Small and medium scale direct shear test of the Bremanger sandstone rockfill

Transcription

1 AES/GE/10-14 Small and medium scale direct shear test of the Bremanger sandstone rockfill July-2010 Xiaoshan Sun

2 Title : Small and medium scale direct shear test of the Bremanger sandstone rockfill Author(s) : Xiaoshan Sun Date : July 2010 Professor(s) : dr.ir. D.J.M. Ngan-Tillard Supervisor(s) : dr.ir. D.J.M. Ngan-Tillard TA Report number : AES/GE/10-14 Postal Address : Section for Geo-engineering Department of Applied Earth Sciences Delft University of Technology P.O. Box 5028 The Netherlands Telephone : (31) (secretary) Telefax : (31) Copyright 2010 Section for Geo-engineering All rights reserved. No parts of this publication may be reproduced, Stored in a retrieval system, or transmitted, In any form or by any means, electronic, Mechanical, photocopying, recording, or otherwise, Without the prior written permission of the Section for Geo-engineering

3 Acknowledgement First, I greatly appreciate the help of my supervisor dr. ir. D. Ngan-Tillard (CiTG) who advised and encouraged me during the compilation of this thesis. I would like to thank dr. R.B.J.Brinkgreve for providing Plaxis 10 Beta version software to me. I would also like to thank A. Mulder and H. de Visser for helping me install the experimental equipments and M. van der Linden for conducting the medium size shear box tests with me. It was a very enjoyable experience working with all of you. Last but not least, I would like to thank my parents, my family, my boyfriend, all of my friends for everything they have done for me, especially for their support during my study.

4 Table of content 1 Introduction Literature review Factors affecting the shear strength of rockfill The direct shear test Factors affecting shear strength Scale effects, determination of the maximum particle size Scale effect Determination of the maximum particle size Shear strength models Apparatus, material and test procedure Experiment apparatus Small size shear box (100mm*100mm*40mm) Medium size shear box (500mm*500mm*400mm) Rockfill material Experiment procedure Small size shear box experiment procedure Medium size shear box experiment procedure Overview of experiments Experimental results and discussion Small size direct shear box experiment results General trends Secant friction angle and dilatancy angle Strain at failure Factors affecting shear behavior Stress-dilatancy Particle breakage Repeatability Medium size direct shear box experiment results General trends

5 4.2.2 Secant friction angle and dilatancy angle Strain at failure Factors affecting shear behavior Particle breakage Repeatability Comparison and discussion The general trend Secant friction angle and dilatancy angle at failure Factors affecting shear behavior Rockfill shear strength model Introduction Mohr-Coulomb Model Introduction Data Process Method Result Power Curve Strength Model Introduction Data process method Result Hoek -Brown Model Introduction Data process method Result Barton Model Introduction Data process method Result Comparison and conclusion of modeling results Plaxis modeling of the crane walk-way Introduction Method

6 6.3 Result Conclusions and recommendations Conclusions Recommendations Reference Appendix AppendixⅠ: Hoek-Brown criterion detail curve fitting information

7 Table of tables Table 2.1: The comparison between the direct shear test and the triaxial test Table 2.2: Summary of factors affecting the friction angle (Douglas, 2002) Table 2.3: Various shear strength model for rockfill (Douglas, 2002). In addition to Douglas models, the Hoek Brown model and Lee s model are also included Table 2.4: Shear strength of heavily compacted sample of rockfill at low normal stress (Charles & Watts, 1980) Table 2.5: Shear strength parameters for some fills when using power curve strength model (Charles, 1991). I D is the rockfill relative density Table 2.6: Shear strength parameters for some fills when using power curve strength model (Estaire & Olalla, 2005) Table 3.1: Properties of the Bremanger sandstone Table 3.2: The category name, category symbol, test detailed information of the small and medium shear box tests Table 4.1: The internal friction angle of six categories when using three low normal stress and all six normal stress of the small size shear box test Table 4.2: The uniformity coefficient of category NB, MS and MB Table 4.3: The influence of particle size, normal stress, density and uniformity coefficient on shear strength, friction angle and dilatancy of the small shear box test 45 Table 4.4: The internal friction angle of the medium size shear box test Table 4.5: The influence of particle size and density on shear strength, internal friction angle and volume expansion of the medium size shear box test Table 4.6: The influence of particle size, density and normal stress on shear strength, internal friction angle and volume expansion of both the small and medium size shear box test Table 5.1: The overview of four model application condition Table 5.2: The value A, B and R^2 when using the parabolic expression modeling Table 5.3: The influence of UCS, density and maximum particle size on value A Table 5.4: The UCS, m i and D for the Bremanger sandstone rockfill Table 5.5: The best fit GSI and corresponding friction angle and cohesion calculated by RocData Table 5.6: The influence of maximum particle size and density on GSI value Table 5.7: The calculated R, B and R 2 value from the experimental result

8 Table 5.8: The d 50 and estimated S value from Barton's figure Table 5.9: The general comment on the models Table 6.1: Detailed input data for the dense sand and the Bremanger sandstone rockfill material property Table 6.2: The safety factor and total displacement of the design

9 Table of figures Figure 1.1: The layout of the crane walk-way design (Krane, 2010) Figure 2.1: Estimated variation of under toe and beneath downstream slope of dam (Barton & Kjaernsli, 1981). The triangular shape of the slope is associated to a triangular distribution of the vertical stress due to self-weight Figure 2.2: The explanation of normal stress, shear stress and displacement Figure 2.3: Estimate of Geological Index GSI based on geological descriptions (Hoek & Brown, 1997) Figure 2.4: Selection of Geological Strength Index (Marinos et al., 2006) Figure 2.5: Method of estimating equivalent roughness (R) based on porosity of rockfill (Barton & Kjaernsli, 1981) Figure 2.6: Method of estimating equivalent strength (S) of rockfill based on uniaxial compression strength and d 50 particle size (Barton & Kjaernsli, 1981) Figure 2.7: Principle of tilt test for rock fill (Barton, 2008). Note the expression of R, the equivalent roughness for the rock fill in 5 derived by applying the Barton s model to the tilt test conditions. is the tilt angle and σ no, the normal stress on the sliding surface Figure 3.1:The small size shear box at laboratory of Geo-engineering department of TU Delft (Left: 4.5 kn loading ring; Right: 20 kn load cell) Figure 3.2: General arrangement of small shear box apparatus (Mulder & Verwaal, 2006) Figure 3.3: The TU Delft medium size shear box Figure 3.4: Sketch of the medium size shear box (van der Linden, 2010) Figure 3.5: Movement of the upper box caused by particle trapped between the box. Problem solved by inserting wooden blocks between the upper shear box and the steel frame Figure 3.6: Tilted dead weight Figure 3.7: Manual compaction in the medium scale shear box Figure 4.1: Horizontal displacement vs. corrected shear stress of small shear box test Figure 4.2: Horizontal displacement vs. vertical displacement of small shear box test Figure 4.3: Correct normal stress vs. the secant friction angle at failure Figure 4.4: Corrected normal stress vs. dilatancy angle at failure

10 Figure 4.5: Corrected normal stress vs. strain at failure Figure 4.6: Dilatancy vs. stress ratio of the small shear box test Figure 4.7: Particle breakage at different normal stress Figure 4.8: The stress-strain and dilatancy figure of three specimens under the same test condition Figure 4.9: The stress-strain, vertical - horizontal displacement, dilatancy-stress ratio figures for the medium size shear box test Figure 4.10: Corrected normal stress vs. the secant friction angle at failure of the medium size shear box test Figure 4.11: Corrected normal stress vs. dilatancy angle at failure of the medium size shear box test Figure 4.12: Corrected normal stress vs. strain at failure Figure 4.13: Particle breakage of the medium size shear box (left: the position where the rock was caught; right: the broken rock) Figure 4.14: Corrected normal stress vs. the secant friction angle at failure Figure 4.15: Corrected normal stress vs. the dilatancy angle at failure Figure 4.16: The internal friction angle of category NS, NB and M Figure 5.1: The shear and normal stress relationship and the internal friction angle of the small shear box test Figure 5.2: The shear and normal stress relationship and the internal friction angle of the medium size shear box test Figure 5.3: The relationship between the GSI value and maximum particle size (category NS, NB and M2) Figure 5.4: Corrected normal stress vs. basic friction angle at failure Figure 5.5: Pictures of the small shear box (left: 3.35<P<6.30 mm; right: 3.35<P<6.30mm) Figure 5.6: Pictures of the medium shear box (left: 31.5<P<50 mm; right: 31.5<P<80 mm) Figure 5.7:Estimating the equivalent roughness R (blue line for small shear box; red line for medium size shear box) (Barton & Kjaernsli, 1981) Figure 5.8: Estimating S/UCS reduction factors for estimating S (Barton & Kjaernsli, 1981) Figure 6.1: The layout of the crane walk-way design Figure 6.2: The dimension and detailed information of the design

11 Figure 6.3: GSI value vs. safety factor of the crane walk-way design Figure 6.4: The total displacement when the normal load is in the middle and GSI equal to Figure 6.5: The vertical effective stress when the normal load is in the middle and GSI equal to Figure 6.6: The total displacement when the normal load is at the outer edge and GSI equal to Figure 6.7: The vertical effective stress when the normal load is at the outer edge and GSI equal to Figure 9.1: The power trend line curve of normal-shear strength value from category NS test data Figure 9.2: The best fit curve with category NS test data when using Hoek-Brown criterion Figure 9.3: The power trend line curve of normal-shear strength value from category NB test data Figure 9.4: The best fit curve with category NB test data when using Hoek-Brown criterion Figure 9.5: The power trend line curve of normal-shear strength value from category HS test data Figure 9.6: The best fit curve with category HS test data when using Hoek-Brown criterion Figure 9.7: The power trend line curve of normal-shear strength value from category HB test data Figure 9.8: The best fit curve with category HB test data when using Hoek-Brown criterion Figure 9.9: The power trend line curve of normal-shear strength value from category MS test data Figure 9.10: The best fit curve with category MS test data when using Hoek-Brown criterion Figure 9.11: The power trend line curve of normal-shear strength value from category MB test data Figure 9.12: The best fit curve with category MB test data when using Hoek-Brown criterion Figure 9.13: The power trend line curve of normal-shear strength value from category M1 test data

12 Figure 9.14: The best fit curve with category M1 test data when using Hoek-Brown criterion Figure 9.15: The power trend line curve of normal-shear strength value from category M2 test data Figure 9.16: The best fit curve with category M2 test data when using Hoek-Brown criterion Figure 9.17: The power trend line curve of normal-shear strength value from category M3 test data Figure 9.18: The best fit curve with category M3 test data when using Hoek-Brown criterion

13 Abstract This study focuses on the shear strength of the Bremanger sandstone used as rockfill for a crane walkway. The rockfill was tested in a small (100*100*40mm) and a medium scale (500*500*400mm) direct shear boxes to quantify the effect of particle size, packing density and uniformity, specimen size, and normal stress on shear strength. The laboratory data were fitted with four different models (Mohr-Coulomb Model, Power Curve Strength Model, Hoek-Brown Model and Barton Model). The Hoek-Brown model, initially developed for rock masses, was found to be suitable for rockfills. Finally, a crane walk-way was simulated with Plaxis 10 Beta version to assess its stability. 11

14 1 Introduction Rockfill is generally produced at quarries and increasingly used as a fill or base material for offshore structures, dams, road embankment and foundation for buildings (Lee et al., 2009; Charles, 1991). Therefore, it is indispensable to make precise research on the behavior of rockfill materials. The two most important factors influencing the design of a rockfill structure are the shear strength and the compressibility of the rockfill material (Marachi et al., 1972). However, it is difficult to conduct shear tests on rockfill material mostly because it requires using large-scale equipments and applying high stresses to cause failure in the specimen. As a result, the small or medium size equipments are generally used. There are two major problems that should be considered: 1) determination of the maximum particle size, and 2) the scale-effect of the equipment (Asadzadeh & Soroush, 2009). Previous studies indicated that the behavior of rockfill materials depends on factors such as normal effective stress, particle size, density, uniformity coefficient, maximum particle size, particle roughness, particle crushing strength, particle shape and moisture content. Figure 1.1: The layout of the crane walk-way design (Krane, 2010) In this study, a small size shear box (100mm*100mm*40mm) and a medium size shear box (500mm*500mm*400mm) were employed to determine the shear strength properties of crushed sandstone from Dyrstad, Bremanger in Norway for constructing a cobble beach and a crane walk way in the Maasvlaakte 2 project (MV2)of the Netherlands (Figure 1.1). The cobble beach will form a transition between the soft dunes and the rigid seawater breaker protecting the MV2 and the crane is used to put in place the 40 tonne armourstones of the sea water breaker (Loman, 2009). This 12

15 project is constructed by the PUMA consortium, a joint venture of Boskalis and Van Oord. The main targets of this study are as follow: Understand the shear strength behavior of the Bremanger sandstone rockfill; Find out the influence of the particle size, density, uniformity and specimen size on the direct shear test results; Select a proper modeling method for this rockfill material; Construct a rough 2D Plaxis (Plaxis bv, 2010) model for visualizing the deformation and the distribution of stresses. 13

16 2 Literature review 2.1 Factors affecting the shear strength of rockfill The direct shear test The vast application of rockfill materials in geotechnical engineering makes the study of the behaviour of these materials indispensable. However, due to the difficulties of conducting shear tests on rockfill, the study results are limited. This chapter presents a summary of the main factors affecting rockfill shear strength from the literature. It is evident from existing research that triaxial, plane strain and direct shear have been employed for studying the shear behaviour of rockfill materials. In this study, the focus is on the direct shear tests. The direct shear test has been used in geotechnical engineering over 50 years because of its simplicity and repeatability (Cerato & Lutenegger, 2006). A direct shear test is a laboratory test used by geotechnical engineers to find the shear strength parameters. The U.S. and U.K. standards defining how the test should be performed are ASTM D 3080 and BS :1990 respectively. During the test, a specimen is placed in a shear box which has two stacked rings to hold the sample; the contact between the two rings is at approximately the mid-height of the sample. A confining stress is applied vertically to the specimen, and the upper ring is pulled laterally until the sample fails, or through a specified strain. The load applied and the strain induced is recorded at frequent intervals to determine a stress-strain curve for the confining stress. In this study, the friction angle ( ) is the main focus of the analysis, because cohesion in rockfill is normally less of a concern in the design practice for civil structures (Lee et al., 2009). Many test results have shown that the friction angle of rockfill in direct shear test is higher than that of triaxial test (Ghanbari et al., 2008; Yan, 2004). As a result, it is necessary to consider a higher safety factor when using the friction angle estimated from direct shear test. There are two different friction angle concepts used in this study, secant friction angle and internal friction angle. Secant friction angle ( ) is the arctangent of the shear strength over the normal stress at failure ( ). A different secant friction angle is derived from each specimen. Internal friction angle ( ) is determined from Mohr-Coulomb linear failure envelopes constructed as best-fit lines. A different internal friction angle is derived from each test category.. 14

17 Table 2.1: The comparison between the direct shear test and the triaxial test The direct shear test The triaxial test Failure surface The failure surface is predetermined The failure surface is not fixed Friction angle Higher Lower Advantages Simple, low cost The test result is much more close to reality, but Factors affecting shear strength the test procedure is more complex According to previous research, the main factors affecting the behaviour of rockfill material are: normal effective stress, density, particle size, particle roughness, particle shape, uniformity coefficient and moisture content. Marsal (1973) performed tests on the shear strength and found out the strength of rockfill is positively correlated -with normal effective stress, dry density, particle roughness, particle crushing strength and inversely with grain size, uniformity of grading, and particle shape. The failure envelops of rockfill material are usually non-linear and stress dependent (Marsal, 1973; Asadzadeh & Soroush, 2009; Lee et al., 2009). The friction angle is the most important parameter regarding the shear strength property Normal stress and low normal stress The results of previous research on shear tests demonstrated that the shear stress-strain curve for rockfill is non-linear, particularly at low normal pressure (Marachi et al., 1969; Leps, 1970; Bertacchi & Bellotti, 1970; Penman et al., 1982; Indraratna et al., 1993; Anagnosti & Popovic, 1982; Al-Hussaini, 1983). Indraratna (1994) indicated that the frictional angle decrease with the increase of normal stress. This can be explained by the theory that as normal stress is increased, dilation is suppressed, therefore shear strength increase is reduced (Douglas, 2002). This curved strength envelop of rockfill has a large impact on the stability analysis of rockfill dam due to the fact that a lower safety factor will be produced for the shallow slip surface when using constant friction angle (Indraratna, 1994; Douglas, 2002; Barton & Kjaernsli, 1981). In other words, the high friction angles associated to low normal stresses are favourable to resistance against ravelling (Barton & Kjaernsli, 1981), at the slope toe and close to the downstream face of the slope (Figure 2.1). 15

18 Figure 2.1: Estimated variation of under toe and beneath downstream slope of dam (Barton & Kjaernsli, 1981). The triangular shape of the slope is associated to a triangular distribution of the vertical stress due to self-weight Maximum Particle size Different researches obtain contradictory results in terms of the effect of particle size on shear strength (Douglas, 2002). Most results indicate that the shear strength decreases with particle size (Marachi et al., 1972; Marsal, 1973), while some studies show the opposite effect (Anagnosti & Popovic, 1982) or no effect at all (Charles & Watts, 1980) Density It is generally accepted that the shear strength of rockfill increases with a higher relative density (Leps, 1970; Marsal, 1973). Douglas (2002) indicated that the shape of Mohr-Coulomb failure envelope is affected by this factor. The dense rockfill specimens show a marked curvature on the stress-strain curve, which shows a distinct drop in the friction angle while the loose rockfill specimens shows minimal curvature and drop in friction because the loose material require less dilation as particle have more freedom to move or rotate during shearing (Douglas, 2002). Cerato & Lutenegger (2006) used five sands with different properties to test in three square shear boxes of varying size, each at three densities: dense, medium and loose. The result turned out to be that the friction angle increases with increasing relative density in each of the three boxes. 16

19 Uniformity coefficient Douglas (2002) concluded that a poorly-graded rockfill, which is with low uniformity coefficient, would have a higher strength than a well-graded rockfill because well-graded material would be more likely to reduce the amount of dilatancy due to the fact that the gaps in rockfill are being filled with small particles. The impact of type of grading on the friction angle is about 2 to 3 degrees (Ghanbari et al., 2008). Brauns (1968) found that in well graded material the percentage of crushed rock is less and the friction angle will be higher (Ghanbari et al., 2008). Marachi et al (1969) found out that if both rockfills were compacted to their maximum density then the well graded material could be expected to be stronger as it would have the greater density. However, Douglas (2002) indicated that a poorly-graded rockfill would have a higher strength than a well-graded material assuming a constant void ratio for both because a well-graded material would be more likely to reduce the amount of dilation required due to the gaps in the gravel matrix being filled with smaller particles Particle breakage The particle breakage generally increases when the stress level increases. However, the breakage, which is dependent on the particle property, can happen even at low normal stress. Furthermore, there are several factors influencing particle breakage, apart from stress level, such as uniaxial compressive strength, particle size, particle angularity, uniformity, relative density, stress path, water content, etc (Lee et al., 2009; Asadzadeh & Soroush, 2009; Marachi et al., 1969) Summary Douglas (2002) summarized the factors affecting the friction angle and pointed out that the most significant effects on the friction angle are caused by normal pressures, density and maximum particle size (Table 2.2). 17

20 Table 2.2: Summary of factors affecting the friction angle (Douglas, 2002) Parameter Effect on with increase in parameter Comment Normal pressure Decrease Significant effect. The rate of decrease in will drop with increasing normal pressure Unconfined compressive strength of intact rock Increase Effect will depend on the ratio of confining stress to compressive strength Uniformity coefficient Decrease Minor effect and may reverse if samples are compacted to their maximum density Density Increase Maximum particle size (assuming the ratio of maximum particle size to sample diameter is constant) No consensus reached Ratio of maximum particle size to sample diameter Increase Angularity Increase The effect will be most noticeable with highly angular material Percent finer than gravel size in sample Decrease The effect will not be significant at low percentages. At higher percentages, strength will approach that of the finer material 2.2 Scale effects, determination of the maximum particle size Scale effect The effect of the apparatus size on direct shear test is a very important issue because a lot of small shear box tests are used to determine the friction angle of content material. It is still questionable that whether the current practice of using small shear boxes to find the friction angle is appropriate (Cerato & Lutenegger, 2006). Cerato & Lutenegger (2006) found that the friction angle of well-graded, angular sands decreases as direct shear box size increase. The friction angle should be 18

21 determined using the largest box size. On the other hand, the and ratios, where H is the height of the box, W is the width of the box and d max is the maximum particle size, need to be taken into consideration. If the material cannot meet the ASTM Standard , then the friction angle should be reduced by 10% to ensure an accurate strength parameter Determination of the maximum particle size In the experimental apparatus, the maximum particle size is determined by the minimum dimension of the apparatus. There are several different standard systems to determine the maximum allowable particle size for a shear box test. The first one is the Japanese standard, where the maximum allowable particle size for a large shear box test is 1/10-1/5 of the box length, 1/7-1/5 of the box height and 1/9-1/5 of the smaller of the box length or height (Lee et al., 2009). The second one is the ASTM D standard. It requires a minimum specimen thickness of six times the maximum particle diameter and a minimum specimen width of 10 times the maximum particle diameter in determining what size shear box should be used for testing sands. A minimum specimen width to thickness ratio 2:1 is required. The second set of standards will be used in this study Shear strength models There are a number of different models for describing the strength of rockfill materials. Table 2.3 shows the shear strength model for rockfill as summarized by Douglas (2002). Table 2.3: Various shear strength model for rockfill (Douglas, 2002). In addition to Douglas models, the Hoek Brown model and Lee s model are also included. 19

22 Reference Equation Parameters De Mello (1977) Charles & Watts (1980) Indraratna et al (1993) Indraratna (1994) Sarac & Popovic (1985) A,B=4.4,0.81 (Sandy gravel); A,B=4.2,0.75 (Soft rockfill); A,B=1.4,0.90 (Soft rockfill); a,b=0.25,0.83 (lower bound, ) a,b=0.71,0.84 (upper bound, ) a,b=0.75,0.98 (lower bound, ) a,b=1.80,0.99 (upper bound, ) A increase with ; B increase with ; =0.1-1 MPa; =0.1-1 MPa; =1-7 MPa; =1-7 MPa; Indraratna et al (1993) Indraratna (1994) Indraratna et al (1998) Doruk (1991) a,b = 84.98, (gradation A) a,b = , (gradation B) m, a ; ; ; ; Barton & Kjaernsli(1981) ; R equivalent roughness; S equivalent strength; Charles (1991) ; ; Gonzalez (1985) Hoek Brown (1997, 2002) Lee (2009) ; - standard crushing grain strength; and are the major and minor effective principal stresses at failure; is the uniaxial compressive strength of the intact rock material; s and a are constants for the rock mass UCS is the uniaxial compressive strength of the parent rock in MPa, is the internal friction angle in degrees 20

23 = Normal stress; = Unconfined compressive strength of the intact rock pieces; = Coefficient of uniformity; = Unit weight; = Particle diameter at which 50% of the material is finer; In this study, the four most widely used and accepted strength models for soil and rock (Mohr-Coulomb model, Power Curve strength model, Hoek & Brown model and Barton s model) are used to analyse the direct shear tests data. The basic concept of these models is explained below Mohr-Coulomb Model Mohr-Coulomb model is the most common failure criterion encountered in geotechnical engineering. This model describes a linear relationship between normal and shear stresses (or maximum and minimum principal stresses) at failure (Rocscience Inc., 2004). The direct shear formulation of this criterion can be represented by the equation: Where τ is peak shear stress; is peak normal stress; is the angle of friction; c is the cohesive strength; Figure 2.2: The explanation of normal stress, shear stress and displacement Failure occurs according to Mohr Coulomb criterion of failure when the applied shear stress less the frictional resistance related to the normal stress on the failure plane becomes equal to the rock cohesion. The model will be analyzed under two hypotheses. One is assuming without cohesion (hypothesis 1) and the other is assuming an apparent cohesion (hypothesis 2): 21

24 Where τ is the peak shear stress; is the peak normal stress; is the angle of friction; c is the cohesive strength; Power Curve Strength Model Large amount of experimental evidence suggests that the failure envelopes of many geotechnical materials are not linear, particularly in the range of small normal stresses. The relationship between shear and normal stresses of curved envelopes can be described with the Power Curve model (Rocscience Inc., 2004): where a, b and d are the parameters of the model. For rockfill material, various power curve strength criteria have been found (Charles & Watts, 1980; Charles, 1991; Indraratna, 1994; Estaire & Olalla, 2005). In this study, the parabolic expression is chosen for fitting the direct shear box test result: The interpretation using parabolic expression has been performed by several authors. De Mello (1977) interpreted tests performed by Marsal (1973) and indicated that the parabolic expression is suitable for the curved rockfill strength envelope and obtained value B between 0.81 and Matsumoto & Wanatabe (1987) fitted 49 triaxial tests and indicated that value B ranges from 0.77 to 0.97 with an average value of Charles & Watts (1980) also used the parabolic expression to analyze the shear strength of rockfill from large size triaxial data (Table 2.4). Furthermore, Charles (1991) suggested value A and B for different rockfill (Table 2.5). Table 2.4: Shear strength of heavily compacted sample of rockfill at low normal stress (Charles & Watts, 1980) Rock type A B Sandstone Slate Slate Basalt

25 Table 2.5: Shear strength parameters for some fills when using power curve strength model (Charles, 1991). I D is the rockfill relative density Rock type I D A B Sandy gravel Soft rockfill Soft rockfill Estaire & Olalla (2005) conducted 1 m 3 direct shear box tests on armourstone and found value A and B for both poured armourstone and compacted armourstone. Table 2.6: Shear strength parameters for some fills when using power curve strength model (Estaire & Olalla, 2005) Rock Type Density (Mg/m 3 ) A B R 2 Poured armourstone Compacted armourstone Asadzadeh & Soroush (2009) worked on direct shear box of limestone rockfill, which has a UCS value of 84 MPa, and found that the A value was around and the B value was around Hoek -Brown Model Hoek-Brown model is an empirical failure criterion that establishes the strength of rock in terms of major and minor principal stresses. It predicts strength envelops that agree well with values determined from experimental triaxial test of intact rock, and from observed failures in jointed rock masses (Rocscience Inc., 2004). The generalized Hoek-Brown failure criterion is expressed as: Where and are the major and minor effective principal stresses at failure; is the uniaxial compressive strength of the intact rock material; s and a are constants for the rock mass given by the following relationships: 23

26 s is the strength reduction factor, i.e. the ratio of the uniaxial compressive strength of the rock mass and rock material. is a reduced value of the material constant. It represents the degree of interlocking of the rock mass and quality of discontinuity walls and is given by m b and s are rock constants while m i is a material constant for intact rock that plays the role of friction angle for a curved failure envelop. GSI, known as the Geological Strength Index, relates the failure criterion to visual geological observations in the field. Its value ranges from 100 for fully intact rock down to 0 for very poor and laminated / sheared rock sections. The GSI parameter can be selected on the basis of the well-known charts as depicted in Figure 2.3. D is a factor which depends upon the degree of disturbance to which the rock mass has been subjected by blast damage and stress relaxation. It varies from 0 for undisturbed in situ rock masses to 1 for very disturbed rock masses. Figure 2.3: Estimate of Geological Index GSI based on geological descriptions (Hoek & Brown, 1997). 24

27 Figure 2.4: Selection of Geological Strength Index (Marinos et al., 2006) The rock fill might be treated as a rock mass that is highly damaged (D=1), poorly interlocked (low GSI), without any significant uniaxial compressive strength and tensile strength (s=0). This assumption will be checked from the Bremanger rock fills in chapter 5.4 of this report. However, contrary to the Barton s model, the Hoek and Brown model does not capture the dilatancy behavior observed during shearing. It allows for volume expansion due to tensile stresses rather than volume expansion due to shearing (Brinkgreve, 2010) Barton Model The Barton failure criterion (Barton, 1973; Barton, 1976; Barton & Choubey, 1977) is an empirical relationship widely used in modelling the shear strength of rock discontinuities (Rocscience Inc., 2004). Barton and Kjaernsli (1981) compared the behaviour of natural rock joint with that of rockfill (Barton & Kjaernsli, 1981; Barton, 2008). They found that rockfill and rock joints have several features in common, including dilatancy behaviour under low effective normal stress, and significant crushing of contact points with reduced dilation under high normal stress. The Barton failure criterion has the non-linear form: where is peak shear stress; is peak normal load; is the basic friction angle; 25

28 R is equivalent roughness of rockfill; S is equivalent strength of rockfill particles; i is the structural component of strength; reflects the texture of the rock material; it depends on the mineralogy and grain size of the rock material. can be obtained by carrying out direct shear box tests or tilt tests on smooth saw cut or sand blasted discontinuities. Alternatively, it can be derived from a table in which Barton summarized values of the basic friction angle values published in the 1960 ies and early 1970 ies for a number of rock types (Barton, 1973). It is probable that values derived from sand blasted surface are low estimates of the basic friction angle. Damage cracks have been found at a distance of 0.1 mm behind the sand blasted surface (Verhoef, 1987). These cracks are likely to cause an early grain failure during shearing (Verhoef, 2010). R and S values can be estimated using empirical charts. R is a function of porosity of the rockfill and particle origin, roundedness and smoothness (Figure 2.5). S can be estimated empirically by the S/UCS reduction factors once the mean particle size is known (Figure 2.6). Barton and Kjaernsli (1981) explains that the S-shape of the curve is probably due to the fact that large rock samples contain many micro-cracks and sand grains, none. The reduction of particle strength with decreasing mean particle size is stronger in triaxial than in plane strain conditions. It reaches up to 70% when the mean particle diameter varies between 5 and 20 mm in triaxial conditions and, up to only 30 % when the mean particle diameter varies between 3 and 15 mm in plane strain conditions. According to Barton s model, an increase in mean particle size will result in a decrease in rock fill strength. Any difference in grading is captured in the achieved porosity, and therefore in the equivalent roughness parameter. 26

29 Figure 2.5: Method of estimating equivalent roughness (R) based on porosity of rockfill (Barton & Kjaernsli, 1981) Figure 2.6: Method of estimating equivalent strength (S) of rockfill based on uniaxial compression strength and d 50 particle size (Barton & Kjaernsli, 1981) 27

30 Figure 2.7: Principle of tilt test for rock fill (Barton, 2008). Note the expression of R, the equivalent roughness for the rock fill in 5 derived by applying the Barton s model to the tilt test conditions. is the tilt angle and σ no, the normal stress on the sliding surface. Once S and b are known, it is possible to back-calculate R from a tilt test as explained in Figure 2.7. R and S are used to estimate i, the structural component of strength. i corresponds to an increase of strength due to interlocking of rock fill particles. It is the equivalent for rock discontinuities of the contribution of interlocked asperities. For discontinuities, the structural component of strength is related to discontinuity dilatancy. When shearing causes slight damage of discontinuity walls, they are equal (Barton & Choubey, 1977). In a similar way, for rock fills made of strong rocks with respect to applied stresses, one can expect that the structural component of strength is equal to the dilatancy at failure. i = Ψ with Ψ, the rock fill dilatancy at failure. Dilatancy is strongly stress dependent which explains partly the non-linearity of the failure envelop of rock fills. As stress increases towards the equivalent particle strength, crushing at contact points between particles becomes dominant and i decreases. By measuring shear strength and dilatancy during direct shear box shearing under different normal stresses, the parameters of the Barton s model might be derived. This assumption is checked in chapter 5.5 of this report. The obtained values (in case of a 28

31 reasonable fit) can be compared to values either derived using the table proposed by Barton for the basic friction angle and the charts developed to estimate the equivalent particle strength and roughness or back-calculated from tilt test results. Barton (1973) indicated that at low values of normal stress, a maximum value of secant friction angle of 70 degree seems to occur with some frequency on rock joint although it is quite possible for rough, continuous joints to have friction angle up to 80 degree at extremely low normal stresses. Leps (1970) assembled a significant number of large-scale triaxial shear test data for rockfills of various types. Barton (1981) used these data to fit in the Barton s model and suggest that R ranges from 5 to 10 and S ranges from 10 to 100 MPa. 29

32 3 Apparatus, material and test procedure 3.1 Experiment apparatus Small size shear box (100mm*100mm*40mm) The small direct shear test apparatus consists of a direct shear box of dimensions W= 100 mm, L=100mm, H=40mm, a steel frame, a thyristor controlled drive unit, a loading ring, weight hanger, loading yoke and a data acquisition system. The vertical load is applied by the yoke which is placed on the loading cap and by putting weight on the weight hanger. For greater normal load, the slotted weights can put on the hanger from the level. In this case, the applied weight is multiplied by a factor of 11 because of the length of the beam (Figure 3.1). The lower shear box is fixed to a carriage. The shearing load is applied to the carriage as well as the lower shear box while the upper shear box is fixed (Figure 3.2). The maximum load of the loading ring is around 4.5 kn, so a 20 kn load cell was replaced for higher normal load tests (normal load: kg and kg). The dial gauges and the force transducers are connected to the data acquisition system WINCLISP program v4.51. Figure 3.1:The small size shear box at laboratory of Geo-engineering department of TU Delft (Left: 4.5 kn loading ring; Right: 20 kn load cell) 30

33 Figure 3.2: General arrangement of small shear box apparatus (Mulder & Verwaal, 2006) Medium size shear box (500mm*500mm*400mm) The medium size shear test apparatus consists of a direct shear box that is 500 mm wide and long and 400 mm high, vertical and shearing loading units, a steel frame, force and displacement measuring devices, and a data acquisition system. The vertical load is exerted on the specimen with a loading plate with steel dead weight on top. As a result, it is low. At the maximum, 800 kg of steel plates are applied onto the top plate which corresponds to a normal stress of 32 kpa. The plates are prevented from toppling down by safety straps hanging loosely onto the portal crane. The shearing load is applied by an electric motor with a worm wheel and reduction gear to the lower shear box while the upper shear box is onto the steel frame. The load cells placed between the steel frame and the upper box record the horizontal force applied by the content of the lower box being sheared against the material contained in the upper box. The capacity of each load cells is 50 kn so that the maximum shear strength that can be generated during testing is 500 kpa at 20% horizontal strain. The friction between the upper and lower box is less than 85 N. It was measured by conducting shear tests with empty boxes. The range of the horizontal displacement is 20 cm while the maximum allowable horizontal displacement is 10 cm, which corresponds to 20% horizontal strain. The range of the vertical displacement is only 2 cm so that the transducer needs to be re-set during testing when testing strongly dilatant materials. The dial gauges and the force transducers are connected to the data acquisition system mp3, an in-house software developed at TU Delft. Shearing is conducted at a rate of 10 mm per min. To prevent rocks from getting trapped in between the edges of the boxes during shearing (Figure 3.3), the vertical movement of the top shear box was restricted by inserting wooden blocks between the top shear box and the steel frame. As the aggregates tend to lift up the upper box when they dilate, friction between the steel surfaces of the upper and lower boxes is not increased after 31

34 the insertion of the wooden blocks. The lateral movement of the boxes is not prevented. During shearing, the horizontal forces measured by both load cells can differ. In this report, they are averaged. During shearing, the top plate that transmits the dead weight provided by the steel plates to the aggregates, is tilted when the aggregates are sheared and dilate. As a result, the dead weight applies both a normal and shear load component onto the aggregates (van der Linden, 2010). Figure 3.3: The TU Delft medium size shear box. Figure 3.4: Sketch of the medium size shear box (van der Linden, 2010) 32

35 Figure 3.5: Movement of the upper box caused by particle trapped between the box. Problem solved by inserting wooden blocks between the upper shear box and the steel frame. Figure 3.6: Tilted dead weight 3.2 Rockfill material The rockfill used in this research is the Bremanger sandstone, which is used to create a cobble beach as well as a walk way for a crane in the Maasvlaakte 2 project (MV2) (the seaward extension of the Port of Rotterdam) of the Netherlands. The Bremanger sandstone is a dark colored rock with alternating black, grey and white layers. As it has sustained some metamorphism, it is a meta-sandstone rather 33

36 than sandstone. This sandstone is mined in an open pit operation situated on a mountain plateau meters at Dyrstad, in Norway then shipped to the Yangtze harbor in Rotterdam. Preliminary physical tests were carried out to identify the basic properties of this sandstone (Alnaes et al., 1999) (Table 3.1). The uniaxial compressive strength of the intact rock pieces is high, 188 MPa in average. The density of this material ranges from 2.67 to 2.74 Mg/m^3. The shape of rock used in the rockfill is elongated and angular. Table 3.1: Properties of the Bremanger sandstone Parameter Name Average Value Unit Modulus of Elasticity 93.5 GPa Poisson s ratio 0.31 Uniaxial compressive strength MPa Sonic velocity 5664 m/s Bulk density Mg/m^3 3.3 Experiment procedure Small size shear box experiment procedure Sieving Four sieves (1.18mm, 3.35mm, 6.3mm, 10mm) are used to separate the Bremanger sandstone into three categories (1.18mm<P<3.35mm, 3.35mm<P<6.3mm, 6.3mm<P<10mm). ASTM D requires a minimum specimen thickness of six times the maximum particle diameter and a minimum specimen width of 10 times the maximum particle diameter and the specimen used in this direct shear test is 100*100*40 mm. In this case, only two categories (1.18mm<P<3.35mm, 3.35mm<P<6.3mm) were used in the test. The dmax/w is 1/15.8 and dmax/h is 1/6.3, so the Japanese standard has been fulfilled as well. Preparation of specimen From each specimen, the material is weighed before being placed inside the shear box and the mass was determined to 0.01 gram. A layer of sandstone aggregates is placed into the shear box, and compacted with a hammer. The surface layer is loosened before adding more sandstone to avoid forming separate layers. These steps are 34

37 repeated until the shear box is filled. Then the unused sandstone is weighted and the initial mass of the specimen is determined. For the high density specimen, the above steps are conducted in a vibration equipment to achieve a better compaction. Preparation of test After placing the compacted specimen in the shear box, the horizontal displacement, the vertical displacement and shear force measurement gauges are installed. The shearing speed is fixed to 1mm/min (Mulder & Verwaal, 2006). The data record software is opened, the test parameters set-up and the initial conditions are entered. Recording data The motor is started and readings are taken on the measuring devices at regular intervals (5 seconds) until the vertical displacement is around 11 mm (around 10% shear strain). Particle breakage data For category NB and HB, particle breakage data was measured. Each specimen was sieved after the direct shear test and the weight of each size category was recorded Medium size shear box experiment procedure The test procedure for the medium size shear box was similar with that of the small shear box. The differences are listed as follows: Sieving Three sieves (31.5mm, 50mm, 80mm) are used to separate the Bremanger sandstone into two categories (31.5<P<50mm, 31.5<P<80mm). Shear box calibration The friction between the upper box and the lower box was calibrated by running the testing device several times without any material in the shear box and any load on the shear box. A friction of 83.8 N was measured and applied to all testing series for correction. Shear speed These tests were conducted at the same speed (10 mm/min). This speed was determined by running several calibration tests and comparing the results with the testing speed of the small shear box test. Shear strain Following the small shear box test, a 10% shear strain was insufficient; therefore a 20% shear strain was used for the medium size shear box. Compacting high density specimen For normal density tests, the box was filled in by pouring buckets of material in the 35

38 shear box, without physical compaction. For high density tests, the material was divided in four parts. After pouring a part, compaction with a tamping rammer weighting 90 N took place (Figure 3.7). Each layer was around ten centimeter high after compaction. Figure 3.7: Manual compaction in the medium scale shear box 3.4 Overview of experiments In this research, 48 direct shear tests were performed, in which 36 tests were performed in the small shear box and 12 tests were performed in the medium size shear box. The small shear box tests can be subdivided into six different categories while the medium size shear box test can be classified into three categories (Table 3.2). The porosity can be calculated by the following equations where n is the porosity; e is the pore index; is the specific weight of the rock mass material; is the specific weight of the in situ rockfill; 36

39 W is the moisture content of the rockfill. The specific weight of the Bremanger sandstone is 2.7 Mg/m^3, the specific weight of the in situ rockfill is known. The moisture content of the rockfill is assumed to 0%; The pore index can be calculated, and then the porosity can be calculated. The porosity of the Bremanger sandstone is between %; Table 3.2: The category name, category symbol, test detailed information of the small and medium shear box tests Category Full Name Category Symbol Tests Density (Mg/m 3 ) Porosity (%) Normal density (1.18mm<P<3.35mm) NS Six tests (5.98 kg, kg, kg, kg, kg and kg) Normal density (3.35mm<P<6.30mm) NB Six tests (the same as NS) Small Shear Box High density (1.18mm<P<3.35mm) High density (3.35mm<P<6.30mm) HS Six tests (the same as NS) HB Six tests (the same as NS) Mixture (70%small, 30% big) MS Six tests (the same as NS) Mixture (30%small, 70% big) MB Six tests (the same as NS) Normal density (31.5mm<P<50mm) M1 Three tests (34.12 kg, kg, kg) Medium Size Shear Box High density (31.5mm<P<50mm) Normal density (31.5mm<P<80mm) M2 M3 Three tests (34.12 kg, kg, kg) Six tests (two kg, two kg, two kg)

40 4 Experimental results and discussion 4.1 Small size direct shear box experiment results General trends The general shear characteristics of the Bremanger sandstone rockfill from the small shear box tests are summarized as follows: The shear stress-strain behavior of the Bremanger sandstone rockfill is nonlinear and stress dependent. An increase in normal stress is associated with a decrease of volume expansion and an increase in shear strength. Typical mixed behavior is observed in the relation between volume change and shear-strain. At low normal pressure, this rockfill behaves as dense materials, while at high normal pressure it behaves as loose materials. (1) Under high normal stress ( kpa and kpa), most specimen stay strain hardening when horizontal displacement is 10 mm (the shear strain is 10%). Volume expansion is not very large, starting with a significant compression then followed by dilation. (2) Under intermediate normal stress ( kpa), slight strain softening occurs and the volume expansion is more obvious, starting from a slight initial compression followed by a significant dilation. (3) Under low normal stress, strain softening or shearing at constant shear stress occurs. A pronounced peak is not observed in the stress-strain curves. Volume expansion is significant. 38

41 Figure 4.1: Horizontal displacement vs. corrected shear stress of small shear box test 39

42 Figure 4.2: Horizontal displacement vs. vertical displacement of small shear box test Secant friction angle and dilatancy angle Failure is defined at the maximum stress ratio. The secant friction angle at failure is the arctangent of the shear stress at failure over the normal stress at failure ( ). The secant friction angle at failure is derived for each specimen. According to Figure 4.3, the secant friction angle at failure decreases with an increase in normal stress. The relationship between friction angle and normal stress is non-linear with a quick decrease when normal stress is between kpa and comparatively slower when normal stress is higher than 100 kpa. The friction angle varies between 65 and 78 degree at the lowest normal stress and between 42 and 50 40

43 degree when the normal stress is 1 MPa (Figure 4.3). The same as the friction angle, the dilatancy angle decreases from 30 to 8 degrees as the normal stress increases from 0 to 1000 kpa, however, the rate of decrease is more even (Figure 4.4). Category HB and NB have the highest secant friction angle as well as dilatancy angle while category MS and NS have the lowest friction angle and dilatancy angle. Figure 4.3: Correct normal stress vs. the secant friction angle at failure Figure 4.4: Corrected normal stress vs. dilatancy angle at failure Strain at failure The strain at failure varies from 4.0 to 11.8%. The shear strain at failure increases as the normal stress increases, however there are some points that does not follow the trend. Higher density categories have a much lower strain at failure value than that of normal density category. 41

44 Figure 4.5: Corrected normal stress vs. strain at failure Factors affecting shear behavior Normal stress In this section, the internal friction angle is used for discussion. The internal friction angle is determined from Mohr-Coulomb s linear failure envelopes constructed as best-fit lines. The internal friction angle is derived for each category. The normal stress is a very important factor on the internal friction angle. According to Table 4.1, the higher the normal stress the lower the internal friction angle. When only using three low normal stress data, the average internal friction angle is degree. When using all six normal stress data, the average internal friction angle is degree, which is around 11 degree lower than that of the low normal stress. Similar results were found in previous studies (Douglas, 2002; Asadzadeh & Soroush, 2009). 42

45 Table 4.1: The internal friction angle of six categories when using three low normal stress and all six normal stress of the small size shear box test. Category Normal stress kpa Internal friction angle (degree) Hypothesis 1 (without cohesion) Normal stress kpa Internal friction angle (degree) Friction angle difference (degree) NS NB HS HB MS MB Hypothesis 2 (with cohesion) NS NB HS HB MS MB Average Maximum particle size Big particle categories have higher shear strength and larger volume expansion than small particle categories (Figure 4.2). The internal friction angle of big particle categories is around 4 degree higher than that of small particle categories (Table 4.1). Big particle categories approach the peak shear stress value later than the small particle categories. Strain hardening is observed for most big particle categories experiments while most small particle categories approach the peak shear value while horizontal displacement is 4-8 cm (Figure 4.1) Density The shear strength and the volume expansion of the high density categories are slightly higher than the normal density categories. The internal friction angle of the high density categories is about 2 degree higher than that of the normal density categories (Table 4.1). The stress-strain curves of the high density categories (1.71 Mg/m^3) show a marked curvature and a distinct drop after failure while that of the normal density categories (1.63 and 1.65 Mg/m^3) show minimal curvature and less drop in the friction angle. In other words, a slightly higher strain softening occurs in the high density categories. 43

46 The same trend was found in previous research (Douglas, 2002; Lee et al., 2009). This can be explained by the dense material requiring more dilation to fail as particles have less room to move during shearing which cause a distinct drop in the friction angle after failure. The compression stage of the high density categories when under high normal stress is much shorter than the normal density categories. This is because the pressure on the high density specimen is lower due to a larger contact area between particles Uniformity coefficient The uniformity coefficient can be calculated by the following equation: Where, d 60 is the particle size for which 60% is finer; d 10 is the particle size for which 10% is finer. Assuming the grade distribution in each particle category (1.18<P<3.35 mm and 3.35<P<6.30 mm) is evenly distributed, the uniformity coefficient calculation results list as follow: Table 4.2: The uniformity coefficient of category NB, MS and MB Category Full Name Category symbol Density (Mg/m 3 ) d 10 (mm) d 60 (mm) Normal density (3.35mm<P<6.30mm) NB Mixture (70%small, 30% big) MS Mixture (30%small, 70% big) MB Category NB, MS and MB have the same value (6.30 mm) and density, but different uniformity coefficient. The shear strength, internal friction angle and volume expansion of these three categories follow the same trend, category NB shows the highest values, followed by category MB then MS. However, the trend of uniformity coefficient of these three categories is different, category MB is the least uniform, followed by category MS than NB. This result shows that uniformity coefficient has a complicated effect on the shear strength and further research is required. The same result was found in most of the previous researches Summary Table 4.3 sums up the influence of factors affecting shear strength, friction angle and volume expansion on the small size shear box test: 44

47 Table 4.3: The influence of particle size, normal stress, density and uniformity coefficient on shear strength, friction angle and dilatancy of the small shear box test Effect factors Shear strength Friction angle Dilatancy Particle size Normal stress Density Uniformity coefficient Unknown Unknown Unknown Stress-dilatancy The energy-based theory accounts for the added stress associated with volumetric dilation as follows (Lee et al., 2009; Wood, 1990; Taylor, 1948): Where is the normal stress; the shear stress; the friction coefficient of the particles sliding against each other; the horizontal displacement; the vertical displacement; the secant friction angle and the dilatancy angle; The stress ratio-dilatancy figure can combine the strain-stress-volume information into a single graphical representation. As a result, the shearing process (compression, expansion, failure and softening/hardening) can be easily explained (Lee et al., 2009): For most experiments (except for those under low normal pressure), the stress ratio increases up to the peak stress ratio while the dilatancy changes from compression to expansion in the experiment. For categories NS, NB, HS, HB, the dilatancy-stress ratio relationship of all specimens for the intermediate normal stresses is nearly delineated as a unique straight relation until the stress reaches its peak value. Therefore, it can be concluded that the dilatancy-stress ratio relationship of crushed rock is only slightly influenced by the level of normal stress up to the peak behavior in that 45

48 intermediate normal stress range. The dilatancy-stress ratio relationship of category MS and MB is not as delineated as a unique straight relation as category NS, NB, HS, HB. It might be caused by a lower uniformity in these categories. Both the stress ratio at failure and dilatancy at failure follow a similar trend. They both decrease with increasing normal stress. This can be explained by the fact that shearing under low normal load is resisted by interlocking of particles rather than crushing of particles and causes dilatancy. This leads to an increase in the friction angle. By comparing the six categories dilatancy-stress relationship, big particle categories have higher peak stress ratio and corresponding peak dilatancy than small particle categories. The post peak behavior of big particle categories has more strain hardening behavior than small particle categories. High density categories have higher magnitude of stress ratio and dilatancy than corresponding normal density categories (NS and NB). Maximum dilatancy does not always correspond to maximum stress ratio. This result was not observed by (Lee et al., 2009) The post peak behavior is different at different normal stress level. When the normal stress is low (5.86 kpa, kpa, kpa) strain softening took place while at high normal stress ( kpa, kpa and kpa) strain hardening occurred for most specimens. Most curves (except those recorded under high normal stress) show a reversal trend around the peak area. After the turning point, as dilatancy decreases, the stress ratio decreases faster than it has increased with increasing dilatancy before the turning point. As a result, extrapolating the curves for the Bremanger sandstone to zero dilatancy would lead to a negative stress ratio at critical state.. This trend was not observed by Lee and his co-workers. The observation made on the Bremanger sandstone might be due to the fact that strain localization occurred in a dilatant shear band that did not affect the whole sample thickness. A dilatancy averaged over material within and outside the shear was measured. If the shear band did affect the whole sample thickness, it is possible that the smooth interface between the gravels and the top and bottom shear box surfaces affected the measured vertical displacement. 46

49 Figure 4.6: Dilatancy vs. stress ratio of the small shear box test Particle breakage The particle breakage is measured by sieving the specimen after the direct shear box test and weighing the particles under 3.35 mm. However, the splitting of particles that led to changes in grain size between 3.35 mm and 6.30 mm was not captured in this analysis of particle breakage. Only category NB and HB specimens are employed to test the particle breakage. The test result shows that the particle breakage increases rapidly with the normal stress for both categories HB and NB (Figure 4.7). The particle breakage of category HB is slightly higher than category NB. It can be concluded that the normal stress has a significant effect on the particle breakage, while the density has a limited effect on it. 47

50 Figure 4.7: Particle breakage at different normal stress Repeatability Test april 28-1, test april 28-2 and test april 10-1 specimens were under the same testing conditions (normal stress: kpa; density: 1.71 Mg/m^3; particle size: 3.35<P<6.30 mm). The general trend of the three tests are similar, however small variation occurred in both stress-strain and dilatancy figures. It is advisable to conduct at least two parallel tests in the future tests. Figure 4.8: The stress-strain and dilatancy figure of three specimens under the same test condition. 48

51 4.2 Medium size direct shear box experiment results General trends The general shear characteristics of the Bremanger sandstone rockfill from the medium size shear box tests are summarized as follows: The stress-strain behavior of the Bremanger sandstone rockfill is nonlinear, stress dependent. The behavior of shear strength is similar for all specimens. An increase in normal stress is associated with an increase in shear strength. Since all specimens are under very low normal stress (1.34 kpa kpa), the change in vertical displacement is significant. For a given test category, dilatancy increases after the peak stress linearly as function of the horizontal displacement. Whatever the normal stress is, the dilatancy is the same. The observations mentioned above can be derived from the stress ratio- dilatancy graphs instead of considering in parallel the stress-strain curves and the vertical displacement- horizontal curves Secant friction angle and dilatancy angle For all three categories, the secant friction angle decreases with an increase in normal stress. The secant friction angle of the medium size shear box test varies from 70 to 87 degree (Figure 4.10), which is around 25 degree higher that of small shear box test. The dilatancy angle of the medium size shear box test varies from 17 to 30 degree, which is comparable to that of small shear box test. Category M2 (medium size particles, high density) has the highest friction angle as well as dilatancy angle. Category M1 (medium size particles, low density) has the lowest friction angle and category M3 (bigger particles) has the lowest dilatancy angle. This last result is surprising. Test duplication shows that a high spreading of dilatancy results. 49

52 Figure 4.9: The stress-strain, vertical - horizontal displacement, dilatancy-stress ratio figures for the medium size shear box test 50

53 Figure 4.10: Corrected normal stress vs. the secant friction angle at failure of the medium size shear box test. Figure 4.11: Corrected normal stress vs. dilatancy angle at failure of the medium size shear box test Strain at failure The strain at failure varies from 6.0 to 18%. Most of the points have a higher strain at failure than that of small shear box. The strain at failure does not increase with the normal stress, which might be due to the low normal stress as well as the short normal stress range. Higher density specimens (Category M2) has a much lower strain at failure value than that of normal density specimens (Category M1), the same trend was observed in the small shear box test. 51

54 Figure 4.12: Corrected normal stress vs. strain at failure Factors affecting shear behavior Maximum particle size The big particle category (category M3) has higher shear resistance than the small particle category (category M1), the same trend was observed in the small shear box test results. The internal friction angle of category M3 is around 4 degrees higher than category M1. The dilatancy angle is similar for both categories (Figure 4.11,Table 4.4). Table 4.4: The internal friction angle of the medium size shear box test Hypothesis 1 (without cohesion) Hypothesis 2 (with cohesion) Category Full Name Category Symbol Cohesion Internal Friction Cohesion Internal Friction (kpa) Angle (kpa) Angle (deg.) (deg.) Normal density (31.5mm<P<50mm) M High density (31.5mm<P<50mm) M Normal density (31.5mm<P<80mm) M

55 Density High density category (Category M2) has a larger shear strength and larger volume expansion than normal density category (Category M1). Category M2 has a friction angle 5 degree higher than that of category M1. In addition, category M2 approaches the peak shear stress value earlier, showing a much more marked curvature and a distinct drop after failure. The same trend is found in the small shear box test Summary The following table sums up the influence of effect factors on the medium size shear box test: Table 4.5: The influence of particle size and density on shear strength, internal friction angle and volume expansion of the medium size shear box test Effect factors Shear strength Friction angle Dilatancy Particle size similar Density Particle breakage Generally, particle breakage should not occur at such low normal stress. However, particle breakage of category M3 occurred because some big rocks were caught between the top and the lower shear box (the yellow point) and caused a big variation in the stress-strain data. According to this, it can be concluded that a maximum particle size of 80 mm is too big for the medium size shear box. A maximum particle size 50 mm should be employed for future tests. Figure 4.13: Particle breakage of the medium size shear box (left: the position where the rock was caught; right: the broken rock) 53

56 4.2.6 Repeatability The repeatability can be easily observed from the experiment data of category M3. The variation between two specimens under the same experimental conditions is bigger than that of the small shear box test. It is advisable to conduct a few tests under the same experimental conditions and use the average value for further analysis in future studies. 4.3 Comparison and discussion The general trend The stress-strain behavior of the 48 direct shear box tests is similar, which is nonlinear, inelastic and stress dependent. The stress-strain curves of the small shear box tests contain less variation Secant friction angle and dilatancy angle at failure The secant friction angle ( ) of the medium size shear box test is around 10 degree higher than that of the small size shear box test. The dilatancy angle at failure for the medium size shear box test is similar with that of the small size shear box test. Contrary to the small shear box tests, no reduction of dilatancy is observed in the medium scale shear box tests. This might be due to a limitation of the medium scale set-up. Figure 4.14: Corrected normal stress vs. the secant friction angle at failure 54

57 Figure 4.15: Corrected normal stress vs. the dilatancy angle at failure Factors affecting shear behavior Maximum particle size The internal friction angles of category NS, NB and M2 were compared because they have similar density (NS:1.63 Mg/m^3; NB: 1.65 Mg/m^3; M2: 1.56 Mg/m^3). Figure 4.16 shows that the internal friction angle increases with the maximum particle size. The result is in contrast with some previous researches. Further research is recommended to find out whether this is due to material property or the difference in the two equipment properties. Figure 4.16: The internal friction angle of category NS, NB and M Density The same trend was found in both the small shear box test and the medium size shear box test, the higher density, the higher shear strength and dilatancy are. The stress-strain curves of the high density categories show a much more marked 55

58 curvature and a distinct drop after failure than the normal density category Summary To sum up, the influence of particle size, density and normal stress on the shear strength, friction angle and dilatancy is concluded in Table 4.6. Further study is suggested to conduct for verifying this conclusion. Table 4.6: The influence of particle size, density and normal stress on shear strength, internal friction angle and volume expansion of both the small and medium size shear box test Effect factors Shear strength Friction angle Dilatancy Particle size unknown Density Normal stress 56

59 5 Rockfill shear strength model 5.1 Introduction There are a number of rockfill shear strength model from literature. In this chapter, four different empirical models (Mohr-Coulomb Model, Power Curve Strength Model, Barton Model and Hoek-Brown Model) will be compared to find the most appropriate model for the Bremanger sandstone rockfill. Table 5.1: The overview of four model application condition Model Name Small shear box test Medium size shear box test Mohr-Coulomb Model Power Curve Strength Model Hoek -Brown Model Barton Model 5.2 Mohr-Coulomb Model Introduction The first way to interpret the experimental results is by using the Mohr-Coulomb model, which is the most widely used model in geotechnical engineering. The Mohr-Coulomb model criterion describes a linear relationship between normal stress and shear stress at failure. However, this model is not accurate for this study since the non-linear relationship between the shear stress and normal stress at failure can be easily observed from the two shear box test data. The model will be analyzed under two hypotheses. One is assuming no cohesion (hypothesis 1) and the other is assuming an apparent cohesion (hypothesis 2): Where τ is the peak shear stress; is the peak normal stress; is the angle of friction; 57

60 c is the cohesive strength; Data Process Method Step 1: Plot the shear stress and corresponding normal stress at failure for each experimental category, the shear stress is plotted on the y axis while the normal stress is plotted on the x axis; Step 2: For hypothesis 1, add a linear trend (intercept =0) for points of each category and get an equation of the linear trend (y=ax), so A is equal to. Step 3: For hypothesis 2, Add a linear trend (intercept 0) for points of each category and get an equation of this linear trend (y=ax+b), so A is equal to, B is equal to the cohesive strength Result Small shear box test The general trend for both hypothesis 1 and 2 is similar, the model underestimated the shear strength value when the normal stress is lower than 600 kpa and overestimated the shear strength value when the normal stress is higher than 600 kpa. The regression coefficient of hypothesis 2 is higher than that of hypothesis 1. However, since apparent cohesion in rockfill is normally less of a concern; as hypothesis 1 is more widely used in practice. The following discussion will be based on modeling results of hypothesis 1. In hypothesis 1, friction angles range from 44.3 degree to 50.5 degree. Big particle categories (Category NB, HB and MB) have higher friction angle than small particle categories (Category NS, HS and MS). High density categories (HS and HB) are around 2 higher than corresponding normal density categories (NS and NB). The friction angles of categories MS and MB are higher than category NS and lower than category NB. Category MS is much closer to category NS (only 0.3 difference) while category MB is much closer to category NB (2.16 difference). The largest friction angles are obtained with high density and big particle size. 58

61 Category NS, φ=44.25, c=0; Category NB, φ=49.70, c=0. Category NS, φ=42.30, c=43.65; Category NB, φ=47.15, c= Category HS, φ=46.32, c=0; Category HB, φ=50.47, c=0. Category HS, φ=44.16, c=50.13; Category HB, φ=47.47, c= Category MS, φ=44.54, c=0; Category MB, φ=47.54, c=0. Category MS, φ=42.05, c=54.97; Category MB, φ=45.11, c= Figure 5.1: The shear and normal stress relationship and the internal friction angle of the small shear box test Medium size shear box test The medium size shear box test data is not as stable as the small shear box data and only few pairs of shear stress and normal stress are available. It is recommended to conduct more tests at different stresses in the low stress range and to adapt the 59

62 equipment to be able to conduct tests at higher normal stresses. The internal friction angles for the medium size shear box range from 74.0 to 79.1 degree, which is around 25 degree higher than that of the small shear box test. This can be explained by the low normal stress and the larger particle size. On one hand, previous research has shown that the friction angle decreases rapidly with an increasing normal stress when under low normal stress condition. On the other hand, there is no unanimous agreement on the positive influence of particle size on aggregate strength. Category M1, φ=69.06, c=26.27; Category M2, φ=75.63, c=36.46; Category M3, φ=76.22, c= Category M1, φ=74.02, c=0; Category M2, φ=79.10, c=0; Category M3, φ=78.19, c=0 Figure 5.2: The shear and normal stress relationship and the internal friction angle of the medium size shear box test To sum up, the Mohr-Coulomb model can only be used as a rough estimate for shear strength and friction angle for this rockfill because of the non-linear relationship between the normal stress and shear stress. 60

63 5.3 Power Curve Strength Model Introduction A number of previous studies suggest that a parabolic expression can be used to analyze the shear strength of rockfill (Charles & Watts, 1980; Charles, 1991; De Mello, 1977; Matsumoto & Wanatabe, 1987). De Mello (1977) indicated that the following equation is suitable for representing the curved strength of rockfill. Where A and B are empirical values, dependant on the type of material Data process method Step 1: Plot the shear stress and corresponding normal stress for different normal stresses of each experimental category, the shear stress is plotted on the y axis while the normal stress is plotted on the x axis; Step 2: Add a power trend to each category and get an equation of this power trend ( ), so A, B and values for each category can be read directly from the equation Result The regression coefficients of these parabolic curves are higher than the ones corresponding to the linear curves, which indicate a non-linear shear stress behavior at failure of the Bremanger sandstone rockfill. The fitting result is listed in Table 5.2. The modeling result of the medium size shear test will not be discussed due to the fact that the very low normal stress and big variation in the test results. For the small shear box test, value B is stable and ranges from 0.71 to 0.81 while value A varies from to This result is comparable with Charles result (1991), where sandy gravel has value of A equal to 4.4 and value B equal to However, Charles research was based on the large scale triaxial test, the difference caused by the difference of triaxial test and direct shear box test on A and B value is unknown. By comparing the results of previous research, high regression coefficients (bigger than 0.9) and similar values of B (around 0.8) were found for sandstone rockfill. Value B determines the basic shape of curve. From all the rockfill research data, value B is comparatively stable around 0.8, which indicates the fact that the shear strength of rockfill increases rapidly under low normal stress and slowly under high normal stress. By comparing the modeling results and the previous research results, a value of B ranged from is recommended for the Bremanger sandstone rockfill in future applications. This value should be verified by high normal stress medium scale tests in the future. 61

64 Table 5.2: The value A, B and R^2 when using the parabolic expression modeling Category Full Name Category A B Symbol Normal density (1.18mm<P<3.35mm) NS Normal density (3.35mm<P<6.30mm) NB High density (1.18mm<P<3.35mm) HS High density (3.35mm<P<6.30mm) HB Mixture (70%small, 30% big) MS Mixture (30%small, 70% big) MB Normal density (31.5mm<P<50mm) M High density (31.5mm<P<50mm) M Normal density (31.5mm<P<80mm) M Since value B is determined, value A is the only parameter left to be determined when using the parabolic expression model. However, it is difficult to quantitatively estimate value A. The influence of different factors on the value A will be discussed. From the modeling results, the big particle categories have higher value A than that of the small particle categories. By summing up previous research result (Charles, 1991; Charles & Watts, 1980; De Mello, 1977; Asadzadeh & Soroush, 2009; Estaire & Olalla, 2005), the influence of the effective factors (the UCS, density, particle size) on the value A are listed in Table 5.3. Value A around 4.4 is suggested for further application of the Bremanger sandstone rockfill. Table 5.3: The influence of UCS, density and maximum particle size on value A Effective Factor Value A UCS Desity Maximum particle size To sum up, regression coefficient of this parabolic curve model is high, however the variation of value B is uncertain and it is hard to quantitatively analyze value A. Further research is required for this model fitting. 62

65 5.4 Hoek -Brown Model Introduction The main principle of this method is to find the best-fit normal - shear stress curve, which is made by using the RocData software (Rocscience Inc., 2004), with the parabolic curve from the lab data. RocData is a software for determining soil and rock mass strength parameters through analysis of laboratory or field triaxial or direct shear data. The program can fit the linear Mohr-Coulomb strength criterion and three other non-linear failure criteria, the generalized Hoek-Brown, Barton-Bandies and Power Curve strength models (Rocscience Inc., 2004) Data process method Input data of RocData The four input parameters for RocData of the Generalized Hoek-Brown model is the intact uniaxial compressive strength, GSI, material constant and disturbance factor D. Three of the four parameters are fixed for the Bremanger sandstone rockfill, only the GSI can be varied. Table 5.4: The UCS, m i and D for the Bremanger sandstone rockfill. Parameter name Parameter symbol Value Remark Intact uniaxial compressive strength σci 188 MPa Material constant index 19 Metasandstone Disturbance factor D 1 Blasting rockfill When these four parameters are entered, the, which is derived from the principal stresses based on the geometric calculation from shear stress and normal stress, is chosen. After this, RocData will automatically give the result of the Hoek-Brown criterion, Mohr-Coulomb fit, rock mass parameters, major stress-minor stress curve and normal stress-shear stress curve. In this study, the normal stress-shear stress curve and Mohr-Coulomb fit data will be used for further comparison. The basic mathematical equations for these two calculations are listed as follows. The equations can easily be inserted in an excel sheet. Normal stress-shear stress curve In RocData, the following equation were used to calculate normal and shear stress 63

66 from the Hoek-Brown parameters (Hoek et al., 2002)(Balme,1952). where RocData will give a normal stress-shear stress curve when all the Hoek-Brown parameters were entered. Mohr-Coulomb criterion The Mohr-Coulomb criterion fits an average linear relationship to the curve generated by solving the generalized Hoek-Brown equation for a range of minor principal stress values defined by. The fitting process involves balancing the areas above and below the Mohr-Coulomb plot. The following equations are used in calculating the friction angle and cohesive strength (Hoek et al., 2002): where Note that the value of, the upper limit of confining stress over which the relationship between the Hoek-Brown and the Mohr-Coulomb criteria is considered, has to be determined for each individual case Curve fit The curve provided by RocData for each category was manually compared with the 64

67 parabolic curve by varying the GSI value. When the best fit GSI was found, corresponding Mohr-Coulomb fit cohesion and friction were automatically calculated by RocData. For the small shear box test, the parabolic curve can fit very well with the normal stress-shear stress curve estimated by RocData while the fit of the medium size shear box test are not that accurate because of short normal stress range and unstable data. The detailed curve fitting information can be found in appendix GSI determining factors In the RocData, the GSI is related to the structure and surface condition. In this study, the disintegrated condition is chosen for the rockfill structure. The variation of GSI can be explained as the surface condition change due to the particle size and density variation (Figure 2.3) Result The similarity between the two curves (parabolic curve based on the shear test data and the Hoek-Brown curve from RocData, see Appendix 9.1) shows that it is possible to apply Hoek-Brown criterion by using the direct shear test data to estimate the shear strength of the Bremanger sandstone rockfill (Table 5.5). The advantage of this method is that GSI is the only parameter that needs to be determined. The friction angle estimated by RocData is 5-10 degree lower than the value calculated by the Mohr-Coulomb model result. The cohesion estimated by RocData is around twice the Mohr-Coulomb model result. By comparing the GSI values of the nine different categories, the influence of density and particle size can be compared. Category NB, NB and M2 have similar density (1.63, 1.65 and 1.56 Mg/m^3) but different maximum particle size, the GSI variation indicated that the higher the particle size the higher the GSI value. Figure 5.3 shows the power trend line plotted for these categories, where GSI increase rapidly when d max ranges from 0 to 20 mm and increase slowly when d max is bigger than 20 mm. The accuracy of this curve needs to be verified by further study because the density and normal stress of these three categories is not exactly the same and the error caused by two equipments is unknown. 65

68 Table 5.5: The best fit GSI and corresponding friction angle and cohesion calculated by RocData Category Full Name Category Symbol Density (Mg/m 3 ) Best Fit GSI (MPa) Mohr-Coulomb Fit Friction Cohesion angel (MPa) (Degree) Normal density (1.18mm<P<3.35mm) NS Normal density (3.35mm<P<6.30mm) NB Small Shear Box High density (1.18mm<P<3.35mm) High density (3.35mm<P<6.30mm) HS HB Mixture (70%small, 30% big) MS Mixture (30%small, 70% big) MB Medium Shear BOX Normal density (31.5mm<P<50mm) High density (31.5mm<P<50mm) Normal density (31.5mm<P<80mm) M M M Figure 5.3: The relationship between the GSI value and maximum particle size (category NS, NB and M2) 66

69 The influence of the density can be compared by three pairs (Category NS&HS, NB& HB, M1&M2). The higher density categories have 5-10% higher GSI values. To sum up, the influence of the effective factors on the GSI value are as follows: Table 5.6: The influence of maximum particle size and density on GSI value Effective Factor GSI Value Maximum particle size Density In conclusion, this method is comparably more applicable for estimating shear strength of the Bremanger sandstone rockfill because there is only one parameter that needs to be determined. It is also possible to quantify the factors affecting the GSI value. Further research is recommended to verify the applicability of this method and find the influence of other factors on the GSI value (such as normal stress, the grade distribution, the uniformity coefficient etc.) to better estimate it. With GSI values between 20 to 40 and damage factor of 1, the Hoek-Brown criterion of failure predicts a uniaxial strength of the rockfill of zero in comparison the UCS of intact rock (the s is very small). Note that the dilatancy measured during testing is not used when determining the parameters of generalized Hoek-Brown criterion of failure. 5.5 Barton Model Introduction Barton (1981) compared the shear strength of rockfill with rock joints and suggested that the friction angle of rockfill can be estimated from knowing the following parameters: (1) the uniaxial compressive strength; (2) the d 50 particle size; (3) the degree of particle roundedness; and (4) the porosity following compaction. The general equation is as follows: where is the peak shear stress; is the peak normal stress; is the basic friction angle; R is the equivalent roughness of rockfill; S is the equivalent strength of rockfill particles; 67

70 i is the structural component of strength; Data process method Step 1: Equation rewriting Rewrite the basic equation as follows: Calculate value and value for each specimen and plot value and value for each experimental category on the y and x axis respectively; Step 2: Calculate R value Add a linear trend (intercept 0) to the points of each category and get the equation of this linear trend line (y=-ax+b). A is equal to R, so the R value can be determined directly. S value can be calculated by the following equation. S value can calculated from the expression of the intercept B: as follows: Step 3: Estimate basic friction angle The basic friction angle is a fundamental parameter of intact rock, and seems to be a key parameter in describing the shear strength of rockfill. It usually ranges from about 25 degree to 38 degree (Barton & Kjaernsli, 1981). Douglas (2002) summarized the shear strength of rockfill and indicated that the shear strength of rockfill at a particular confining stress may be seen as the combination of a basic friction angle, plus a dilation angle caused by asperity or particle crushing and reorientation of particles. where is the friction angle; is the basic friction angle; i is the dilation angle; is the particle crushing and reorientation angle; In this study, the basic friction angle is calculated by subtracting the secant friction angle at failure by the dilatancy angle at failure for each specimen, assuming no 68

71 crushing. The dilatancy angle at failure can be calculated by the arctangent of the slope of the horizontal displacement-vertical displacement curve at failure (max. stress ratio). The secant friction angle at failure can be calculated by the arctangent of the slope of the shear stress-normal stress at failure. Figure 5.4: Corrected normal stress vs. basic friction angle at failure Figure 5.4 shows the calculation result of the basic friction angle. is relatively constant under the same normal stress. When the normal stress is very low (5.86 kpa), is around 45 degree. decrease rapidly when the normal stress changes from 5.86 kpa to kpa and is constant when the normal stress change from kpa to around 1 MPa. This can be explained by the crushing of particles. When the normal stress is low, there is no crushing effect; the crushing effect increase a lot when the normal stress increase from 5.86 kpa to kpa, then keep in the same level when the normal stress increase from kpa to around 1 MPa. For further calculation, the basic friction angle is assumed to be 35 degree for this rockfill. Previous research at TU Delft shows that the basic friction of the Bremanger sandstone cannot be measured easily. Diamond saw cutting produces polished surfaces on which the quality of the polishing rather than the basic friction angle is measured during direct box shearing (Ngan-Tillard & Mulder, 2010). Sandblasted has been used to produce smooth surfaces whose texture reflects that of the natural rock. Sandblasting causes micro-cracks that extend up to 0.1 mm below the blasted surface (Verhoef, 2010). As a result, it leads to a low estimation of the basic friction angle. In addition, deciding whether or not sandblasting simulates well the natural texture of the rock is subjective. 69

72 Step 4: Calculate the S value S value can be calculated by. Step 4: Compare the calculation results obtained from the shear box tests with those derived from Barton s R and S (Figure 2.5 and Figure 2.6). Four parameters (the uniaxial compressive strength, the d 50 particle size, the degree of particle roundedness, the porosity following compaction) need to be provided. The uniaxial compressive strength is 188 MPa; The d 50 can be calculated by assuming the particle size is distribute evenly in each category; Talus rock is chosen for the degree of particle roundedness(figure 5.5,Figure 5.6); The porosity has been calculated in chapter 3.4 (Table 3.2) Figure 5.5: Pictures of the small shear box (left: 3.35<P<6.30 mm; right: 3.35<P<6.30mm) Figure 5.6: Pictures of the medium shear box (left: 31.5<P<50 mm; right: 31.5<P<80 mm) 70

73 5.5.3 Result Experimental result Table 5.7: The calculated R, B and R 2 value from the experimental result Category Full Name Category Symbol R B S(MPa) Normal density (1.18mm<P<3.35mm) Normal density (3.35mm<P<6.30mm) High density (1.18mm<P<3.35mm) High density (3.35mm<P<6.30mm) NS NB HS HB Mixture (70%small, 30% big) MS Mixture (30%small, 70% big) MB Normal density (31.5mm<P<50mm) High density (31.5mm<P<50mm) Normal density (31.5mm<P<80mm) M M Very large M Very large The modeling result by Barton s estimation figures From Barton s R and S value estimating figures (Figure 2.5 and Figure 2.6), the R value is 4.5 for small shear box and for medium size shear box is 4.2 (Figure 5.7). The S value can be estimated from Figure 2.6 when assuming the grade is evenly distributed (Figure 5.8,Table 5.8). 71

74 Figure 5.7:Estimating the equivalent roughness R (blue line for small shear box; red line for medium size shear box) (Barton & Kjaernsli, 1981) Figure 5.8: Estimating S/UCS reduction factors for estimating S (Barton & Kjaernsli, 1981) 72

75 Table 5.8: The d 50 and estimated S value from Barton's figure Category Symbol (mm) S (triaxial test) (MPa) S (plane test) (MPa) NS, HS NB,HB MS MB M1,M M Comparison between two results When comparing the calculation result with the modeling result, the difference is very obvious. The estimated R value is lower than the calculated S value while the calculated S value is unstable. Barton (1973) indicated that at low values of normal stress ( ), the friction angle becomes very high. The small shear box has a of 188 while the medium size shear box has a of The very high value causes the instability of the calculated result. To sum up, the application of Barton s model on this study is not good. 73

76 5.6 Comparison and conclusion of modeling results The comparison of these four different models is listed as follows: Table 5.9: The general comment on the models Model Name Mohr-Coulomb Model Power Curve Strength Model Hoek -Brown Model Barton Model General Comment The estimation is simple, but not accurate The regression coefficients of these parabolic curves are high, However there are two parameters that needs to be determined, the influence of effective factors on these two parameters is not clear. Only one parameter needs to be determined; further study is recommended. The fitting result is not good It can be concluded that the Mohr-Coulomb model can be used for rough estimation and Hoek-Brown Model can be used for more detailed estimation for the Bremanger sandstone rockfill. 74

77 6 Plaxis modeling of the crane walk-way 6.1 Introduction The Plaxis 2D program is a special purpose two-dimensional finite element program used to perform deformation and stability simulations for various types of geotechnical applications. The detailed design of the crane walk-way of the MV2 project is not known to us. A model was assumed for this study. The Bremanger sandstone rockfill layer is assumed to be 2 meters high and 30 meters wide (Figure 6.1). A plane strain model was used for this project. The Plaxis model is shown in Figure 6.2. Figure 6.1: The layout of the crane walk-way design Figure 6.2: The dimension and detailed information of the design 75

78 6.2 Method The Plaxis 2D 10 Beta version, provided by Plaxis bv, is employed for this project. In this beta version, the Hoek-Brown model has been added for modeling the behavior of the rock mass and, here, rockfill. The software is used as follows: Step 1: Creating the input The basic parameters of the finite element model are entered in the software. A geometric contour of the design is drawn (Figure 6.2) and the boundary condition is defined. The property of dense sand and the Bremanger sandstone rockfill material are entered. HS small model is chosen for the dense sand material while Hoek-Brown model is chosen for the rockfill. The detailed input data can be seen in Table 6.1. A mesh is automatically generated by the software. The rockfill layer area is chosen to create a finer mesh for more accurate modeling. Step 2: Performing calculations Three construction stages are defined (the first one is constructing the dense sand layer, the second one is constructing the rockfill layer, the third one is adding the normal load). In each stage, the water level is defined (Figure 6.2). A surcharge of 300 kpa is applied, either, at the middle of the fill or at the outer edge. One point is selected at the top right corner of the rockfill layer and two points right under the normal load to generate the load-displacement curves. An additional stage for the Mohr-Coulomb safety factor calculation is added. The calculation is not straightforward, for additional information, refer to Draft presentation of the Hoek and Brown criterion of failure in PLAXIS by Brinkgreve (2010). Step 3: Viewing output result Safety factor can be read directly from the calculation procedure. The deformation and stress distribution information can be extracted from the 2D pictures. Step 4: Varying the model for comparing the influence of the effective factors The GSI value and the corresponding Young s modulus are varied based on the generalized Hoek-Brown strength criterion from RocData. Table 6.1: Detailed input data for the dense sand and the Bremanger sandstone rockfill material property 76

79 Dense sand Model HS small model Density 90% 1. General properties Saturated weight sat KN/m^3 Unsaturated weight unsat KN/m^3 2. Parameters for stiffness Secant stiffness in standard drained triaxial test E-50 ref 5.40E+04 KN/m^2 Tangent stiffness for primary oedometer loading E-oed ref 5.40E+04 KN/m^2 unloading/reload stiffness at engineering strains E-ur ref 1.62E+05 KN/m^2 Power for stress-level dependency of stiffness power(m) 3. Advanced parameters for stiffness Poisson's ratio for unloading-reloading 0.20 Reference stress for stiffness p-ref KN/m^2 Ko-value for normal consolidation Parameters for strength Effective cohesion c'ref 0.00 KN/m^2 Effective angle of internal friction degree Angle of dilatancy 9.25 degree 5. Advanced parameters for strength Failure ratio qf/qa Rf Parameters for small strain stiffness Reference shear modulus at very small strains G-0 ref 1.21E+05 KN/m^2 Shear strain at which Gs=0.722Go Gamma E-04 Bremanger sandstone rockfill Model Hoek-Brown model 1. General properties Saturated weight sat KN/m^3 Unsaturated weight unsat KN/m^3 2. Parameters for stiffness Young's modulus of rock mass E' 2.50E+06 KN/m^2 Poisson's ratio v' Hoek-Brown parameters Uniaxial compressive strength of rock material σci 1.88E+05 KN/m^2 Material constant for the intact rock mi Geological Strength Index GSI Disturbance factor D Dilatation angle Maximum dilatancy angle ψmax degree The normal pressure when the dilatancy angle become zero ψ KN/m^2 77

80 The maximum dilatancy angle and normal pressure when the dilatancy angle becomes zero is extracted from Figure Result The Plaxis modeling results show that the crane walk-way design has a high safety factor. The total displacement is around mm, which is acceptable for this design. The influence of varying the GSI, and consequently the Young s modulus (calculated by RocData), on the factor of safety and displacement was investigated (Table 6.2) (Brinkgreve, 2010). As expected, the safety factor increases with an increase of GSI. Normal surcharge in the middle model has a higher safety factor than normal load at the edge model. Figure 6.3 shows that there is a linear relationship between the GSI and safety factor for both loading methods. The safety factor approaches 1 when the GSI value is 10. According to the discussion in charpter 5.4, an increse in density will result in a higher GSI value. It is recommended to conduct some field test to find the proper compaction density for the atucal project construction. The total displacement decreases with an increase of GSI (Table 6.2,). The variation of vertical displacement and horizontlal displacement is not significant with changes in GSI. Additionally, the difference between using the Hoek-Brown model and the Mohr-Coulomb model for rockfill are recommended to be studied in the future. Table 6.2: The safety factor and total displacement of the design Normal load in the middle Normal load at the edge GSI Young s modulus 8.89E E E E E E+06 Safety Factor Total displacement (mm) Horizontal displacement (mm) Vertical displacement (mm)

81 Figure 6.3: GSI value vs. safety factor of the crane walk-way design Figure 6.4: The total displacement when the normal load is in the middle and GSI equal to 38 Figure 6.5: The vertical effective stress when the normal load is in the middle and GSI equal to 38 79