ stresses were applied to the m odel boundary and dom ain. Then the m easuring points ( for both displacem ents and stresses) were set up and the program run to establish the 135

157 Chapter 5 Two-Dim ensional Models equilibrium conditions to initialize stresses. The sim ulations were designed such that they represented the actual sequence of events leading to the shaft excavation at Boulby m ine. After the initial equilibrium was established, the next st eps were the shaft excavation and the installation of the support. I n the practical situation, the shaft lining is not installed im m ediately after shaft excavation. An im portant issue in these stages is the am ount of st ress relief and redistribution and consequent ground m ovem ent due to the shaft excavation that occurs prior t o support placem ent. This is known as the head- end effect in tunnel design. The m ajor im plication of the head- end effect is that a support installed at a distance behind the face will not be subjected t o the full loading and deform ation as a result of the full overburden pressure ( Whittaker and Frith 1990). So if no change in loads acting on the support is assum ed to occur, t he pressure acting on the support will be over- predicted. I f com plete st ress relaxation at the shaft periphery is assum ed t o occur, zero loads will develop in the support at the installation step, provided that the relaxation state is at equilibrium. I n fact, even if the support is installed at the face, a degree of stress relief and m ovem ent will have already taken place in the im m ediate ground in front of the face, see Figure 5.8 ( Muir Wood 1979). I t is necessary t o t ake account of stress relaxation in shaft excavation and support installing stages of the m odel, for econom ic reasons and to m ake the num erical sim ulation as close to the real engineering situation as possible. It will result in a support m ore correctly m atched to the expect ed ground behaviour rather than one over- designed if the full overburden pressure is considered. 136

158 Chapter 5 Two-Dim ensional Models Tangential stress 2q 1.75q 1.5q 1.25q u m ax 0.75u m ax 0.5u m ax 0.25u m ax Radial convergence 1q 80r 60r 40r 20r 0-20r -40r Distance from face 2r q = in situ hydrostatic stress Figure 5.8 Radial convergence and tangential stress in vicinity of tunnel face ( Muir Wood 1979) However, it is difficult to choose the am ount of st ress relief at the point of support installation and the result of over-estim ating this effect m ay lead to false conclusions concerning the stability of the support in question. One way to m odel the relaxation is to decrease the Young s m odulus of the shaft core, equilibrate, rem ove the core and install the support. The m odels are then cycled to equilibrium, with stresses and displacem ents being m onitored throughout the cycling process. I n this research, according to m odelling experience, the Young s m odulus of the shaft core was decreased by 50% to m odel the stress relaxation. The flow chart (Figure 5.9) shows the detailed operations for the shaft excavation and support installation in the m odels for the m ine shaft project, which have been designed to take the practical construction situation into account in the num erical m odelling. 137

159 Chapter 5 Two-Dim ensional Models The initial equilibrium Decrease the shaft core s Young s m odulus 50% to sim ulate the stress relief Solve (Run program to equilibrium ) Rem ove the shaft core, install the support Solve (Run program to equilibrium ) End Figure 5.9 Modelling sequence flow chart in the two- dim ensional m odels 5.3 Modelling Results of t he Param et ric Studies As described in section 5.1, param etric studies in the m odels for the m ine shaft linings focus on t he effects of rock properties of the un- weathered Marl, the extent of weat hered Marl and the ground stress field (hydrost atic or not) on the st ress and deform ation conditions of the shaft linings, using the original lining as an exam ple. The m odelling results from all the param et ric studies are presented in this section, respectively. I t should be not ed that in the following figures, the shaft lining closures refer to the radial inwards displacem ent of the inner surface of the concret e lining in the num erical m odels. I t was chosen as the deform ation index in studying the effect of the properties of the un- weathered Marl on the stability of the shaft lining, since the space left in the shaft is 138

160 Chapter 5 Two-Dim ensional Models im portant to the m ining work. The m ax. 1 is the m axim um m ajor principal stress in the concrete lining in the num erical m odels. To com pare different rock properties effects on the stability of the original shaft lining in this research, the shaft lining closure and m axim um m aj or principal stress 1 in the lining have been plotted against percentage of the basic properties, which are the Patchet s (1970) tests results after reduction (shown in Table 5.2) The Effect of t he Propert ies of t he Marl Figures 5.10~ 5.11 show the m odelling results of the param etric study on the effect of properties of the un- weathered Marl on the stress and deform ation conditions of the original shaft lining. I t can be seen from Figures 5.10~ 5.11 that the shaft lining closure and the m axim um m ajor principal stress 1 increased with a decrease in property value (strength cohesion C and friction angle F, and stiffness E). 120 Shaft lining closure (m m ) % 20% 40% 60% 80% 100% Percentage of the basic properties Basic E = 0.41 GPa Basic C = 0.97 MPa Basic F = 18 Figure 5.10 Shaft lining closure vs. the properties of the Marl 139

161 Chapter 5 Two-Dim ensional Models 70 Max. 1 in lining (MPa) % 20% 40% 60% 80% 100% Percentage of the basic properties Basic E = 0.41 GPa Basic C = 0.97 MPa Basic F = 18 Figure 5.11 Max. 1 in shaft lining vs. the properties of the Marl When the friction angle and the Young s m odulus of the Marl decreased to be lower than 16 and 0.3 GPa, respectively, the original shaft lining closure increased dram atically ( Figure 5.10, from approxim ately m to nearly 0.12 m ) in num erical m odels. However, the m axim um m ajor principal stress curve ( Figure 5.11) in the original shaft lining gradually increased at the early stage ( from approxim ately 48 MPa to 60 MPa) but tended to be st eady around 62 MPa at the later stage when the properties of the Marl decreased in num erical m odels. Corresponding to each m axim um m ajor principal stress 1 in the original shaft lining, the m inor principal stress 3 was approxim ately 8 MPa in all m odels in this part of the param et ric study. This im plies that corresponding to the end stage of the m axim um m ajor principal stress curve ( Figure 5.11), the principal stress difference ( deviator st ress ( 1-3 ) ) in the shaft lining becam e increasingly greater, threatening the stability of the shaft lining. 140

162 Chapter 5 Two-Dim ensional Models A decrease in the value of each single property in the Marl m eans a m ore severe ground st ress from the surrounding Marl acting on the shaft lining, leading to greater deform ation and stress conditions in it. I t can be seen from the m odelling results shown and described above that, in t his research case, the stability of the original shaft lining was m ost sensitive to the friction angle of the surrounding Marl, and least sensitive to the cohesion of the Marl. That is to say, for shear strength properties of the Marl, the cohesion has less effect on the stability of the shaft lining than the friction angle. I t is thought by the author that it is because in the num erical m odels in this research, soft Marl with fairly low cohesion (lower than 1 MPa in Table 5.2) in an environm ent of high ground stress field ( nearly 30 MPa in Table 5.1). The following Equations (5.3~ 5.5) are used to dem onstrate this condition in this research. τ = c + σtgϕ (5.3) τ c = c (5.4) = σtgϕ σtg (5.5) τ ϕ 1 ϕ 2 Where, τ is shear stress, σ is norm al st ress, c is cohesion, c is cohesion difference, ϕ is friction angle, ϕ is friction angle difference, τ c is shear st ress differ ence caused by c, τ is shear stress difference ϕ caused by ϕ = ϕ 1 ϕ. 2 According to Tables 5.1~ 5.2, let σ = 29.43MPa, ϕ 1 = 18, ϕ 2 = 17 and c = = 0. 22MPa, t hen τ c = 0. 22MPa and τ = 0.56MPa. I t can ϕ be seen obviously that > τ. c τϕ 141

163 Chapter 5 Two-Dim ensional Models The Effect of the Extent of the W eathered Marl Figures 5.12~ 5.13 show the m odelling results of the param etric study on the effect of the ext ent of the weathered Marl on the stress and deform ation conditions of the original shaft lining. As shown in Figures 5.12~ 5.13, the shaft lining closure increased gradually at the early stage and dram atically at the later stage with the increasing extent of the weathered Marl in the num erical m odels. Shaft lining closure (m m ) The thickness of the weathered Carnallitic Marl ( m ) Figure 5.12 Shaft lining closure vs. the thickness of the weathered Marl 70 Max. 1 in lining (MPa) The thickness of the weathered Carnallitic Marl ( m ) Figure 5.13 Max. 1 in shaft lining vs. the thickness of the weathered Marl 142

164 Chapter 5 Two-Dim ensional Models When there was 6 m (1.5 tim es the shaft excavation radius) thick weathered Marl surrounding the shaft in the m odel, up to 0.39 m closure occurred in the original shaft lining, which was 14% of the original shaft lining inner radius. This m agnitude closure would be a serious problem for shaft operations and severely com prom ise the shaft lining stability. The m axim um m ajor principal stress curve in the original lining (Figure 5.13) gradually increased then tended to be st eady when the extent of the weathered Marl increased in the num erical m odels. However, when the weathered Marl was 6 m thick, the ground stress field was so severe that the original lining could not provide support and becam e plastic in m ost area. Therefore, the m axim um m aj or principal stress 1 in it started decreasing. This confirm s that 6 m thick weat hered Marl caused a serious problem for the original lining stability in the two- dim ensional m odels. The m odelling results im ply that the increasing extent of the weathered Marl leads to an increasingly severe ground stress field working on the original shaft lining and all relinings, resulting in higher deform ation and stress conditions in them. As seen from Figures 5.12~ 5.13, it is suggested by the author that in this research case, 4 m ( approxim ately equal to the shaft excavation radius) is a critical value for t he ext ent of the weathered Marl. When the weathered Marl ext ent is greater than 4 m, the original lining confronts a severe ground st ress field, threat ening its stability The Effect of t he Ground St ress Field The m odelling results of the param etric study on the effect of ground stress field (hydrostatic or not) on the stress and deform ation conditions of the original shaft lining are shown in Figures 5.14~ The m odelling results in Figures 5.14~ 5.15 show that the shaft lining closure and the 143

165 Chapter 5 Two-Dim ensional Models m axim um m ajor principal stress 1 increased with the background st ress ratio decreasing. However, when the background stress ratio decreased to 0.5, extrem ely large closure (nearly 0.25 m, 9% of the original lining inner radius) occurred in the original shaft lining and the m axim um m ajor principal stress 1 decreased dram atically. These were because the original lining becam e plastic under severe ground stress field and lost som e of its supporting capacity. 300 Shaft lining closure (m m ) Background stress ratio Figure 5.14 Shaft lining closure vs. background stress ratio 70 Max 1 in lining (MPa) Background stress ratio Figure 5.15 Max. 1 in lining vs. background stress ratio 144

166 Chapter 5 Two-Dim ensional Models When the background stress ratio was 0.6 and 0.5, tensile stress occurred in the original shaft lining and caused tension failure (shown in Figure 5.16). These im ply that the severe non- hydrostatic stress field with background stress ratios, equal to 0.5 and 0.6 caused serious problem s for the shaft lining stability in the two- dim ensional m odels. Original shaft lining * Shear failure Tension failure Y X Figure 5.16 Failure stat e of the original shaft lining under background stress ratio = 0.5 The m odelling results described and discussed above im ply that nonhydrostatic stress field would result in uneven loading on the circular shaft linings and threaten their stabilities. However, when the background stress ratio was close to 1 im plying a hydrostatic stress field, the original shaft lining was less com prom ised. 5.4 The Possible Point Loading on t he Original Lining I n practical engineering, the cross- section of t he shaft excavation cannot be a perfect circle. However, the concret e lining was designed t o be a perfect circle. That m eans the backfill m aterials in the gap between the 145

167 Chapter 5 Two-Dim ensional Models surrounding rock and concrete lining was not of an even thickness. I n the original concrete lining system, the backfill m aterial was very soft polyurethane through t he Marl stratum, which can be easily and highly com pressed. The polyurethane could not accom m odate t he high pressure from the surrounding Marl. This situation m ay well have caused uneven loading on the original concrete lining. Usually, the circular concret e st ructure can exhibit good stability under even loading, but it has a m uch lower ability to resist uneven loading, which has been confirm ed by the num erical m odelling results shown in section 5.3. A sim ple ext rem e case of the possible uneven loading ( called point loading) on the original concret e lining system was sim ulated and discussed in this section Model Configurat ions The artificial boundary and the hydrostatic ground stress field shown in Figure 5.4 described in section 5.2 were also em ployed in this m odel. For the sim ulation of the possible point loading on the original lining, a full circular shaft m odel has been utilized. Therefore, the m odel dom ain for this m odel was 80 m 80 m. At the sam e tim e, the concept of the weathered Marl zone introduced in section 5.2 has been used in this possible point loading m odel. According to the m odelling results in section 5.3, 4 m was chosen as the extent of the weathered Marl, which was approxim ately equal to the shaft excavation radius. Figure 5.17 shows the point loading s position, 1m in length along the periphery of the original shaft lining, and the different m at erial groups in this m odel. 146

168 Chapter 5 Two-Dim ensional Models Polyurethane Shaft lining Unevenly thick polyurethane Weathered Marl Un- weathered Marl Figure 5.17 Mesh for possible point loading m odel (not full window) The input m aterial properties for the weathered and un- weathered Marl can be found in Table 5.3. As described in section 5.2, the input properties for the in situ cast concrete and the polyurethane can be found in Tables 3.10 and Modelling Result s and Discussion Figure 5.18 shows the failure state of the original shaft lining under possible point loading caused by unevenly thick distribution of the polyurethane along its periphery. I t can be seen that a m assive tension failure and shear failure occurred near the point loading position in the concret e lining. I n t his num erical m odel, the m axim um radial inwards displacem ent (closure) of the original lining at the point loading area was approxim ately 0.2 m, m uch bigger than those of other parts of the 147

169 Chapter 5 Two-Dim ensional Models concret e lining (0.03 m ). Additionally, the original shaft lining m oved slightly in a horizontal direction because of the point loading, schem atically shown in Figure This result was consistent with the lining condition indicated by in- situ m easurem ents described in Cook s thesis (1974) shown in Figure However, Cook s figure ( 1974) showed no shape change of the shaft lining. I t is thought by the author that Cook just em phasized the lateral m ovem ent of the lining but ignored its shape change. Shaft original concret e lining * Shear failure Tension failure Lining initial shape Lining after deform ation Figure 5.18 Failure stat e and schem atic shape change of the original shaft lining under possible point loading Shaft original lining m oved slightly in horizontal direction Shaft original lining initial position Figure 5.19 Lateral m ovem ent of the original lining (Cook, 1974) 148

170 Chapter 5 Two-Dim ensional Models Based on these m odelling results, it was deduced that a possible reason for the original shaft lining s failure m ay be due to uneven loading on the concret e lining caused by uneven thicknesses of the backfill m aterial. Uneven loading could lead to high tensile stress and shear st ress in the concret e which causes a severe threat to t he stability of the circular concret e structure. However, the cem ent grout, a rigid backfill m aterial when com pared with polyurethane, was em ployed in the shaft relinings and would accom m odate the high pressure before they affected the concret e linings. The buffering cem ent grout layer transferred high ground pressure t o the concret e blocks gradually and facilitated the avoidance of possible uneven loading on the concrete linings, which would have threatened the stability of the shaft lining system. 5.5 Modelling for t he Original Lining and Relinings The stress and deform ation conditions of the shaft s concret e linings at Boulby m ine have been num erically sim ulated, from the cast concret e lining that were originally installed when the shafts were sunk to their first, second and third entire relinings through the Marl stratum. The assum ptions m ade during the m odelling and the m odelling results have been present ed and discussed in this section Model Configurat ions One limitation affecting the finite difference m esh in all the num erical m odels is that the m esh cannot be changed once the program m e starts running. However, the original shaft lining and relinings through the Marl zone at Boulby m ine did not have the sam e dim ensions. I n fact, the circular shaft relinings through the Marl zone gradually increased in radius as shown in Table

171 Chapter 5 Two-Dim ensional Models I n: Lining s I nner Radius (m ) Lining s Outer Radius (m ) Shaft s Excavation Radius (m ) Original lining st relining nd relining rd relining Table 5.4 Dim ensions of shaft linings through the Marl zone at Boulby To solve this problem in the m odels, all the shaft s relinings through the Marl zone have been sim ulated in their own true dim ensions, which m eans that three new finite difference m eshes were required, one for each relining system, and each different from the one for the original shaft lining. The artificial boundary and the hydrostatic ground stress field shown in Figure 5.4 described in section 5.2 were em ployed in all the quarter m odels for the original shaft lining and relinings. As with the m odel configuration set for the m odel of point loading on the original lining, there was a 4 m thick weathered Marl surrounding the original shaft concret e lining, from the shaft excavation face to the un- weathered Marl. Additionally, it has been assum ed by the author that during the shaft relining process and working tim e, the weat hered Marl zone ext ended outwards slightly. Table 5.5 shows the detailed dim ensions used for the weathered Marl in different relining stages in the m odels. The input m aterial properties for the in situ cast concrete, the polyurethane, the weathered and un- weat hered Marl can be found in Tables 3.10, 3.19 and

172 Chapter 5 Two-Dim ensional Models Materials Original lining Radial thickness in m odels (m ) 1 st relining 2 nd relining 3 rd relining Excavation radius Weathered Marl Un-weathered Marl The rem ainder of the m odel Table 5.5 Dim ensions of the weathered Marl zone in the two- dim ensional m odels I nt erfaces bet w een Concret e Block s For all the shaft relining system s at Boulby m ine, HSC blocks were em ployed, with different m aterials filled between the concret e blocks each tim e. Adhesive m aterials, epoxy resin and cem ent m ortar, were em ployed between the concret e blocks in the first relining and squeezable plywood packs were used in the second and third relinings. These j oints were actually very thin but are im portant to the m echanical behaviour of the whole concrete lining system s. Because of m esh generation lim itations, solid elem ents with som e thickness cannot be used t o represent these m aterials in the num erical m odels. To solve this problem, interface elem ents with appropriate properties have been built into the m odels to be used t o represent the j oints between concret e blocks in the num erical m odelling in this research. Figure 5.20 illustrates t he detailed finite difference m esh in the zone close to the lining in the shaft lining system s. The input properties for the interface elem ents representing these j oints can be found in Tables 3.12 and

173 Chapter 5 Two-Dim ensional Models Original lining 1 st relining Un- weathered Marl Polyurethane Weathered Marl I nt erface Grout I n situ cast concret e Y HSC blocks Y X X 2 nd relining 3 rd relining Grout Grout I nt erface I nt erface HSC blocks Y HSC blocks Y X X Figure 5.20 Detailed finite difference m esh of the shaft linings Modelling Result s and Discussion The num erical m odelling results for the m ine shaft s original lining and relinings are presented and discussed in this section, including the radial closures of each concrete lining system and principal stress conditions in the shaft linings Concret e linings radial closure The radial closures of t he shaft lining system s taken from the num erical m odels are shown in Figure Figure 5.22 shows the ratios of concrete lining s closure with the lining s inner radius of each lining system. 152

174 Chapter 5 Two-Dim ensional Models 10 Lining closure (m m ) All historic cases of concrete lining Figure 5.21 Shaft linings closure from the two- dim ensional m odels Lining closure/ lining inner radius 0.5% 0.4% 0.3% 0.2% 0.1% 0.0% All historic cases of concrete lining Figure 5.22 Ratio of lining s closure with inner radius of each lining I t can be seen that the biggest lining s closure occurred in the second relining a double ring of concret e blocks ( Figure 5.21). The ratio of shaft lining s closure with its inner radius also reached its peak in the second relining ( Figure 5.22). For the newly designed third thicker relining, m odelling results show that its closure and the ratio of its closure with its inner radius were lower than those of the first and second relinings. 153

175 Chapter 5 Two-Dim ensional Models As described in section 5.3, the shaft linings closure should be as sm all as possible to keep the space inside the shaft large enough to allow unaffect ed shaft conveyance operations. I n achieving this, the num erical m odelling results im ply that the single ring concrete blocks lining (the first and third relinings) was m ore effective, leaving m ore space in the shafts. I t was thought by the author that m ore plywood packs between concret e blocks involved in second relining ( double ring concret e blocks lining) m ade the relining m ore flexible in deform ability com pared with the first and third relinings. The m odels also show that the newly designed third relining should perform better than the previous relinings in term s of lining closure. I t can be noticed that t he closures of the shaft relinings were bigger t han that of the original lining. This was because of the filled m aterials between the HSC blocks in the relining, especially the squeezable plywood packs, which were designed to allow som e radial displacem ents of the concret e blocks to im prove the flexibility of the whole lining system s (William s and Auld, 2002) Principal st ress conditions in concrete linings Figure 5.23 shows the principal stress tensors in the num erical m odel for the first relining. I t can be seen that the major principal stress ( 1 ) was a tangential hoop stress, norm al to the radial direction and its m axim um value always occurred at the inner surface of linings as expect ed. The minor principal stress ( 3 ), in the radial direction, usually was very low com pared with the m aj or principal stress ( 1 ), even less than 1% of the m aj or principal stress ( 1 ) at som e positions in the second relining. 154

176 Chapter 5 Two-Dim ensional Models Y X Long: m ajor principal stress Short: m inor principal stress FLAC 2D m esh and zones White lines: I nterfaces Figure 5.23 Principal stress tensors in the first relining The difference between the principal stresses led to a very high deviator stress ( 1-3 ) in the concrete lining in the num erical m odels. The m axim um value of the deviator stress ( 1-3 ) also always occurred at the inner surface of linings. High deviator stress ( 1-3 ) would threat en the stability of the concrete lining system, since higher deviator st ress ( 1-3 ) will bring the Mohr circle closer to the strength envelope in the Mohr- Coulom b failure criteria ( shown in Figure 5.24). 155

177 Chapter 5 Two-Dim ensional Models C = Cohesion = Friction angle C Figure 5.24 Mohr circles and strength envelop in the Mohr- Coulom b failure criteria Figures 5.25~ 5.26 show the m axim um m aj or principal stress 1 and the m axim um deviator st ress ( 1-3 ) in the shaft linings in the num erical m odels and the ratio of the m axim um deviator stress ( 1-3 ) with the corresponding characteristic strength of the HSC in each relining system at the m ine. 100 Stress in linings (MPa) All historic cases of concrete lining Deviator stress Maj or principal stress Figure 5.25 Max. m aj or principal stress 1 and m ax. deviator stress ( 1-3 ) in shaft linings 156

178 Chapter 5 Two-Dim ensional Models 1 Max. deviator stress/ concrete strength All historic cases of concrete lining Figure 5.26 The ratio of the m ax. deviator stress ( 1-3 ) in shaft linings with the corresponding HSC strength As seen from the Figure 5.25, under high ground stress com pression, the m axim um m aj or principal stress 1 and the m axim um deviator st ress ( 1-3 ) in different linings increased with the increasing concret e st rength, reaching the peak in the second relining and decreasing in the newly designed third relining. This result again im plies that the single ring concret e blocks lining (the first and third relinings) was m ore effective than the double rings. Figure 5.26 shows that the m axim um deviator st resses ( 1-3 ) in the shaft s original lining and the first relining were very close to the st rength of the concrete (approxim ately 80% ). However, the ratio of the m axim um deviator st resses ( 1-3 ) with the HSC characteristic strength decreased in the second and third thicker relining in the m odelling, to only approxim ately 46% in the third relining. These m odelling results illustrate 157

179 Chapter 5 Two-Dim ensional Models again that the newly designed third relining should perform better t han the previous relinings in term s of the lower value of m axim um deviator stress ( 1-3 ) in the concrete lining. Figure 5.27 shows the m aj or principal stress 1 contour of the first relining at the m ine in the num erical m odel. Stress concentration zones along the inner surface of the relining at the end tips of the epoxy resin MPa 67.5 MPa 62.5 MPa Y displacem ent X Figure 5.27 Maj or principal stress contour and direction of displacem ent in the first relining I t can be seen that there were st ress concentration zones along the inner surface of the concrete lining at the end tips of the interfaces (epoxy resin in the first relining). A sim ilar phenom enon happened in the m odels of the second and third relining. I t dem onstrat ed that interface m at erials between HSC blocks in shaft relinings im proved the flexibility of the shaft lining system s successfully but caused st ress concentrations at the inner surface of the concret e linings thus decreasing the strength of the whole lining system. 158

180 Chapter 5 Two-Dim ensional Models 5.6 Conclusions This chapter present ed the results of param et ric studies on the effect s of rock properties of the Marl, the extent of weathered Marl and the ground stress field (hydrostatic or not) on the stress and deform ation conditions of the shaft linings through the Marl zone. The possible point loading on the original shaft lining due to unevenly thick polyurethane was t hen sim ulated. Based on the m odelling results of the param etric studies, a series of num erical m odels have been carried out to sim ulate the stress and deform ation conditions in the various historic stages of the lining syst em s em ployed in the Boulby m ine shafts since the tim e that they were sunk. According to the m odelling results presented above, som e conclusions are drawn as follows: 1) I n this research case, t he param etric studies in the m odels im ply that the stability of the original shaft lining was m ost sensitive to the friction angle of the surrounding Marl, and least sensitive to the cohesion of the Marl, because of soft Marl with fairly low cohesion (lower than 1 MPa) in an high ground stress field (nearly 30 MPa). 2) The concept of the plastic zone of the weathered Marl adjacent t o the shaft has been introduced. Assum ptions about the properties of the Marl have been largely based upon the results of t est s conducted at the NCG and the RSM. The extent of the weathered Marl has been increased with each successive relining in num erical m odels indicating likely change to the Marl rock m ass with tim e. 3) The increasing extent of the weathered Marl result ed in bigger deform ation and stress conditions in the shaft s linings. I t is suggest ed 159

181 Chapter 5 Two-Dim ensional Models by the author that 4 m (approxim ately equal to the shaft excavation radius) is a critical value for the extent of the weathered Marl in this research case. This critical value has been used in the later m odels. 4) The non- hydrostatic stress field would result in uneven loading on the circular shaft linings and threat en their stabilities. 5) A possible reason for t he original shaft lining s failure m ay be due t o uneven (point) loading on it, due to uneven thicknesses of backfill m aterial. The cem ent grout backfilled in the relinings transferred high ground pressure to the concret e blocks gradually and facilitated the avoidance of potential uneven loading on the concret e linings. 6) I n the m odels the m axim um m aj or principal stress ( a hoop st ress) and the m axim um deviator stress always occurred at the inner surface of shaft linings as expected. A high deviator st ress would threat en the stability of the concret e lining system. 7) The single ring concret e blocks are a m ore effective lining than the double rings, because m ore plywood packs involved in double rings concret e blocks lining m ade the relining m ore deform able. 8) For the newly designed third thicker relining, the ratio of lining s closure with its inner radius was lower than those of the previous relinings. The ratio of the m axim um deviator stress with the HSC charact eristic strength was only approxim ately 46% in the third relining. These m odelling results illustrate that the newly designed third relining will perform better than the previous ones. 9) Stress concentration zones were evident along the inner surface of the shaft relining at the end tips of the interfaces. This dem onst rated that interface m at erials between HSC blocks in shaft relinings im proved the flexibility of the lining syst em s successfully but these weak j oints decreased the st rength of the whole lining system s. 160

182 Chapter 5 Two-Dim ensional Models Based on the two- dim ensional m odelling results presented in this chapter and conclusions listed in 1~ 9 above, it is thought that the Marl with weak m echanical properties should not be the only reason for the failure of the shaft linings through t his stratum since the m odelling results show that even in the second relining, the lining s closure was less than 0.3% of the lining s inner radius. To find other reasons for the failure of the shaft linings and the effect of surrounding strata on the shaft lining s stability in three- dim ension, three- dim ensional num erical m odels of the shaft linings at Boulby m ine have been conducted, which are presented in detail in the following Chapter

183 Chapter 6 Three-Dim ensional Models CHAPTER 6 THREE- DI MENSI ONAL NUMERI CAL MODELLI NG OF SHAFT LI NI NG SYSTEMS 6.1 I ntroduction The FLAC 3D num erical code has been used to set up three dim ensional m odels for the m ine shaft relining s stability analysis, considering the effect of the shaft inset and the roadway leading to it, on the st ress distribution and subsequent displacem ent of the shaft lining wall above the inset at Boulby m ine. The shaft inset is schem atically shown in Figure 6.1. Foundation Roadway Shaft Foundation Figure 6.1 Schem atic inset of the shaft and the roadway As described in Chapter 5, all num erical m odels in this chapter have been based on the m an shaft, and the solid three- dim ensional elem ents have been utilised to m odel the shaft linings. Due to the lim itation of the finite 162

184 Chapter 6 Three-Dim ensional Models difference m esh in num erical m odels and the difference between the dim ensions of the m ine original shaft lining and relinings through the Marl zone, two m odelling m ethods have been developed in three- dim ensional m odels in this research to sim ulate each stage in the shaft linings. The detailed m odelling m ethodology, m odel configurations and m odelling results are presented and discussed in this chapter. 6.2 Modelling Methodology - A Continuous Model for the Original Lining and All Relining Syst em s As stated and shown in Chapter 5 ( section 5.5, Table 5.4), the original shaft lining and relinings through the Marl zone at Boulby m ine did not have the sam e dim ensions. However, the finite difference m esh in num erical m odels cannot be changed once the program m e starts running. Additionally, joint fillings (epoxy resins, cem ent m ortar and plywood packs) between the concret e blocks m ake the relining syst em s and the num erical m odelling of them m ore com plicated and tim e- consum ing. To solve t hese problem s, t wo m odelling m ethods have been utilised in the threedim ensional m odels to sim ulate each stage in the shaft construction and lining at the m ine. The aim s and particular procedures of these two m ethods are described and discussed as follows. The first m ethod used was to sim ulate the shaft s original lining and all subsequent relinings through the Marl zone continuously in one finite difference m esh. By this m ethod, the effect of the historic changes in the stress field on each shaft lining s stability could be investigated from the shaft s initial construction, original lining installation, the construction of the inset and the roadway leading from the shaft, and subsequent relining phases. However, only one set m esh was involved in this m ethod, in which 163

185 Chapter 6 Three-Dim ensional Models all the relinings through the Marl zone have t he sam e dim ensions as the original shaft lining, which were originally sm aller than their own particular dim ensions. At the sam e tim e, j oints between concret e blocks were not directly included in the num erical m odelling in this m ethod to save num erical calculation tim e. However these existed in all relinings at Boulby m ine: epoxy resin and cem ent m ortar in the first shaft s relining, plywood packs in the second and third shaft s relinings. Due to these differences between the real situation and num erical m odelling of the relinings through the Marl zone, values of the actual m aterial properties for the high strength concret e ( HSC) used in the relinings, which had been obtained through the laboratory t est s conducted at the NCG (shown in Appendix I I I ) cannot be utilised in the num erical m odelling directly. A set of equivalent m aterial properties for the HSC relining syst em is required to be used in the num erical m odelling in the first proposed m ethod. The problem is then how to calculate accurately the equivalent properties for the HSC relining system? Sim ple three- dim ensional m odels were em ployed m odelling the lining alone to obtain the equivalent properties for the shaft s relining syst em s through the Marl zone. The shaft s first relining syst em was taken as an exam ple to dem onstrat e the process of obtaining the equivalent properties for the relining system s. Firstly, a m esh was set up representing three layers of concret e block rings in the first relining system through the Marl zone, using the actual dim ensions of the first relining system shown in Table 5.4. I nterfaces elem ents have been introduced into this m esh to represent the j oints between concrete blocks filled with epoxy resin and cem ent m ortar. This m esh is shown in Figure 6.2. Only a quarter of a circular shaft s lining was 164

186 Chapter 6 Three-Dim ensional Models m odelled since it is a sym m etrical problem. The blue zones in the m esh ( Figure 6.2), representing concrete blocks, were assigned with the act ual material properties (cohesion C, friction angle and tensile strength t ) for the HSC blocks used in the shaft s first relining. The red planes in Figure 6.2 indicate the interface elem ents and were assigned interface properties which have been described in Chapter 3 (section 3.4). Figure 6.2 Mesh in the dim ensions of the first relining system The t op plane and the inner surface of the m odel in Figure 6.2 were free. The bottom plane in Figure 6.2 was fixed in the Z direction. A series of radial com pressive st resses were applied onto the outer surface of t he m odel in Figure 6.2. The boundary planes in Y- Z and X-Z planes in Figure 6.2 were fixed in X and Y directions, respectively. Horizontal displacem ents of several points on the inner surface of the m odel were m onitored during the m odelling calculations. Vertical displacem ents were very sm all com pared with horizontal displacem ents and neglected in this exercise. Each concret e lining s inner radius decreasing ratio ( r/r) plotted against radial loading curve was obtained after a series of m odels of increasing load were com pleted. This is called the TARGET curve ( shown as black line) in Figure

187 Chapter 6 Three-Dim ensional Models Radial loading ( MPa) Concrete liner inner radius decreasing ratio ( r/ r) Target curve: I n Actual Dim., 1 (E,C,F,T) Basic curve: I n Ori. Dim., 1(E,C,F,T) Equivalent curve: I n Ori. Dim., 0.228E, 1.7C, 0.58F, 1T Figure 6.3 Curves obtained in the process of calculating equivalent properties for the shaft s first HSC relining syst em Secondly, another m esh was built up representing three layers of concrete block rings in the shaft s first relining system through the Marl zone, but using the dim ensions of the original lining system shown in Table 5.4, without interface elem ents to represent the j oints between concret e blocks. This m esh is shown in Figure 6.4. The actual m aterial properties ( cohesion c, friction angle and t ensile strength t ) for t he HSC used in shaft s first relining were assigned to the whole m odel. The boundary conditions and displacem ents m onitoring were set to be the sam e as the previous m odel. Another concret e lining s inner radius decreasing ratio - radial loading curve was obtained aft er a series of m odels were com pleted. This was called the BASI C curve (shown as the red line) in Figure

188 Chapter 6 Three-Dim ensional Models Figure 6.4 Mesh in the dim ensions of the shaft s original lining What was needed next was to adjust input m aterial properties for the HSC used in the shaft s first relining in the m odel shown in Figure 6.4, to obtain an EQUI VALENT curve as close to the target curve as possible shown in Figure 6.3. This was achieved through an iterative trial and error process. Only the Mohr- Coulom b properties ( cohesion c and friction angle ) have been changed in this procedure since the num erical test exam ples show that the tensile strength t has little effect on the curve. The input m aterial properties determ ined corresponding to the equivalent curve in Figure 6.3 are called equivalent m aterial properties for the HSC used in the shaft s first relining for the first m odelling m ethod. This process was then repeated for the other relinings. All the equivalent properties for the HSC used in the relining system s at Boulby m ine are shown in Table

189 Chapter 6 Three-Dim ensional Models Young s m odulus (GPa) Cohesion (MPa) Friction angle ( ) Tensile st rengt h (MPa) 1 st relining concrete 7.48 (0.228) (1.7) 27 (0.58) 5.47 (1) 2 nd relining concrete (0.46) (1.7) 25 (0.55) 7.41 (1) 3 rd relining concrete 17.0 (0.52) (1.19) 48 (1.17) 8.31 (1) Note: the values in brackets are the ratios of equivalent properties to the corresponding actual properties. For friction angles, they are the ratios of equivalent tangents to the corresponding actual tangents. Table 6.1 Equivalent input properties for the HSC used in shaft s relining syst em s at Boulby m ine 6.3 Modelling Methodology - I ndependent Models for the Original Lining and All Relining Syst em s The second m odelling m ethod sim ulated all the shaft s relinings through the Marl zone in their own true dim ensions, which m eans that three new finite difference m eshes were required, one for each relining system, and each different from the one for the shaft s original lining. Figures 6.5~ 6.6 show the vertically consistent and non- consistent finite difference m eshes used to m odel the m ine shaft s original lining and the first relining ( the term s consistent and non-consistent are related t o the inner surface of the shaft linings). 168

190 Chapter 6 Three-Dim ensional Models CL Upper Anhydrite Concrete lining and foundation of the interm ediate tower I nner surface Marl Concrete lining (restoration part) Potash Middle Halite Figure 6.5 Consistent m esh for the original lining part of vertical section CL I nner surface Upper Anhydrite Concrete lining and foundation of the interm ediate tower Marl Changed inner radius Cem ent grout 1 st relining Potash Middle Halite Figure 6.6 Non- consistent m esh for the 1 st relining part of vertical section 169

191 Chapter 6 Three-Dim ensional Models By this m ethod, the actual m aterial properties for the HSC used in relinings through the Marl zone were utilised directly in the num erical m odelling. Joints (epoxy resin, cem ent m ortar and plywood packs) between concret e blocks have also been included in the m odels in this m ethod, and are represented by interface elem ents ( shown in Figure 6.7). Model m esh Y X Y X I nterfaces Concrete blocks a. The first relining b. The second relining Figure 6.7 I nterfaces in the relining system s in the num erical m odels Although this m ethod m odels the geom etry accurat ely it is not possible to carry over st resses induced by previous relining, with the stress having to be reset back to its original hydrostatic value for each m odel. The ot her disadvantage of this m ethod is that it is fairly tim e- consum ing due to the large num ber of interface elem ents involved in each shaft relining m odel representing j oints between concrete blocks. Lots of interfaces m ake the num erical calculation very slow. In the three- dim ensional m odel for the first, second and third relining system s at the m ine, there were 205, 146, 152 interface elem ent s, respectively ( 326 interface elem ents will be required in the second relining system if they were set up according to the practical situation. To reduce the num ber of the interface elem ents, 16 layers of concrete rings have been replaced in the m odel by 7 big rings ). 170

192 Chapter 6 Three-Dim ensional Models I t takes approxim ately 24 hours to finish the whole m odel calculation if using the continuous m odel for the original lining and all relining syst em s, with equivalent propert ies for the relining system s. However, nearly 70 hours are taken to finish calculation using the independent m odels for the original lining and all relining system s with all practical dim ensions and interface elem ents. 6.4 Modelling Methodology - Excavat ion and Relining Sequences To avoid a catastrophic collapse failure in the m odel (especially in soft stratum like the Marl) and to m ake the num erical sim ulation as close to the real engineering situation as possible, the excavations of the shaft/ roadway and the relinings through the Marl zone in all num erical m odels were carried out in m ultiple- steps. Shaft excavation (from the top down direction) sequences in different st rata used in the m odelling are shown in Table 6.2. The roadway excavation, m ade after the whole shaft had been fully excavat ed, included four st eps, around 9 m forward each step. Therefore, there are in total 17 excavation steps in all num erical m odels before all relining work. I n which strata Upper Anhydrite Strata thickness in m odel (m ) 1 st step (m ) 2 nd step (m ) rd step (m ) 4 (3 m foundation inclusive) 4 th st ep (m ) Marl Potash th step (m ) Middle Halite (6.8 m foundation inclusive) Table 6.2 Shaft excavation sequences used in the num erical m odels 171

193 Chapter 6 Three-Dim ensional Models The following flow chart (Figure 6.8) shows the detailed operations in excavation m odelling for the Boulby m ine shaft proj ect, which have been designed to take the practical construction situation into account in the num erical m odelling. I n the practical situation, the shaft lining is not installed im m ediately after shaft excavation. During this tim e period before the lining installation, stress relief usually occurs in the surrounding rock near the excavation face (described in Chapter 5, section 5.2). This stress relief in the surrounding rock was sim ulated by running the program to equilibrium ( Solve part in Figure 6.8) after a one st ep excavation but before installing the lining in this step excavation in num erical m odels. First step excavation Solve (Run program to equilibrium ) More excavation I nstall lining for the form er step excavation + Next step excavation Solve (Run program to equilibrium ) No m ore excavation End Figure 6.8 Excavation st eps flow chart in num erical m odels I n all three- dim ensional m odels, the shaft s relining was sim ulated after the excavations of the shaft and roadway, also in m ultiple- steps, but from 172

194 Chapter 6 Three-Dim ensional Models the bott om up direction. I n fact, shafts at Boulby m ine have been relined through the Marl zone in different lengths each tim e. According to the figures quoted by William s and Auld (2002), approxim ately 15.8 m of the original shaft lining through the Marl and Potash strata was replaced in the first relining; in the second relining, approxim ately 11.4 m of the first relining was replaced. I t is reported by the m ine that in the third relining, approxim ately 10.8 m of the second relining will be replaced. Figure 6.9 shows schem atically the Boulby m ine shaft s relining sequences through the Marl zone used in all three- dim ensional m odels. 0.6 m 70.5 Marl stratum top Marl Marl stratum bottom & Potash stratum top Potash stratum bottom & Halite Stratum top Middle Halite HSC1 HSC2 HSC3 Cem ent grout Figure 6.9 Schem atic shaft relining sequences in the continuous m odel 173

195 Chapter 6 Three-Dim ensional Models The horizontal gaps bet ween shaft lining sections in the first and second relining syst em s, have been backfilled with cem ent grout in the m odels instead of being left open during num erical m odelling, to avoid m assive inwards displacem ents of the host rock at these levels. This cem ent grout possessed the sam e properties as that backfilled into the gap between the relining and shaft s excavation face. These horizontal cem ent grout layers divided the first and second relining system s into 3 and 4 sect ions, respectively. These practical engineering sections have been treated as relining steps in all m odels, from the bottom up direction which is the practical construction direction. For the third relining, 18 layers of concrete rings have been evenly separated into 3 st eps, 6 layers each st ep. I n each independent m odel for the shaft relinings, firstly, the original NSC lining was installed through the whole shaft during the shaft excavation from the t op down (though the dim ensions of the lining through the Marl and Potash strata are actually bigger than those of the original NSC lining and interface elem ents have to be kept in the m odel because of the limitation of the finite difference m esh generation). Then the roadway excavation was carried out, followed by the corresponding shaft HSC relining from the bott om up. 6.5 Model Configurat ions Model Dom ain and M esh Design As described in Chapter 5 (section 5.2), due to the num erical m odelling const raints on com puter m em ory and analysis tim e, it is not possible t o cover the whole length of the m ine shaft in the num erical m odels. Artificial boundaries have been placed around the m odel dom ain. Therefore, not all strata beneath the ground surface were included in the m odels. 174

196 Chapter 6 Three-Dim ensional Models The artificial top and bottom boundaries of the whole m odel dom ain in this research were set to be 1075 m and 1155 m beneath the ground surface, respectively. This dom ain contains the Upper Anhydrite stratum (above the Marl), the Marl stratum, the Potash, the Middle Halite and the Middle Anhydrite strata (beneath the Marl), shown in Figure The roadway was driven in the Middle Halite and its roof was located 8 m below the Potash floor. The dim ensions for the whole dom ain are shown in Figure Lat erally, the m odel was about t en tim es the shaft excavation radius. Because this is a sym m etrical problem, only a quarter shaft with inset and one side roadway has been m odelled to save the program m e running tim e and m em ory m Upper Anhydrite 10 m Marl 10 m Potash 2 m Roadway roof Middle Halite 53 m m Middle Anhydrite 5 m Figure 6.10 Geological stratigraphy in the study 175

197 Chapter 6 Three-Dim ensional Models 40 m 40 m Roadway 80 m Shaft Figure 6.11 Num erical m odel dom ain and m esh in the study Dim ensions Used in t he Models I n order to obtain dim ensions used in the num erical m odels, two CAD drawings from Cleveland Potash Ltd. have been referred t o: Manshaft: Vertical Sect ions Through N/ S Axis July 1976 ( ~ ), 176

198 Chapter 6 Three-Dim ensional Models Manshaft: Miscellaneous Sections (JULY 1976) These CAD drawings show that the thickness of the shaft s original concret e lining at Boulby m ine varied through the whole shaft, and was approxim ately 0.61~ 0.75 m thick and at the t op end of this range in the Marl and Potash strata. Polyurethane was backfilled in the gap between surrounding rock and original shaft lining through the Marl and Pot ash strata. Meanwhile, verm iculite powder was used as backfill m aterial in the gap between surrounding rock and concrete lining in the Upper Anhydrite and Middle Halite strata. These gaps were about 0.45 m in thickness. I n later shaft relinings, polyurethane was replaced by the cem ent grout, and the gap between surrounding rock and shaft relinings through the Marl and Potash strata was around 0.4 m in thickness. For sim plification of the three- dim ensional m odels in this research, the shaft s original lining was kept at a uniform thickness, 0.75 m, and 0.4 m was used for the gaps between the concrete linings and the surrounding rock through the whole m odel dom ain. The detailed dim ensions for the original shaft lining and relinings are shown in Table 5.4. The CAD drawings from Cleveland Potash Ltd. also show that the roadway was driven approxim ately 6 m wide and 4.6 m high. I n this study, 6 m wide by 4.5 m high has been used for the dim ension of the roadway in the Middle Halite, with roadway height adjusted a little according to the finite difference m esh density in the num erical m odels. I t was assum ed that the roof of the roadway in the Middle Halite was 8 m beneath the Potash floor Support for t he Roadw ay To support the roadway, it is known by the author that steel sets have been applied at Boulby m ine and it has been assum ed that st eel sets with 177

199 Chapter 6 Three-Dim ensional Models heavy section were utilised. A table of m axim um support pressures (Hoek and Brown, 1980) for various steel set syst em s was referred to. Based on this table and the available inform ation of the steel sets used at the m ine, the m axim um support pressure of these st eel sets is 2.53 MPa when the tunnel radius is 5 m wide and st eel set spacing is 1 m. This was chosen for supporting the roadway s roof and sidewalls in the num erical m odels. At the area near the roadway inset with the shaft, st ronger support was needed because of the anticipated severe stress conditions caused by the m assive excavation. Therefore, for the first 5 m (away from the shaft inner surface) roadway, 3.5 MPa as a support pressure has been used for the roof and a pressure of 2.53 MPa has been applied to the floor. During sim ulating the shaft relinings in the three- dim ensional m odels, m assive upwards displacem ents in the whole roadway floor occurred due to high ground stress in the underlying rock strata. To solve this problem, a 0.5 m thick concret e slab, the sam e m aterial as the original concret e lining in the Marl, has been em ployed for the roadway s floor in num erical m odels Det ailed Engineering Design Modelling To obtain as accurat e num erical m odelling results as possible, an attem pt has been m ade to set up the three- dim ensional m odels for the Boulby m ine s shaft proj ect according to the practical situation. I t is known that the com plete m ine shaft com prises three parts: the t op tower, the interm ediate t ower and the lower t ower. Each tower has a foundation at its base. The foundations of the interm ediate tower in the Upper Anhydrite stratum and the whole m an shaft in the Middle Halite stratum have been included in the m odels. Additionally, the wing walls at the shaft inset level have also been considered in setting up the m odels. The dim ensions and the finite difference m esh for these st ructures are presented in this section. 178

200 Chapter 6 Three-Dim ensional Models Foundations in the Man Shaft The dim ensions of the reinforced foundation of the interm ediate tower can be found in Figure According to the CAD drawing Manshaft: Vertical Sections Through N/ S Axis July 1976, the m an shaft at Boulby m ine is seat ed on a concret e foundation about 1144 m deep beneath the ground surface, i.e. the foundation of the lower tower of the m an shaft. The dim ensions of this foundation can be found in Figure Concrete 25.9 MPa (Min.) 1.37 m Verm iculite Top of foundation ( m ) Reinforced foundation 1.83 m Concrete 25.9 MPa (Min.) Concrete 34.5 MPa (Min.) 1080 m 1082 m Figure 6.12 Foundation of the interm ediate tower - vertical section (Manshaft: Vertical Sect ions through N/ S Axis July 1976) 179

201 Chapter 6 Three-Dim ensional Models 7.88 m 5.48 m Verm iculite m Concrete 25.9 MPa (Min.) m 8.8 m m Figure 6.13 Foundation of the Manshaft - vertical section ( Manshaft: Vertical Sections through N/ S Axis July 1976 ) Because of the lim itations of the rectangular m eshes utilized in the threedim ensional m odels, these two foundations shapes have been approxim ately m odelled using a step- shape in this study. Figure 6.14 shows the whole m odel m esh in the X-Z plane ( vertical section of the shaft) used for this study. 180

202 Chapter 6 Three-Dim ensional Models CL Concrete lining of the interm ediate tower Model top boundary Foundation of the interm ediate tower Concrete lining through the Marl and Potash strata Wing wall Surrounding rock Concrete lining of the lower tower Foundation of the m an shaft Z X Model bottom boundary Figure 6.14 Vertical section of the whole m odel m esh for this study (through X- Z plane) Wing Wall at Shaft I nset Level Wing walls were built at the shaft inset level, shown in Figure 6.15, to resist high stresses caused by the m assive excavation in this area. Figure 6.15 shows that the wing walls are a little thicker than the original shaft lining (0.75 m ) and wider than the outer diam eter of the lining (6.98 m ). The CAD drawings m entioned in section 6.5 show that the wing walls are 0.91 m thick and 12.2 m high. 181

203 Chapter 6 Three-Dim ensional Models East Side Wing wall 7 m 4.9 m 4.9 m 7 m Trench 3 m 3 m West Side Concrete lining 1.83m 3.05m 3.05m 1.83m Figure 6.15 Plan of shaft inset level at m below shaft collar (BSC), the inset of the roadway and the shaft, Manshaft: Miscellaneous Sections (July 1976) Again, the wing walls were sim plified to a step shape because of the lim itation of the rectangular m eshes in this study. Their m odel m esh is shown in plan view in Figure The wing walls m odelled were about 1.2 m thick, 7.8 m total width and 12.2 m high. 182

204 Chapter 6 Three-Dim ensional Models CL Roadway Sidewall Surrounding rock Y Concrete lining X Wing wall Figure 6.16 Plan view of wing walls m odelled in this study (through the X- Y plane) 6.6 Boundary and I nit ial St ress Condit ions Boundary and initial stress conditions in num erical m odels define the in situ state (i.e., the boundary and stress condition before a change or disturbance in the problem state is introduced) of the geom echanical problem. The boundary and initial stress conditions utilised in the threedim ensional m odels are present ed in this section, and shown in Figure

205 Chapter 6 Three-Dim ensional Models Figure 6.17 Boundary conditions in the three- dim ensional m odels in this study As described in Chapter 5 ( section 5.2), the hydrostatic initial stresses were reconst ructed in the num erical m odels according to Equation (5.1). Based on the description in section 6.5, h = 1075 m for the top boundary, and h = 1155 m for the bottom boundary were used in the m odels. The front boundary plane (X- Z plane in Figure 6.17) and back boundary plane were fixed in the horizontal direction ( Y direction). A vertical ground stress MPa, calculated using Equation (2.7), was applied on the top boundary plane. Gradient ground stresses changing with depth were applied to all the elem ents inside the whole m odel dom ain, i.e. σ = σ σ x y = z = = MPa for the elem ents at the top of the m odel dom ain, and 184

206 Chapter 6 Three-Dim ensional Models σ x = σ y = σ z = = the m odel dom ain. MPa for the elem ents at the bottom of 6.7 Material Properties Various m aterials are involved in this research ( the surrounding rock types, concret es, cem ent grout etc.) which have been described in Chapter 5 ( section 5.2). The detailed m ethodology for obtaining the input m aterial properties and the final version of them used in the num erical m odels has been presented and discussed in Chapter 3. I n this section, only the final input m aterial properties used in the m odels are briefly introduced Surrounding Rock As described in Chapter 3 (sections 3.1~ 3.2), to account for the influence of scale and the presence of discontinuities in the rock m ass, strength and stiffness properties of the rock m aterials used in the num erical m odels were obtained by reducing various test results shown in the database in Appendix I using the RocLab software. GSI and triaxial com pressive t ests data were em ployed in the RocLab software Upper Anhydrit e, Middle Potash, Middle Halite and Middle Anhydrite For the Upper Anhydrite, Middle Potash, Middle Halite and Middle Anhydrite, the RMR (Rock Mass Rating) of 89 is assum ed, which indicates the relatively consistent and stable condition of the in situ rock m ass (Hoek et al., 1995; Swift and Reddish, 2005). Then the GSI for these four rock types was calculated by Equation (3.1) described in Chapter 3 ( section 3.1) : GSI = RMR 89 5 = 89 5 = 84. The final reduced rock 185

207 Chapter 6 Three-Dim ensional Models m aterial s Mohr- Coulom b properties with GSI of 84 used in the m odelling can be found in Appendix I I Marl The concept of the plastic zone of weathered Marl, which has been introduced in Chapter 5 (section 5.2), has also been em ployed in the three- dim ensional m odels, with further developm ent. I t has been further assum ed by the author that the plastic zone of weathered Marl was m odified in grade away from the shaft excavation face because of it s exposure in the shaft excavation process and its subsequent relinings. To take account of this condition and variations in the properties of the Marl as the distance from the shaft lining increases, another concept of a graded weathered Marl has been introduced into the three- dim ensional m odels in this research, schem atically shown in Figure Figure 6.19 shows how this concept was sim ulated in num erical m odels Shaft 1 Heavily weathered Marl 2 Slightly weathered Marl 3 Un- weathered Marl (not to scale) Figure 6.18 Conceptual graded plastic zone around the shaft 186

208 Chapter 6 Three-Dim ensional Models Y Shaft lining X Heavily weathered Marl Slightly weathered Marl Un-weathered Marl Figure 6.19 Plan view of graded weathered Marl sim ulated in the three- dim ensional m odels The m odel configurations for the extent of the weathered Marl used in two-dim ensional m odels for the original shaft lining and relinings, which have been described in Chapter 5 (section 5.5), were also em ployed in the three- dim ensional m odels with further developm ent. I n the t hreedim ensional m odels, the developing weathered Marl zone with the shaft relining process and working tim e have been separat ed into two graded parts: heavily weathered Marl and slightly weathered Marl. Table 6.3 shows the detailed dim ensions used for the graded weathered Marl in different shaft lining stages. 187

209 Chapter 6 Three-Dim ensional Models Materials Original lining Radial thickness in m odels (m ) 1 st relining 2 nd relining 3 rd relining Excavation radius Heavily weathered Marl Slightly weathered Marl Un-weathered Marl The rem ainder of the m odel Table 6.3 Dim ensions used for the weathered Marl zone in the threedim ensional m odels For the m aterial properties, sim ilarly as described in Chapter 5, the RSM (2000) test results and Patchet s t est (1970) results after reduction were chosen for the heavily weathered and un- weat hered Marl, respectively. For the Marl, the GSI was estim ated to be a lower value (30) according to previous report ed in situ experience. The m ean values of the above two groups values were chosen for the slightly weathered Marl. Table 6.4 shows the input propert ies for the Marl in the three-dim ensional m odels. Materials Heavily weathered Marl Slightly weathered Marl Unweathered Marl Elastic m odulus (GPa) Poisson's ratio Cohesion (MPa) Friction Angle ( ) Tensile strength (MPa) GSI estim ated N/ A Table 6.4 I nput properties for the Marl used in three- dim ensional m odels Figure 6.20 shows t he Mohr- Coulom b strength envelopes for the laboratory test data and input properties for the highly weathered, slightly weathered and un- weat hered Marl used in the three- dim ensional m odels. 188

210 Chapter 6 Three-Dim ensional Models Drawn from Patchet s tests (1970) Drawn from RSM s tests (2000) Slightly Weathered Marl Un- weathered Marl Heavily Weathered Marl Figure 6.20 Mohr- Coulom b strength envelopes for the Marl in the threedim ensional m odels Concret e and Cem ent Grout Based on all the available laboratory t est results and references in Chapter 3 (section 3.3), input properties for all concrete m aterials used in the num erical m odels for the original shaft lining and relining system s at Boulby m ine can be found in Table The input properties for cem ent grout used in m odels for the relining system s can be found in Table I nt erfaces I t has been described in Chapter 5 ( section 5.5) that different m at erials had been filled between the high strength concret e blocks in each relining at the m ine: epoxy resin and cem ent m ortar in the first relining and squeezable plywood packs in the second and third relinings. Because of limitations of finite difference m esh generation, the interface elem ents with appropriate properties have been built into the num erical m odels in 189

211 Chapter 6 Three-Dim ensional Models this research t o represent these very thin j oints between concrete blocks, which were im portant t o the m echanical behaviour of the whole concret e lining system s. The input properties for the interface elem ents representing these j oints only used in the independent m odels for the shaft relining system s can be found in Tables 3.12, 3.14 and Polyuret hane and Verm iculit e Polyurethane and verm iculite were the backfill m aterials in the gap between the shaft linings and surrounding rocks at Boulby m ine ( introduced in Chapter 2, section 2.6). At the very beginning of the threedim ensional m odelling research, the polyuret hane and verm iculite had been charact erised as pure elastic m aterials in the m odel for the original shaft lining system, as they were in the two- dim ensional m odels in Chapter 5 (section 5.2). Very low stiffness properties com pared with the surrounding rock were assigned to these backfill m aterials, which are shown in Table 6.5. Surrounding rock stiffness E rock ( GPa) Backfill m aterials and stiffness E backfill ( GPa) E rock / E backfill Upper Anhydrite Heavily weathered Marl Verm iculite 1e Polyurethane 5e Potash 6.65 Polyurethane 5e Middle Halite 3.87 Verm iculite 1e Table 6.5 Stiffness com parison between rocks and backfill m aterials These soft backfill m aterials caused som e difficult sim ulation problem s in the early three- dim ensional m odels for the original lining syst em, such as 190

212 Chapter 6 Three-Dim ensional Models unacceptable deform ation and stress conditions. For exam ple, it is known that the soft backfill materials were severely com pressed in the original shaft lining system at Boulby m ine. However, the m odelling results show that m assive deform ation (0.6~ 6.6 m, even bigger than the excavation radius) occurred in the original shaft concret e lining while deform ations of the soft backfill m aterials and surrounding rock were very sm all (0.01~ 0.1 m ) in com parison. Acceptable behaviour of t he backfill m aterials in the early three- dim ensional m odels was only in the Marl stratum, where the polyurethane was severely com pressed by the surrounding rock, from the original 0.45 m to approxim ately 0.1 m, and sm aller closure (approxim ately 0.11 m ) occurred in the original shaft concret e lining. Table 6.5 shows that the surrounding Marl s stiffness was 34 tim es that of the polyurethane which was acceptable in the three-dim ensional m odels, m eanwhile the surrounding rock s stiffness was 17,550 tim es, 1,330 t im es and 3,870 tim es that of the soft backfill m aterials which show huge differences. I t was thought that the soft backfill m aterials between the m uch stiffer m aterials (concrete and surrounding rocks) m ade the behaviour of stiffer concret e lining unrealistically out of cont rol in the three-dim ensional m odels, especially when the stiffness difference between the soft backfill m aterials and surrounding rocks was very high. To avoid these problem s, these soft backfill m aterials have been ignored in the three- dim ensional m odels presented in this Chapter since they were severely com pressed and did not supply any support. 6.8 Modelling Result s A significant num ber of m odelling results have been obtained including deform ation and stress conditions of the surrounding rock and shaft linings, since the whole shaft and the roadway were excavated in m ultiple- steps in 191

213 Chapter 6 Three-Dim ensional Models the m odels. I t is not thought necessary to present all m odelling results in this thesis. Therefore, for both the continuous and independent m odels for the shaft s original lining and relinings, the m odelling results of the following stages are shown and discussed in this section: After the shaft excavation but before the roadway excavation (original lining) After com pletion of the roadway excavation (original lining) After com pletion of the first shaft relining After com pletion of the second shaft relining After com pletion of the third shaft relining The areas that this research focuses on are the part of shaft concrete linings through the Marl and Potash st rata, and the inset of the shaft with the roadway. Therefore, em phasis in this section has been placed on presenting and discussing the m odelling results of deform ation and st ress of the shaft linings above the roadway roof through the Potash and Marl strata, and the inset of the shaft with the roadway Results of the Cont inuous Model Deform ation of the Concrete Lining ( I nner Surface) Several points at different height levels were chosen to m easure the displacem ents of the inner surface of the concrete linings ( points A and B ) and the rock excavation face ( points A and B) in Figure Measurem ents were taken aft er each key stage. 192

214 Chapter 6 Three-Dim ensional Models Figure 6.21 Displacem ent m easure points in the three- dim ensional m odels (not to scale) I t should be noted that the displacem ents after the roadway excavation presented in this section were accum ulated during the shaft and roadway excavations. However, t he displacem ents aft er each relining were j ust the displacem ents generat ed during each relining being carried out. The displacem ents here refer to both those of the inner surface of the shaft linings and of the rock excavation face. Figure 6.22 shows the horizontal displacem ent s ( inwards closure) of the inner surface of the original shaft lining through the Potash and Marl strata after the five different stages in the continuous m odel. Figures 6.23~ 6.24 show the horizontal displacem ent cont our of the original shaft lining through the Potash and Marl strata before and after the roadway excavation. 193

215 Chapter 6 Three-Dim ensional Models Distance above the roadway roof (m ) I n Marl I n Marl I n Marl I n Potash Horizontal displacem ents (m m ) A'- after shaft excav. A'- after roadway excav. B'-after shaft excav. B'-after roadway excav. Figure 6.22 Horizontal displacem ents of the original lining s inner surface 9.2~ 10 m m 10~ 10.1 m m 36.9~ 38 m m 38~ 40 m m 40~ 40.8 m m 6.2 m above the roadway roof in the Potash stratum 9.8 m above the roadway roof in the Marl stratum 123.1~ 125 m m 125~ 130 m m 130~ 135 m m 135~ m m 251~ 260 m m 260~ 270 m m 270~ 277 m m 12.2 m above the roadway roof in the Marl stratum 15.8 m above the roadway roof in the Marl stratum Figure 6.23 Horizontal displacem ent contour of t he original shaft lining before the roadway excavation (Roadway direct ion: Y) 194

216 Chapter 6 Three-Dim ensional Models 6~ 10 m m 10~ 15 m m 15~ 19.3 m m 32.9~ 35 m m 35~ 40 m m 40~ 44.4 m m 6.2 m above the roadway roof in the Potash stratum 9.8 m above the roadway roof in the Marl stratum 123.4~ 125 m m 125~ 130 m m 130~ 135 m m 135~ m m 12.2 m above the roadway roof in the Marl stratum 15.8 m above the roadway roof in the Marl stratum 250.9~ 255 m m 255~ 260 m m 260~ 265 m m 265~ 270 m m 270~ 275 m m 275~ m m Figure 6.24 Horizontal displacem ent contour of t he original shaft lining after the roadway excavation (Roadway direction: Y) I t can be seen from Figure 6.22 that in this continuous m odel, before and after the roadway excavation, the horizontal displacem ents of the original shaft lining was larger in the Marl stratum than in the Potash stratum ( also shown in Figures 6.23~ 6.24). This im plied that the original shaft lining through the Marl strat um suffered m ore severe stress conditions during the excavations of the shaft and roadway. Figure 6.22 shows that the horizontal displacem ents of the points A and B in the original shaft lining were similar ( the repeated black lines) before the roadway excavation. I t can be seen in Figure 6.23 that the horizontal displacem ent contours of the original shaft lining were evenly distributed. This im plied even horizontal deform ation of the original shaft lining before the roadway 195

217 Chapter 6 Three-Dim ensional Models excavation. This is also shown in Figure 6.25 displacem ent vectors of the concret e lining. 6.2 m above the roadway roof in the Potash stratum 9.8 m above the roadway roof in the Marl stratum Y Y X X Colours: Red - original concrete lining, white - surrounding rock Figure 6.25 Horizontal displacem ent vect ors of t he original shaft lining before the roadway excavation After the roadway excavation, different horizontal displacem ents occurred at points A and B in the inner surface of the original shaft lining (red lines in Figure 6.22), especially at the positions close to the roadway. The displacem ent of point A increased and that of point B decreased aft er t he roadway excavation (Figure 6.22). The biggest displacem ent difference between the points A and B was in the Potash st ratum, around 10 m m and 13% of the thickness of the original lining. I t can be seen in Figure 6.24 that the horizontal displacem ent contours of the original lining were unevenly distributed. The original shaft lining through the Marl and Potash strata changed from a circular shape to an ellipse during the roadway excavation, with the m ajor axis parallel to the roadway direction, the m inor axis perpendicular t o the roadway direction. This im plied that the nearby roadway excavation caused uneven horizontal deform ation of t he original lining through t he Marl and Potash strata, shown in displacem ent vect ors of the concret e lining ( Figure 6.26). 196

218 Chapter 6 Three-Dim ensional Models 6.2 m above the roadway roof in the Potash stratum 9.8 m above the roadway roof in the Marl stratum Y (Roadway direction) Y (Roadway direction) X X Colours: Red - original concrete lining, white - surrounding rock Figure 6.26 Horizontal displacem ent vect ors of t he original shaft lining after the roadway excavation This uneven horizontal deform ation of the lining through the Potash and Marl strata also occurred in all relinings, even if the biggest displacem ents difference between the points A and B was fairly sm all (Figure 6.27, 2~ 5 m m ) com pared with the thicknesses of the relinings (about 1~ 1.2 m ). Distance above the roadway roof (m ) I n Marl I n Marl I n Marl I n Potash Horizontal displacem ents (m m ) A'- 1st relining B'- 1st relining A'- 2nd relining B'- 2nd relining A'- 3rd relining B'- 3rd relining Figure 6.27 Horizontal displacem ents of the shaft relinings inner surface 197

219 Chapter 6 Three-Dim ensional Models Figures 6.28~ 6.29 confirm the uneven horizontal deform ation of the shaft relinings through the Marl and Potash strata. The horizontal displacem ents of the inner surface of all the shaft HSC relinings through the Marl and Potash strata were far sm aller than those in the shaft s original NSC lining. This im plied that HSC relinings through the Marl and Potash st rata perform ed far better t han the shaft s original NSC lining, which was expected. The horizontal displacem ent of the inner surface of the shaft s first relining through the Marl and Potash st rata was bigger than those of the second and third relinings (Figure 6.27~ 6.30). This im plied that the later two HSC shaft relinings supplied stronger support than the first relining. Although the shaft HSC relinings through the Marl and Potash strata were also ellipses in plan, their m aj or axes were perpendicular to the roadway direction ( Figures 6.27~ 6.29, displacem ent of point B was bigger than that of point A ), totally contrary to that of the original lining. 1.7~ 2 m m 2~ 4 mm 4~ 6 mm 6~ 8 mm 8~ 8.7 m m 2~ 3 m m 6.2 m above the roadway roof in the Potash stratum 8 m above the roadway roof in the Marl stratum Figure 6.28 Horizontal displacem ent contour of the first relining (Roadway direction: Y) 198

220 Chapter 6 Three-Dim ensional Models < = 1 m m 1~ 1.2 m m 2.3~ 3 m m 3~ 4 mm 4~ 4.2 m m 6.2 m above the roadway roof in the Potash stratum 8 m above the roadway roof in the Marl stratum 1~ 2 m m 9.8 m above the roadway roof in the Marl stratum Figure 6.29 Horizontal displacem ent contour of t he second relining (Roadway direction: Y) < = 1 m m 6.2 m above the roadway roof in the Potash stratum Figure 6.30 Horizontal displacem ent contour of t he third relining (Roadway direction: Y) 199

221 Chapter 6 Three-Dim ensional Models I t can be noticed from Figures 6.22~ 6.24 and Figures 6.27~ 6.30 that before the shaft relinings through the Marl and Potash st rata, m axim um horizontal displacem ent occurred in the inner surface of the original shaft lining through the upper part of the Marl stratum. However, contrary t o this, during the shaft relining stages, the m inim um horizontal closure occurred in the inner surface of the shaft HSC relinings through the upper part of the Marl stratum. This was because of different m odelling directions during the shaft excavation and relinings through the Marl and Potash strata. I t was from the t op down during the shaft excavation, as the original shaft lining through the upper part of the Marl stratum was installed at the first step. However, it was from the bottom up during the relinings, as the shaft HSC relinings through the upper part of the Marl stratum were installed at the last step. The horizontal displacem ents of the rock excavation face were 5~ 35 m m bigger than those of the inner surface of the shaft linings through the Marl and Potash st rata after five different stages in the continuous m odel. This was expect ed during the m odelling since the linings were com pressed under severe ground st ress, especially in the original shaft lining system through the Marl stratum (approxim ately 35 m m horizontal displacem ents difference between the rock excavation face and the inner surface of t he original lining). Due t o the vertical stress acting on the m odel and lining weight during the shaft and roadway excavations, the whole shaft linings and surrounding rock m oved downwards approxim ately 70 m m. The whole Marl stratum had been com pressed during the shaft excavation. The roadway excavation resulted in m ore downwards m ovem ents in the roadway roof area (up to 85 m m ) and som e upwards m ovem ents (approxim ately

222 Chapter 6 Three-Dim ensional Models m m ) in the roadway floor area due to the vertical stress relief caused by the roadway excavation. The horizontal displacem ent of the rock excavation face and the vertical displacem ents at m easured points show sim ilar t rends with Figure 6.22 and Figure 6.27, respectively. Before the roadway excavation, even deform ation ( horizontal and vertical) occurred in the circular original shaft lining; after the roadway excavation and relinings, uneven deform ation ( horizontal and vertical) occurred in the circular original lining and relinings through the shaft inset adjacent strata, especially the roadway im m ediate roof and floor horizon in this m odel Stress Conditions Figures 6.31~ 6.35 show the vertical stress ( z ) contours of the whole m odel aft er different stages in the continuous m odel. I t should be rem em bered that the negative values m ean com pressive st ress and positive values m ean tensile stress in these figures. I t can be seen from Figures 6.31~ 6.35 that in this continuous m odel: The shaft excavation resulted in a vertical stress relief zone in the surrounding rock in the Marl and Potash strata, which becam e bigger during the shaft relinings being carried out. The roadway excavation led to: a) the vertical stress concentration in the roadway roof corner and floor corner, and b) vertical stress relief in the roadway im m ediate roof and floor within the Middle Halite stratum and in the original shaft lining (Figure 6.32). During relinings, significant tensile stress developed in the relinings in the Marl and Potash strata (Figure 6.33) and wing wall (Figures 6.34~ 6.35). At the sam e tim e, the vertical stress concentration in the 201

223 Chapter 6 Three-Dim ensional Models roadway roof corner and floor corner also becam e m ore severe with the relining being carried out. Upper Anhydrite Marl Potash Middle Halite Middle Anhydrite ~ -30 MPa -30 ~ -20 MPa -20 ~ -10 MPa -10 ~ 0 MPa 0 ~ 1.78 MPa Figure 6.31 Vertical stress z in the original lining after the shaft excavation 202

224 Chapter 6 Three-Dim ensional Models Upper Anhydrite Marl Potash Middle Halite Middle Anhydrite ~ -50 MPa -50 ~ -40 MPa -40 ~ -30 MPa -30 ~ -20 MPa -20 ~ -10 MPa -10 ~ 0 MPa 0 ~ 3.12 MPa Figure 6.32 Vertical stress z in the original lining after the roadway excavation 203

225 Chapter 6 Three-Dim ensional Models Upper Anhydrite Marl Potash Middle Halite Middle Anhydrite ~ -50 MPa -50 ~ -40 MPa -40 ~ -30 MPa -30 ~ -20 MPa -20 ~ -10 MPa -10 ~ 0 MPa 0 ~ 4.93 MPa Figure 6.33 Vertical stress z in the first relining 204

226 Chapter 6 Three-Dim ensional Models Upper Anhydrite Marl Potash Middle Halite Middle Anhydrite ~ -50 MPa -50 ~ -40 MPa -40 ~ -30 MPa -30 ~ -20 MPa -20 ~ -10 MPa -10 ~ 0 MPa 0 ~ 6.36 MPa Figure 6.34 Vertical stress z in the second relining 205

227 Chapter 6 Three-Dim ensional Models Upper Anhydrite Marl Potash Middle Halite Middle Anhydrite ~ -50 MPa -50 ~ -40 MPa -40 ~ -30 MPa -30 ~ -20 MPa -20 ~ -10 MPa -10 ~ 0 MPa 0 ~ 7.57 MPa Figure 6.35 Vertical stress z in the third relining 206

228 Chapter 6 Three-Dim ensional Models Again, points A and B shown in Figure 6.21 were used to m easure the principal stresses conditions of the concrete linings in the strata near to the shaft inset. Tables 6.6~ 6.7 show the principal stresses m easurem ent results from this continuous m odel. Measure points position above the roadway roof I n strata Before the roadway excavation (MPa) After the roadway excavation (MPa) After 1 st relining (MPa) After 2 nd relining (MPa) After 3 rd relining (MPa) (m ) A B A B A B A B A B Marl Marl Marl Potash Table 6.6 Maj or principal stress 1 of the shaft linings inner surface Measure points position above the roadway roof I n strata Before the roadway excavation (MPa) After the roadway excavation (MPa) After 1 st relining (MPa) After 2 nd relining (MPa) After 3 rd relining (MPa) (m ) A B A B A B A B A B Marl Marl Marl Potash Table 6.7 Minor principal stress 3 of the shaft linings inner surface I t should be not ed that in this continuous m odel, equivalent properties (shown in Table 6.1) were utilised for the HSC in all shaft relinings. The equivalent Young s m odulus of the HSC used in the m odel was only 0.23~ 0.52 that of the HSC obtained from t he laboratory t ests. This resulted in equivalent principal stresses in the shaft relinings (colum ns in 207

229 Chapter 6 Three-Dim ensional Models light gray in Tables 6.6~ 6.7), which were fairly low com pared with those in the original shaft lining (colum ns in light blue and green). Although they were not the practical principal stresses developed in the shaft relinings in the m odel, they show the developing principal stress t rends during the shaft relining being carried out in the m odel. I t can be seen clearly from Tables 6.6~ 6.7 (colum ns in light blue) that the principal stresses in the original shaft lining at points A and B in this m odel were approxim ately equal to each other at the sam e vertical level through the Marl and Potash strata before the roadway excavation, i.e. A B, n= 1, 3 This m odelling result im plied that the original shaft lining was under an even loading condition before the roadway excavation in this m odel. This is also shown in Figure B B ~ -40 MPa -40 ~ -35 MPa -35 ~ -30 MPa -30 ~ -25 MPa -25 ~ -20 MPa -20 ~ MPa Principal stress vectors A ~ -4 MPa -4 ~ -2 MPa -2 ~ MPa Y Principal stress vectors X A (a) Minor principle stress 3 (b) Maj or principle stress 1 Figure 6.36 Principal stress contours for the original lining: 9.8 m above the roadway roof in the Marl stratum, before the roadway excavation 208

230 Chapter 6 Three-Dim ensional Models Figure 6.36 shows that there was a large difference between the m aj or principal stress 1 and the m inor principal stress 3 in the concret e lining in this m odel, and the inner surface of the concrete lining suffered higher com pression stress com pared with the outer surface of the lining. The directions of the principal stresses in the concrete lining are also shown in Figure 6.36: the m inor principal stress 3 was a hoop st ress ( long red lines), the m ajor principal stress 1 was in the radial direction ( short red lines, perpendicular with the long red lines). However, the roadway excavation changed the even loading condition of the original shaft lining and relinings, which can be seen from Tables 6.6~ 6.7 (colum ns in light green and gray). St ress m easurem ent results in Tables 6.6~ 6.7 show t hat the roadway excavation caused a reduction of the m inor principal stress 3 at point A and an increasing of the m inor principal stress 3 at point B in the original shaft lining, which was a severe one through the bottom of the Marl and the Potash strata. The m inor principal stress 3 difference between points A and B was especially large in the original shaft lining through the bott om of the Marl, the Potash strata and the roadway im m ediate roof and floor. The 3 at point B was up to 182% the 3 at point A at the position of 6.2 m above the roadway roof in the Potash st ratum. The 3 at point B was approxim ately 126% the 3 at point A at the position of 9.8 m above the roadway roof in the Marl stratum. I n the shaft relinings, the differences between the m inor principal stresses ( 3, colum ns in light gray in Table 6.7) at points A and B through both the Marl and Potash strata were also significant, e.g. in the first relining, 209

231 Chapter 6 Three-Dim ensional Models the 3 at point B was up to 167% the 3 at point A at the position of 6.2 m above the roadway roof in the Potash stratum. The 3 at point B was approxim ately 102% the 3 at point A at the position of 9.8 m above the roadway roof in the Marl stratum. After the roadway excavation, the principal stresses in the original lining and relinings at points A and B in this m odel do not equalise to each other anym ore at the sam e vertical level through the Marl and Potash strata. i.e. A B, n= 1, 3 This uneven distribution of the principal stresses in the shaft linings im plied that the original shaft lining and relinings were under an uneven loading condition due to the shaft inset with the roadway in this m odel which is also shown in Figure B B ~ -40 MPa -40 ~ -35 MPa -35 ~ -30 MPa -30 ~ -25 MPa -25 ~ -20 MPa -20 ~ MPa Principal stress vectors A ~ -11 MPa -11 ~ -10 MPa -10 ~ -9 MPa -9 ~ -8 MPa -8 ~ -7 MPa -7 ~ MPa Y (Roadway direction) X A a. Original lining after the roadway excavation b. 3 rd relining Figure 6.37 Minor principal stresses 3 contour of the shaft linings: 9.8 m above the roadway roof in the Marl stratum I t can be noticed from Figure 6.37 that the uneven stress condition (the position of the m axim um absolute value of the 3) in the shaft HSC relining is different from that in the original shaft NSC lining through the 210

232 Chapter 6 Three-Dim ensional Models Marl and Potash strata. This difference is sim ilar to the direction difference of the ellipses m aj or axis between the original lining and relinings, which has been described in section These m odelling results need validation with the in situ observation Discussion I n this continuous m odel, the deform ation (horizontal and vertical) and stress conditions in the original shaft lining were evenly distributed before the roadway excavation. However, these conditions disappeared after t he roadway excavation in the num erical m odel. The uneven deform at ion (horizontal and vertical) and uneven distribution of the principal stresses (especially the m inor principal stress 3) of the original lining through the Marl and Potash strat a caused by the roadway excavation was quite significant: approxim ately 15 m above the roadway roof and 15 m below the roadway floor in this continuous m odel, including the Marl, the Pot ash and the Middle Halite strata (the roadway im m ediate roof and floor). However, for the shaft HSC relinings, the extent of the uneven deform ation and uneven distribution of the principal stresses caused by the existence of the nearby roadway was not as m uch as that of the original shaft lining. The existence of the roadway has m ore effect on the deform ation and st ress conditions of the shaft relinings through the Potash and the bottom of the Marl strata (less than 10 m above the roadway roof). That is to say, the uneven deform ation and uneven st ress distribution conditions in the shaft relinings through the Marl and Potash strata were not as severe as those in the original shaft NSC lining. This was expect ed, as the HSC relinings should perform bett er than the NSC lining at Boulby m ine. Figure 6.30 shows that even in the Potash st ratum, the shaft HSC 211

233 Chapter 6 Three-Dim ensional Models lining suffered little uneven horizontal deform ation, which im plied that the third shaft relining would perform better than the previous shaft relinings. These uneven deform ations ( schem atically shown in Figure 6.38) and uneven stress conditions in the shaft linings in the continuous m odel were caused by uneven loading on the annular concret e linings from the surrounding rock. This uneven loading (vertical and horizontal) can bring high shear and t ensile stress threatening the stability of the circular concret e structures, as shown in Figure 2.16 in Chapter 2, and m assive shear failure in the shaft s second relining system. Roadway position and direction Concret e lining Deform ed concret e lining Roadway position and direction Figure 6.38 Schem atic horizontal closure of the shaft lining through the Marl and Potash strata in the m odel The uneven loading originated from the rock surrounding the shaft. That is to say, the st resses and failure conditions of the rock surrounding the shaft controlled the shaft linings stability. The roadway caused severe uneven stresses and failure conditions of the surrounding rock ( shown in 212

234 Chapter 6 Three-Dim ensional Models Figure 6.39), leading to uneven loading on the shaft concret e linings through the nearby st rata in this m odel, especially the weak Marl and the Potash. Therefore, the shaft concrete linings through the Marl and Potash strata suffered the m ost severe displacem ent in this m odel. Original lining, after shaft excavation Original lining, after roadway excavation Y X Y X After 1 st relining After 2 nd relining Roadway direction Y X Y X After 3 rd relining Y X n: Now, active at the final state p: Past, at an historical earlier state Figure 6.39 Plastic states of the shaft linings at 7 m above the roadway roof in the Potash st ratum (the inside two rings are the shaft linings) 213

235 Chapter 6 Three-Dim ensional Models Results of the I ndependent Models Deform ation of the Concrete Lining ( I nner Surface) I n these independent m odels, fairly low displacem ents occurred in the shaft relinings (less than 0.5 m m, take the m odel of the first relining as an exam ple shown in Figure 6.40), which were ext rem ely low when com pared with the thicknesses of the shaft linings (0.75~ 1.2 m ) and displacem ents of the shaft NSC/ HSC linings in the continuous m odel (in Figures 6.22, 6.27). This was very difficult to understand since the shaft lining system s were under very high ground st ress field (around 30 MPa) and severe underground in situ conditions (very soft surrounding rock m ass - Marl). Model m esh Concret e lining Cem ent grout Max. dis.: 0.15 m m Marl Potash Middle Halite Figure 6.40 Displacem ent vect ors of the first relining in independent m odel (Roadway direction: Y) 214

236 Chapter 6 Three-Dim ensional Models Deform ation and St ress Conditions of the I nterfaces The obtained shear displacem ents of the interfaces between concret e blocks were even lower ( less than 0.01 m m ) in the shaft HSC relinings through the Marl and Potash strata. Shear and norm al stresses in the interfaces in the independent m odels for the first and third relinings were very low ( MPa~ 0.01 MPa) com pared with the stress in the surrounding rock (around 30 MPa. However, the shear and norm al stresses in the interfaces in the independent m odel for the second relining shown in Figures 6.41~ 6.42 cannot be ignored. Marl Potash 0~ 1 MPa 4~ 5 MPa 9~ 10 MPa 12~ 13 MPa Model m esh Concret e lining Cem ent grout Figure 6.41 I nterface norm al stress in the second relining in independent m odel (Roadway direction: Y) ( For clarity, only interfaces at the bottom part of relining are shown, since stress in other interfaces are very low, between 0~ 1 MPa) 215

237 Chapter 6 Three-Dim ensional Models Marl Potash 0~ 0.5 MPa 0.5~ 1 MPa 1~ 1.5 MPa 1.5~ 1.53 MPa Model m esh Concret e lining Cem ent grout Figure 6.42 I nterface shear stress in the second relining in independent m odel (Roadway direction: Y) ( For clarity, only interfaces at the bottom part of relining are shown, since stress in other interfaces are very low, between 0~ 0.5 MPa) At the bottom part of t he HSC lining in the Pot ash stratum, the shear and norm al stresses in the interfaces were up to 13 MPa and 1.5 MPa, respectively. High shear and norm al stresses that developed in the interfaces in the second relining were thought to threat en the stability of the whole relining system. Figures 6.43~ 6.45 show the interfaces shear failure conditions in the inner surface of the shaft HSC linings in each independent m odel. I t can be seen that m assive interface shear failure occurred in the second and third relinings through the Marl and Potash strata during the num erical 216

238 Chapter 6 Three-Dim ensional Models calculation in the three- dim ensional m odels. Less historical shear failure occurred in the first relining due to epoxy resin s higher adhesive st rength with the concret e blocks com pared with the plywood packs (Tables 3.12 and 3.17). However, at the final equilibrium state, som e interface shear failure stayed active only in the second relining. These m odelling results im plied again that the single ring of concrete blocks as shaft lining (the first and third relinings) was m ore effective than the double rings of concret e blocks (the second relining). Model m esh Concret e lining Cem ent grout Marl Potash Middle Halite Figure 6.43 I nterface shear failure in the first relining in independent m odel (Roadway direction: Y) 217

239 Chapter 6 Three-Dim ensional Models Model Concret e lining Cem ent Marl Potash Shaft lining inner surface Surface between double rings Figure 6.44 I nterface shear failure in the second relining in independent m odel (Roadway direction: Y) Model m esh Concret e lining Marl Potash Figure 6.45 I nterface shear failure in the third relining in independent m odel (Roadway direction: Y) 218

240 Chapter 6 Three-Dim ensional Models Stress Condition of the Concret e Lining Figures 6.46~ 6.48 show the vertical stress z contours of the whole m odel dom ain after relining in each independent m odel. I t can be seen that the independent m odels for shaft relinings show very consistent m odelling results with the continuous m odel for shaft relinings (Figures 6.33~ 6.35), which have been described in the early part of the section and are not repeat ed in this section. However, for the stress relief zone in the Marl and Potash strata caused by the shaft excavat ion and subsequent original lining and relinings, its extent in the independent m odels for shaft relinings was bigger than that in the continuous m odel. This can be found by a com parison of t he st ress zones ( - 20~ - 10 MPa) between Figures 6.33&6.46, 6.34&6.47, 6.35&

241 Chapter 6 Three-Dim ensional Models Upper Anhydrite Marl Potash Middle Halite Middle Anhydrite ~ -50 MPa -50 ~ -40 MPa -40 ~ -30 MPa -30 ~ -20 MPa -20 ~ -10 MPa -10 ~ 0 MPa 0 ~ 8.23 MPa Figure 6.46 Vertical stress z in the first relining in independent m odel 220

242 Chapter 6 Three-Dim ensional Models Upper Anhydrite Marl Potash Middle Halite Middle Anhydrite ~ -40 MPa -40 ~ -30 MPa -30 ~ -20 MPa -20 ~ -10 MPa -10 ~ 0 MPa 0 ~ 4.12 MPa Figure 6.47 Vertical stress z in the second relining in independent m odel 221