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On the use of shear wave velocity to characterize changes in fines content of a silty sand Campbell, Jessica E. 2006

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O N T H E U S E O F S H E A R W A V E V E L O C I T Y T O C H A R A C T E R I Z E C H A N G E S IN F I N E S C O N T E N T O F A S I L T Y S A N D by JESSICA E. C A M P B E L L B.Sc. (Geological Engineering), University of New Brunswick, 2001 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R OF A P P L I E D SCIENCE in The Faculty of Graduate Studies (Civil Engineering) U N I V E R S I T Y OF BRITISH C O L U M B I A August 2006 © Jessica E . Campbell, 2006 A B S T R A C T Seismic, waves are commonly used to characterize the mechanical properties of soils, either through in-situ techniques or laboratory measurement. Several factors are known to influence shear wave velocity, including stress, void ratio and soil fabric. In the case of internally unstable soils, where a seepage-induced fines loss occurs over time, the phenomenon may be well-suited to geophysical monitoring. This laboratory program investigates the relation between shear wave velocity and fines content of a silty sand, and examines how that relation varies with seepage flow. Specimens of varying fines content (Sf = 0, 13, 18, 23, 28 and 33 %) were reconstituted as a slurry in a rigid-walled permeameter outfitted with bender elements. Shear wave velocities of the specimens were found to be influenced primarily by stress, and, to a lesser degree, changes in fines content and hydraulic gradient. The change due to fines content is small (15 m/s at o-m' = 12 kPa and 34 m/s at o"m' = 200 kPa) but the trend is consistent across the range of mean effective stresses examined in testing. Shear wave velocity was found to diminish with increasing fines up to a threshold value of approximately 23 %. At, and beyond, the threshold fines content, a subtle increase in shear wave velocity is observed; the relation becomes more pronounced with increase in stress. The influence of hydraulic gradient on shear wave velocity is solely due to the change in confining stress imposed by the downward seepage force. The findings of the study and comparison to triaxial test data for similar gradations, show that a subtle change in shear wave velocity occurs with change in fines content, however, shear wave velocity is more sensitive to change in mean effective stress. Comparison of field and laboratory data indicates differences in shear wave velocity between the moist-tamped/compacted materials and the slurry-deposited materials, and a convergence of shear wave velocities with increasing mean effective stress. Change in fines content in the field caused by possible fines migration may be detected using seismic surveying techniques, however, it would appear difficult to correlate shear wave velocity to fines content since the mechanism of fines loss also affects the structure of the soil. i i TABLE OF CONTENTS Page ABSTRACT ii TABLE OF CONTENTS iii LIST OF TABLES vi LIST OF FIGURES viii ACKNOWLEDGEMENTS xii 1.0 INTRODUCTION 1 1.1 Purpose of the study 1 1.2 Organization of the thesis 2 2.0 LITERATURE REVIEW 4 2.1 Principle of shear wave velocity 4 2.1.1 Techniques of measurement 5 2.1.1.1 Resonant column 8 2.1.1.2 Bender elements 9 2.1.2 Experience and reported trends 15 2.2 Small strain shear modulus and influencing factors 18 2.2.1 Stress condition 19 2.2.1.1 Isotropic conditions 19 2.2.1.2 Anisotropic conditions 20 2.2.2 Void ratio function 22 2.2.3 Material constant 25 3.0 APPARATUS, MATERIALS AND TEST PROCEDURE 27 3.1 Permeameter 27 3.1.1 Vertical loading system 27 3.1.2 Water flow control system 29 3.1.3 Data acquisition system 31 3.2 Bender elementsystem 31 3.2.1 Element configuration 31 3.2.2 Peripheral electronics 34 ii i 3.3 Materials 35 3.3.1 Fraser River sand 35 3.3.2 Core material: W A C Bennett dam 36 3.4 Test procedure 36 3.4.1 Slurry preparation 38 3.4.2 Specimen reconstitution 38 3.4.3 Test setup 39 3.4.4 Multi-stage testing procedure 40 3.5 Test program 41 3.5.1 Preliminary tests 41 3.5.2 Main test program 42 4.0 T E S T R E S U L T S 43 4.1 Consolidation behavior 43 4.1.1 Specimen repeatability 45 4.2 Homogeneity 45 4.2.1 Post-test grain size distribution 46 4.2.2 Water head distribution 46 4.3 Hydraulic conductivity 53 4.4 Shear wave velocity 54 4.4.1 Influence of stress 55 4.4.2 Influence of fines content 56 4.4.3 Influence of hydraulic gradient 59 5.0 A N A L Y S I S 63 5.1 Structure of the specimen 63 5.1.1 Fines content - void ratio relation 63 5.1.2 Compressibility 68 5.2 Consideration of mean effective stress 69 5.3 Shear wave velocity 71 5.3.1 Influence of stress 72 5.3.2 Influence of void ratio 79 5.3.3 Influences of fines content 80 iv 5.4 Comparison to moist-tamped laboratory data 83 5.4.1 Materials and test procedure 83 5.4.1.1 Materials 83 5.4.1.2 Specimen reconstitution 84 5.4.1.3 Ageing 85 5.4.1.4 Loading 86 5.4.1.5 Determination of shear wave velocity 86 5.4.2 Test results 87 5.4.3 Data comparison 89 5.4.3.1 Void ratio 90 5.4.3.2 Shear wave velocity 92 5.4.3.3 Elastic constants 95 5.5 Comparison to field data 98 5.5.1 Test methodology and materials 99 5.5.1.1 Test methodology 99 5.5.1.2 Core material 104 5.5.2 Test results 104 5.5.3 Data comparison 107 5.5.3.1 Void ratio 108 5.5.3.2 Shear wave velocity 109 6.0 S U M M A R Y A N D C O N C L U S I O N S 1 1 2 6.1 Summary 112 6.2 Conclusions 115 R E F E R E N C E S 1 1 9 A P P E N D I X A 1 2 3 A P P E N D I X B 1 3 4 v L I S T O F T A B L E S Page Table 2.1 Database compiled from new experiments 17 Table 2.2 Anisotropic G m a x stress exponents 22 Table 2.3 Comparison of A parameters between selected studies 25 Table 3.1 Index properties for each gradation of the main test program 38 Table 4.1 Repeatability of consolidation void ratio 44 Table 4.2 Average shear wave velocities for an applied stress of 25 and 400 kPa 56 Table 4.3 Shear wave velocity obtained at each hydraulic gradient for an 61 applied stress of 25 kPa Table 4.4 Shear wave velocity obtained at each hydraulic gradient for an 62 applied stress of 400 kPa Table 5.1 Variation of porosity with fines content 66 Table 5.2 Velocity-stress constants of the current study 73 Table 5.3 Summary of A parameters of the current study 77 Table 5.4 Comparison of A parameters between selected studies 78 Table 5.5 Target sample preparation void ratios 85 Table 5.6 Test code nomenclature and index properties for specimens of the 87 triaxial test program (BCH-GA) Table 5.7 Comparison of shear wave velocities of the triaxial testing program 89 Table 5.8 Comparison of shear wave velocities of both laboratory programs 95 Table 5.9 Summary table of elastic constants of the three programs of study 97 Table 5.10 Details of seismic planes 22 and 26 100 Table 5.11 Generalized shear wave velocities from crosshole seismic surveys; 108 Planes 22 and 26 vi Table 5.12 Core material void ratios obtained in field and laboratory programs 108 Table A . l Mean effective stress computed using upper and lower bound Ko 132 (air-pluviated FRS) Table A.2 Reproducibility of specimen response (Vs) for commissioning tests 133 Table B . l Shear wave velocity versus stress states; test C-0 134 Table B.2 Shear wave velocity versus stress states; test C-13 134 Table B.3 Shear wave velocity versus stress states; test C-18 135 Table B.4 Shear wave velocity versus stress states; test C-23 135 Table B.5 Shear wave velocity versus stress states; test C-28 136 Table B.6 Shear wave velocity versus stress states; test C-33 136 vii LIST OF FIGURES Page Figure 2.1 Deformation and motion of compression (P-) waves and shear 5 (S-) waves through soils Figure 2.2 Schematic of downhole seismic surveying 7 Figure 2.3 Schematic of crosshole seismic surveying 7 Figure 2.4 U B C resonant column apparatus 8 Figure 2.5 Schematic of a resonant column device 9 Figure 2.6 Relaxed and excited bender elements 10 Figure 2.7 General cantilever mounting configuration for bender elements 10 Figure 2.8 Schematic of compression and shear wave generation 11 Figure 2.9 Typical shear wave signal 12 Figure 2.10 Receiver waveforms (a) and cross-correlation function (b) 14 Figure 2.11 Variation of shear wave velocity of sand samples with stresses in 21 three planes Figure 2.12 Variation of shear wave velocity with void ratio and confining 24 pressure for dry round and angular sand Figure 3.1 Details of the rigid-walled permeameter assembly 28 Figure 3.2 Permeameter cell assembly in reservoir bath 28 Figure 3.3 Schematic of permeameter and flow control system 30 Figure 3.4 Transmitter bender element mounted on the top plate 33 Figure 3.5 Post-mounted receiver elements on the cell base 33 Figure 3.6 Schematic diagram of bender element system 34 Figure 3.7 Schematic diagram of peripheral equipment configuration 35 vi i i Figure 3.8 Source core material obtained from the 1996 sonic drilling 37 program at the W A C Bennett dam Figure 3.9 Core material grain size distribution 37 Figure 4.1 Consolidation paths for specimens of various fines content 44 Figure 4.2 Post-test grain size distribution for tests C-0, C-13, C-18, C-23, 47 C-28 and C-33 (a-f) Figure 4.3 Water head distribution for tests C-0, C-13, C-18, C-23, C-28 and 50 C-33 (a-f) Figure 4.4 Hydraulic conductivities for specimens of varying fines content 54 Figure 4.5 Variation of shear wave velocity with vertical effective stress 56 Figure 4.6 Variation of shear wave velocity with vertical effective stress for 58 fines content (Sf) of 0, 13 and 18 % (a) and fines content of 23, 28 and 33 % (b) Figure 4.7 Variation of shear wave velocity with vertical effective stress for 60 tests C-0 and C-13 (a), C-18 and C-23 (b), and C-28 and C-33 (c) Figure 5.1 Variation of void ratio with fines content 64 Figure 5.2 Volume and porosity as a function of fines content for gap-graded 66 material Figure 5.3 Intergranular soil mix classification 67 Figure 5.4 Void ratio - fines content relation for intergranular soil mixes 67 Figure 5.5 Compressibility of specimens of various fines content 69 Figure 5.6 Variation in average shear wave velocity with mean effective stress 73 Figure 5.7 Variation of small strain shear modulus with mean effective stress 74 Figure 5.8 Theoretical versus calculated G m a x 76 Figure 5.9 Variation of shear wave velocity with void ratio for constant fines 79 content Figure 5.10 Variation of shear wave velocity with void ratio for similar applied 80 vertical stresses ix Figure 5.11 Variation of shear wave velocity with fines content for each stage of 82 vertical loading Figure 5.12 Grain size distribution for core and transition material of the Bennett 84 dam Figure 5.13 Variation of shear wave velocity with mean effective stress for 88 specimens with 34 % fines content Figure 5.14 Variation of shear wave velocity with mean effective stress for 90 specimens with 25.9 % fines content Figure 5.15 Consolidation behavior of C-33 material and target void ratios of 91 triaxial testing program for specimens with 34 % fines content Figure 5.16 Consolidation behavior of C-28 material and target void ratios of 92 triaxial testing program for specimens with 25.9 % fines content Figure 5.17 Comparison of shear wave velocities of different laboratory 94 programs; nominal gradation specimens Figure 5.18 Comparison of shear wave velocities of different laboratory 94 programs; fines reduced specimens Figure 5.19 Calculated versus theoretical G m a x for C-28 and C-33 of the current 97 study (A = 320, b = 0.6) Figure 5.20 Calculated versus theoretical G m a x for C-28 and C-33 of the current 98 study (A = 415 and 450, b = 0.42) Figure 5.21 Overview of seismic plane layout at the W A C Bennett dam; 101 Plane 22 and 26 Figure 5.22 Benchmark No. 1 area; borehole DH96-32 of Plane 22 102 Figure 5.23 Benchmark No. 2 area; Plane 26 103 Figure 5.24 Estimated as-placed void ratios for intact core material 105 Figure 5.25 Crosshole seismic profiles; Plane 22 (a) and 26 (b) 106 Figure 5.26 Variation of shear wave velocity obtained in field testing with mean 107 effective stress (Planes 22 and 26) x Figure 5.27 Comparison of shear wave velocities of intact core for field and 109 laboratory programs Figure 5.28 Comparison of shear wave velocities of intact core and fines reduced 110 core for field and current study Figure A . l Grain size distribution for Fraser River sand of commissioning tests 124 Figure A.2 Direct shear test apparatus 127 Figure A.3 Interface friction angle from direct shear tests with Fraser River sand 128 and smooth aluminum Figure A.4 Schematic of force equilibrium of the soil in the rigid-walled 129 permeameter Figure A.5 Fraser River sand shear wave velocity comparison; triaxial (isotropic 131 loading) versus rigid walled permeameter (5= 19.5°, K 0 = 0.5) Figure A.6 Fraser River sand shear wave velocity comparison; triaxial (isotropic 131 loading) versus rigid walled permeameter (8 = 19.5°, Ko = 0.85) xi A C K N O W L E D G E M E N T S I would like to extend sincere thanks and gratitude to my research supervisor, Dr. Jonathan Fannin, for his continued guidance and support throughout the course of this study. I also wish to thank Dr. John Howie for his helpful input and Dr. Dharma Wijewickreme for feedback on this manuscript. Funding support for this research was provided from the National Science and Engineering Research Council of Canada. Findings of the tests at U B C Civ i l Engineering were compared with additional laboratory data on reconstituted soils and field data on core materials of the W A C Bennett dam, through support of Mr . Stephen Garner at British Columbia Hydro. His interest in the project, and input to discussions on the data, are gratefully acknowledged. Further thanks are given to Mr. Saman Vazinkhoo, of B C Hydro, and Mr. Micheal Jefferies, of Golder Associates, for contributions to discussions on the field and laboratory data respectively. Thanks are extended to my colleagues in the geotechnical group (Maoxin L i , Hamid Karimian, A l i Khali l i , Ernie Naesgaard, Mavi Sannin, Pascale Rouse, and Lalinda Weerasekara) for their help and insightful conversations with respect to the research. Thanks are also extended to the technical staff (Scott Jackson and John Wong) and to the C iv i l Engineering workshop (Harald Schremp and B i l l Leung). Finally, I would like to thank my family and friends back East for their constant support, patience and understanding over the course of this study. xi i 1.0 INTRODUCTION Engineering applications for which geophysical surveying can be used are extensive. Whether it is natural resource exploitation, assessment of static and dynamic stability of municipal works or to determine anomalous zones in sensitive structures, seismic surveying has been employed with great success. Seismic waves are commonly used to characterize the mechanical properties of soils, either through in-situ techniques such as crosshole and downhole seismic testing, or laboratory measurement using bender elements. Techniques that allow measurement of shear wave velocity are well-suited to characterization of mechanical properties of soil, because shear wave velocity is dependent on density, confining stress and fabric of a soil. In sensitive structures, where non-intrusive testing is preferred over traditional programs of drilling, mechanical properties of zones of the structure can be characterized or assessed using seismic profiling. Furthermore, in the case of internally unstable soils, where a seepage-induced fines loss occurs over time, the phenomenon may be well-suited to geophysical monitoring. Performance monitoring at the W A C Bennett dam involves crosshole seismic surveying though transition and core units of the dam. Fifteen planes of interest are monitored on an annual basis. Changes in shear wave velocity in these planes over time may indicate a change in the structure or state of the soil. It is of interest to examine the influence of fines content on shear wave velocity of the silty sand core. 1.1 Purpose of the study This laboratory program investigates the relation between shear wave velocity and fines content of a silty sand, and examines how that relation varies with effective stress and seepage flow. Accordingly, a laboratory testing program was undertaken on six gradations of a silty sand from the core of the W A C Bennett dam. As constructed, the core of the dam has a fines content of 33 %. A multistage test procedure was designed with stress, hydraulic gradient and fines content being the test variables. The fines l content of the specimens ranged from 0 to 33 %. They were reconstituted in a rigid-walled permeameter equipped with bender elements, and shear wave data were recorded across the specimen for each stage of loading and induced seepage flow. The influence of stress, hydraulic gradient and fines content on shear wave velocity in these slurry-deposited soils is examined, and comparison then made to shear wave velocities of another laboratory program that involved moist-tamped specimens and also to insitu shear wave velocities of the core from annual crosshole seismic testing at the dam site. The main objectives of the study are: • To examine how shear wave velocity is influenced by fines content of a silty sand; • To examine how those relations may be affected by seepage flow; • To compare shear wave velocity of specimens reconstituted by methods of slurry deposition and moist-tamping; and, • To compare shear wave velocity of the current study to shear wave velocities obtained in the field. 1.2 Organization of the thesis In Chapter 2, a review of literature is presented on shear wave velocity and small strain shear modulus. Shear wave theory is introduced, and field and laboratory measurement described. Empirical relations used in determination of the small strain shear modulus of granular materials, relative influences of stress, material constants and void ratio on the small strain shear modulus, as well as, experience and trends are presented. In Chapter 3, apparatus and materials used in testing, along with the test procedure is described. The configuration of the permeameter, with respect to loading, water control 2 and data acquisition systems, and bender element system is explained, along with a detail on the materials used in testing. A brief explanation of the specimen reconstitution technique, setup and test procedure follows. Results of testing are found in Chapter 4; namely, consolidation behavior, homogeneity, hydraulic conductivities and shear wave velocity data are presented. In Chapter 5, shear wave results are analyzed with respect to influences of stress, fines content and void ratio, and comparison made to other laboratory and field data for core material. Data from the current study are compared to data from testing of another laboratory program (moist-tamped, triaxial) and to field data. Summary of findings and conclusions of the study are given in Chapter 6. In Chapter 5, shear wave velocities are presented and then compared with other studies and empirical relations with respect to mean effective stress. This requires consideration of frictional losses in the rigid-walled permeameter cell. Frictional losses from the sidewall are carefully considered, and values of Ko and interface friction are determined by comparison to a companion set of shear wave data in a triaxial cell. Comparison and discussion with respect to the evaluation of mean effective stress is given in Appendix A . Shear wave velocities are tabulated for applied vertical effective stress, and mean effective stresses using upper and lower bounds of Ko (0.85 and 0.4, respectively) in Appendix B . 3 2.0 L I T E R A T U R E R E V I E W A review of literature regarding shear wave velocity and small strain shear modulus is presented. In section 2.1, mechanics of shear waves and how they are used in the field and laboratory is discussed, along with a summary of trends that have been established over time. Section 2.2 examines empirical relations used in determination of the small strain shear modulus of granular materials. Various empirical formulae are presented, together with a description of governing factors. The influence of stress, material constants and void ratio on the small strain shear modulus is discussed, and experience and trends presented. 2.1 Principle of shear wave velocity There are two types of body waves that can propagate through elastic solids; compression, or primary (P-) waves and shear, or secondary (S-) waves. Compression waves travel by oscillation (compression and expansion) in the direction of wave travel and can pass through both water and soil. Shear waves are of interest in soil stiffness characterization as shearing can only occur through the soil skeleton. Particle motion, or elastic shearing, occurs in a plane transversely oriented to the direction of wave propagation. Elastic deformations and particle motions associated with compression and shear waves are illustrated in Figure 2.1. In this figure the propagation direction of the shear wave is toward the right of the page and particles oscillate backwards and forwards for P-waves, and upwards and downwards for S-waves. By elastic theory, the value of small strain shear modulus, G m a x , can be obtained from the shear wave velocity by: G m a x = pVs 2 2.1 where Vs is the shear wave velocity and p is the material density. It has been found that G m a x of a cohesionless soil depends primarily on stress, stress history, void ratio and age (Santamarina et al. 2001; Mitchell and Soga 2005; Howie et al. 2001; among others). 4 Consequently, shear wave velocity of soils is a valuable measurement that can be used in determination of soil properties for engineering purposes. The following sections describe how shear wave velocity can be measured, both in the field and in the laboratory. 2.1.1 Techniques of measurement The use of seismic waves in characterization of ground conditions is routine: shear waves can be measured both in the field (large scale) and in laboratory testing (small scale). In both applications, shear waves are created by a seismic source which transmits a small perturbation to the soil. The transmitted shear wave propagates through the soil and is recorded at the receiver. Knowing the distance of wave travel between the transmitter and receiver, and the time difference between initial transmission of the shear wave and arrival of the shear wave at the receiver allows determination of the shear wave velocity. Two common survey techniques to measure shear wave velocity in the field are downhole and crosshole seismic surveying. 5 Downhole surveying involves a source which is triggered on the surface, and shear wave data are recorded by receivers mounted vertically down the borehole (Figure 2.2). A n impact hammer is commonly used as a source; the hammer strikes a metallic plate that is coupled to the soil. Single or multiple receivers are secured to the borehole wall at various locations down the borehole and shear wave data are recorded to disk at each interval. The shear wave velocity is determined knowing the distance between the source and receiver, and the time of first arrival of the shear wave. The advantage of this technique is that only one borehole is required and disadvantages are that soil horizons cannot always be easily delineated, and that only a small area is sampled. In crosshole surveying, multiple boreholes are used; shear waves propagate in the horizontal direction and the sampled area is larger. In the general case, a source is lowered down one borehole to a specific depth and the receiver package is located at a similar depth in an opposite borehole (Figure 2.3). Shear wave data are collected across horizontal planes at varying depths within the borehole. Downhole impact sources generally comprise of a mechanical anvil type assembly that couples to the borehole wall. A switch mechanism is used to trigger impact and thereby introduces vertically polarized shear waves to the surrounding soil. Polarity of the source can be reversed by striking the anvil in the opposite direction. Shear wave velocity is deduced knowing the distance between boreholes and the time taken for the signal to arrive at the receiver. Time can be taken as the time of first arrival of the waveform and confirmed using the 'cross-over' method. Reverse polarity of the source permits two waveforms of opposite polarity to be plotted together. Comparing the two waveforms together allows detection of P-waves within the S-wave arrival; only S-waves can be reversed, the polarity of P-waves wil l not change. The first crossover of shear waveforms is taken as the arrival time. Shear waves can also be generated and propagation velocity measured in the laboratory. Two common techniques of laboratory measurement are now considered; namely, the resonant column device and piezoceramic bender elements. 6 Data acquisition system Figure 2.2. Schematic of downhole seismic surveying (after Olsen Engineering, 2005) Figure 2.3. Schematic of crosshole seismic surveying (Olsen Engineering, 2005) 7 2.1.1.1 Resonant column In resonant column testing, a hollow or solid specimen, confined within an axisymmetric cell, is excited until the resonant frequency of the soil is established. First-mode resonance is the frequency at which maximum top-cap motion is observed; for soils, first mode resonance frequency generally starts near 20 Hz (Anderson and Stokoe, 1978). Excitation is driven by a coil magnet assembly that rests on the top platen of the device (Figure 2.4). The system can provide torsional or flexural modes of vibration; a system of four coil magnets, connected in series, provides torque to the specimen and only two are needed to provide a horizontal force which induces flexural excitation. Accelerometers on the top platen relay the specimen response to the signal analyzer for real time evaluation (Figure 2.5). Velocity and small strain shear modulus are then determined knowing the resonant frequency and the dimensions of the specimen. Figure 2.4. U B C resonant column apparatus (after Zavoral, 1990) 8 *nceiru!irunuly/er, A ' D board, or c»cilloicopc_ si una I conditioner / computer A'Uu) pressure vessel siiinal generator / Figure 2.5. Schematic of a resonant column device (from Cascante and Santamarina, The bender element method, developed by Shirley and Hampton (1978), is a laboratory technique to obtain the elastic shear modulus at small strain ( G m a x ) of a soil by measuring the velocity of propagation of a shear wave though a specimen. A bender element consists of two piezoceramic plates bonded, on either side, to a thin metal shim. When an electrical impulse is applied to the element one plate elongates and the other contracts creating a mechanical pulse or 'bending' of the transmitting element (see Figure 2.6). A n epoxy or polyurethane coating protects the element from moisture in soils. Elements are generally mounted such that approximately 1/3 of their length (lb) is mounted in the housing, 1/3 passes through an opening for a filter stone, and 1/3 protrudes into the soil specimen and provides soil-element coupling (Figure 2.7). The length of element embedment into the soil must be selected so that good coupling, and energy transfer to the soil, is obtained without sacrificing the durability of the element (Dyvik, 2006). When the cantilevered length of the element bends, it pushes the soil particles adjacent to the element tip thereby inducing a shear pulse, and additional compression waves, into the surrounding soil (Figure 2.8). The transmitted shear wave travels through the soil sample, perpendicular to the direction of soil particle motion and is intercepted by the receiver elements. The mechanical response at the receivers is 1997) 2.1.1.2 Bender elements 9 converted to an electrical output and the received waveform is recorded to monitor and to disk. Figure 2.6. Relaxed and excited bender elements (after Dyvik and Madshus, 1985) Direchun of. shear* wave-s •• propogations; Direcnon of plemenf hp .„ and soil partirle movemenf EPOXY - H . - BENOIR ' HEMENT, RUBBLK 11 HOLE FOR „ WIKE L t A U l Figure 2.7. General cantilever mounting configuration for bender elements (after Dyvik and Madshus, 1985) 10 compression P-wavc Figure 2.8. Schematic of compression and shear wave generation (after Santamarina, 2000) In early tests with clays (Dyvik and Madshus, 1985), bender elements were installed in the resonant column and excellent agreement was observed between data sets of the two techniques. Comparing the two, the advantage of the bender element technique is that both the test procedures and computations are much more simple. Bender elements can be easily configured for use in triaxial and oedometer cells, both in vertical and horizontal directions. Accurate determination of shear wave velocity, and hence G m a x for soils, however, requires careful consideration be given to distance and travel time between elements. Propagation velocity of shear waves is determined from the tip-to-tip distance (L t t ) divided by the travel time (t) for the signal. Although the travel distance is confirmed as the tip-to-tip distance between bender elements (Dyvik and Madshus 1985; Viggiani and Atkinson 1995), concern with shear wave velocity determination relates to the subjectivity of the arrival (travel) time of the shear wave. Arrival time can be 'picked' directly from the receiver signal both manually or using computer programs and is considered to be the first deflection of the waveform, however, other factors need to be taken into account. A typical output (or receiver) waveform obtained from a square wave, or step, input source is shown in Figure 2.9. In this figure points A , B , C and D may all be considered as points from which the first arrival time of the shear wave is picked; A is the point of first deflection of the wave, B is the reversal point, C is the cross-over point and point D 11 is the first peak. Ambiguity in the determination of the first arrival time is sometimes caused by the arrival of a transverse wave traveling with a velocity of a compressional wave. This 'near-field' effect may obscure the first arrival of the shear wave when the distance between the transmitter and the receiver is small and separation of component waves becomes difficult. In Figure 2.9 the near field effect is marked by the downward deflection of the waveform between points A and B . Point B is suggested as the time of arrival by Jovicic et al. (1996) while point C is thought to be the time of arrival of the shear wave by others (Kawaguchi et al., 2001; Lee and Santamarina, 2004). Input Output Figure 2.9. Typical shear wave signal (after Lee and Santamarina, 2004) Near field effects arise in soils testing as the source is not a perfect point source in an unbounded medium. Sanchez-Salinero et al. (1986) discuss near field effects from spherical spreading wave fronts at different velocities (shear and compressional) and at different values of attenuation. This deflection, caused by near field waves, obscures the first arrival of the shear wave, thus making it difficult to pick an accurate time. Minimizing the near field effect requires maximizing the L t t/A, ratio and minimizing the y i D ratio (Jovicic et al. 1996; Brignoli et al. 1996; Arulnathan et al. 1998). As a general rule, increasing the wavelength to bender element length ratio (A./lb) to greater than 4 allows generation of a waveform that is closer to a point source (Arulnathan et al., 1998). In laboratory testing, however, cell assembly does not always conform to these 12 requirements. As such, it is advantageous to use other methods from which arrival times of shear waves can be assessed. Alternate techniques were developed so that first arrival picking could be avoided. These techniques involve numerical analysis of waveforms in the frequency domain (cross-power) or in the time domain (cross-over and cross-correlation). While frequency domain techniques may be well-suited to sine waves, square waves comprise a spectrum of different frequencies and numerical analysis in the frequency domain is therefore complex. In the field, and wherever the polarity of the input motion can be reversed, the cross-over method can be used. As mentioned in section 2.1.1, the cross-over method involves comparison of opposite polarity waveforms and allows detection of the true arrival time of the shear wave. Compression wave arrivals are not reversible and can therefore be detected upon analysis of the oppositely polarized waveforms. Another common time domain technique involves cross-correlation of two signals. The cross-correlation function, CCxy (x), indicates the degree of correlation between two signals, X(t) and Y(t), versus time shift (r) imposed to the signals. The analytical expression of cross-correlation follows as (Mancuso et al., 1989): where T is the length of the time record. The signals are correlated against one another and amplitudes of each waveform are multiplied together and then summed over a specified unit of time. This is done for each increment of time, or time shift (T), until a maximum sum is found. The maximum sum of amplitude, or maximum correlation, coincides with an almost perfect match between signals. Figure 2.10 shows (a) two receiver waveforms of the current study and (b) the cross-correlated waveform. Knowing the tip-to-tip distance between receivers of similar frequency content and the time taken to travel, the shear wave velocity can be calculated. The peak-to-peak time difference, t(p-p), indicated in Figure 2.10a, also provides direct measurement of travel time. This method, though 13 14 similar in concept to cross-correlation, is preferred since the peak values are clearly defined in each waveform and there is very little effect from attenuation of the waveform. The difference in arrival time using these two methods is due to attenuation of the waveform; the cross-correlation method correlates the entire waveform unlike peak-to-peak where only the first strong motion is compared between signals. Using the peak-to-peak time difference between receiver waveforms (or cross-correlation technique), allows some of the ambiguity caused by this near field component to be decreased and the arrival time of the received signals can be computed and validated. 2.1.2 Experience and reported trends Pioneering research in the area of elastic waves and soils are found in laboratory studies conducted by Hardin and Richart (1963), Hardin and Black (1966), Hardin and Drnevich (1972), Iwasaki and Tatsuoka (1978), Anderson and Stokoe (1978), Roesler (1979), Y u and Richart (1984), Stokoe et al. (1985), Hardin and Blanford (1989), among others. Most of these studies involved testing in the resonant column device. This section addresses some basic trends noted in the study of shear wave velocity. The purpose here is to establish confidence in the use of shear wave velocity to characterize the mechanical behavior of granular soils. Parameters influencing shear wave velocity, and hence small strain shear modulus, are discussed separately in section 2.2. Some of the early experimental programs, conducted by Hardin and Richart (1963), Hardin and Black (1966) and Hardin (1978), considered the influence of confining pressure, time, void ratio and grain characteristics on shear wave velocity of soils. In these tests, rounded Ottawa sand, crushed quartz sand and silt were reconstituted and tested in a resonant column device. For isotropic loading, shear wave velocity data for specimens were fit by trendlines of the form; Vs = a a m , p 2.2 15 where o"m' is the mean effective stress, and a and P are experimentally determined. More specifically, this is written for coarse and fine-grained soils as; Vs = a CT. m (for coarse grained materials) 2.3 Vs = a i CTm' p O C R k (for fine grained materials) 2.4 where O C R is the overconsolidation ratio and k is a material property which was later found to be influenced by plasticity. Results from these experimental programs established important trends of shear wave velocity. Generally speaking these findings are: - shear wave velocity varies with approximately }A power of the mean stress - shear wave velocity varies linearly with void ratio - shear wave velocity of silt is highly dependent on age It was later recognized that stress anisotropy can also effect shear wave velocity and that velocity may be dependent on effective stress in the plane of wave propagation (aa') as well as effective stress in the plane of particle motion (CTp') (Roesler, 1979). Generally, however, the relative contribution of velocity for each plane of stress is not widely varying (Yu and Richart, 1984). Velocity-stress exponent P is applied to the average effective stress in the two planes. For anisotropic stress states, shear wave data are fit to trendlines of the form: In equation 2.2 through 2.5, coefficient a is dependent on grain properties and packing of the soil, and can be separated into the terms A and F(e), respectively. The velocity-stress exponent p is dependent on contact behavior between particles and fabric (Santamarina and Aloufi 1999; Santamarina et al. 2001). Cho et al. (2006) provide a detailed summary of trends relating to material and packing coefficient, a, and velocity-stress exponent, p (see Table 2.1). They compiled a database from new experiments and examined the influence of grain sphericity, roundness and regularity on coefficients a and p. It was Vs = a[(CTa' + CTp)/2] P 2.5 16 Table 2.1. Database compiled from new experiments (after Cho et al., 2006) Particle soape t'.-tr retettaa Soil 15 pe R S P 'Nevada sand -'' 0.60 0.85 0.73 56.3 0.242 Tkim> sand *,'0.40 0.80 0.60 70.7 0.231 Margaret river sand1 • 0.70- 0.70 0.70 93.2 0.21 <J ASTM 20/10 sand n.so 0.90 0.S5 ' 72.7 0.223 Pome Vedra sanu*"' 0 50 0.S5 0.58 160.6- 0.161 SMS crashed sand' 0.20 0.70 0.45 55.7 0.252 9C1 crushed sand • 0.25 0.70- 0.48 54.0' 0.297 Jekyll island ssndr'" 0 30 0.S5 " 0.5S 0.17? ASTM graded sand 0.80 0.90 0.S5 — — Blasung sand 0.30 055_ 0.43 — — Glass beads 1.00 LOO •1.00 — — Granite powder 0.40 " 0.24 0252 — — Ottawa #20/30 sand 0.90 0.90 o.yo — — Oliawa F-liO sand 0.70 0.70 0.70 — — 7U7-crushed sand 0.20 O.SO 0.50 — • — IK9-crashed nod " 0.20 0.40 0.30 35.0 0.350 2Z8-crashsd sand O.iO 0.60 035 25.0 0.360 5Z9-crusbed sand 0.30 0.90 0.60 68.9 0 2 IS 61! t-crushed sand 0.20 O.SO 0.50 53.0 0.272 9Ff-crusiied sand 0.20 0.S0 0.50 41.8 0.510 3P3-crushed sand 0.20 0.70 0.-+5 41.0 0.280 6A2-cns»hed sand 0.20 0.75 0.4S 50* 0.260 5UI-crushed a^nd 0.35 0.70 0.43 42.6 0.266 Sandboii sand 0.55 0.70 0.63 — — Paytona Beach sand1" 0.62 o.;o 0.66 — — Fraxer River sand" 0.25 0.50 0.38 — — Michigan dune sand' 0.77 0.87 0.82 — — Onawa #20/70 sand1' 0.76 0.8! 0.79 — — Ottawa #45 sand' 0.45 0.68 - ;o.57 — — Ottawa #60/80 sand"" 0.65 0.78 0.72 - —j Oitawa;? 90 sand"' , 0.40 0.60 " 0.50 — Syncrude Tailings' , 0.47 0.62 ' 0-5S-" — — i 02-crushed sand 0.25 0.80 033 — — 106-crushcd sand 0.30 O.70 0.50 — — 6F5-enished sand 011 0.80 0.53 — — 8B8-crushed sand '0.25 0.80 OS3 — — 3C7-crushed sand '0.25 O.SO 0.53 — — 2L.6-eroshed sand - 0.25 1)80 0.53 — — Note: D%i xm'-m VTA:. (mm|, C « V U K fan sn.stomiitit c.t^.f.w--* *uu. ti\ p = K U i M m i =*i8* *< « J tf*^h£.u- -A-AW vdodry imfe) at •*Its icAinr<; is ray <n*>:*h. found that as sphericity, roundness and regularity of grain particles decrease, a also decreases and p increases. Two consequences of irregularity are a lower stiffness (indicated by decrease in a) and higher sensitivity to stress (indicated by an increase in P). Additionally, as particle irregularity increases, compressibility under Ko loading increases. From Table 2.1, a varies from 25.0 to 160.6 and P varies from 0.16 to 0.36. These data 17 broadly confirm the equation postulated by Santamarina et al. (2001) which relates velocity-stress exponent (3 to a by: p = 0.36 - a/700 2.6 As discussed above, trends are observed from shear wave velocity. Consider now selected studies that examine the influences of stress state, void ratio and grain characteristics on the small strain shear modulus, G m a x . 2.2 Small strain shear modulus and influencing factors Small strain shear modulus is an important parameter in engineering design, especially with regard to soils that are subject to dynamic loading. G m a x can also be indirectly correlated to other soil parameters such as liquefaction potential, fabric and density. Types of equation are used to estimate G m a x of sands; one for isotropic stress conditions and another for anisotropic stress conditions. Hardin and Black (1966) postulated: where A is a material constant which depends on elastic properties of the grain particles, F(e) is the void ratio function which accounts for the soil density or packing, P a is generally taken as the atmospheric pressure and is used only in constant normalization, <rm' is the mean effective stress, and b is a stress exponent generally taken as 0.5. The other form of the equation, for anisotropic stress conditions, takes into consideration stresses in planes of wave propagation (rja) and particle vibration (a p) and can be written as (Yu and Richart, 1984): G m a x = A F ( e ) P a ' - b a, , b 2.7 G m a x = A F ( e ) P a u f e [(o-a+rjp)/2]* 2.8 18 2.2.1 Stress condition Equations 2.7 and 2.8 indicate that G m a x is very sensitive to a change in stress. Research in this area has generally found that a stress exponent of b = 0.5 provides a close fit to the data for specimens in a state of isotropic stress and for specimens in a state of anisotropic stress. The relative influences of stress on G m a x for both isotropic and anisotropic states are now considered. 2.2.1.1 Isotropic conditions As previously discussed, many experimental studies indicate that G m a x of granular soils is a function of confining pressure to a power of approximately 0.5 under isotropic stress conditions (Hardin and Black 1966; among many others). This empirical relation for Gmax is, however, different from the analytical expression developed in classical contact theory. The Hertz-Mindlin contact theory, developed for perfectly smooth, rounded, elastic spheres, indicates that at value of 1/3 is appropriate; this is validated from results of experimental work done on glass beads and high precision steel spheres (Santamarina et al. 2001; Cascante and Santamarina 1996, respectively). Naturally occurring granular soils, however, are rarely perfectly smooth and rounded. Particle roundness together with roughness (Santamarina and Cascante 1998; Yimisri and Soga 1999) lend an expected deviation from classical elastic theory as not only particle contact coordinations change but stress-induced fabric changes may occur as well (Santamarina and Aloufi, 1999). From Table 2.1, presented in section 2.1.2, stress exponents may range from 0.32 up to 0.72 for natural and crushed sands depending on the contact behavior and fabric. 19 2.2.1.2 Anisotropic conditions Roesler (1979) developed a technique with a torsional exciter to measure the velocity of polarized shear waves in cubical sand box. This setup enabled the separation of different shear wave velocities caused by stress anisotropy in a subsoil. Figure 2.11 shows the variation of shear wave velocity of sand samples with stress in three planes. As shown in the figure, shear wave velocity is dependent on stresses in the direction of the wave propagation (rja) and in the direction of particle vibration (rj p), but not in a plane orthogonal to both (rj s). The following empirical relation was noted: V s « o - a crp rj s l.y For anisotropic stress conditions, the empirical equation becomes: G m a x = A F ( e ) P a 1 - a - p o - a a r j p P 2.10 Although there is a slight difference in velocity-stress exponents between the planes of particle motion and wave propagation, shear wave velocity does not change widely between them for the range of stresses examined. Y u and Richart (1984) identified that testing in the resonant column device is axially symmetric and therefore a two dimensional condition. Accordingly, the empirical equation for anisotropic stress conditions can be taken as Equation 2.8, where b represents the sum of the stress exponents as they are approximately equal (a = 0.298 and p = 0.214, Roesler 1979). Another program of testing carried out by Yan and Byrne (1990) investigated stress anisotropy effects on shear wave velocity obtained using downhole and crosshole seismic surveys. In their laboratory program, the hydraulic similitude method was used to invoke high body forces and hence high stresses similar to those of the field condition. Shear wave velocities were measured between vertically and horizontally mounted bender elements within a sand box. In loading, downhole tests gave higher shear wave velocities 20 3 « mfeec 2SQ ft) sample 1 sample- 2 r 15 . Nftm2 Figure 2.11. Variation of shear wave velocity of sand samples with stresses in three planes: (a) rj a; (b) rj p; (c) ors (after Roesler, 1979). than the crosshole tests under the same applied stress condition. Therefore, in the framework of the current discussion, stress acting in the direction of particle motion was found to have a stronger effect on shear wave velocity than stress in the direction of propagation. 21 From resonant column tests with Ottawa sand (Santamarina and Cascante, 1996) it was also found that stress acting in the direction of particle motion has a stronger effect on the propagation velocity than does the stress in the direction of propagation. Gmax-stress regression parameters from the study are presented in Table 2.2. Slightly larger differences are noted between stress exponents where the sample is subjected to stress ratios greater than unity. Table 2.2. Anisotropic G m a x stress exponents (Santamarina and Cascante, 1996) Parameter a P a + p = b Related stress On Axial extension (stress ratio < 1) 0.24 0.32 0.56 Axia l compression (stress ratio >1) 0.20 0.34 0.54 Most studies on sand indicate that stiffness is greatest in the horizontal direction, but other studies disagree. Because anisotropy in sands is related to both fabric (contact) anisotropy and stress-induced anisotropy, mixed results obtained in the literature may be due to differences in sample preparation procedures (Mitchell and Soga, 2005). It is anticipated that the relative contribution from different planes of stress is more pronounced in platy or lenticular shaped sand particles. Furthermore, a negligible difference in stress exponents between stress planes may be anticipated in natural sands whose grain shapes are rounded or sub-angular. 2.2.2 Void ratio function A void ratio function, F(e), accounts for the effect of specimen density or packing on G m a x . A small void ratio implies a greater number of contacts, and a higher number of contacts typically increases the stiffness of the material. Because grain shape has a direct influence on the number of contacts and stiffness, G m a x , of a material, different void ratio functions have been postulated which depend on grain shape. 22 As mentioned earlier, research conducted by Hardin and Richart (1963) involved laboratory testing of rounded Ottawa sand, crushed quartz sand and crushed quartz silt. Shear wave velocities of specimens of different grain shapes (rounded Ottawa sand and angular crushed quartz sand), prepared to various void ratios, were examined and it was found that shear wave velocity varies linearly with void ratio, independent of grain size, gradation and relative density. In terms of small strain shear modulus, these are expressed as: G m a x = 700 [(2.17-e) 2 / l + e] a m ' 0 5 2.11 for rounded Ottawa sand and, G m a x = 326 [(2.97 - e) 2/l + e ] o V 0 5 2.12 for angular crushed quartz sand. Figure 2.12 shows the variation of shear wave velocity with void ratio and confining pressure for dry round and angular sand. At low pressures the velocity of the angular sand is higher than rounded sand at comparable void ratios, however, at higher stresses of approximately 390kPa (6000psf) the velocities approach each other. From these results it was concluded that shear wave velocity is influenced by void ratio (F(e) function) and stress (oV); specifically, shear wave velocity in sands decreases linearly with void ratio, independent of grain size gradation and relative density. It was also noted that shear wave velocity is influenced by particle shape at low confining pressure and that grain shape also affects velocity through its effect on the range of possible void ratios. Two void ratio functions were defined for rounded and crushed sand, respectively: F(e) = (2 .17-e) 2 / l+e " 2.13 F(e) = (2.97 - e) 2 / l + e 2.14 23 -tool i I I I ,\ I ,—I '.—I 1—IJJ Oi 0<\ 0 5 OS 07 0.8 05 10 II 12 '3 VOID R'ftTIO , -," ' " Figure 2.12. Variation of shear wave velocity with void ratio and confining pressure for dry round and angular grained sand (after Hardin and Richart, 1963) These equations are based on a linear fit to the data, which yields problems at the high and low end of stress. Pestana and Whittle (1995) note that the use of these forms of the void ratio function wil l result in negative void ratios at high stresses. A different form of the void ratio function which is based on critical state testing of Erksak sand relates to a value of e m j n * (Jefferies and Been, 2000). The definition of emin* is the void ratio at which soil behavior changes from particulate to that of a rock-like solid. This void ratio function takes the form; F ( e ) = l / ( e - e m i n * ) 2.15 24 2.2.3 Material constants The material constant, A, is a correlation constant which depends on the grain properties of the soil. Theoretically, it relates to the elastic properties of the grain particles (Santamarina et al., 2001). The following experimental programs are selected for comparison since they all use the form of the void ratio function expressed in Equation 2.15. Comparison is also made between material constants of clean sands and silty sands (see Table 2.3). Table 2.3. Comparison of A parameters between selected studies; F(e) = (2.17 - e) / l + e Study Material description A value A value (S f=0) (S f >0) Rounded, uniform Ottawa 700 sand Clean (Toyoura and Iruma 700-900 < 700* sands) and natural sand Ottawa sand with silt 612 207-454 * Authors note significant scatter with natural sand but that the shear modulus is lower than that for a clean sand at the same void ratio, stress and strain. Iwasaki and Tatsuoka (1978) investigated the shear wave velocities of clean and natural sands. It was found that empirical equations could be used to estimate shear moduli of clean sands tested irrespective of grain shape and size. In their tests they found that empirical equation for G m a x (Equation 2.7) with an A value of 700 and void ratio function (Equation 2.13) for rounded Ottawa sand provided a good fit to the experimental data at a shear strain of 10"4%. For natural sands, however, shear moduli decrease with increase in uniformity coefficient and decrease with increase in content of fines. Values less than 700 were found in testing of the natural sands. Salgado et al. (2000) tested Ottawa sand with varying amounts of silt. The authors observed that G m a x decreases with an increase in silt content up to 20 % silt. The Hardin and Richart (1963) Iwasaki and Tatsuoka (1978) Salgado et al. (2000) 25 decrease in G m a x was reflected in back-calculated A values of 454, 357, 238 and 207, for fines content of 5, 10, 15 and 20 %, respectively. For Ottawa sand without fines, and using the same void ratio function, excellent correlation is observed between A values of the two different test programs (Hardin and Richart 1963; Salgado et al. 2000). This correlation of material constant A helps lend confidence on the use of empirical equations to estimate G m a x knowing the level of stress and void ratio, or conversely, in estimation of stress or void ratio from field calculated G m a x . The relevance of this discussion to the current study is that the A value is a material parameter which is unique for a given soil. One of the objectives of the research is to compare shear wave velocities specimens reconstituted by methods of slurry deposition and moist-tamping for the same material. Since the A value is a unique material property, comparison of shear wave velocity for similar materials allows assessment of other influencing factors, such as soil fabric and density. In summary, shear wave velocity, and hence small strain shear modulus, can be obtained for soils in the field using seismic surveying techniques, and in the laboratory using the resonant column device or bender elements. Review of literature has demonstrated that shear wave velocity can be used to characterize the mechanical behavior of granular soils as it is influenced by mean effective stress, density and fabric. Several empirical relations exist in which shear wave velocity, or small strain shear modulus, can be estimated. Coefficient a is dependent on grain properties and packing of the soil, and can be separated in the terms A and F(e), respectively. The velocity-stress exponent p is dependent on contact behavior between particles and fabric. Material constant, A, can be defined for the soils of the main test program. Although much research has focused on defining parameters for clean sands and uniformly graded materials, the database is relatively small for well-graded naturally silty sands. Therefore, interest lies in the comparison of empirical constants from this study to another laboratory program with the same material, and also with other findings for various sands. 26 3.0 APPARATUS, MATERIALS AND TEST PROCEDURE The following sections describe the apparatus, materials and test procedure used in the laboratory investigation. Each test specimen was reconstituted in a rigid-walled permeameter. The permeameter assembly was outfitted with a bender element system from which shear wave velocity could be deduced across the specimen. Two materials were used in testing: Fraser River sand was used in the commissioning of the test device, and select gradations of a silty sand core material from the W A C Bennett dam site were used in the main test program. 3.1 Permeameter The permeameter cell used in this study is made of anodized aluminum, the cell has an inner diameter of 100 mm and the walls are 16 mm thick. The soil specimen (a) is laterally confined by the rigid wall of the permeameter (1) and vertical load is applied to the top of the specimen by way of a perforated rigid top plate (c), shown schematically in Figure 3.1. A n inlet port (j) in the top of the cell (e) allows water flow to be introduced to the cell and a top plate with 5 mm holes allows for uniformly distributed seepage flow across the specimen. A very fine bottom wire mesh was selected based on the grain size of the material so that loss of fines would be negligible. The wire mesh together with the perforated rigid base plate allow throughflow of water with only minor loss of fines. Any soil passing the bottom mesh is captured in a bottom collection trough (g). The permeameter cell assembly is submerged in a reservoir bath (m) made of Plexiglas. A photograph of the entire cell assembly is reproduced as Figure 3.2. 3.1.1 Vertical loading system Vertical load is applied to the top surface of the specimen through a top plate. The loading piston is threaded to the top plate. A high precision Fairchild Model 10 pressure regulator is used to regulate air pressure from the diaphragm cylinder. The 27 a- soil sample b - bottom wire mesh c - perforated rigid top plats d-piston e - cell top f -cetlbase g • collection trough h-LVDT i - port* 1 to 7 j -water Wet k - perforated rigid base plate I - permeameter cell wai m - reservoir bath n - constant head overflow tube P - vertical load Q - inlet flow rate Figure 3.1. Details of the rigid walled permeameter assembly (after Fannin et al., 1996) Figure 3.2. Permeameter cell assembly in reservoir bath 28 vertical top effective stress is calculated from measurements of a compression load cell with a maximum capacity of 400 kg. The low profile, pancake style load cell is made of beryllium copper and is manufactured in-house. The load cell yields a resolution of stress of +/- 0.1 kPa. Axia l displacement is measured with a linear voltage differential transformer (LVDT) accurate to +/- 0.1 mm. The L V D T , which was also manufactured in-house, measures the displacement of the top plate in contact with the specimen. 3.1.2 Water flow control system Hydraulic gradient is applied across the specimen by varying the level of constant head across the length of the specimen. A schematic diagram of the flow control system is shown in Figure 3.3. A Model 7529-20 Masterflex peristaltic pump is used to supply de-aired water from the reservoir to the constant head inlet tank; the constant head outlet tank, in which the permeameter rests, then feeds the discharge from the specimen back to the reservoir. The constant head inlet tank is connected to a port on the top cap of the permeameter and downward flow is imposed through the perforated top plate. As depicted in Figure 3.3, the applied system gradient (in) is defined as the hydraulic head (H) divided by the length of the specimen (L). System gradient is established by changing the height of the inlet tank. Port 1, located at the top of the cell assembly, enables a measurement of head at the top of the specimen, as does Port 7 at the bottom of the reservoir bath. Differential water head is measured across ports 1, 3, 4, 5, 6 and 7 (hn, 1134,1145, hs6, and \%i respectively) as illustrated in Figure 3.1. Five Setra model C230 wet/wet differential pressure transducers are used to establish the differential water head between ports. Four ports of the permeameter cell are connected to differential pressure transducers with a range of +/- 7 29 Constant head inlet tank Reservoir bath SL Applied constant head, H Constant head outlet Specimen length, L RESERVOIR PUMP Figure 3.3. Schematic of permeameter and flow control system kPa (h]3, I145, h56 and h67) and one port is connected to a differential pressure transducer with a range of+/- 17 kPa (I134). The accuracy of these transducers is believed equivalent to +/-lmm of water. Local hydraulic gradients (ijk) were computed from measured differential water head, knowing the center-to-center spacing between ports. The hydraulic conductivity of each specimen was calculated based on volumetric flow rate and the applied system hydraulic gradient. Flow rate is obtained by collecting a volume of water from the constant head outlet over a discrete time interval. The time 30 interval over which the volumetric flow rate was obtained varied depending on the conductivity of the specimen being tested. 3.1.3 Data acquisition system Output voltages from the load cell, L V D T and differential pressure transducers were recorded by a data acquisition system. The acquisition system comprises a power supply, signal conditioning unit which amplifies output signals and a Metrabyte DAS-16 board connected to a desktop computer. The multifunction D A S board has a 12 bit resolution and digital input and output. Data were collected at a rate of 1 Hz and written to output file using Labtech Notebook software (Laboratory Technologies Corporation). 3.2 Bender element system Piezoceramic bender elements were used to deduce the shear wave velocity across the specimen. As discussed in Section 2.1.1, bender elements are electro-mechanical transducers which can apply mechanical displacement to the surrounding soil from an electric driving signal and can also output electrical signals, or waveforms, upon receipt of mechanical vibration. 3.2.1 Element configuration The bender elements used in this study were fabricated at U B C . Each element is cut from a piezoceramic sheet obtained from Piezo Systems, Inc. to a size of 12 x 12 x 0.6 mm thick. High performance two-layer piezo element sheets (material type PSI-5H-S4) were selected to provide the highest motion, force and response ratings. These properties are important when voltage or force is limited. The elements are then cantilever-mounted, wired and moisture sealed using polyurethane. 31 The bender elements are arranged vertically within the permeameter cell; the system comprises one transmitter and two receivers. The transmitter is mounted cantilever style in the top plate such that two thirds of the element length is embedded in flexible silicon sealant filling the opening in the plate, and one third of its length (4 mm) protrudes into the soil specimen (see Figure 3.4). This embedment length provides adequate soil-element coupling and signal strength. Received waveforms have signal amplitudes of approximately 2 mV at the near receiver and 0.5 mV at the far receiver. The two receivers are mounted on a vertical post and have a fixed tip-to-tip separation of 40. mm (see Figures 3.5 and 3.6); they are at distances of approximately 40 mm and 80 mm from the transmitter. The post-mounted receiver design follows from experimental laboratory research conducted by Byrne and Yan (1990). The vertical post is supported using a rubber coupling which fits into one of the openings of the perforated rigid base plate. The rubber coupling minimizes inherent vibration noise down the posts induced from 'bending'. Having two receivers is advantageous as a direct correlation can be made between the two waveforms of similar frequency content. As described in section 2.1.1.2, 'picking' of first arrival of the shear wave can be difficult due to near field effects. Having two waveforms of similar frequency content allow peak-to-peak interval time to be used in deducing shear wave velocity instead of using the first arrival times at each receiver. The difference in time between the first high amplitude peak at each receiver is taken as the interval time required for the shear wave to travel between receivers (see Figure 2.1 la). The peak-to-peak technique is preferred because it removes any discrepancy caused by the near field effect and picking of first arrival time. The fixed separation of 40mm between post-mounted elements, as shown in Figure 3.6, also reduces any ambiguity of travel distance. A fixed distance greatly reduces travel distance errors thereby improving the resolution of the velocity computation. No shear wave velocity interference effect was observed due to the presence of the middle receiver. This was confirmed by comparison of shear wave velocities computed at each receiver. 32 Side view Top view Figure 3.4. Transmitter element mounted on the top plate Figure 3.5. Post-mounted receiver elements on the cell base 33 40mm Front view H Scale: 10mm Profile view Loading piston Top plate Perforated rigid top plate Soil specimen Transmitter Receivers Rubber coupling Perforated bottom plate Figure 3.6. Schematic diagram of bender element system 3.2.2 Peripheral electronics Peripheral equipment used in shear wave generation and recording is illustrated in Figure 3.7. A n Exact model 7030 function generator provided an excitation voltage to the transmitter element. The driving signal used in testing was a square pulse with a voltage of 10 V . Although some researchers have favored using a single pulse sine wave to minimize near field effects (or 'masked' first arrival of the shear wave), the square pulse used in this program of testing resulted in clear received signals and was preferred for convenience of use. It is thought that the effect of a masked arrival of a shear wave increases with increase in stress or stiffness of soil. At high stresses the true signal can be more attenuated than at lower stresses, and it may become difficult to distinguish the first arrival of the shear wave from the background noise and p-wave arrival. The phenomenon was not encountered in this study. 34 Exact 7030 function generator Nicolet 4094B digital oscilloscope Figure 3.7. Schematic diagram of peripheral equipment configuration A Nicolet 4094B digitizing oscilloscope was used to record system output. A sampling rate of 5 psec on the oscilloscope was selected to allow proper resolution of the waveform. Three channels provided real-time output to an oscilloscope monitor, and to disk for further analysis. 3.3 Materials Two materials were used in this laboratory study: Fraser River sand was used in commissioning tests, and soil from the W A C Bennett dam was used for the main program of testing. 3.3.1 Fraser River sand Fraser River sand was used in the commissioning of the test device. Fraser sand is uniformly graded with angular to sub-angular shaped particles (d5o= 0.3 mm, Cu= 2.5). The nominal grain size distribution is shown in Figure A . l of Appendix A . 35 3.3.2 Core material: W A C Bennett dam The material selected for construction of the zoned earthfill dam originated from extensive glacial moraine deposits near the site. The moraines comprise interbedded sands and gravels with a predominance of silty gravels containing 10-20 % silt (Morgan and Harris, 1967). The silty sand selected for the core was supplemented, at the time of construction, with a small amount of non-plastic silt from another nearby sandy silt deposit. Core material originally shipped to U B C was obtained from a program of sonic drilling at the Bennett dam (Figure 3.8). The core material is a broadly graded silty sand with gravel with sub-angular particle shape and a specific gravity of 2.7 (Moffat, 2005). A portion of the material was sieved, washed and divided into selected grain size ranges. Desired gradations were achieved by mixing different size ranges. The gradation believed representative of the core of the Bennett dam, is depicted as 'nominal' in Figure 3.9. Gradations of varying fines content were then produced by scaling percentages from the nominal gradation with the incremental removal of fine material (< 0.075 mm) passing the #200 sieve. In this way, six different gradations with a fines content of 0, 13, 18, 23, 28 and 33 % were established. Test codes follow as C-0, C-13, C-18, C-23, C-28 and C-33, respectively. Grain size distributions of each sample are given in Figure 3.9 and the coefficient of uniformity, Q j , for each gradation is listed in Table 3.1. 3.4 Test procedure Segregation is a primary concern when reconstituting broadly graded soils in the laboratory. A reconstitution technique introduced by Kuerbis and Vaid (1988) involves preparation of soil as a slurry followed by a method of discrete disposition. This modified slurry deposition technique yields a saturated, homogeneous and loose specimen and was used in this study. 36 Figure 3.8. Core material obtained from the 1996 sonic drilling program at the W A C Bennett dam 100.000 Grain size analysis - Core material 10.000 1.000 0.100 Grain size (mm) 0.010 0.001 Figure 3.9. Core material grain size distribution 37 Table 3.1 Index properties for each gradation of the main test program Test gradation Fines content (% <75um) D 8 5 (mm) D , s (mm) D 6 0 (mm) Dio (mm) Cu C-0 0 4.2 0.140 0.78 0.104 8 C-13 13 3.8 0.090 0.65 0.041 16 C-18 18 3.4 0.045 0.60 0.025 24 C-23 23 3.2 0.032 0.53 0.019 28 C-28 28 2.9 0.028 0.48 0.014 34 C-33 33 2.5 0.020 0.42 0.011 38 3.4.1 Slurry preparation Four containers of core material totaling 2000 g were portioned, saturated with de-aired water and placed under vacuum for a minimum of 48 hours to evacuate any entrained air. During this period of air evacuation the soil was gently agitated to promote de-airing. To prepare the cell before receiving the slurry material, the permeameter cell assembly was first submerged in a reservoir bath and left for an hour to free any air from the assembly. Saturation of pressure lines was then checked by visual observation to ensure any air bubbles were discharged. Bubbles were removed by allowing flow of water through the lines. Air-free connections to the ports were made by injecting de-aired water into the fitting of the port and then by connecting the lines under a condition of low flow. 3.4.2 Specimen reconstitution A modified slurry deposition technique was used to reconstitute the sample as it is well-suited to well graded granular materials. Homogeneous slurry was achieved by continuous mixing of the sample followed by discrete deposition under a thin film of water (5 mm or less). This technique minimizes any propensity for segregation, and 38 yields a homogenous and saturated sample. Care was taken to not to disturb the vertical receiver post in the center of the sample and to ensure that material was placed around the elements in a homogeneous and consistent manner. 3.4.3 Test setup The specimen was reconstituted on top of a fine wire mesh (0.038 mm opening size) to a target height of 110 mm. The very small opening size was selected with the expectation that little or no fine material would pass through, and this was confirmed by visual observation. Any fine material passing through the bottom wire mesh was collected in the bottom collection trough. It was found that fines only passed through the mesh during reconstitution of the very bottom of the specimen. This material was dried and weighed for the first two tests and the amount was found to be negligible (< 1 g). Once the specimen is built to desired height, the initial height is measured so that the initial void ratio (e0) can be computed. The surface of the top layer is then gently agitated to ensure that any fines rich layer that may have developed, due to settlement of suspended fines in the thin film of water above the top of the soil specimen, is eliminated. The latter modification to the test setup procedure was made after observation of a very thin layer (< 1 mm thick) of fines after running test C-13. After agitation, clean de-aired water is added to dilute the excess suspended fines, and then siphoned out. The top wire mesh is attached to the perforated rigid top plate (see Figure 3.1) and the assembly is carefully placed so as not to disturb the sample. Care is taken to ensure that the transmitter element is in the same alignment as the post-mounted receiver elements. Vertical load was applied through the top plate. The vertical loading is applied to the top of the specimen by slowly opening the air regulator. A target vertical effective stress of 25 kPa was achieved by gradually increasing the load, whereupon the specimen is left to consolidate. The period over which the load is applied is such that full dissipation of 39 excess pore water pressure occurs. A n elapsed time of 10 minutes was nominally observed. Because medium and fine grained soils may undergo a noticeable increase in small strain shear modulus with time (Hardin and Richart 1963; Anderson and Stokoe 1978), it was necessary to limit any time-dependent ageing effects from the shear wave data collected in this study. Accordingly, each specimen was aged for a period of 1000 min before testing commenced. 3.4.4 Multi-stage testing procedure The objectives of the study are to examine relations between shear wave velocity and fines content and how those relations may be affected by effective stress and seepage flow. The testing procedure is therefore designed in a multistage fashion for which there are three test variables. The test variables were vertical effective stress on the top of the specimen, hydraulic gradient across the specimen and fines content of the specimen. Top vertical effective stresses of 25, 50, 100, 200 and 400 kPa are applied and hydraulic gradients of 0, 2, 4 and 8 are imposed across the specimen. It is recognized that a limitation of these staged test is that void ratio is not constant at each stage of stress, however the intent is to compare to another staged test where void ratio is not constant and to field data for which there is more uncertainty in void ratio. Void ratio comparisons between the different programs of interest are discussed in section 5.5.3.1. For each specimen the following test procedure was adopted: 1. Impose a vertical effective stress of 25 kPa for 1000 min; 2. Holding this stress constant, stages of hydraulic gradient (in) are applied; 3. A hydraulic gradient of 2 is applied and maintained for 15 min, after this time shear wave data were recorded to disk; 4. In the same fashion, gradients of 4 and then 8 are applied for 15 min each; 40 5. After applying a gradient of 8, the inlet tank is then lowered so that there is a near zero gradient; 6. Vertical top stress is slowly increased to the next stage by adjusting the regulator; this is done at a rate such that minimal excess pore pressures are developed. Conditional on the magnitude of the stress increment, loading times ranged from 10 to 30 min; and 7. Repeat steps 2 through 6 for each stage of effective stress. Volumetric flow rates were taken at the end of each stress increment at ( in = 8) for tests C-0 and C-13. For these tests the flow rate was sufficiently large that the elapsed time for measurement of volumetric flow did not interfere with the timing sequence of the tests. The permeability of test specimens C-18 and C-28 an extended period of time (> 15 min) was required in order to collect a representative volume of water from which a flow rate could be deduced. Accordingly, volumetric flow rate was measured at a hydraulic gradient of 8 under an applied vertical effective stress of 400 kPa. In the case of tests C-23 and C-33 it was not possible to obtain a volumetric flow rate as the hydraulic conductivity of the specimen was too low. 3 . 5 Test program The test program had two components. Preliminary tests with Fraser River sand were undertaken to commission the test device. Commissioning was performed so that conditions could be established before the main program of testing commenced. 3.5 .1 Preliminary tests A series of preliminary tests was used to commission the test device. The objective of these tests were two fold; to establish relations from which a value of mean 41 effective stress in the rigid-walled permeameter could be determined and to determine the repeatability of shear wave velocity data. A summary of setup and results of these tests can be found in Appendix A . The relations determined from these tests are called upon in later chapters of this report. 3.5.2 M a i n test program Once the test device was commissioned, the main program of testing was commenced. Six different gradations of a silty sand core material with fines content ranging from 0 to 33 % were tested (specimens C-0, C-13, C-18, C-23, C-28 and C-33). Gradations of maximum and minimum fines content (C-33 and C-13) were tested first in order to determine the expected range of void ratios and shear wave velocities which would be encountered. Tests were then executed based on the incremental increase of fines content (C-18, C-23 and C-28), followed by that with no fines content (C-0). Each test was prepared, reconstituted, aged and tested in stages using a consistent and systematic procedure. The specimens were subjected to identical stages of loading and hydraulic gradient as detailed in section 3.4.4. 42 4.0 T E S T R E S U L T S Results from the main program of testing are presented in the following sections. The consolidation behavior of test specimens is first presented, followed by results that verify the reproducibility and homogeneity of the test specimens. Permeability is compared for several gradations, and the variation of measured shear wave velocity for each gradation reported for a range of effective stress and hydraulic gradient. In this chapter void ratio and shear wave velocity are plotted against vertical effective stress. Vertical effective stress is computed at each stage of loading and hydraulic gradient knowing the applied vertical effective stress, the effective unit weight of the specimen and the seepage force. Sidewall friction is not taken into consideration in this section but is addressed in Chapter 5.0. 4.1 Consolidation behavior Specimens with fines content ranging from 0 to 33 % were reconstituted, consolidated and then aged in a rigid-walled permeameter. A standard routine of reconstitution, consolidation and aging was used in the program of testing (see section 3.4). The consolidation void ratio, or e25, is the void ratio obtained after initial loading and subsequent ageing at 25 kPa for 1000 minutes. Void ratio is computed knowing the specific gravity, dry weight and volume of the specimen. Throughout the course of any test, void ratios are subsequently determined from measured axial displacement at each stage of loading. The respective void ratios are denoted as eso, eioo, e2oo and e^o. Consolidation (e-log crv') paths for each of the six gradations tested are reported in Figure 4.1. Observe that void ratio diminishes with increasing stress, but the change is relatively small. The initial void ratio of gradations C-13 to C-33 are similar, with an e25 range of approximately 0.06 (0.34-0.40), see Table 4.1. The consolidation trend with stress is consistent between specimens with different fines content. Although there is no clear 43 0.55 0.45 o a tm •a o > 0.35 0.25 —4— C-0 + C-0 r1 • C-13 C-13 r1 A— C-18 ll C-18 r1 —* C-23 C-23 r1 C-28 X C-28 r1 C-33 • C-33 r1 10 100 1000 Vertical effective stress (kPa) Figure 4.1. Consolidation paths for specimens of various fines content relation between void ratio and fines content (Sf), observe that void ratios for C-0 are the highest, void ratios are almost identical for C-18 and C-23, and void ratios are the smallest for C-28. Table 4.1. Repeatability of consolidation void ratio (e2s) Gradation (Sf) e2s e25_rl % Deviation C-0 0.503 0.505 0.4 C-13 0.397 0.389 2.0 C-18 0.350 0.350 0.0 C-23 0.347 0.350 0.9 C-28 0.336 0.326 3.0 C-33 0.376 0.332 12 44 4.1.1 Specimen repeatability Confidence in the findings of this experimental study requires the method of reconstitution yield reproducible specimens. Consolidation void ratio was selected as the indicator of specimen reproducibility. The repeatability of this void ratio for each test was established by reconstituting duplicate, or repeat, specimens of the same gradation. Upon completion of a test, the specimen was exhumed, reconstituted again as a slurry deposit in the permeameter, consolidated and aged according to the standard routine. The void ratio (^25) of this duplicate specimen was then computed as before, knowing the new specimen volume and weight. The repeat specimens, denoted as r l , are included in Figure 4.1 and are tabulated together with percentage deviation in Table 4.1. A generally good repeatability is observed between specimens, with the exception of C-33, which was more difficult to reconstitute due to the large fines content of the slurry. The compression index, Q , ranges from 0.02 to 0.03 for the gradations of core material tested in this program. This is in good agreement with other compression indices found for silty sands (Huang et al. 1999; Cho et al. 2006). 4.2 Homogeneity In any laboratory investigation it is of primary importance to ensure that the test specimens are homogeneous. In this study, homogeneity throughout the specimen is confirmed through observation of post-test grain size distribution and also from observation of water head distribution induced by seepage through the specimen. Post-test grain size distribution is considered appropriate in assessing specimen uniformity as there is no migration of fines through the specimen under the relatively small hydraulic gradients applied in testing (in < 8). As discussed in section 3.4.3, only a negligible amount of fines passed through the fine wire mesh located at the bottom of the permeameter during specimen reconstitution. 45 4.2.1 Post-test grain size distribution At the end of each test the specimen was removed from the cell in four layers (upper, upper mid, lower mid and lower) of equal thickness approximately 25-30 mm. Materials from each of these layers were oven-dried and sieved, and the grain size distributions compared to the original gradation of the test material. Post-test grain size distributions together with the original gradation for each test are presented in Figures 4.2 (a-f). Although there is a general good match to the nominal gradations (see for example, C-0 and C-13) slight differences are seen for some specimens (in particular, tests C-23 and C-28). In these cases a small deviation from the original curve at larger grain sizes (ie. 4.75 mm) appears to shift the remainder of the distribution as well. The effect is attributed to the influence of a few coarser grained particles in comparison to the relatively small mass of each layer (-400 g). In all grain size distributions the trend of the post-test data are consistent with that of the original, and no layer is considered to be consistently rich or poor in fines or coarser fraction. 4.2.2 Water head distribution Another method used as a check on specimen homogeneity was the differential water head distribution across the length of the specimens. The advantage of using water head distribution, over the post-grain size distribution, is that the former is more sensitive to subtle changes in gradation across the five differential ports of the permeameter (see Figure 3.1 for details of the permeameter port locations). Differential water head distributions for the six gradations tested are shown in Figures 4.3(a-f). Water head at each port location is-plotted against distance above the bottom wire mesh upon which the specimen rests. Distributions are shown for all stages of 46 GRAVEL SAND SILT CLAY 100 90 80 70 60 50 40 30 20 10 0 VI I I I I I IIVI i i i 111 I M I ! M i l l 1 - •—C-0 _ 111 l " ^ J I 111 I I I I I Ml 1 —A— upper —1— upper rrid —x— low er rrid —e—lower 111 I I I I I I 11 I I ! I I I I I I I 1 1 1 M i l l 1 I I I I I I I ! R k i i i i i i 1 1 % . i i 1 I I ! I I I I I 111 \ % i i 1 III 1 1 1 1 1 I I I I I I I I i n i I \ I i 1111 i i % i I ! I I I I I I 1 1 1 1 1 1 ' \ N L 1 1 1 I I 1 I I I I I ! I ! 1 1 1 1 1 1 1 1111 i i i i^ Ss. I I I I I I I ! Iii i i i i i ^ ^  10 0.1 Grain size (mm) 0.01 0.001 Figure 4.2a. Post-test grain distribution for test C-0 GRAVEL | SAND | SILT | CLAY | -•—C-13 -I I I l % J I i II —I— upper mid x low er mid —e— low er III 111 I I ^ i n i i i i i ili'Mtoi I I Ml I M M i \ i i i i II I I ! I I I I I " ' > ^ I J n i l i i i \S i I I I I I I I I I I I 11111 i | | ^ i 1111 I I I I 11111 i i i MM I I I I 100 90 80 70 60 50 40 30 20 10 0 10 0.1 Grain size (mm) 0.01 0.001 Figure 4.2b. Post-test grain distribution for test C-13 47 GRAVEL | SAND | SILT | CLAY 0.001 Grain size (mm) Figure 4.2c. Post-test grain distribution for test C-18 | GRAVEL | SAND | SILT [CLAY] 0 I 1 1 1 1 1 I 1 I I II M I ! I | I I I I I 1 1 1 I I I I I 1 1 1 j 10 1 0.1 0.01 0.001 Grain size (mm) Figure 4.2d. Post-test grain distribution for test C-23 48 GRAVEL SAND SILT CLAY 100 90 80 70 60 50 40 30 20 10 0 II I I I I I I I I I I I I I I 1 i 1 1 I I 1 1 _*_C-28 A upper —I— upper mid x low er mid —e— low er -II I I I I I I 1 1 1 1 1 1 1 1 | X M M I I 1 1 1 1 1 1 1 1 1 TJVN! ' ' ' « ^ i • i 1 1 1 1 1 1 1 1 I I I M N ^ I i 1 1 1 1 1 1 1 1 l l l l 1 1 1 1 n I i i 1 1 1 I I 1 1 1 1 I N I 1 1 1 1 | | I 1 1 1 I 1 T ^ S . ^ W 1 1 1 1 1 1 1 1 II II 1 1 1 1 I I I 1 1 1 1 ^ I I I ! 1 1 1 1 II 1 1 1 1 1 1 | | 1 | | | | | m i l l ! i 11 ! 1 1 1 1 I l l I I I I I II 1 1 1 1 1 1 M l : 1 I I I 10 0.1 Grain size (mm) 0.01 0.001 Figure 4.2e. Post-test grain distribution for test C-28 I GRAVEL I SAND | SILT | CLAY | 100 90 80 70 60 50 40 30 20 10 0 V l l I I I I I I rx*B«L I I I I I I I I I I I | | | | | | | 11 | i 1 | i | -•—C-33 —A— upper —I— upper rrid x low er rrid —e— low er I I I I I I I I III 1 1 1 1 1 I MI111 r^5^ Mil i i i i 11 1 1 1 1 1 1 1 V ^ M . I I i i 1 1 1 M 1 1 I I j | l 111111 i i 111 I N ^ J 1 1 1 1 II 1 1 M M II 1 1 11111 i i 1111 i i I I I i i i ^ ^ ^ f t ^ \ II 1 1 1 I 1 1 111111 i i M I N I I r ^ ^ s ^ ; I I I I I I I I \ ^ 1 ' 1 I l l 1 II 1 1 111111 i i I I I I I I I I III II 1 1 1 II'! I I II I I I I I I M I N I I I I I I I I I I I "M '1—1—1 1 1 1 1 1 1 1 1 1 1. 1 . 10 0.1 Grain size (mm) 0.01 0.001 Figure 4.2f. Post-test grain distribution for test C-33 49 Water head-C-0, 25kPa 12\ 0 20 40 60 80 100 Water head (cm) Figure 4.3a. Water head distribution for test C-0 Water head - C-13, 25kPa Water head (cm) Figure 4.3b. Water head distribution for test C-13 50 Water head - C-18, 25kPa 100 Water head (cm) Figure 4.3c. Water head distribution for test C-18 Water head - C-23, 25kPa Water head (cm) Figure 4.3d. Water head distribution for test C-23 51 Water head - C-28, 25kPa 12, Water head (cm) Figure 4.3e. Water head distribution for test C-28 Water head - C-33, 25kPa Water head (cm) Figure 4.3f. Water head distribution for test C-33 seepage flow (i = 0, 2, 4 and 8) after an elapsed period of 15min at each stage, and under a top vertical effective stress of 25 kPa. C-13 was one of the initial tests conducted and it was observed that higherthan expected heads existed in the top portion of the specimen. Upon post-test analysis it was noticed that a fines rich layer had developed on the top surface of the specimen. This thin layer, 52 estimated at less than 1mm thick, is believed to have developed after completion of specimen reconstitution by slurry deposition over a period of time during which suspended fines in the overlying thin film of water settled out. The effect of this thin top layer of fines is seen in the bi-linear shape of curves (Figure 4.3b). The post-test grain size distribution shown in Figure 4.2b reaffirms that there is no significant difference in gradation of the top layer (-30 mm) hence the increased gradient observed in the top portion of the specimen is attributed to the very thin "fines rich" layer. The test setup for each subsequent test was modified to minimize the potential formation of such a fines rich layer. This was achieved by gently agitating the top surface and diluting the fines rich water before siphoning it off as described in section 3.4.3. With the exception of the aforementioned deviations at the port 3, which is 7.6 cm from the bottom wire mesh (see Figure 3.1), the trend of water head through the specimen appears to be fairly linear. This linear relation confirms the homogeneity of each test specimen. 4.3 Hydraulic conductivity Hydraulic conductivity of the specimens was calculated based on volumetric flow rate and the measured system hydraulic gradient (in). As mentioned in section 3.4.4, volumetric flow rates were taken at the end of each stress increment ( in = 8) for tests C-0 and C-13 (oV = 400 kPa, i ] 7 = 8), for tests C-18 and C-28 as they required more time to get a representative volume of water. In the case of test C-33 it was not possible to obtain a volumetric flow rate as the hydraulic conductivity of the specimen was too low. Additionally, flow rate was insufficient to enable a reliable value of hydraulic conductivity for test C-23. Hydraulic conductivities obtained in this study are plotted in Figure 4.4 together with data obtained from testing of core material in a companion study using a large permeameter (Moffat, 2005). As expected, a decrease in hydraulic conductivity is noted 53 1.E+00 -.-1.E-01 -1.E-02 -;m/s) 1.E-03 '! > 1.E-04 -3 TJ c 1.E-05 -o u _o 1.E-06 -2 TJ >. 1.E-07 -X 1.E-08 -1.E-09 -1.E-10 -10 15 20 Fines content, Sf (%) 25 X C-0 X C-13 X C-18 - » — C - 2 0 (Modal 2005) X C-28 - S — C - 3 0 (Moffat, 2005) 30 35 Figure 4.4. Hydraulic conductivities for specimens of various fines content with increase in fines content. A n excellent correlation is observed between data sets for similar material in different test apparatus (large and small permeameter). This further confirms the repeatability of the specimens, observed in different programs of testing. 4 .4 Shear wave velocity The propagation velocities of shear waves are established for each specimen using a configuration of three piezoceramic bender elements as detailed in section 3.2.1. Interval arrival time of the seismic wave between receivers is taken as the peak-to-peak time difference. The fixed receiver separation is then divided by the interval time to compute the shear wave velocity. In this fashion shear wave velocities are obtained, for each stage of stress and hydraulic gradient, for each gradation of the main test program. 54 4.4.1 Influence of stress Shear wave data from testing of all specimens are plotted together in Figure 4.5: computed shear wave velocities are those obtained at a vertical effective stress of 25 kPa applied to the top of each specimen. The consolidation void ratio at 25 kPa is also reported for each specimen. Each data point represents the shear wave velocity obtained for each gradient ( i , 7 = 0, 2, 4 and 8) at each applied stress (oV = 25, 50, 100, 200, 400 kPa). Power-fit trend lines define the relation of shear wave velocity with increasing stress. As seen in Figure 4.5, shear wave velocities range from approximately 110 to 125m/s at an applied vertical stress of 25 kPa and range from approximately 250 to 280m/s at an applied vertical stress of 400 kPa. Average shear wave velocities for each specimen at applied vertical stresses of 25 and 400 kPa are presented in Table 4.2. These shear wave velocities represent the average of values obtained at hydraulic gradients of 0, 2, 4 and 8. The general trend of shear wave velocity is observed to increase with vertical effective stress and can be fit by Equation 2.2. Stress exponents are in close agreement with exponents found in other laboratory and field experiments for sands (Hardin and Richart 1963; Santamarina et al. 2001'; Cho et al. 2006). A best fit to the test data yields a material constant (a ) and stress exponent (p) that range from 34 to 43 and 0.30 to 0.33, respectively. The trend of shear wave velocity with stress is similar for specimens of different fines content. As noted above, the stress exponent varies slightly between specimens although the material constant varies a bit more. At the low end of stress (25-50 kPa) velocities for all specimens are similar in magnitude with a maximum spread of 18 and 25 m/s respectively. As stress is increased, trends specific to each specimen begin to emerge and the maximuirrvelocity difference between specimens continues to increase with 30, 32 and 34 m/s (observed at applied vertical stresses of 100, 200 and 400 kPa, respectively). Consider now the influence of fines content and hydraulic gradient. 55 300 50 100 150 200 250 300 Vertical effective s t ress (kPa) 350 400 450 Figure 4.5. Variation of shear wave velocity with vertical effective stress Table 4.2. Average shear wave velocities at 25 and 400 kPa Test code Fines content. S f (%) Average shear wave velocity (m/s); 0 < i n < 8 oV = 25 kPa oV = 400 kPa C-0 0 123 272 C-13 13 112 255 C-18 18 109 255 C-23 23 113 267 C-28 28 122 281 C-33 33 115 266 4.4.2 Influence of fines content Although not widely varying, velocity trends specific to the fines content of each specimen appear related to increasing stress. More specifically, the trend of increasing 56 shear wave velocity with stress is consistent for tests C-0, C-13 and C-18. As seen in Figure 4.6a, C-0 velocities are consistently higher than both C-13 and C-18, and velocities for C-13 are consistently higher than those for test C-18. Accordingly, for fines content between zero and 18 %, the shear wave velocity is found to decrease with increasing fines content. This relation holds true regardless of magnitude of stress in the range of 25 to 400 kPa. For tests C-23, C-28 and C-33 however, the trend changes with fines content. The most pronounced relative change of shear wave velocity with stress is observed in test C-28 and to lesser extent tests C-23 and C-33 (see Figure 4.6b). Velocities obtained from tests C-23 and C-33 are nearly identical. Comparison with Figure 4.6a reveals the magnitude of shear wave velocity is between those of tests C-0 and C-13 at applied vertical stress above 100 kPa. However, a different relation is observed with test C-28. Although shear wave velocities are slightly lower than test C-0 at low stress (25 < a v t ' < 50 kPa), as stress increases the velocity increases at a higher rate. These relative differences between minimum and maximum shear wave velocity for each specimen (at 25 and 400 kPa respectively) are quantified in Table 4.2. The largest relative difference between average shear wave velocity is observed for C-28; this specimen also exhibits the highest shear wave velocity at 400 kPa. Implications of these relations are discussed in Chapter 5.0. As stated earlier in this chapter, the slurry deposition method yields specimens with only a moderate difference in initial void ratios (following consolidation to 25 kPa) regardless of fines content. Initial void ratios obtained in testing vary between 0.34 and 0.40 for tests C-13, C-18, C-28 and C-33 but test C-0 has a much greater void ratio of 0.50 (see Table 4.1). Note that although void ratios are very different between C-0 and C-28, for example, they plot with similar shear wave velocities. In contrast, void ratios of C-18 and C-23 are almost identical but very different shear wave velocities are observed. The influence of fines on void ratio and shear wave velocity is also examined in more detail in Chapter 5. 57 300 250 200 a > ra 3 i 100 50 + C-0 (e25 = 0.50) » C-13(e25 = 0.40) i C-18(e25 = 0.35) . . . . . -—" A ...JMi w 50 100 150 200 250 300 Vertical effective stress (kPa) 350 400 450 Figure 4.6a. Variation of shear wave velocity with vertical effective stress for fines content (S f) of 0, 13 and 18 % 300 250 200 9 150 iS 100 50 A C-23 (e25 = 0.35 * C-28 e25 = 0.34 . C-33 (e25 = 0.38 50 100 150 200 250 300 Vertical effective stress (kPa) 350 400 450 Figure 4.6b. Variation of shear wave velocity with vertical effective stress for fines content (Sf) of 23, 28 and 33 % 58 4.4.3 Influence of hydraulic gradient It was of interest to determine the effect, i f any, that seepage flow imparts to shear wave velocity. Accordingly, each specimen was subjected to a hydrostatic condition (i = 0) and unidirectional downward flow at hydraulic gradients (I17) of 2, 4 and 8 at each stage (25 < a v t ' < 400 kPa) of loading. Shear wave velocities for each test are plotted against vertical effective stress in Figures 4.7a-c. To observe the relation of hydraulic gradient more effectively, two tests are plotted in each figure with an inset showing an enlarged portion of the plot. Test results are plotted in Figure 4.7a for tests C-0 and C-13, in Figure 4.7b for tests C-18 and C-23 and in Figure 4.7c for tests C-28 and C-33. The inset located in the lower right hand corner of each figure depicts the shear wave velocity obtained under each hydraulic gradient for applied vertical effective stresses of 25 and 50 kPa. These represent the lower end of the applied stress regime. Inspection of the main plots show considerable scatter at low stresses. This scatter is not apparent at high stresses. The scatter observed at low stresses (25 < o V < 50 kPa) is attributed to a seepage-induced change in effective stress. To better understand velocity-gradient relations at low stresses, see the companion insets. Some specimens exhibit a fairly strong relation between shear wave velocity and effective stress, attributed to increasing gradient. Specifically, C-18 and C-23 show a strong relation, C-28 and C-33 to a lesser extent, and the weakest relation is observed with C-0 and C-13. This trend is quantified in Table 4.3 where shear wave velocities obtained at each hydraulic gradient, for an applied stress of 25 kPa, are presented. Due to disk recording malfunction, three data points are missing from the data set. As can be seen in each of the insets, there is a pattern of increasing velocity with increasing gradient in the lowerstress range. This pattern follows the velocity-stress trend line of the data quite closely in most cases, with minor deviations as noted above. 59 300 250 -g 200 o _o §> 150 > ra i S 100 s: 50 + C-0 (e25 = 0.50) - C-13(e25 = 0.40) * • - ' ' J M a i = o 0 i = 2 + l"4 1 I-8 ^ 6 A i 8 " ' " ^ • + A • O o -4 A • o + 50 100 150 200 250 300 Vertical effective stress (kPa) 350 30 35 40 45 SO 55 60 400 450 Figure 4 13 tests; 7a. Variation of shear wave velocity with vertical effective stress for C-0 and C-includes hydraulic gradient insert 300 250 200 g 150 > ra i 3 1 0 0 1 50 4 C-18 (e25 = 0.35) C-23 (e25 = 0.35) Ms' 0 l»0 o ( = 2 + l« 4 • + + 3 A 50 100 150 200 250 300 Vertical effective stress (kPa) 350 400 450 Figure 4.7b. Variation of shear wave velocity with vertical effective stress for C-18 and C-23 tests; includes hydraulic gradient insert 60 Figure 4.7c. Variation of shear wave velocity with vertical effective stress for C-28 and C-33 tests; includes hydraulic gradient insert Table 4.3. Shear wave velocity obtained at each hydraulic gradient for an applied stress of 25 kPa Test code Shear wave velocity (m/s); o^ ' -25 kPa i = 0 i = 2 i = 4 i = 8 C-0 125 123 122 C-13 110 110 112 118 C-18 - 107 109 110 C-23 112 112 113 115 C-28 125 120 120 123 C-33 113 115 - 116 With increase in gradient, and therefore increase in applied stress, velocities follow the general velocity-stress curve. Although a relation is observed at lower stresses it is not observed at higher values (o\t' > 100 kPa). Table 4.4 shows shear wave velocities for each specimen at hydraulic gradients of 0, 2, 4 and 8 for an applied stress of 400 kPa. For tests C-0, C-13 and C-28 there is no detected change in velocity with gradient, and in the remaining tests, there 61 Table 4.4. Shear wave velocity obtained at each hydraulic gradient for an applied stress of400kPa Test code Shear wave velocity (m/s); oV = 400 kPa i = 0 i = 2 i = 4 i = 8 C-0 272 272 272 -C-13 255 255 255 255 C-18 - 255 263 247 C-23 272 - - 263 C-28 281 281 281 281 C-33 263 263 272 272 does not appear to be any systematic relation of velocity and gradient. Due to disk recording malfunction, four data points are missing from the data set. For each of these tests, velocity varies only to the nearest resolution of arrival time (5 psec) at each stage of gradient; there is no systematic increase noted. Predicated on these observations, there does not appear to be a direct influence of hydraulic gradient on shear wave velocity, apart from an increase in confining stress induced by downward seepage forces. This effect is observed at lower stress where the seepage force imparts a relatively larger influence on stress level. At higher stress levels deviations between points are only observed due to change in arrival time. 62 5.0 ANALYSIS As the propagation velocity of shear waves is largely governed by mean effective stress (Hardin and Richart, 1963), results of the main program of testing are now analyzed with reference to this computed variable. However, consideration is first given to the structure of the test specimens as structure varies with fines content. A discussion of the test data then follows, with emphasis on the influences of stress, fines content and void ratio. Comparison is then made to moist-tamped laboratory data made available to this study, and also to field data obtained by annual seismic testing at the W A C Bennett dam. 5.1 Structu re of the specimen The fines content of the water-pluviated test ranges from 0 to 33 % and it is therefore anticipated that the structure of the reconstituted soil wi l l vary significantly. More specifically, the fines wil l exert an influence on packing structure and void ratio trends. Accordingly, the concept of skeletal void ratio and threshold fines content is introduced from the literature. Further consideration is given to the addition of fines and its control on compressibility of the structure. 5.1.1 Fines content - void ratio relation Variation of void ratio with fines content for the current study is presented in Figure 5.1. As mentioned in section 4.1, void ratios were computed from measurements of volume and weight of specimen. For each test of different fines content, void ratios are computed at every stage of applied vertical effective stress (rj v t ' ) . The void ratios plotted represent the values at which consolidation has occurred at applied vertical effective stresses of 25, 50, 100, 200 and 400 (e25, e50, el00, e200 and e400, respectively). Void ratios of duplicate specimens are also shown (e25 only). A best-fit 63 curve is shown for void ratios at 25 kPa. A trend of decreasing void ratio is noted in specimens with fines content of 0 % to about 23 or 28 %. The dashed lines depict the range of threshold fines content, or fines content at which the lowest void ratio is observed. Beyond the threshold value, additional fines result in slightly higher void ratios. As can be seen from Figure 5.1, this trend is consistent at each level of stress. It is believed that a portion of the fines occupy void spaces of the coarse-grained sand skeleton and others separate the skeleton. A continued increase in fines leads to further dispersion of the sand skeleton. Beyond the threshold fines content, at the minimum void ratio, the structure of the soil is fully dispersed and the sand skeleton is supported by the fines-dominant matrix. Threshold fines content is dependent on the gradation and mean particle size of the soil, and the threshold values for the current study are in excellent agreement with findings from other investigations with silty sand and gap-graded sandy gravels. A n experimental investigation conducted by Skempton and Brogan (1994) identified a similar critical content of fines, denoted as S* in gap-graded sandy gravels. They found that below this critical value, fines do not completely fill the voids in the coarse, or clast supported matrix, and above the critical value, clasts are floating in a fines supported 0.6 0.5 o 0.3 * e25 • e50 e100 a e200 ° e400 a ^^^^ • • ~~ _1 o c • A Figure 5.1. Variation of void ratio with fines content 64 matrix. The critical content of fines was found to range from 24 to 29 %. A relation for the critical value was postulated based on the coarse and fine porosities (nc and « f , respectively): S * = A / ( 1 + A ) 5.1 where A = nc (1 - nj)l( 1 - « c) 5.2 As fines increase from 0 %, fines fill void spaces and the overall porosity of the soil decreases (see Figure 5.2). No major change is observed for the porosity of the coarse fraction until the threshold value, or critical value S*, of fines is reached. The critical fines content of the silty sand of the current study is believed to occur within the dashed lines represented in the figure. Beyond the critical value, the porosity of the coarse fraction increases with fines as dispersion of the coarse skeleton occurs. The overall porosity of the soil also increases. For purposes of comparison, overall porosities of the current study are presented in Table 5.1. At an applied stress of 25 kPa, porosities range from approximately 33 % at 0 % fines content, 24.9 % at a threshold fines content of 28 % and up to 26 % at a fines content of 33 %. In comparison to the values obtained in the gap-graded sandy gravel mixtures, the values of the current study undergo relatively smaller change in porosity with fines content, but the threshold values of fines content found in the current study (23-28 %) is in excellent agreement with the findings of Skempton and Brogan (1994) for a gap-graded soil (24-29 %). In experiments with silty sands (Thevanagayam 1998; Thevanagayam et al. 2002) a transition from a sand dominated behavior to a fines dominated behavior was also observed at a threshold fines content. Threshold fines content, denoted in these studies as F C m , is equivalent to S* defined above by Skempton and Brogan (1994). A schematic diagram (Figure 5.3) illustrates how the structure of a silty sand changes with increase in fines content. Adding fines to an initially coarse-grained soil mix results in some fines confined within voids of the coarse skeleton and some fines acting as separators, pushing 65 Figure 5.2. Volume and porosity as a function of fines content for gap-graded material (after Skempton and Brogan, 1994) Table 5.1 Variation of porosity with fines content Fines content, S f (%) Overall porosity, r\ (%) 0 13 18 23 28 33 T| (rV = 25 kPa) 33.5 28.2 25.9 25.9 24.9 26.3 r| (oV = 400 kPa) 32.3 27.0 24.4 24.3 23.2 25.8 apart the coarse grains. As the fines content is increased past the threshold value, there is a transition to a fine-grained soil mix where the coarse grains are fully dispersed and 'float' in a fines dominated matrix. This behavior is also depicted in Figure 5.4 which shows the variation of void ratio with fines content. 66 (a) Coarse qrain soil mi* (b) Ffno grain soil m\xv (c) Layered soil mix .Primary Grains Contact S&condaryGrains Contact : fn-ier Coarse Grain: FC^FC* Rr)'» fitFtu» Gf»lii ••J -"• ^Contact Dommani.-•i | R«8«Coaise6<ai i>, | : -4 • Fully CGT«(?W(J w.it'Sn vela T pertmlfytn contact: .5^pf rotor Ol? * « y i f 4 « grain-i . ;^ disperse^:: rc»f-C. v Partis liy dispersed; • rfitnJrjtarttl element:: Grain Contact I o s =<o«fc)/{i-lo) II (e,)„ = («+(1 h)te!'(t-{1-b)'c) If e , » 6 f c |[ (o,|„»c'(IC4(1-(c)/R,' Density index 1 'I II l l •b=f»rtion otsthB (iw Figure 5.3. Intergranular soil mix classification (after Thevanagayam et al., 2002) 0.0 J > * » 1 I ! I I I J ' Ii I i n ' j n j i I j '"- I i j . | ; Fines Content [%] Figure 5.4. Void ratio - fine content relation for intergranular soil mixes (after Thevanagayam, 1998) 67 In order to explain the observed behavior of a silty sand with varying fines content, Kuerbis et al. (1988) make reference to a sand skeleton void ratio. The skeletal void ratio is determined from the weight of the coarse fraction only and the total volume of the mixture. In their testing with clean and silty sands, no substantial differences were found in the undrained response with varying amounts of silt (up to 20 % silt content) although widely different void ratios were found for the materials. It was postulated that silt of the silty sand was only fdling in void spaces of the sand skeleton and therefore the behavior of the silty sand is controlled by the skeleton void ratio solely. Although very different void ratios were obtained, the skeletal void ratio remained relatively constant with increasing fines up to about 20 %. A consistent trend of void ratio and fines content was observed in the current study and confirmed by similar trends for gap-graded and silty sands in the literature. Given the framework of coarse sand skeleton and shift to a fines dominated matrix, consider now the role of compressibility in the structure of the soil specimen in the current study. 5.1.2 Compressibility Compressibility of a soil changes with the amount of fine-grained particles present; in the current study, compressibility changes with fines content. In the case of fines dominated specimens, large strains are encountered as the applied vertical stresses are increased. As stress is applied and the specimen is compressed, the relative participation of fine and coarse particles in load sharing also changes. The compressibility of each specimen is computed from the difference between the current void ratio for a given stress and the initial void ratio at a stress of 25 kPa, divided by the initial void ratio at 25 kPa. Compressibility for all test specimens at each stage of applied vertical effective stress is shown in Figure 5.5. Compressibility increases with increasing stress, and also with increasing fines content. 68 0.10 0.08 in 0.06 CM 0.02 0.00 > • — - -, * ~ " " _ * -A. , ^ ^  , , . i + C-0 a C-13 A C-18 C-23 x C-28 * C-33 50 100 150 200 250 300 Vertical effective s t ress (kPa) 350 400 Figure 5.5. Compressibility of specimens of various fines content 450 Test C-0 displays very little compressibility, C-13 shows more compressibility than C-0, and C-18 and C-23 have a very similar compressibility. Test C-28 shows the highest compressibility with stress. This trend of increasing compressibility implies that the specimens with fines dominated matrices have structures that are more compressible than those that are primarily sand dominated. The role of participation of fines and coarse particles in skeletal load transfer is related to shear wave velocity in a later discussion (section 5.3.3). 5.2 Consideration of mean effective stress In Chapter 4, shear wave velocity and consolidation data were plotted against vertical effective stress at the mid-height of the specimen. The latter was calculated taking into account the applied top vertical effective stress, effective unit weight of the specimen and seepage force. Since the propagation velocity of shear waves through granular material is governed by the mean effective state of stress (Hardin and Richart, 1963), it is most appropriate to present shear wave data of the current study in terms of 69 mean effective stress. This also allows evaluation and comparison with empirical relations, as mentioned previously in Chapter 2. Computation of mean effective stress for the rigid-walled permeameter requires (1), a value of Ko for the reconstituted specimen, and (2) a relation for the interface friction (5) between the soil and the inside wall of the permeameter. Accordingly, a series of commissioning tests were performed in the rigid-walled permeameter. Thesetests were conducted on Fraser River sand, because a companion set of laboratory triaxial data (Naesgaard et al., 2005) were available from which comparison of shear wave velocity and stress could be evaluated. Details of those triaxial tests are found in Appendix A . Fraser River sand was reconstituted into the rigid-walled permeameter using a method of air and water pluviation. As the void ratios of the reconstituted specimens are similar, the shear wave velocity of two test programs can be directly compared. The comparison of shear wave velocity from the commissioning tests to the shear wave velocity from the triaxial test program allows mean effective stress to be determined for the rigid-walled permeameter. A value of Ko for Fraser River sand in the rigid-walled permeameter may be computed from back-analysis, given a value of interface friction angle (obtained from direct shear testing). Once parameters are defined for Fraser River sand in the rigid-walled permeameter, consideration is given to defining parameters for core material in the rigid-walled permeameter. Six direct shear tests were conducted on Fraser River sand in contact with a block of anodized aluminum considered representative of the inside wall of the permeameter. A n efficiency factor of 0.53 was found for the smooth rigid-walled permeameter and Fraser River sand (see Appendix A) . This was determined from the tangent of the interface friction angle (5) divided by the tangent of the friction angle (<|> = 33° for Fraser River sand). A n interface friction angle for core material and the rigid-walled permeameter was then computed knowing the efficiency factor (0.53) and the friction angle of the core material. A friction angle of 37° for core material (Morgan and Harris, 1967) yields an interface friction angle of 21 0. 70 A best fit of the shear wave velocity for the Fraser River sand of the commissioning tests to the shear wave velocity of Naesgaard et al. (2005) data occurs when a value of Ko = 0.85 is used (see Figure A.6). While this value appears larger than the typical value of 0.5 for a rigid-walled boundary, upon immediate reconstitution and loading of a slurry, a value near to 1 would reasonably be expected. Given the structure of a slurry deposited specimen, a different value for Ko may be appropriate. Testing of various clean sands at comparable void ratios (~ 0.8) yield values of K 0 ranging from 0.4 to 0.7 (Mesri and Hayat, 1993) and 0.3 to 0.6 (Mayne and Kulhawy, 1982). Tests conducted on silica sand in a split ring consolidometer indicate Ko of 0.42 (Landva et al., 2000). The aforementioned laboratory data on sands address the suitability of the classic Jaky expression which allows Ko to be determined from the internal friction angle. Their data also confirm that the Jaky expression provides a good estimate of Ko for sedimented, normally consolidated young clays and granular soils. Using this equation, a Ko of 0.5 might be expected for Fraser River sand (cp' = 33°) and 0.4 for core material (cp' = 37°) of the main test program. In summary, two parameters required for the determination of mean effective stress in the rigid-walled permeameter have been evaluated. A n interface friction angle of 21° between the core material and the inside wall of the permeameter is considered appropriate, however, an argument is put forward regarding the value of Ko to be used in the determination of mean effective stress. For the core material with a friction angle of 37°, the classic Jaky expression indicates Ko = 0.4, and best-fit of commissioning test data to Naesgaard et al. (2005) data indicates Ko = 0.85. Accordingly, for purposes of analysis, mean effective stress is defined with reference to an upper bound (Ko = 0.85) and lower bound (Ko= 0.4). 5.3 Shear wave velocity Shear wave velocity for uncemented granular soils is recognized to be a function of stress and void ratio and also a function of age (Hardin and Richart 1963; Hardin and 71 Black 1966; Iwasaki and Tatsuoka 1978, among others). Age, and specifically the influence of time, was not considered in this study given the standard elapsed time (1000 min) between the initial consolidation of the specimen and subsequent measurement of shear wave velocity. In this section, shear wave data obtained in testing are discussed regarding the influences of stress, void ratio and fines content. 5.3.1 Influence of stress The variation of shear wave velocity with mean effective stress is shown in Figure 5.6. Shear wave velocity (Vs), deduced from travel distance and arrival time between receivers, is reported as the average of lower and upper bound mean effective stresses (rjra') at each stage of loading. As described above in section 5.2, lower and upper bounds based on K o = 0.4 and 0.85, respectively, are considered appropriate for the smooth rigid-walled permeameter cell of the current study. Upper and lower mean effective stresses are represented as maximum and minimum stress bars. Stress differences of approximately 16 % (+/- 8 % from average am ') are observed from calculation of mean effective stress at K o of 0.4 and 0.85. Velocities are also tabulated for each bound of stress in Appendix B . It is noted that relative stress-velocity trends between different specimens remain as discussed in Chapter 4; namely, shear wave velocity increases with increasing stress. Relative trends of shear wave velocity and fines content are also consistent when plotted against mean effective stress; shear wave velocity decreases with increasing fines up to fines content of 18 %, and shear wave velocity of specimens with fines content of 23 % and greater show a subtle increase in shear wave velocity. The magnitude of these shear wave velocities increases with increase in stress. As discussed in Chapter 2.1, the trend of shear wave velocity varies with mean effective stress. The velocity-stress relation (Equation 2.2) comprises a velocity-stress exponent (P) and a material constant (a). The trend of shear wave velocity with mean effective stress is similar for specimens of different fines content; specifically, a best fit to the test 72 100 -I 1 , 1 i 1 0 50 100 150 200 250 Mean effective stress (kPa) Figure 5.6. Variation of average shear wave velocity with mean effective stress data yields a and P values that range from 44 to 54 and 0.30 to 0.33, respectively (see Table 5.2). Stress exponents (P) are within the range of exponents found in other laboratory experiments for sands (Hardin and Richart 1963; Santamarina 2001), falling within the range of 0.17 to 0.36, as shown in Table 2.1. Material constants (a) of the current study also fall within the range observed in sands by Cho et al. (2006), see Table 2.1. Table 5.2 Velocity-stress constants of the current study Test specimen Fines content, Material constant, oc Velocity-stress R 2 value S f(%) exponent, p C-0 0 54 0.30 0.9986 C-13 13 49 0.31 0.9998 C-18 18 44 0.33 0.9931 C-23 23 47 0.33 0.9981 C-28 28 49 0.33 0.9959 C-33 33 47 0.33 0.9966 73 Further confidence in shear wave velocities obtained for the current study is gained from comparison of calculated and theoretical values of small strain shear modulus, Gm ax-Gmax rnay be calculated from shear wave velocity and specimen density by Equation 2.1 and is plotted against mean effective stress in Figure 5.7. Minimum-maximum bars again represent the mean effective stresses at upper and lower bound values of Ko. The variation of G m a x with stress is similar in trend to that of the shear wave velocity stress trends apart from a few deviations. G m a x increases with increasing stress, but the relative trends of G m a x for each test specimen are different due to the additional influence of specimen density. The G m a x of specimens with fines content of 23, 28 and 33 % are now all higher in magnitude than the G m a x of C-0. The difference is attributed to the higher densities, or lower void ratios, of the fines dominated matrices in comparison to clean sand of test C-0 (see Table 4.1). The trend of decreasing shear wave velocity with increase in fines content between C-0, C-13 and C-18, is still observed but now the magnitude of the difference between C-0 and C-13 is less. 200 -150 I 100 " £ CD 50 0 Figure 5.7. Variation of small strain shear modulus with mean effective stress 74 Salgado et al. (2000) used bender elements to measure shear wave velocity, and hence shear modulus, of reconstituted specimens of Ottawa sand mixed with silt contents of 5, 10, 15 and 20 %. G m a x was found to decrease with increasing fines up to 20 % fines. The trend of decreasing G m a x with increase in fines content (Sf = 0, 13 and 18 %) of the current study agrees with this finding. Calculated Gmax values of the current study are now compared to theoretical values of Gmax obtained from empirical relations. As discussed in section 2.2, various empirical relations for G m a x have been recognized by Hardin and Richart (1963), Hardin and Drnevich (1972), Iwasaki and Tatsuoka (1977), Hardin (1978), Roesler (1979), and Y u and Richart (1984), among others. Two forms of the equation, one for an isotropic stress state (Equation 2.7) and the other for an anisotropic stress state (Equation 2.8), are used to obtain theoretical G m a x . In these equations, G m a x relates to a material constant (A) which depends on the elastic properties of the grain particles, a void ratio function (F(e)) which accounts for the density or number of contacts per particle, o V is the mean effective stress, and b is a stress exponent. For anisotropic conditions, rj a' is the effective stress in the direction of wave propagation (crv'), crp' is the effective stress in the direction of particle vibration (oV). Figure 5.8 shows Gmax as calculated with Equation 2.7 using the shear wave velocity of all gradations of the current study under each stage of stress and hydraulic gradient. Parameters A , F(e) and b are varied to obtain theoretical Gmax which fit within +/- 10 % of the measured values. The best fit occurs when the following parameters are used: - Material constant, A , of 460 for clean sand (C-0) and 365 for other tests - Void ratio function, F(e), of the form observed by Hardin and Richart (1963) - Stress exponent, b, of 0.6 Before discussing the parameters used to fit the experimental data, consideration is given to the fit of the data with respect to the isotropic and anisotropic stress states. The inset of Figure 5.8 shows the comparison, for C-13 only, between Equation 2.7 and 2.8 (listed 75 Theore t i ca l G m a x (MPa) Figure 5.8 Theoretical G m a x versus calculated G m a x . Inset illustrates comparison between empirical formulas for test C-13 above) with a common stress exponent (b - 0.6). As is seen in the inset, the difference in Gmax as computed using the two equations is small. This might imply that although the specimens of the current study were anisotropically consolidated, G m a x is not sensitive to stress in the different directions of wave propagation and particle movement over the range of applied stresses (10 < rj m ' < 200 kPa). As presented in section 2.2.1, many authors have found that G m a x varies with the square root of mean effective stress. Using this stress exponent (b = 0.5) did not fit the data across all magnitudes of stress. However, fit was achieved using an exponent of 0.6. Although this value is slightly higher than the traditional empirical value of 0.5, it is not outside the range of values encountered in the literature (see section 2.2.1). It has been observed that stress exponents range from 0.32 up to 0.72 for natural and crushed sands (Cho et al., 2006) depending on contact behavior and fabric. It is speculated that as stress is increased, the slurry-deposited specimens compress and both the nature of fine particle contacts, and fabric, change. The 76 combination of effects may relate to the slightly higher than typical sensitivity of G m a x to stress for the reconstituted specimen. As discussed in section 2.2, three main forms of the void ratio function are commonly used. Equations 2.15 and 2.16 were observed from testing of rounded and crushed quartz sand by Hardin and Richart (1963), respectively, and Equation 2.17 was developed from critical state testing of Erksak sand by Jefferies and Been (2000) and relates to em i n*. O f the three functions used, the first function best fits the experimental data and the third fits the data reasonably well. In Chapter 5.4 both functions are used in comparison of results from other laboratory studies. The second form of the relation did not provide a fit to the data across all magnitudes of stress. Gmax for all tests are fit to the line of equivalence (within +/- 10 %) by varying the A parameter on a test by test basis. The resulting A values are tabulated in Table 5.3. These A values are obtained through best fit using a stress exponent of 0.6 and void ratio function of Equation 2.15. A higher value of A (460) is obtained for gradation C-0 and a slightly lower A value (320) was obtained for gradation C-18. A difference in material constant A is expected for the clean sand (C-0) as the structure of the clean sand is much different from the structure of the silty sand (as discussed in section 5.1). It is unclear why the A value of test C-18 is lower. A n average value of A = 365 is considered appropriate for the silty sand of the current study; this average is based on A values from C-13, C-23, C-28 and C-33 test data. Table 5.3 Summary of material constant, A , of the current study Test material Fines content (%) A C-0 C-13 C-18 C-23 C-28 C-33 0 13 18 23 28 33 460 360 320 360 370 370 77 A substantial range of A values may be expected for soils (Mitchell and Soga, 2005). Furthermore, A can change significantly depending on the form of the void ratio function used. Three studies are selected for comparison of A parameter as the forms of the Gmax equation are similar and the same void ratio function is used in each (Equation 2.15). Material descriptions and A parameters for those clean and silty sands are reproduced in Table 5.4. Table 5.4 Comparison of A parameters between selected studies Study Mater ia l description A parameter (Sr=0) A parameter (SF>0) Current study Hardin and Richart (1963) Iwasaki and Tatsuoka (1977) Sub-angular, non-uniform silty sand Rounded, uniform Ottawa sand Clean and natural sand Ottawa sand with silt 460 700 700-900 612 365 N / A <700* 207-454 ' Authors note significant scatter with natural sand but that the shear modulus is lower than that for a clean sand at the same void ratio, stress and strain. A n A parameter of 460 was found in the current study, this value is slightly lower than that reported by others for uniform sands. This difference is likely due to differences in material properties, such as grain shape and gradation, as well as fabric differences. The potential range of A parameters for silty sands from the other studies is large, namely 200 to 700, and the average A parameter found in the silty sand of the current study is within this range. Interestingly, while the spread of A parameters obtained with the addition of fines (13, 18, 23, 28 and 33 %) in the current study is small (360-370, with a possible outlier of 310), the spread of A parameters for the Salgado et al. (2000) study is more pronounced. In the latter case, a fines content of 5, 10, 15 and 20 % yields A parameters of 454, 357, 238 and 207, respectively. 78 5.3.2 Influence of void ratio Figure 5.9 shows the relation between shear wave velocity and void ratio. Shear wave velocity is plotted against void ratio at each corresponding stage of gradient (0 < /' < 8) and at each increment of stress. Shear wave velocity increases linearly with void ratio, independent of gradation (or fines content). Regardless of void ratio, the observed range of shear wave velocities is very similar between specimens. Examination of the void ratio-shear wave velocity relation for each specimen under comparable effective stress is also of interest (see Figure 5.10). The slope of the best-fit lines of equal stress implies that a large change in void ratio, and hence fines content, yields a relatively a small change to shear wave velocity. The result is in agreement with findings presented by Hardin and Richart (1963), who also examined void ratio-velocity relations. As mentioned in section 2.1.1, they found that for rounded Ottawa sand and crushed quartz silts, velocity varies linearly with void ratio, and increases with decreasing in void ratio, independent of grain size, gradation and 300 280 260 240 220 200 180 160 140 120 100 + C-0 a C-13 „ A C-18 a C-23 -Ht-X C-28 • C 33 • • a / * / / * • / • / * # X ' / / i i r * i i i ff i * j : / * J 1 f h J * 1 * # f •M W i 0.55 0.5 0.45 0.4 Void ratio 0.35 0.3 0.25 Figure 5.9. Variation of shear wave velocity with void ratio for constant fines content 79 300 280 260 I 240 > o 220 o > § 200 « a 180 to 160 140 120 100 + C-0 C-13 X A X C-18 C-23 C-28 C-33 = 400k Pa • ' — • • JL • i • = 200kPa m • I = 100k Pa i j»— I * . ... I = 50kPa • — , = 25k Pa • 4 i 0.55 0.5 0.45 0.4 Void ratio 0.35 0.3 0.25 Figure 5.10. Variation of shear wave velocity with void ratio for similar applied vertical stress relative density (see Figure 2.13). They attributed that the only effect of grain size and gradation is to change the void ratio. In their program of investigation sands and silts were tested but not sand-silt mixtures. To analyze the deviation from trends for tests conducted with varying amounts of fines content, consider now the influence of fines content. 5.3.3 Influence of fines content Propagation velocities of shear waves through soils are directly dependent on the stiffness of the soil skeleton. The stiffness of the soil skeleton, in turn, depends on soil fabric and interparticle forces. In Chapter 5.1, soil structure and skeleton changes with the addition of fines was discussed. Aside from a different structure with changing fines content, consideration also needs to be given to how stresses are transferred through the soil skeleton and how the transfer may change with the addition of fines. so A continuous sequence of how fines content influences shear wave velocity is illustrated in Figure 5.11. Five plots of shear wave velocity against fines content, one for each stage of vertical loading, are shown. The first three data points, for fines content of 0, 13 and 18 %, all confirm the trend of decreasing shear wave velocity with increasing fines content. This trend is consistent across all levels of stress, although the relative change is small at an applied stress of 25 kPa. The dashed lines in each of the plots represent the postulated threshold fines content; this range was observed in Figure 5.1 which illustrated the variation of void ratio with fines content. In each plot the shear wave velocities at fines content of 23 % and 28 % are higher than the subsequent velocity at 18 %. The increase is subtle at low stress but becomes more pronounced at higher stresses. The increase in shear wave velocity may be partially attributed to the difference in compressibility of the specimens. Although compressibility of test C-18 and C-23 are similar, the compressibility of C-28 and C-33 are higher in relation to the others. It is speculated that as stress is increased, the specimens that are more compressible yield a stiffer response as the fine particles begin to stabilize the floating sand skeleton and actively participate in load transfer. The highest stiffness is noted for a fines content of 28 %, this fines content may represent the optimum structure for load sharing where fines stabilize or cushion the sand skeleton. At stresses of 200 and 400 kPa, shear wave velocities for C-28 are higher than the sand structure of test C-0. Comparison of tests C-23, C-28 and C-33 indicates that velocities for C-28 are the highest and velocities obtained for tests C-23 and C-33 are almost the same (Figure 4.18). Perhaps with increase in fines from 23 % to 33 % a balance is found between fragility and stiffness of the differing structures. A decrease in small strain modulus, or shear wave velocity, with increase in fines content is also noted by various researchers. Iwasaki and Tatsuoka (1977) found that the shear moduli of sands decreases with increase in uniformity coefficient and decreases with increase of fines content for the same values of stress, void ratio and strain. Likewise, Huang et al. (2004) observed that, for similar void ratios, shear wave velocity of narrowly-graded silty sand decreases with increasing fines. Kuerbis et al. (1988) studied 81 Figure 5.11. Variation of shear wave velocity with fines content for each stage of vertical loading. the effect of gradation and fines content on the undrained response of well graded silty sands and found that the shear strength of the slurry-deposited specimens did not vary significantly with fines contentjup to 20 % fines). Increase in shear wave velocity with increase in fines past the threshold point, is postulated by Salgado et al. (2000) and Thevanayagam (2002). Both authors note that once the threshold fines content is passed 82 the fines begin to support and cushion the sand skeleton in a silty sand. Although only small change in shear wave velocity with fines content is observed from the C-23, C-28 and C-33 test data, the same trend is observed for each stage of stress with the relative changes most pronounced at higher stress (rjm ' « 200 kPa). 5.4 Comparison to moist-tamped laboratory data In 2003, B C Hydro retained Golder Associates Ltd. to conduct laboratory testing on three gradations of core material and one representative gradation of transition material from the W A C Bennett dam. In that B C H - G A study, core and transition materials were tested in a triaxial cell equipped with bender elements. It is of interest to compare shear wave data obtained in the current study, for slurry-deposited (s-d) specimens of core material loaded anisotropically in a rigid-walled permeameter, to those data for moist-tamped (m-t) specimens of core material loaded isotropically in a triaxial cell. 5.4.1 Materials and test procedure 5.4.1.1 Materials Core materials used in both laboratory programs were obtained from sonic drill samples originally shipped to U B C from the Bennett dam site. As described in section 3.3.2, the six target gradations of the current study were achieved by mixing different particle sizes, to attain a fines content of 0, 13, 18, 23, 28 and 33 %. Specimens used in the B C H - G A study were processed by adding or removing material passing the #100 sieve, to attain three gradations of about 26, 33 and 34 % fines content. Grain size distribution curves of soils tested in the triaxial program are shown in Figure 5.12 and, 83 for purposes of comparison, grain size distribution curves for the current study are found in Figure 3.5. 5.4.1.2 Specimen reconstitution Specimens of the current study were reconstituted as a slurry using a modified slurry deposition technique (described in section 3.4.2) whereas, specimens in the B C H - G A study were reconstituted by moist tamping to a target void ratio (see Table 5.5). Each specimen was prepared to three target states, characterized as dense, medium and loose (state parameters of -0.07, 0 and 0.05, respectively). Target void ratios, at 50 kPa, were achieved by moist tamping at moisture content of 5 %. Specimens were reconstituted to a nominal height and diameter of 150 mm and 70 mm in the triaxial cell and 110 mm and 100 mm in the permeameter cell, respectively. X :i • 1 i n W » 1 » 20 -to SO ICO 200 Hi N; Ill ! j ! mm i i Cork 34% (nas Com Si.6% fines Cora 25.9% fines Transition — i l l 1 i ! II ! ! * • • 4 9 w v | j 1 in i | j 1 | I i HI { i 1 | ii • [ 1 ) | 1 I * I ; 1 s v HI \ •* c \\ ; il JI \ i \ III sill | Ml \ I 111! •> : i \ i 1 II \I' ';| j1 [j j •i i j | | 1 i i i A± 1 III a. : J i too :o io o.i aoi m»i 30001 G R A I N S I Z E , m m 30UIDER SOS C O M U GRAVEL SiZE SAND size FINE GRAINED Krojao H». .MtW.IMS.1. 0^w»> X.?;. ........ Reviewed 'vv.. OM> mm— C-A' «oMer GRAIN SIZE DISTRIBUTION BENNETT DAM CORE and TRANSITION Figure 6 Figure 5.12. Grain size distribution for core and transition material of the Bennett dam (Golder, 2005) 84 Table 5.5. Target sample preparation void ratios (after Golder, 2005) Density State parameter, \|/ Target void ratio; mean effective stress of 50 kPa Core with 32.6% Core with 34% Core with 25.9 % fines fines fines Dense -0.07 0.317 0.317 0.280 Medium 0 0.387 0.387 0.350 Loose 0.05 0.437 0.437 0.400 5.4.1.3 Ageing Ageing may have a significant effect on the shear wave velocity and small strain shear modulus of granular materials (Hardin and Richart 1963 ; Anderson and Stokoe, 1978). More generally, it has been found that ageing time has a significant effect on stiffness of loose sands and the effect becomes more pronounced at higher initial stress ratios (Howie et al., 2001). To account for this phenomenon in the current study, all specimens were aged for a period of lOOOmin at an applied effective stress (o"vt' = 25 kPa). Additionally, each stage of testing was sequenced so that measurements were taken at exact elapsed times (lhr/stage, see section 3.4.4). The effect of ageing time was also recognized in the triaxial laboratory program. Through initial testing, in which shear wave data were collected over prolonged periods of time (several days) and at different consolidation stresses, it was found that the ageing effect could be removed from the shear wave data i f the specimen was left a period of 2 hours at mean effective stress of 50 kPa. After 2 hours, or 120min, no change in shear wave velocity with time was observed at this stress level. As such, each specimen was aged for a minimum of 2 hours at a mean effective stress of 50 kPa before shear wave data were recorded. 85 5.4.1.4 Loading In the current study, top vertical effective stress, along with varying levels of unidirectional downward seepage flow, are applied to each specimen confined within the rigid boundary of the permeameter cell. Loading in the laterally confined (zero strain) rigid-walled cell is essentially a Ko loading condition and the specimen undergoes anisotropic consolidation. Discussion of force equilibrium within the permeameter cell is found in section A.2.2 of Appendix A . In contrast, specimens in the BCH-GA study were isotropically consolidated in a triaxial cell. The flexible boundaries around the specimen, together with a stress control system, allow confining pressure to be systematically applied both laterally and axially. Consolidation increments were nominally 20, 50, 100, 200, 500 and 1000 kPa. After reaching the maximum consolidation increment the specimens were sheared to failure. For purposes of comparison only shear wave data collected during isotropic loading will be considered (50 > rjm ' > 1000 kPa). 5.4.1.5 Determination of shear wave velocity The bender element system of the current study comprises one transmitter and two receivers, which were fabricated at UBC. A square pulse of 10 volts was used for excitation, and shear wave velocity is deduced knowing the fixed receiver-to-receiver distance and the peak-to-peak interval time between the receivers. In the BCH-GA study a system of two bender elements was used. These elements, supplied by Global Digital Systems Ltd. (GDS), were incorporated into the top and bottom caps of the triaxial cell. Both shear and compression waves are generated at the top of the specimen and received by the element at the bottom of the specimen. A single sine pulse of 10 kHz frequency was selected for use in testing and shear wave data were recorded to disk every 1 to lOmin during consolidation. Each time shear wave data were 86 recorded, the transmitting bender element is triggered several times. In this way multiple waveforms were obtained at the receiver. The multiple waveforms were then stacked to reduce random noise from the waveform, thus increasing the signal-to-noise ratio. Stacking of seismic signals is performed within the GDS acquisition software. The first arrival time of the shear wave is determined from the stacked waveform. Shear wave velocity is deduced knowing the tip-to-tip separation and the time difference between the trigger and the first arrival of the waveform at the receiver. Peak-to-peak arrival time method (as used in the current study) was not used in the triaxial testing program, because the source wave and received wave frequency components were different. 5.4.2 Test results Shear wave velocities obtained from the B C H - G A study are presented below. The variation of shear wave velocity with mean effective stress is presented for a gradation considered representative of intact core (34 %) and for a gradation of reduced fines content (25.9 %). Test data are obtained from B C Hydro (Vazinkhoo, 2006) and from Golder Associates (Golder, 2005). Test nomenclatures, together with index properties of the gradations, are listed in Table 5.6. Table 5.6. Test code nomenclature and index properties for specimens of the triaxial test program Test specimen S,(%) (<0.075mm) Density ^ m a x BASE34CID-1 34.0 Dense 0.26 0.73 -BASE34CID-2 Medium BASE34CID-3 Loose BASE25.9CID-1 25.9 Dense 0.37 0.560 0.285 BASE25.9CID-2 Medium BASE25.9CID-3 Loose BASE25.9_dupl_CID-3 Loose * BASE25.9_dupl._CID-3 indicates a duplicate of the loose test BASE25.9CID-3 87 The variation of shear wave velocity with mean effective stress, for specimens with fines content of 34 % prepared to three target densities, are illustrated in Figure 5.13. The data for each test specimen are plotted on a log-log plot and a general trend of increasing shear wave velocity with increasing mean effective stress is observed. The dashed lines in the figure represent upper and lower bounds to the shear wave velocity for dense and loose specimens, respectively. The trend lines are parallel in relation to each other and represent velocity-stress exponents (b) of 0.21. Best fits to each test specimen yield velocity-stress exponents of 0.21, 0.25 and 0.19 for the dense, medium and loose condition, respectively. Shear wave velocities of the dense specimens are greater than those of the loose specimens for the same fines content; this trend is consistent across the entire range of stress (50 > a m ' < 1000 kPa). The trend lines of the dense and loose specimens differ by approximately 50 m/s at 50 kPa and 100 m/s at 1000 kPa (Table 5.7). 1000 E I • BASE34CID-1 BASE34CID-2 BASE34CID-3 100 Mean effective stress (kPa) 1000 Figure 5.13. Variation of shear wave velocity with mean effective stress for specimens with 34 % fines 88 Table 5.7. Comparison of shear wave velocities of the triaxial testing program Test specimen Density Shear wave velocity (m/s) r j m ' = 50 k P a am' = 1000 k P a Upper trend line BASE34 Lower trend line BASE34 Dense Loose 274 223 513 417 Upper trend line BASE25.9 Lower trend line BASE25.9 Dense Loose 291 240 546 449 Figure 5.14 shows the variation of shear wave velocity with mean effective stress for specimens with 25.9 % fines content which were also reconstituted to three target densities. Similar trends are noted: the shear wave velocities of the dense specimens are greater than those of the loose specimens for the same fines content for all stresses. Best fits to each test specimen yield velocity-stress exponents which range from 0.21 to 0.28. As is observed for specimens with 34 % fines content (see Figure 5.13), the trend lines of the dense and loose specimens are separated by approximately 50 m/s at 50 kPa and 100 m/s at 1000 kPa (Table 5.7). Comparison indicates the shear wave velocities in the fines-reduced specimens (25.9 % fines) are slightly higher than those of the 34 % fines specimens. The influence of density, or void ratio, on shear wave velocity was demonstrated for moist-tamped specimens (Figure 5.13 and 5.14). Accordingly, before shear wave velocities are compared for the different methods of reconstitution used in each study, consideration is given to the void ratios of the respective specimens. Void ratios of the slurry-deposited specimens of the current study are presented together with the target void ratios used in the triaxial program. Consolidation data from test C-33 (with 33 % fines content) are compared with void ratios of moist-tamped specimens with 34 % fines, 5.4.3 Data comparison 89 1000 t-O o • BASE25.9CID-1 oBASE25.9_dupl_CID-1 BASE25.9CID-2 BASE25.9CID-3 BASE25.9_dupl_CID-3 100 10 100 1000 Mean effective stress (kPa) Figure 5.14. Variation of shear wave velocity with mean effective stress for specimens with 25.9 % fines and data from test C-28 (with 28 % fines content) are compared with void ratios of moist-tamped specimens with 25.9 % fines. This comparison is followed by a discussion of corresponding shear wave data. Consolidation data for test specimen C-33 of the current study, together with initial target void ratios for specimens of 34 % fines content, are presented in Figure 5.15. Observe that the void ratio of the slurry-deposited (s-d) C-33 specimen decreases with increasing stress, but the range of void ratios attained over the applied stress range is small. Target void ratios for moist-tamped specimens (m-t) at a mean effective stress of 50 kPa (see Table 5.5) are plotted in Figure 5.15. Although the methods of specimen reconstitution are significantly different, the resulting void ratios using both methods are comparable. Void ratio comparability is also noted considering the range between 5.4.3.1 Void ratio 90 0.4 0.3 t > — * — C-33 (s-d) • BASE34CID-1 target • BASE34CID-2 target A BASE34CID-3 target I i t 10 100 1000 Mean effective st ress (kPa) Figure 5.15. Consolidation behavior of C-33 material and target void ratios of triaxial testing program for specimens with 34 % fines maximum and minimum void ratios for the core material (see Table 5.6). A t 50 kPa, the void ratio of the C-33 specimen lies between the medium and dense target densities of the moist-tamped triaxial specimens with 34 % fines content. Similarly, Figure 5.16 shows the consolidation data for test C-28 of the current test program together with target void ratios for specimens of 25.9 % fines content (also tabulated in Table 5.5). A t 50 kPa, the void ratio of the C-28 specimen again lies between the medium and dense target densities of the moist-tamped triaxial specimens with 25.9 % fines content. Recognizing that the void ratio or density of the slurry-deposited specimens of the current study are similar to those of the medium-dense target voids ratio of the B C H - G A study prepared using moist-tamping, consider now a comparison of shear wave velocities from 91 0.3 — * — C-28 (s-d) • BASE25.9CID-1 target • BASE25.9CID-2 target A BASE25.9CID-3 target i * < I 10 100 1000 Mean effective stress (kPa) Figure 5.16. Consolidation behavior of C-28 material and target void ratios of triaxial testing program for specimens with 25.9 % fines the two programs of testing. 5.4.3.2 Shear wave velocity Shear wave velocities are compared for nominal core gradations (34 and 33 % fines content) and reduced fines content (25.9 and 28 %), from B C H - G A and the current study, respectively. The objective is to determine similarities and differences in the shear wave velocity of both laboratory programs, and to examine relative trends in each. For purposes of comparison, only shear wave velocities of the dense (CID-1) and medium density (CID-2) moist-tamped triaxial specimens are included. To account for the relative influence of void ratio, shear wave velocities of the current study are compared with average values that lie between medium and dense moist-tamped data. The data are 92 reported in Figures 5.17 and 5.18: the minimum-maximum stress bars indicate the range of mean effective stress computed using K o values of 0.4 and 0.85, respectively. Although all data show a clear linear relation, between mean effective stresses of 50 and 200 kPa, the shear wave velocities of the moist-tamped specimens are higher than those of the slurry-deposited specimens (see Table 5.6). The average difference between shear wave velocity of the current study and the medium and dense data of the B C H - G A study is greatest (approximately lOOm/s, or 38 % difference) at the lowest common mean effective stress (oV = 50 kPa). A t the highest common stress (oV = 200 kPa), the average difference in shear wave velocities decreases to approximately 80m/s (24 % difference). Slopes of a best fit to the data of each test program are different. It is postulated that the fabric of the slurry-deposited specimens is more sensitive to a change in stress than the moist-tamped specimens. However, convergence of shear wave velocities of the two different programs occurs with increasing stress. The trends imply that similar shear wave velocities might be obtained i f testing continued up to mean effective stresses of approximately 1000 kPa. In both programs of testing, the shear wave velocities of the fines-reduced specimens (approximately 26-28 %) are slightly higher than those of the nominal gradations (approximately 33-34 %). Average shear wave velocities of test C-28 are slightly higher than those of C-33 (see Table 5.8); the difference is small but the trend is consistent across the range of stress (10 < rj m ' < 200 kPa). The difference is approximately 10 and 15m/s at mean effective stresses of 50 and 200 kPa, respectively. For the B C H - G A study, the same relation is observed comparing specimens with 34 and 25.9 % fines content. As mentioned in section 5.4.2, a 20 to 30 m/s difference in shear wave velocity is observed between the trendlines of the different gradations (Table 5.7). Although the difference is not as apparent looking at the individual test shear wave velocities at 50 and 100 kPa, it is noted thatat 200 kPa and greater, the trend becomes more apparent. 93 1000.0 100.0 10 100 Mean effective stress (kPa) OC-33 • BASE34CID-1 BASE34CID-2 1000 Figure 5.17. Comparison of shear wave velocities of different laboratory programs; nominal gradation specimen (33 - 34 % fines content) 1000 100 10 • H H * C-28 • BASE25.9CID-1 o BASE25.9_dupl_CID-1 BASE25.9CID-2 100 Mean effective stress (kPa) 1000 Figure 5.18. Comparison of shear wave velocities of different laboratory programs; fines reduced specimen (25.9 - 28 % fines content) 04 Table 5.8. Comparison of shear wave velocities of the current study and the triaxial program Test specimen Density Shear wave velocity (m/s) 50 kPa 100 kPa 200 kPa C-33 BASE34CID-1 BASE34CID-2 Dense Medium 165 285 246 209 315 275 266 364 334 C-28 BASE25.9CID-1 BASE25.9_dupl_CID-l BASE25.9CID-2 Dense Dense Medium 175 290 234 243 222 293 287 292 281 394 346 337 5.4.3.3 Elastic constants As discussed in section 5.3.1, further confidence in shear wave velocities of the current study is gained from back calculation of the small strain shear modulus, G m a x . Using Equation 2.1, the small strain shear modulus, G m a x , is calculated from deduced shear wave velocity and specimen density. The calculated G m a x is then compared to theoretical values of G m a x . Following the literature review (section 2.2), G m a x is directly influenced by the mean effective stress, void ratio, and particle size and shape. Three elastic constants, as observed in Equation 2.7 for an isotropic and elastic material are: A , which represents a material constant for a given soil and takes into account the size and shape of the soil grains, the void ratio function, F(e), which accounts for soil density or void ratio influence, and stress exponent, b, which is the slope of the linear trendline of data on a G m a x - l o g stress plot. While a value of 0.5 is traditionally assigned to b (square root of stress), values can range from 0.5 to 1.0 in some cases (Hardin and Drnevich, 1972). The determination of elastic constants from the back calculation of G m a x of the current study is described in section 5.3. A good fit between calculated G m a x in the laboratory and theoretical G ^ T i s obtained using an A value of 460 for the C-0 test (clean sand) and 365 for tests C-13, C-18, C-23, C-28 and C-33 (silty sands), see Table 5.8. The void ratio function of Hardin and Richart (1963), Equation 2.13, provides the closest fit to the 95 calculated data for the current study although the fit using Jefferies and Been (2000) e m i n relation, Equation 2.15, provides a good fit to the data as well. A stress exponent of 0.6 is obtained from the data. Elastic constants of the core material were also investigated in the B C H - G A study. A good fit between calculated G m a x in the laboratory and theoretical G m a x was obtained using an A value of 450 for core material with 34 % fines and 415 for core material with 25.9 % fines content. In their study, the Jefferies and Been (2000) form of the void ratio function was confirmed most appropriate from results of critical state experiments on core material. Stress exponents (b = 0.42) were determined from isotropic loading data and a value of A was determined at each measurement of mean effective stress and void ratio. Simultaneous iteration was used to estimate values of A and emj n; this was accomplished by picking an approximate value of emj n and then iterating to minimize error in estimated A . A summary of elastic constants for the two laboratory programs is shown in Table 5.9. So that direct comparison can be made between the programs, elastic constants of the current program were also computed using the Jefferies and Been (2000) void ratio function (Equation 2.15). Back-calculated A values of the current study using the are lower in magnitude than those obtained in B C H - G A study, however, the values are still within relatively good agreement. The difference in the stress exponent (b), as discussed previously, may be the result of the differing fabrics from specimen reconstitution. It might be anticipated that a higher sensitivity of shear wave velocity, or small strain shear modulus, with stress change would occur for a slurry-deposited fabric. In Figure 5.19, current study data for tests with 28 and 33 % fines content are compared to theoretical G m a x using elastic constants that yield the best fit to the data. Using the same void ratio function, a good fit to theoretical G m a x is obtained with A values of 320 and higher stress exponents (b = 0.6). In contrast, Figure 5.20 illustrates theoretical versus calculated G m a x of the current study with the elastic constants of the B C H - G A study, for a stress exponent of b = 0.42 and A = 415 and 450 for C-28 and C-33 data, 96 Table 5.9. Summary table of elastic constants of the three programs of study Test program Fines content, Sf{%) A F(e) b Current study; 33 460 Eqn. 2.13 0.6 Slurry-deposited, anisotropic 320 Eqn.2.15* 0.6 28 365 Eqn. 2.13 0.6 320 Eqn. 2.15* 0.6 Triaxial study; 34 450 Eqn. 2.13* 0.42 Moist-tamped, isotropic 25.9 415 Eqn.2.15* 0.42 * Jefferies and Been (2000) form of the void ratio function; emin* of 0.11 and 0.12 are used for core material with 34 and 25.9 % fines content, respectively respectively. The lower stress exponent of 0.42 and higher values of A of the B C H - G A study does not allow the data of the current study to be fit within +/- 10 %. Theoretical Gmax (MPa) Figure 5.19. Calculated versus" theoretical G m a x for C-28 and C-33 of the current study (using elastic constants; A = 320, b = 0.6) 97 5.5 Comparison to field data Shear wave data are obtained from annual crosshole seismic testing at the W A C Bennett dam. They are compared here to shear wave data obtained from laboratory tests on core material. The objective is to examine trends of shear wave velocity obtained in the field relative to those calculated in the laboratory. The use of crosshole shear wave velocity testing at the W A C Bennett dam began in response to the 1996 sinkhole program. O f the various types of seismic techniques tried at the dam, crosshole testing was considered to have the best ability to determine the spatial extent of unusual zones, and subsequently, to establish changes as a result of ground improvement. As part of a program of performance monitoring at the dam, crosshole surveys have been conducted on an annual basis since 1996. Each year shear wave velocity profiles are computed in fifteen planes (cross-sections) through the dam 98 and shear wave velocities are plotted with depth for each measurement plane. The integrity of the core is assessed using these data in two ways: first, by monitoring temporal changes, and second, by monitoring the deviation from expected values. Any temporal change in specific areas of the core can be monitored from year to year. A 'real' change in shear wave velocity is considered where the difference exceeds the error threshold of the velocity determination (~ 30 m/s). Shear wave data obtained in annual testing are also compared to expected velocities that are computed using correlation models. Models were established based on the results of testing conducted in the field during sinkhole remediation and from results of additional laboratory testing commissioned by B C Hydro (discussed previously in section 5.4). Seismic crosshole testing methodology (equipment, survey layout and shear wave velocity determination) along with details of the as-placed core material, are briefly discussed. Thereafter, results are presented for two planes of interest and a comparison made of the two data sets. 5.5.1 Test methodology, materials and stress state 5.5.1.1 Test methodology In crosshole seismic testing, shear waves generated from the source, travel through the surrounding soil, and are recorded at the receivers (as described in section 2.1). The source in the field program at the W A C Bennett dam consists of a hydraulic packer with metal anvils at either end. The assembly is lowered down to a specific depth and a vertically polarized shear wave is generated when the metal hammer impacts the anvil. Triggering is enabled when the hammer strikes the anvil and effectively closes the circuit. Receiver packages are lowered down to a specific depth in a borehole opposite to the borehole in which the source is located. The source and receiver packages are generally lowered to concurrent depths so that horizontal profiles are obtained. Receiver 99 packages are comprised of vertically oriented geophones secured to the borehole wall using a spring steel carrier (Vazinkhoo, 2006). Seismograph acquisition software is used to record the data. Signal traces, or waveforms, are digitally sampled every 0.0625 msec. For longer distance planes, signal stacking was used to obtain a detectable signal at the receiver. As discussed in section 5.4.1.5, stacking increases the signal-to-noise ratio and effectively filters random noise from the waveform. The first arrival of the shear wave at the receiver is identified as the first break on Automatic Gain Control plots (Vazinkhoo, 2006). In each seismic plane, shear wave data are typically obtained at depth increments of 1.5 m and shear wave velocity is determined by dividing the arrival time by the borehole separation, or ray path length. In total, shear wave velocity profiles are obtained with respect to depth across 15 different seismic planes. Borehole numbering, separation and maximum depths for the two planes of interest are listed in Table 5.10 (Vazinkhoo, 2006). The location of these planes is given in Figures 5.21-23. Plane 22 extends from Benchmark #1 area (Figure 5.22) hole DH96-32 to observation well #7 that is outside the close up view in Figure 5.22. The entire extent of Plane 22 is seen in Figure 5.21. Plane 26 is within the Benchmark #2 area, as shown in Figure 5.23, between hole DH96-33 and observation well #9. Some of the seismic planes cross through both core and transition materials. Plane 22 and 26, which pass through core material only, are presented. These planes represent velocity profiles near to those expected for intact core (Plane 22: DH96-32 to OW7) and for lower than expected velocities downstream of remediated sinkhole location (Plane 26: DH96-33 to OW9). Table 5.10. Details of seismic planes 22 and 26 (after Vazinkhoo, 2006) Plane Drill Holes Separation Maximum depth tested (m) Source Receiver On crest (m) Source Receiver 22 DH96-32 OW-7 68 111 137 26 DH96-33 OW-9 11 99 99 100 Figure 5.21 Overview o f seismic plane layout at the W A C Bennett dam; Plane 22 and 26 (Vazinkhoo, 2006) 5.5.1.2 Core material The Bennett dam, constructed between 1963 and 1967, is a zoned earthfill dam. Material used for the core was a naturally occurring silty sand from moraine deposits which was supplemented with more non-plastic fines (section 3.3). The fines content of the core was specified between 25 and 35 % for construction (Morgan and Harris, 1967) and the nominal fines content for intact core is approximately 33 % (Vazinkhoo, 2006). The core of the dam was placed at a moisture content of 6 % and compacted in 0.25 m (10 in) lifts to achieve unit weight of approximately 20.2 kN/m 3 (128 lb/ft3). Each lift was compacted using pneumatic loading with a minimum pressure of approximately 700 kPa (lOOpsi) (Low and Lyel l , 1967). Four passes were completed for each lift of the core. Estimated void ratios from drill hole data and construction documentation indicate a range of approximately 0.25 to 0.35 (Figure 5.24) for compacted, as-placed, core material. From this figure, an average void ratio of 0.31 to 0.32 could be reasonably assigned to intact core. 5.5.2 Test results The two planes are selected for comparative analysis because one represents intact core (Plane 22) and the other is a plane in which lower than expected shear wave velocities are observed (Plane 26). As a result, these two planes represent approximate upper and lower limits of shear wave velocities for core material determined in the field. The plane in which zones of lower velocity are observed may represent a location of reduced fines content or perhaps a location of increased void ratio, reduced stress or a combination of these phenomena. Data obtained from crosshole seismic profiles of Plane 22 and 26 are reported in Figures 5.25a and b, respectively. Shear wave velocity is plotted here against elevation for each plane. Solid and dashed lines in the figures represent shear wave velocity expected for 104 CMmalW A r f t ooed Void Ratio 0«! R to Comlreciion Void Ratio Dm Cntxai State VoW Ratio 2200 2100 „ 2000 P i l l ul o & 1900 Ul _t Ul 1800 1700 1600 0.2 0.4 VOID RATIO Figure 5.24. Estimated as-placed void ratios for intact core material (Vazinkfioo, 2006) core material dense of critical state, Vj/ = -0.1 and -0.07, respectively. Shear wave velocity is observed to increase with depth. For purposes of comparison with laboratory data, it is of interest to report shear wave velocity in terms of mean effective stress. Mean effective stress is estimated for core material using a Ko of 0.4 and a pore pressure equal to 0.26 times the overburden stress (Vazinkfioo, 2006). It is emphasized that field shear wave velocities are shown for estimated mean effective stresses, and recognized that mean effective state of stress may vary in the field. The variation of shear wave velocity with mean effective stress, for Planes 22 and 26, is given in Figure 5.26. The profiles are generalized from field data at 50 ft intervals. Shear wave velocities of both planes are observed to increase with increasing stress (or 105 Figure 5.25a. Crosshole seismic profiles; Plane 22 (Vazinkhoo, 2006) Oct. 2003 Sept 2004 Base Expected (ea-0.1) — Base Expected (es-0.07) I 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Shear Wave Velocity (feet/s) Figure 5.25b. Crosshole seismic profiles; Plane 26 (Vazinkhoo, 2006) 106 1000 100 - e— Plane No. 22: DH96-32 to OW7 - A — Plane No. 26: DH96-33toOW9 10 100 1000 Mean effective s t ress (kPa) 10000 Figure 5.26. Variation of shear wave velocity obtained in field testing (Plane No. 22 and 26) with mean effective stress depth). Values obtained in Plane 22 are in agreement with those expected for intact core (Vazinkhoo, 2006). At a stress of approximately 400 kPa, which represents an elevation of 670 m in the dam, the velocities are approximately the same for each plane. However, those for Plane 26 become progressively lower than Plane 22 with increasing stress. A maximum difference of approximately 170 m/s and mean difference of about 100 m/s is observed between the two (Table 5.11). 5 . 5 . 3 Data comparison Analysis of shear wave velocities acquired in the core of the dam requires consideration be given to the void ratios estimated in the field and those obtained in the laboratory. Therefore, a comparison of void ratio is first presented, and a comparison of shear wave velocities follows thereafter. 107 Table 5.11. Generalized shear wave velocities from crosshole seismic surveys (Planes 22 and 26, B C H 2002-2003) Mean effective stress Shear wave velocity (m/s) (kPa) Plane 22 Plane 26 0 373 265 369 -426 373 369 1043 463 389 1660 530 422 2277 546 474 2894 572 456 3511 600 463 4128 652 482 4745 680 -5362 674 -5.5.3.1 Void ratio Void ratios estimated from the field are compared with the target void ratios used in the triaxial program and void ratios obtained in the current study. Void ratios for the different programs of testing are summarized in Table 5.12. The void ratio for intact core material was observed to range from 0.25 to 0.35, as shown in Figure 5.24, with an average value of approximately 0.32. The average value for intact core in the field is close to that of the specimens prepared to a dense state by moist tamping (0.32). Void ratios of the slurry deposited specimen (0.35 - 0.38) are observed to be slightly higher. Although there is not a constant void ratio for all specimens, it appears entirely reasonable to compare the data. Table 5.12. Core material void ratios obtained in field and laboratory programs Test program Void ratios Current: Laboratory (slurry-deposited) 0.35 (at 200 kPa) < e < 0.38 (at 10 kPa) Triaxial: Laboratory (moist-tamped) e (target) = 0.32 (at 50 kPa) Field.(compacted) 0.25 < e < 0.35 ; e a v e r a g e « 0.32 108 5.5.3.2 Shear wave velocity Figure 5.27 shows the variation in shear wave velocity for nominal core material between the three different test programs. C-33 (s-d) denotes the slurry-deposited specimen with 33 % fines content and BASE34CID-1 denotes the dense moist-tamped specimen with 34 % fines content. The shear wave velocity profile for Plane 22 is also shown in the figure. Data obtained from the current program of testing for C-33 are shown as points connected with a linear best fit. Minimum-maximum stress bars indicated for these data represent the value of mean effective stress using a K o of 0.4 to 0.85. The mean effective stresses, over which the shear wave velocities are calculated, are different between the two programs. The maximum stress of the current study is approximately 200 kPa while the minimum stress at which the shear wave velocity is calculated for Plane 22 is approximately 300 kPa. Although there is no stress overlap from which shear wave velocity can be directly compared between the current study and the field data, comparative trends are discussed. 100 -I 1 ' ' ' i • '•—1—'———:-i ; : —l 10 100 1000 10000 Mean effective stress (kPa) Figure 5.27. Comparison of shear wave velocities of intact core for field and laboratory programs 109 As plotted in Figure 5.27, shear wave velocities obtained in each of the three test programs show similar trends of increasing shear wave velocity with increase in stress, with the magnitude of field shear wave velocity between those obtained in the two laboratory programs. Although the rate at which shear wave velocity increases with stress are slightly different between the slurry-deposited specimens (b = 0.33), and the moist-tamped and compacted field data (b - 0.21 and 0.22, respectively), the shear wave velocities of all programs appear to merge at approximately lOOOkPa. Therefore, the data sets, taken together, indicate reasonable values of shear wave velocity for core material. Consideration is also given to shear wave velocities of both intact, or nominal core materials, and those with reduced-fines, or profiles in which lower velocities are observed. Shear wave velocities of test C-18 with 18 % fines content and Plane 26 in the field are compared in Figure 5.28. Data from test C-18 of the current study represent the lowest shear wave velocities obtained in the test program. In both cases, shear wave velocity of the comparative C-18 and Plane 26 are lower than those that represent a nominal fines content or intact core; C-33 and Plane 22 respectively. This trend is consistent for each 1000 en 1 100 r 1 —o— Plane No. 22: DH96-32 to OW7 fgjf • C-33 (s-d) <-W —A— Plane No. 26: DH96-33 to OW9 ff*7f A C-18 (s-d) 10 100 1000 Mean effective stress (kPa) 10000 Figure 5.28. Comparison of shear wave velocities of intact core of and fines-reduced specimens for field and current study 110 level of stress, and in both programs, the magnitude of the difference increases with increasing stress. In the current study, however, only negligible differences in shear wave velocity (5-10 %) are observed between tests C-33 and C-18. There is no difference in shear wave velocity between planes 22 and 26 at stresses near 400 kPa but greater differences (170 m/s or 25 %) as stress in increased (Table 5.11). The current study examined the variation of shear wave velocity data with varying fines content. Specimens with very different fines content and similar void ratio did not result in widely different shear wave velocities over the stress range tested (10 < o V < 200 kPa). The implications of the study suggest that a difference in fines content alone is not responsible for the large difference in shear wave velocities seen in the field. Namely, the lower than expected shear wave velocities consistently encountered in Plane 26 may be influenced by a stress reduction in response to potential fines loss. I l l 6.0 S U M M A R Y A N D C O N C L U S I O N S 6.1 Summary The objectives of the study were to examine how shear wave velocity is influenced by changes in fines content of a silty sand, and how those relations may be affected by seepage flow. Specimens of varying fines content (Sf = 0, 13, 18, 23, 28 and 33 %) were reconstituted as a slurry in a rigid-walled permeameter outfitted with bender elements^ A multistage test procedure was implemented, and shear wave data recorded for each of the six gradations (0 < Sf < 33 %) at multiple stages of stress (25 < o V < 400 kPa) and at different values of hydraulic gradient (0 < /' < 8). The configuration of bender elements comprises a transmitting element, mounted in the top cap of the permeameter assembly, and two receivers elements mounted vertically on a post located in the center of the reconstituted specimen. Shear wave velocity of the specimen is deduced knowing the tip-to-tip distance between the two receivers and the difference in travel time of shear waves between them. A n advantage of the two receivers is that a direct correlation can be made between two waveforms of similar frequency content. Peak-to-peak interval time is used in deducing shear wave velocity, instead of using the first arrival times at each receiver. The peak-to-peak technique is preferred because it removes discrepancy introduced by the near field effect and picking of first arrival time. A modified slurry deposition technique was used to reconstitute the test specimen in the permeameter cell. This technique is well-suited to well-graded granular materials as it minimizes the potential for segregation and yields a homogenous and saturated sample. Homogeneous slurry was achieved by continuous mixing of the soil followed by its discrete deposition under a thin film of water. Specimen homogeneity was confirmed through analysis of both water head distribution during testing, and a post-test grain size analysis. Specimen reproducibility was assessed by means of the initial void ratio (after 112 consolidation to 25 kPa) obtained in the main test program and duplicate specimens of the same gradation. Results of testing were presented in Chapter 4. The general trend of shear wave velocity is observed to increase with vertical effective stress, and is similar for specimens of different fines content. A t relatively low stress (oV = 25 kPa), velocities for all specimens are similar in magnitude (maximum spread 18 m/s), however, at higher stress (o"vt' = 400 kPa), the range in velocity increases (maximum of 34 m/s). For a fines content 0 < Sf < 18 %, the shear wave velocity is found to decrease with increasing fines content. This relation is consistent over the range of applied stress (25 < o\t < 400 kPa). For a fines content 23 < Sf < 33 %, the shear wave velocity is found to have a different relation with fines content. The shear wave velocity for fines content Sf = 23 and 33 % are nearly identical in magnitude, however, as applied stress increases, the shear wave velocity for fines content Sf = 28 % is higher in magnitude than the others (oV > 100 kPa). Hydraulic gradient does not appear to have a direct influence on shear wave velocity, apart from an increase in confining stress induced by downward seepage flow. In Chapter 5, shear wave results were analyzed with respect to influences of stress, fines content and void ratio, and a comparison then made to other laboratory and field data for core material. It was observed that shear wave velocity of the slurry-deposited (s-d) specimens are very sensitive to change in stress. Stress exponents (P = 0.33, b = 0.6) are slightly higher than those generally assumed for soils (b = 0.5) but are within the range of encountered exponents for sands. Shear wave velocity was found to vary linearly with void ratio, irrespective of fines content. The structure of the specimen is believed to change with increasing fines content. Void ratio decreases with the addition of fines, up to a threshold value, and increases thereafter. Beyond the threshold value of fines content, defined between 23 and 28 % for the core material of the current study, the sand fraction of the soil is considered fully dispersed by the fines. A similar range has been noted in other studies of gap-graded sandy gravels and silty sands. Shear wave velocities of the specimen with Sf = 28 % are the highest in magnitude. The structure of this specimen, 113 which has a fines content near the threshold value, may represent an optimal packing where fines help stabilize the sand skeleton as it is compressed. A n increased number of particle contacts yields a stiffer response from the specimen, and higher shear wave velocities are therefore observed. Data from the current study were compared with data from testing in another laboratory program (moist-tamped, triaxial) and with field data. Shear wave velocities obtained in each of the three test programs show consistent trends of increasing shear wave velocity with increasing stress. Shear wave velocities of the slurry-deposited specimens are found to be lower in relation to moist-tamped laboratory specimens and field shear wave velocities lie between those obtained in the two laboratory programs. The differences reduce with increasing stress and values appear likely to converge at higher stress (am' « 1000 kPa). A t similar stresses and void ratios, shear wave velocities obtained from moist-tamped (m-t) specimens are higher than for slurry-deposited specimens (10 < rj m ' < 200 kPa) with a variation in shear wave velocity of 38 % at 50 kPa and 24 % at 200 kPa. These differences are not attributed to the influence of void ratio, since these values are comparable between studies. Neither are they attributed to stress condition as it was demonstrated that sidewall friction of the permeameter is accounted for in the selected Ko and interface friction. Accordingly, the fabric of the specimens may play a role in the magnitude of differences observed. Confidence in this explanation derives from comparison of field data on the compacted core material to moist-tamped laboratory data; shear wave velocities between the two programs are very close in magnitude. The rate at which shear wave velocity increases with increasing stress is slightly different between the slurry-deposited specimens (b = 0.33), and the moist-tamped laboratory and compacted field data (b = 0.21 and 0.22, respectively). It is postulated that the fabric of the slurry-deposited specimens is more sensitive to change in stress than the others. Because only small changes (maximum difference of 10 %) are noted in the shear wave velocities of reduced fines content specimens in both laboratory programs, it is speculated that a change in fines content alone is not responsible for the large difference (16 to 26 %) in shear wave velocities obtained in the field. In the current study, 114 specimens with very different fines content and similar void ratio did not result in widely different shear wave velocities over the stress range tested (10 < crm' < 200 kPa). It is postulated that the lower than expected shear wave velocities encountered for Plane 26 may be due. to changes in stress, void ratio or a combination of the two. 6.2 Conclusions The objectives of the study were to examine how shear wave velocity might change with fines content, and how that relation is effected by seepage flow. Through careful investigation of the relative influences of hydraulic gradient, stress, void ratio and fines content, as well as comparison to other laboratory test data and field data, it was found that the shear wave velocities of the current study are influenced primarily by stress, and, to a lesser degree, changes in fines content and hydraulic gradient. Ten main conclusions of this research program are discussed below. The following conclusions are drawn with respect to the equipment and test method; 1. A square wave input signal can be used successfully to determine a value of shear wave velocity for the silty sands tested; and, 2. A bender element configuration comprising two receivers allows arrival time to be determined without discrepancies introduced from near-field effects. Conclusions are drawn for the relative influences of hydraulic gradient, stress, void ratio and fines content on shear wave velocities, as follows: 3. Hydraulic gradient (0 < i < 8) does not appear to have a direct influence on shear wave velocity, apart from an increase in confining stress induced by downward seepage flow; 115 4. Shear wave velocity of the slurry deposited (s-d) specimens is very sensitive to change in mean effective stress. Stress exponents (p = 0.33, b = 0.6) are slightly higher than generally assumed for granular materials (0.25 and 0.5, respectively) but are within the range reported for sands; 5. For s-d specimens, over the range of void ratios obtained in testing, shear wave velocity was not found to change widely. The relative influence of void ratio on shear wave velocity is therefore believed minimal; and, 6. Shear wave velocity is more sensitive to a change in mean effective stress than change in fines content. However, subtle trends are observed for s-d specimens which are consistent over the range of stresses tested (10 < o-m' < 200 kPa). More specifically, shear wave velocity decreases with introduction of fines up to a threshold value, of about 23 to 28 %, beyond which a subtle increase in shear wave velocity is observed (Sf = 23, 28 and 33 %) that becomes more pronounced with increase in stress. Propagation velocity of shear waves through soil is affected by fabric and the nature of the particle contacts. For specimens with fines content at and beyond the threshold value, compression of fines dominated matrix allow the fines to support the sand skeleton, which increases the stiffness of the soil, and hence, the shear wave velocity. The greatest velocity was measured at Sf = 28 %, and that specimen also exhibited the highest compressibility. Comparison to moist-tamped triaxial data and field data yield the following conclusions: 7. Similar trends of increasing shear wave velocity with increase in stress are noted for all three data sets, and the velocities appear to converge at higher stress ( c m ' > 1000 kPa); 8. A t similar stresses and void ratios, shear wave velocities of the s-d specimens are lower than those of the moist-tamped (m-t) specimens; differences of 38 % and 116 24 % are observed (rjm ' = 50 and 200 kPa, respectively). At similar stresses and slightly different void ratios, shear wave velocities obtained in the field are closer in magnitude to those of the m-t specimens; 9. Shear wave velocity of the s-d specimens appear slightly more sensitive to stress than m-t and compacted core material, this is indicated by a higher rate of increase of shear wave velocity with stress (higher stress exponent) Since the state of the specimens (void ratio and mean effective stress) appears to be the same between laboratory programs, the difference in shear wave velocity may be attributed to specimen fabric, or inherent anisotropy, from the different reconstitution techniques. The higher sensitivity of the shear wave velocities to stress for the s-d specimens might also be attributed to fabric differences. Due to the nature of the particle contacts, fabric of the s-d specimens is slightly more fragile than the fabric of the compacted material with randomly oriented particle contacts. A convergence is noted at higher stress, however, this may imply that fabric differences observed at lower stresses no longer have a significant influence on shear wave velocity at higher stresses (rjm ' « 1000 kPa). Additional testing of slurry-deposited core material at higher stresses may confirm this relation. 10. Since only small changes are observed in the shear wave velocities of reduced fines content specimens in both laboratory programs, it is speculated that a change in fines content alone cannot account for the large difference in shear wave velocities observed in the field. It is postulated that the lower than expected shear wave velocities encountered for Plane 26 may be due to changes in stress or void ratio or likely a combination of the two. The objectives of the study were to examine how shear wave velocity might change with fines content, and how that relation is effected by seepage flow. Accordingly, shear wave velocities of the current study were found to be influenced primarily by stress, and, to a lesser degree, changes in fines content and hydraulic gradient. The change due to fines 117 content is small but the trend is consistent across the range of stress examined for the slurry-deposited specimens. With respect to hydraulic gradient, however, the change is only due to the variation in confining stress caused by the downward seepage force. The findings of the study imply that a change in fines content caused by possible fines migration might be identified using seismic surveying techniques. Although a subtle trend of shear wave velocity with fines content might be defined, it is not possible to directly relate shear wave velocity for a given fines content since any fines loss might reasonably be expected to affect the stress in the soil. 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M A S c Thesis, University of British Columbia, Vancouver. 122 A P P E N D I X A : E V A L U A T I O N O F M E A N E F F E C T I V E S T R E S S Propagation velocity of shear waves through granular material, is governed by mean effective stress (Hardin and Richart, 1963). It is therefore appropriate to present shear wave data of the current study in terms of mean effective stress. A consideration of force equilibrium in the rigid-walled permeameter requires a value of interface friction, 8, between the soil and the cell wall and a value for the coefficient of lateral earth pressure, Ko. A series of tests were performed to commission the test device with the objective of establishing a basis for calculating a value of mean effective stress for the test specimen. Shear wave data, from testing conducted in the rigid-walled permeameter, were compared to a companion set of data for testing conducted in a triaxial cell. Direct comparison of shear wave velocities for the same material, prepared to similar densities, allows the state of stress to be determined for the rigid-walled cell. Specifically, a value of Ko can be back-calculated from the data, knowing the interface friction angle. Accordingly, a series of direct shear tests were also performed to establish a relation for interface friction between the inside of the cell wall and the soil specimen. Fraser River sand was selected for comparison due to the availability of companion shear wave data from triaxial testing (Naesgaard et al., 2005). Details of the test material and experimental setup, and a discussion of stress state, are presented below. In addition, the repeatability of shear wave velocity measurement is demonstrated through comparison of commissioning test data. A .1 Test material and setup details Fraser River sand is uniformly graded with angular to sub-angular shaped particles (dso = 0.3mm, Q j .= 2.5). The grain size distribution for the source sand is shown in Figure A . 1. 123 G R A V E L SAND SILT iCLAY Coarse | M edium I Fine Coarse | M edium I Fine - | | | j | -j j j U l l T i 1 T — r H ^ l l I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 M i l l 1 III i 1 I 1 I III 1 IJ 1 1 III 1 1 1 1 1 1 , 1 1 , 1 1 i l 1 1 1 i 1 1 l l 1 i 1 I I I III I I y 1 1 1 1 1 1 1 1 1 1111,11 1 III 1 1 i l l III 1 1 1 1 H H , , , i M i l l I III 1 1 1 \ 1 III 1 I I 1 1 ,11 1 i , 1 , ' M i l ! 1 > l 1 | 11,1111 | II 1 1 1 1 1 1 H I M ! l l 1 I l l 1 I I 1 1 III 1 1 1 1 1 I N I 1 1 1 1 II 1 1 1 1 1 1 III 1 1 1 1 \ III 1 1 1 1 1 III 1 1 1 1 1 M i l 1 I I 1 III 1 1 1 1 1 111 1 1 1 1 l \ III 1 1 1 1 1 III 1 1 1 1 1 M i l l 1 1 1 III 1 1 1 1 1 III 1 1 1 1 1 \ J I M 1 1 1 1 HI 100.000 10.000 1.000 0.100 Grain size (mm) 0.010 0.001 Figure A . 1. Grain size distribution for Fraser River sand of commissioning tests Naesgaard et al. (2005) reconstituted Fraser River sand in a triaxial split-mold using an air-pluviation technique. This technique resulted in relative densities of approximately 20 %. After saturation with methocel (a methyl cellulose pore fluid), the specimens were isotropically loaded. Confining stress was incrementally increased from approximately 20 to 160 kPa, and shear wave data were recorded under the various stages of loading using a system of two bender elements. For purposes of comparison with that triaxial test program, three commissioning tests were performed in the rigid-walled permeameter of the current study and shear wave velocity established using a system of three bender elements. Two of these specimens were reconstituted using water-pluviation (WP1 and WP2), to relative densities of 10 and 12 %, and the other using air-pluviation (API) to a relative density of 17 %. Each specimen was built to a target height of 110 mm while, the program of triaxial testing, specimens were approximately 160 mm in length with a diameter of 75 mm. As described in section 3.2, the bender element system of the current study comprises of one transmitter and two receivers. In contrast, a system of two bender elements was incorporated into the top and bottom caps of the triaxial cell. Global Digital Systems Ltd. 124 supplied these elements along with the data acquisition software. Both shear and compression waves were generated at the top of the specimen and received at the bottom of the specimen; excitation was applied using a single sine wave. Shear wave velocity in the triaxial program is deduced from a known travel distance divided by the observed first arrival of the waveform at the receiver, whereas the shear wave velocity of the current program of study is deduced knowing the travel distance and peak-to-peak interval time between the receivers. In summary, similarities of the two studies include: • material (Fraser River sand); • reconstitution technique and density; and • seismic transducers. Differences include: • loading condition (isotropic versus anisotropic consolidation); • boundary conditions (flexible versus rigid wall); and • pore fluid. It is therefore concluded that the data sets, taken together, provide a very reasonable basis for comparison. A.2 Evaluation of stress state As previously mentioned, it is useful to present shear wave data in terms of mean effective stress. Mean effective stress in the rigid-walled device is computed knowing the applied vertical effective stress, the seepage force, sidewall friction and a coefficient of lateral earth pressure through which horizontal stress can be determined. The main objective of the comparison is to establish a value for the lateral earth pressure coefficient from which sidewall friction and horizontal stress state can be computed. 125 Once the lateral earth pressure coefficient (Ko) and interface friction angle (5) are established from comparison of Fraser River sand data, appropriate Ko and 8 are defined for the core material of the main test program. Consider now the relation for sidewall friction or efficiency for the inside cell wall of the permeameter, and a coefficient of earth pressure at-rest, Ko. A.2.1 Sidewall friction The permeameter cell in this study is made of aluminum with 16 mm thick walls and has a smooth anodized surface treatment. In determining the behavior of the soil-wall interface (or frictional losses), consider must be given to the roughness, or asperity size of the wall surface, in conjunction with the mean particle size (dso) of the soil. In the literature, normalized friction coefficient, fn, or efficiency factor, has been defined as: fn = tan 8 / tan cp A . 1 where 5 is the interface friction angle and cp is the friction angle of the soil. Therefore, an efficiency factor, which characterizes the frictional behavior between soil and cell wall, can be determined knowing the friction angle of the soil and the interface friction angle. To determine an interface friction angle, and hence, an efficiency factor for the cell wall of the current study, a series of six direct shear tests were conducted on Fraser River sand and a smooth anodized aluminum block. The block, with an anodized surface treatment considered representative of the inside cell wall, was placed in the bottom half of a shear box, flush with the plane of shear. The shear box is approximately 76 mm by 76 mm, and the overlying soil specimen was placed to a height of approximately 10 mm. Figure A.2 shows the shear box and equipment used in the direct shear test. 126 Figure A.2 . Direct shear test apparatus Each specimen was prepared to a relative density of 20 % and sheared at a normal stress of 50, 150 and 250 kPa. In Figure A.3 , computed interface friction angle is plotted for shear displacements up to a maximum of 4 mm. A n average value interface friction angle of 19.5° was obtained, and found independent of normal stress up to 250 kPa. The deviation between tests is within the resolution of measurement (+/-1.5°). In relation to the internal friction angle (cp) of the sand, and using Equation B . l , this gives an efficiency factor of 0.53. Various researchers have demonstrated that efficiency factors are influenced by wall roughness, particle size, shape and mineralogy, and soil density. Gachet et al. (2003) observed upper and lower bound interface friction angles of 0.5 and 0.67<p (fn = 0.44-0.64) between glass and silty sand. Another study, conducted by Porcino et al. (2003), found that smooth and very rough aluminum surfaces have efficiencies of 0.45 and 0.92, respectively, in relation to Ticino and Toyoura sand. In their study, a 3 pm 127 25 t 2 10 1.5 2 2.5 Shear displacement (mm) • 50kPa • 50kPa_r1 X 1S0kPa • 250kPa o 250kPa_r1 4 250kPa_r2 Average 3.5 Figure A .3 . Interface friction angle from direct shear tests with Fraser River sand and smooth aluminum peak-to-trough difference is considered smooth and a 30 pm difference is considered very rough. Laboratory testing on sand-steel interfaces (Tejchman, 1995) determined that interface friction angles for very rough surfaces had an upper limit close to that of the angle of friction of the sand, while lower limits for smooth walls were found to be approximately equal to one half the friction angle of quartz against quartz (~ 13°). The computed efficiency of the smooth aluminum cell wall of permeameter (fn = 0.53), obtained from direct shear testing, is in good agreement with expected efficiency factors found for smooth surfaces. Furthermore, as the mean grain size (dso) of Fraser River sand and the core material of the main program of testing are similar (~ 0.3 mm), this efficiency factor (0.53) is deemed appropriate to characterize the interface friction between the core material of the main test program and the inside cell wall. From Equation B . l , given a friction angle of 37° for core material (triaxial testing; Morgan and Harris, 1967), an interface friction angle of 21° is obtained. This friction angle is used to determine interface friction, and subsequently, mean effective stress in the rigid-walled permeameter cell, as described below. 128 A.2.2 Ko condition Mean effective stress (rj m ' ) is computed knowing the top applied vertical effective stress (rjvt'), the seepage force per unit volume (J), sidewall friction (Fsw) and horizontal stress (rjh). Force equilibrium for the soil element in the rigid-walled permeameter is illustrated in Figure A.4. Vertical effective stress, r j v t ' , is computed knowing the applied axial load and area of the perforated top plate. Side wall friction, Fsw, is determined assuming a coefficient of lateral earth pressure (Ko) and interface friction angle (5), where; Fsw = [(aVm' K o ) (tan 5) Ac i r ] / Ac A.2 where A c ; r is the circumferential area, A c is the cross-sectional area of the specimen and ovm' is the mean vertical effective stress at the center of the element. Assuming linearity, rjvm' is the average of the top and bottom vertical effective stresses. Seepage force, J, is determined by adding the seepage component (downward flow) to the effective unit weight of the specimen. Hydraulic gradient is considered uniform throughout the specimen. J i l CJvt' U Figure A.4. Schematic of force equilibrium of the soil in the rigid-walled permeameter 129 Combining stress components and subtracting the sidewall friction, mean vertical effective stress is given by: = [2 ovt' + z (y' + i a v yw)] / [ 2 + ( K 0 tan 5 A c i r ) / A c ] A.3 and, mean effective stress by: = a v m \ ( l + 2Ko) / 3 A.4 Having established a basis to determine mean effective stress of the soil element in the rigid-walled permeameter, a value of Ko is now required. Experimental data from tests conducted with sand address the suitability of the classic Jaky expression for Ko (Mesri and Hayat, 1993; Mayne and Kulhawy, 1982; among others). It relates Ko to the internal friction angle, and suggests a Ko of 0.5 might be expected for Fraser River sand (cp' = 33°). The variation of shear wave velocity with mean effective stress, computed using an interface friction angle, 8 = 19.5° and Ko = 0.5, for Fraser River sand in the rigid-walled permeameter (see Figure A.5). Triaxial test data of Naesgaard et al. (2005) are included for purposes of comparison. Although a close fit is observed between shear velocity of the current study and that of the triaxial study at the lower range of stress (10 < o V < 100 kPa), the difference increases with increasing stress (rjm ' > 100 kPa). The percentage difference at 25 kPa is approximately 2 % whereas the difference at 150 kPa is up to Through trial and error, it was found that the best fit of the current study data to the triaxial data occurs Ko = 0.85 (see Figure A.6). There is a relatively close fit between velocity data of both programs using a value of 0.85; the trend of velocity data for the water pluviated specimens lies within 2 % of the triaxial and the trend of the air pluviated specimen lies within 5 %. The back-calculated Ko value is slightly higher in magnitude than that expected of at-rest coefficients (~0.4 to 0.6) determined using the conventional K Q = 1 - sin q>' A.5 10 %. 130 250 ~ 2 0 0 in £ o o > 150 » > ra OJ to 100 50 —Tr iax ia l eO = 0.88 (Naesgaard et al., 2005) API eO = 0.884 WP1 eO = 0.907 • WP2 eO = 0.901 50 100 150 Mean effective stress (kPa) 200 250 Figure A.5 . Fraser River sand shear wave velocity comparison; triaxial (isotropic loading) versus rigid walled permeameter (5 = 19.5°, Ko = 0.5) 250 ^ 2 0 0 to £ o o 03 > 150 > 100 50 —Tr iax i a l eO = 0.88 (Naesgaard et al. AP1 eO = 0.884 WP1 eO = 0.907 • WP2 eO = 0.901 2005) 50 100 150 Mean effective stress (kPa) 200 250 Figure A.6. Fraser River sand shear wave velocity comparison; triaxial (isotropic loading) versus rigid walled permeameter (8 = 19.5°, Ko = 0.85) 131 Jaky (1944) relation (Equation A.5). However, it is not outside the encountered range of K 0 ( 0 . 3 t o > 1.0). For purposes of data analysis in this study, mean effective stress is determined with reference to upper (0.85) and lower (0.5) bound values of Ko. As shown in Table A . l , mean effective stress does not vary widely for values of Ko = 0.5 and 0.85. The upper bound (Ko = 0.85) for Fraser River sand is used for the upper bound of the core material of the main program. Using the same rational for determining the lower bound of Fraser River sand, namely, the Jaky equation, a lower bound Ko of 0.4 is obtained for core material. Table A . l Mean effective stress computed using upper and lower bound K 0 (air-pluviated FRS) Vertical effective stress (kPa) Mean effective stress K 0 = 0.85 (kPa) Mean effective stress K 0 = 0.50 (kPa) 25 14 13 50 28 25 75 42 37 100 56 49 150 84 74 200 112 98 300 167 147 400 223 196 A . 3 Repeatability Repeatability of specimen response, by way of shear wave velocities obtained in testing, is now demonstrated. Accordingly, direct comparison of shear wave velocities obtained in commissioning tests with water-pluviated specimens (WP1 and WP2) of similar density is made. Shear wave velocity and void ratio are tabulated in Table A.2 for five stages of loading (a v t ' = 100, 150, 200, 300 and 400 kPa). Maximum percentage difference between shear wave velocities of the two tests is 14 %, however as seen in Figures A.5 and A.6 the shear wave velocity of WP2 at 100 kPa does not follow the best-fit trend of the data. Apart from the higher difference observed with velocities at 100 kPa, the percentage difference is small at the other four stages of loading (maximum of 6 %). 132 The comparability of shear wave velocity between these two commissioning tests confirm excellent reproducibility of specimen response. Table A .2 Reproducibility of specimen response (Vs) for commissioning tests Vertical effective stress (kPa) Shear wave velocity (m/s) / Void ratio WP1 WP2 100 158 (0.86) 138 (0.85) 150 172(0.86) 170 (0.84) 200 184(0.85) 185 (0.83) 300 207 (0.84) 199 (0.83) 400 212(0.84) 200 (0.82) 133 A P P E N D I X B : S H E A R W A V E V E L O C I T Y F O R D I F F E R E N T C O M P U T A T I O N S O F S T R E S S S T A T E Table B.l Shear wave velocity versus stress states; test C-0 Sf = 0% Vs ii7 a * ' Upper a m ' Lower am' Avg am' (m/s) (kPa) (kPa) (kPa) (kPa) 125.3 0 26.5 14.4 12.3 13.4 123.4 2 26.5 15.0 12.8 13.9 121.6 4 26.5 15.6 13.3 14.4 8 26.5 16.7 14.3 15.5 138.1 0 49.2 26.3 22.5 24.4 142.9 2 49.2 26.9 23.0 25.0 145.5 4 49.2 27.5 23.5 25.5 142.9 8 49.2 28.6 24.5 26.5 177.1 0 99.9 531 45.4 49.2 181.0 2 99.9 53.7 45.8 49.7 177.1 4 99.9 54.2 46.3 50.3 173.3 8 99.9 55.3 47.3 51.3 220.2 0 201.1 106.6 91.0 98.8 220.2 2 201.1 107.1 91.5 99.3 220.2 4 201.1 107.7 91.9 99.8 214.4 8 201.1 108.8 92.9 100.8 271.5 0 399.0 211.5 180.4 195.9 271.5 2 399.0 212.1 180.9 196.5 271.5 4 399.0 212.7 181.4 197.1 8 399.0 213.8 182.3 198.1 ar wave velocity versus stress states; test C-13 S f= 13% Vs '17 oV Upper am' Lower am' Avg am' (m/s) (kPa) (kPa) (kPa) (kPa) 110.1 0 26.1 14.0 12.0 13.0 110.1 2 26.1 14.6 12.5 13.6 111.6 4 26.1 15.1 13.0 14.1 118.1 8 26.1 16.3 14.0 15.2 131.4 0 49.7 26.2 22.6 24.4 129.3 2 49.7 26.8 23.0 24.9 138.1 4 49.7 27.3 23.5 25.4 135.8 8 49.7 28.5 24.5 26.5 162.9 0 100.9 52.7 45.4 49.0 166.2 2 100.9 53.3 45.9 49.6 . 169.7 4 100.9 53.8 46.4 50.1 8 100.9 55.0 47.3 51.2 203.7 0 200.1 104.1 89.6 96.9 203.7 2 200.1 104.7 90.1 97.4 203.7 4 200.1 105.3 90.6 97.9 208.9 8 200.1 106.5 91.6 99.0 254.6 0 399.8 208.1 178.8 193.4 254.6 2 399.8 208.6 179.3 194.0 254.6 4 399.8 209.2 179.8 194.5 254.6 8 399.8 210.3 180.7 195.5 134 Table B.3 Shear wave velocity versus stress states; test C-18 Sf=18% Vs '17 Upper <7m" Lower CTm" Avg am' (m/s) (kPa) (kPa) (kPa) (kPa) 0 26.4 14.4 12.3 13.4 107.2 2 26.4 15.0 12.8 13.9 108.6 4 26.4 15.5 13:3 14.4 110.1 8 26.4 16.7 14.2 15.4 119.8 0 49.8 26.7 22.8 24.8 123.4 2 49.8 27.3 23.3 25.3 125.3 4 49.8 27.8 23.8 25.8 133.5 8 49.8 29.0 24.8 26.9 150.9 0 100.5 53.5 45.7 49.6 153.7 2 100.5 54.1 46.2 50.1 153.7 4 100.5 54.6 46.7 50.7 156.7 8 100.5 55.8 47.6 51.7 194.0 0 198.9 105.6 90.1 97.8 194.0 2 198.9 106.1 90.6 98.3 194.0 4 198.9 106.7 91.0 98.9 198.7 8 198.9 107.8 92.0 99.9 0 400.9 212.8 181.4 197.1 254.6 2 400.9 213.4 181.9 197.7 262.8 4 400.9 213.9 182.4 198.2 246.8 8 400.9 215.1 183.3 199.2 Table B.4 Shear wave velocity versus stress states; test C-23 Sf=23% Vs I17 Upper am' Lower am" Avg o m ' (m/s) (kPa) (kPa) (kPa) (kPa) 111.6 0 27.9 15.3 13.1 14.2 111.6 2 27.9 15.9 13.5 14.7 113.1 4 27.9 16.4 14.0 15.2 114.7 8 27.9 17.6 15.0 16.3 131.4 0 51.8 28.0 23.9 25.9 138.1 2 51.8 28.6 24.3 26.5 140.4 4 51.8 29.1 24.8 27.0 145.5 8 51.8 30.2 25.8 28.0 166.2 0 100.4 53.9 45.9 49.9 166.2 2 100.4 54.4 46.3 50.4 169.7 4 100.4 55.0 46.8 50.9 173.3 8 100.4 56.1 47.8 51.9 198.7 0 201.0 107.5 91.5 99.5 203.7 2 201.0 108.1 91.9 100.0 208.9 4 201.0 108.6 92.4 100.5 214.4 8 201.0 109.7 93.4 101.5 271.5 0 399.0 213.5 181.4 197.4 2 399.0 214.0 181.9 197.9 4 399.0 214.6 182.3 v 198.5 262.8 8 399.0 215.7 183.3 199.5 135 Table B .5 Shear wave velocity versus stress states; test C-28 S f = 28% V s "17 avt" Upper a m " Lower a m " Avg a m ' (m/s) (kPa) (kPa) (kPa) (kPa) 125.3 0 27.6 15.1 12.9 14.0 119.8 2 27.6 15.7 13.4 14.5 119.8 4 27.6 16.2 13.9 15.0 123.4 8 27.6 17.4 14.8 16.1 138.1 0 49.6 26.8 22.9 24.9 135.8 2 49.7 27.4 23.4 25.4 140.4 4 49.7 28.0 23.8 25.9 8 49.7 29.1 24.8 26.9 173.3 0 101.3 54.3 46.2 50.3 173.3 2 101.3 54.8 46.7 50.8 177.1 4 101.3 55.4 47.2 51.3 177.1 8 101.3 56.5 48.1 52.3 214.4 0 201.9 108.0 91.9 99.9 220.2 2 201.9 108.5 92.4 - 100.4 226.3 4 201.9 109.1 92.8 100.9 226.3 8 201.9 110.2 93.8 102.0 280.9 0 400.9 214.6 182.3 198.5 280.9 2 400.9 215.2 182.8 199.0 280.9 4 400.9 215.7 183.3 199.5 280.9 8 400.9 216.8 184.2 200.5 Table B .6 Shear wave velocity versus stress states; test C-33 S f = 33% Vs •« Upper am' Lower a m ' Avg am' (m/s) (kPa) (kPa) (kPa) (kPa) 113.1 0 27.4 14.6 12.6 13.6 114.7 2 27.4 15.2 13.1 14.2 4 27.4 15.8 13.6 14.7 116.4 8 27.4 17.0 14.6 15.8 127.3 0 50.1 26.4 22.7 24.6 133.5 2 50.1 27.0 23.2 25.1 133.5 4 50.1 27.5 23.7 25.6 131.4 8 50.1 28.7 24.7 26.7 0 98.7 51.5 44.4 47.9 162.9 2 98.7 52.1 44.9 48.5 166.2 4 98.7 52.7 45.3 49.0 166.2 8 98.7 53.8 46.3 50.1 203.7 0 200.1 104.1 89.6, 96.9 208.9 2 200.1 104.7 90.1 97.4 214.4 4 200.1 105.3 90.6 98.0 208.9 8 200.1 106.5 91.6 99.0 262.8 0 400.4 208.5 179.1 193.8 262.8 2 400.5 209.2 179.7 194.5 271.5 4 400.5 209.7 180.2 194.9 271.5 8 400.5 210.9 181.1 196.0 136 

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