Associate Professor John S. McCartney (committee chair) ... I am greatly indebted to my advisor, Professor John Scott McCartney throughout ...... Vianney clay.
Compression Mechanisms of Soils under High Stresses
Woongju Mun M.S. Ajou University, 2007 B.S. Ajou University, 2005
A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirement for the degree of Doctor of Philosophy Department of Civil, Environmental, and Architectural Engineering 2015
ProQuest Number: 10108754
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This thesis entitled:
Compression Mechanisms of Soils under High Stresses
Written by Woongju Mun
has been approved by the Department of Civil, Environmental, and Architectural Engineering
_________________________________________________________ Associate Professor John S. McCartney (committee chair)
_________________________________________________________ Associate Professor Richard Regueiro
_________________________________________________________ Professor Ronald Y.S. Pak
_________________________________________________________ Professor Stein Sture
_________________________________________________________ Professor Dobroslav Znidarčić
Date________________ The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet the acceptable presentation standards of scholarly work in the above mentioned discipline.
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Woongju Mun (Ph.D. Civil Engineering, Department of Civil, Environmental, and Architectural Engineering) Compression Mechanisms of Soils under High Stresses Thesis directed by Professor John S. McCartney ABSTRACT During a buried explosion, the magnitude of upward blast pressure depends partly on the reaction from the surrounding soil. Different reactions are expected for sand and clay, and unsaturated conditions and drainage conditions may play a critical role. In the simulation of buried explosives, the equilibrium compression curve defined using quasi-static compression testing is commonly used in analyses of these problems. There has not been a thorough consideration of the compression characteristics of soils to high stresses with respect to the effects of different initial conditions of soil layers encountered in the field (e.g., degree of saturation, drainage conditions, compaction-induced soil structure, soil type, etc.). Accordingly, not only is there a need for new experimental data that considers these variables, but constitutive relationships need to be developed to represent the behavior of soils under different initial conditions over a wide range of stresses. Therefore, the primary objective of this research is to understand the compression behavior of soils having different initial conditions and drainage conditions under mean stresses up to 160 MPa. To achieve the goal, a new isotropic pressure cell was developed that can be used in tandem with a high-pressure syringe pump operated in displacement-control mode to control the mean total stress and track specimen volume changes. Matric suction control was incorporated in the cell by using the axis translation technique so that various types of drainage conditions can be investigated. Compression tests were performed on three different soils: unsaturated clay, dry and saturated sand, and saturated sand-clay mixtures. For the tests on unsaturated clays, a series of suction-controlled isotropic compression tests performed under different initial degrees of saturation and drainage conditions were performed. The test results permit the evaluation of hardening mechanisms and hypothetical transition points in the compression curve. For the compression tests on the sand, the effect of drainage conditions
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on the compression response of sand was evaluated on saturated and dry specimens. Clear trends in particle breakage quantified using Marsal’s breakage factor with increasing mean total stress were observed. For the compression tests on the sand-clay mixtures, the effect of different portion of clay on the compression response for clay-sand mixtures specimens was assessed. It was found that the stiffness of the mixture increases with increasing the percentage of clay. Based on the experimental findings, the research focused on characterization of different physical mechanisms that change the compression response of saturated and unsaturated soils. These processes include suction-induced hardening, dissolution of air into water, and grain crushing, all of which were characterized and incorporated into a new set of constitutive relationships. These constitutive relationships were found to capture the compression curves of the different soil type well while considering the different physical processes. The outcome of these constitutive models can be used in finite element models to represent the soil behavior when simulating buried explosives.
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ACKNOWLEDGEMENTS I am greatly indebted to my advisor, Professor John Scott McCartney throughout my PhD studies. I have always wanted to follow his footstep as he has been the best advisor and role model I could ask for. All these years that I spent studying and discussing with him greatly inspired and shaped my research and who I am as a scholar. I would like to thank Professors Dobroslav Znidarčić, Richard Regueiro, Ronald Y.S. Pak, and Stein Sture for serving as contributing members of my dissertation committee and for great support. I would also like to acknowledge Dragan Mejic, for offering his expertise in the high pressure isotropic cell, and to Greg Miller for his assistance in the development of the high pressure isotropic cell and supporting software. I would also like to thank Jenna Svoboda, Thayza Teixeira, Fabricio Valente, and Mehmet Can Balci for offering their assistance to perform the experimental tests as members of MURI team. I would also like to thanks to Alexandra Wayllace, Yi Dong, and Ning Lu at Colorado School of Mines for measuring the soil-water retention curve for Boulder clay. I would like to appreciate my father, mother, and brother who have always been there for me during all of my life struggles. I also would like to mention my lovely girlfriend Sojin Jang for her endless love and encouragement. She has been my mentor, teacher, and most importantly an incredible supporter. I would also like to thank my giant baby brother Sang Kim who has also been a great contribution to my work and my focus. He is the one with the greatest potential and talent as a businessman I have ever met in my life. Sang, you are more reliable than Statefarm whenever I encounter challenges and hard moments. I also would like to appreciate my friend Joowook DAM Kim who shared all the good and bad moments together and has offered support everywhere at any time. Additionally, I would like to thank Big mama brother Ahram Kim, P-master Hyunwoo Lim, our Christmas gift Yule Lim and her mother Jimin Park, and a couple that seems to be in their first love - Benjamin LONG Park and Dareum PRE Nam. I also would like to thank Eunjoo Kim who has helped my extra work throughout my school years. I am very grateful to Ismail Ghaaowd, Taeseok Oh, and Moonhee Nam at UCSD, who continuously lend me to feel stable in San Diego. I also would like to thank Professor Atsushi Takai at Kyoto University for his assistance to complete the rest of testings. Additionally, I am grateful to Professor Sangduk Lee at Ajou University. I have great admiration for his enthusiasm towards research. Financial support from Office of Naval Research (ONR) grant N00014-11-1-0691 is greatly and genuinely appreciated.
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TABLE OF CONTENTS TABLE OF FIGURES .....................................................................................................................x LIST OF TABLES .........................................................................................................................xv 1.
INTRODUCTION...................................................................................................................1 MOTIVATION .........................................................................................................................1 PROBLEM STATEMENT .......................................................................................................2 OBJECTIVES AND APPROACH ...........................................................................................6 SCOPE OF DISSERTATION ..................................................................................................7 PUBLICATIONS BASED ON THE PRESENT WORK ........................................................8
2.
DEVELOPMENT
OF
THE
EXPERIMENTAL
SETUP
AND
TESTING
APPROACH ...................................................................................................................................9 EXPERIMENTAL SETUP .......................................................................................................9 SYSTEM CALIBRATION .....................................................................................................14 INSTRUMENTATION CALIBRATION ..............................................................................15 3.
COMPRESSION BEHAVIOR OF SANDS TO HIGH STRESSES ................................18 INTRODUCTION ..................................................................................................................18 BACKGROUND ....................................................................................................................19
3.2.1. High Pressure Behavior of Sand under Quasi-Static Loading .............................................19 3.2.2. Particle Breakage Factors ....................................................................................................21 MATERIAL (MASON SAND) ..............................................................................................22 EXPERIMENTAL APPROACH............................................................................................23 EXPERIMENTAL RESULTS................................................................................................24
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3.5.1. Role of Drainage in the Compression of Sand to High Pressures .......................................24 3.5.2. Loading Effects on Particle Breakage..................................................................................29 FORMULATION OF CONSTITUTIVE MODELS FOR SANDS .......................................31 3.6.1. Drained Compression of Dry or Saturated Sand..................................................................31 3.6.2. Undrained Compression of Saturated Sand .........................................................................34 4.
UNDRAINED COMPRESSION BEHAVIOR OF UNSATURATED CLAY ................36 INTRODUCTION ..................................................................................................................36 BACKGROUND ....................................................................................................................37
4.2.1. Undrained Compression of Unsaturated Soils to High Stresses ..........................................37 4.2.2. Pore Pressure Generation in Unsaturated Soils during Undrained Compression ................38 4.2.3. Modified Hilf Analysis for Pressurized Saturation ..............................................................39 MATERIALS (BOULDER CLAY) .......................................................................................44 EXPERIMENTAL APPROACH............................................................................................46 EXPERIMENTAL RESULTS................................................................................................47 UNDRAINED COMPRESSION MODEL FOR UNSATURATED CLAY .........................49 EVALUATION OF MODELED COMPRESSION CURVES ..............................................54 5.
DRAINED COMPRESSION BEHAVIOR OF CLAY .....................................................56 INTRODUCTION ..................................................................................................................56 BACKGROUND ....................................................................................................................57
5.2.1. Compression of Unsaturated Soils to High Stresses ............................................................57 5.2.2. Limitations of Existing Elasto-Plastic Models of Unsaturated Soils ...................................59
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5.2.3. Rate Effects in Constant Rate of Strain Compression Tests ................................................60 EXPERIMENTAL APPROACH............................................................................................62 5.3.1. Testing Procedures ...............................................................................................................62 5.3.2. Selection of Strain Rate for Compression Tests ..................................................................64 EXPERIMENTAL RESULTS................................................................................................68 5.4.1. Drained Compression Tests .................................................................................................68 5.4.2. Assessment of the Impact of Drainage Conditions ..............................................................75 DRAINED COMPRESSION MODEL FOR UNSATURATED CLAY ...............................78 5.5.1. Zhou et al. (2012a) Model Calibration ................................................................................78 5.5.2. Model Formulation ..............................................................................................................80 EVALUATION OF MODELED COMPRESSION CURVES ..............................................85 6.
BEHAVIOR OF SAND-CLAY MIXTURES .....................................................................87 INTRODUCTION ..................................................................................................................87 BACKGROUND ....................................................................................................................88 SAMPLE PREPARATION (MASON SAND-BOULDER CLAY MIXTURES) .................89 EXPERIMENTAL APPROACH............................................................................................91 EXPERIMENTAL RESULTS................................................................................................93
6.5.1. One Dimensional Oedometer Tests .....................................................................................93 6.5.2. High Pressure Isotropic Tests ..............................................................................................94 7.
CONCLUSIONS AND CONTRIBUTIONS.......................................................................98 COMPRESSION OF SAND TO HIGH PRESSURES ..........................................................98
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UNDRAINED COMPRESSION OF UNSATURATED CLAY ...........................................99 DRAINED COMPRESSION OF UNSATURATED CLAY ...............................................100 BEHAVIOR OF SAND-CLAY MIXTURES ......................................................................101 CONTRIBUTIONS ..............................................................................................................102 8.
REFERENCES ....................................................................................................................103 COMPRESSION BEHAVIOR OF SANDS .........................................................................103 UNDRAINED COMPRESSION BEHAVIOR OF UNSATURATED CLAY....................106 DRAINED COMPRESSION BEHAVIOR OF CLAY ........................................................108 BEHAVIOR OF SAND-CLAY MIXTURES ......................................................................114
APPENDIX .................................................................................................................................116 APPENDIX A: SCHUURMAN’S ANALYSIS (1966) ..............................................................117 APPENDIX B: HILF’S ANALYSIS (1948) ...............................................................................122
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TABLE OF FIGURES Figure 1.1: Shallowly-buried explosion in unsaturated soil ........................................................... 1 Figure 1.2: Isotropic compression response of sand under different drainage conditions (inspired by Whitman 1970 and Veyera 1994) ...................................................................................... 2 Figure 1.3: Transitions in behavior of unsaturated, compacted soils during compression to high stresses under undrained conditions........................................................................................ 3 Figure 1.4: Transitions in behavior of unsaturated, compacted soils during compression to high stresses under drained conditions............................................................................................ 4 Figure 2.1: View of the overall experimental setup ........................................................................ 9 Figure 2.2: Schematic of the pressure control system and connections to the isotropic pressure cell ............................................................................................................................................... 10 Figure 2.3: (a) View of the high pressure syringe pump; (b) View of the pressure control panel 10 Figure 2.4: Isotropic pressure cell: (a) Schematic; (b) Picture ..................................................... 11 Figure 2.5: Bottom platen for suction control: (a) Schematic; (b) Picture of the platen having HAE ceramic disk and sintered porous ring; (c) Picture of the platen with pressure inlet/outlet .. 12 Figure 2.6: Saturation system for the high air entry porous disk: (a) Schematic; (b) Saturation cap; (c) Placement of the saturation cap over the bottom platen .................................................. 13 Figure 2.7: Example of typical pressure and total volume change with time provided by the highpressure syringe pump for the isotropic pressure cell: (a) Raw data; (b) Cumulative data .. 14 Figure 2.8: Machine response curve of the isotropic pressure cell ............................................... 15 Figure 2.9: GPT calibration results ............................................................................................... 16 Figure 2.10: DPT calibration results ............................................................................................. 17 Figure 2.11: Tensiometer calibration results ................................................................................ 17 Figure 3.1: Isotropic compression response of sand under different drainage conditions (inspired by Whitman 1970 and Veyera 1994) .................................................................................... 20 Figure 3.2: Graphical example of the calculation procedure for Marsal’s breakage factor BM for Mason sand isotropically compressed to 160 MPa ............................................................... 21 Figure 3.3: Photo of Mason sand specimen after high pressure compression test under 80MPa . 24
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Figure 3.4: Compression behavior of Mason sand specimens with different drainage conditions: (a) e-logpʹ (drained, dry sand); (b) e-pʹ (drained, dry sand); (c) e-logp (undrained, dry sand); (d) e-p (undrained, dry sand); (e) e-logp (undrained, saturated sand); (f) e-p (undrained, saturated sand) ...................................................................................................................... 25 Figure 3.5: Comparison of compression curves for specimens with different drainage conditions: (a) e-logpʹ or e-logp; (b) e-pʹ or e-p ...................................................................................... 26 Figure 3.6: Grain size distributions of Mason sand before and after compression to different mean stresses: (a) Drained, dry sand; (b) Undrained, dry sand (c) Undrained, saturated sand ...... 27 Figure 3.7: Role of initial relative density: (a) Comparison of compression curves; (b) Comparison of grain size distributions after isotropic compression to 160 MPa...................................... 29 Figure 3.8: Marsal’s breakage factor BM: (a) After isotropic compression to different mean stresses for dry and saturated sands under different drainage conditions; (b) After drained, isotropic compression of sand with different initial relative densities to 160 MPa ............................. 30 Figure 3.9: Comparison of the model results (dashed lines) with the experimental data (solid lines) for isotropic compression of dry sands under different drainage conditions: (a) Dry sand under drained conditions highlighting the unloading model; (b) Dry sand with different initial relative densities under drained conditions; (c) Dry sand under undrained conditions ........ 33 Figure 3.10: Calibration of the model for isotropic compression of saturated sand under undrained conditions: (a) Volume change comparison with water; (b) Undrained compression curve for saturated sand ........................................................................................................................ 35 Figure 4.1: Transitions in behavior of unsaturated, compacted soils during compression to high stresses under undrained conditions...................................................................................... 37 Figure 4.2: Parametric evaluation of the modified Hilf analysis (analytical results): (a) Pore pressure change required for pressurized saturation of soils having different initial degrees of saturation; (b) Pore pressure change during undrained loading for soils having different initial degrees of saturation; (c) Pore pressure change during undrained loading for soils having different mv,u values .............................................................................................................. 43 Figure 4.3: Parametric evaluation of the modified Hilf analysis: (a) Pore pressure change required for pressurized saturation of soils having different initial degrees of saturation; (b) Pore pressure change during undrained loading for soils having different initial degrees of saturation; (c) Pore pressure change during undrained loading for soils having different mv,u values .................................................................................................................................... 46
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Figure 4.4: Evaluation of data to consider machine response curve: (a) Mean stress vs. volume change curves (for a soil specimen with an initial Sr,0 = 1.0); (b) Comparison of the compression response of soil specimens under undrained conditions with that of water .... 47 Figure 4.5: Undrained compression behavior with different Sr,0: (a) e-logp (b) e-p .................... 48 Figure 4.6: Comparison of the initial air volume Va,i of the different soil specimens with the volume of voids at pressurized saturation Vv,ps ................................................................................. 49 Figure 4.7 Undrained compression indices under different Sr,0: (a) Apparent preconsolidation stress pc; (b) Slope of unsaturated soil (u,i) ......................................................................... 51 Figure 4.8 Assessment of pressurized saturation for Boulder clay: (a) Pore pressure change of Boulder clay under different initial degrees of saturation; (b) Comparison of the pressurized saturation under different Sr,0 (prediction vs. experimental data) ......................................... 52 Figure 4.9 Changes in the coefficient u with mean total stress for soil specimens having different initial degrees of saturation ................................................................................................... 53 Figure 4.10 Model Prediction: (a) Comparison of the model calibration (dashed lines) with the experimental data (solid lines) for undrained compression of clay under different Sr,0 (e-logp); (b) Comparison of the model predictions (dashed lines) with the experimental data (solid lines) for undrained compression of clay under different Sr,0 (e-p); (c) Model predictions under different Sr,0 (e-logp); (d) Model predictions under different Sr,0 (e-p) ...................... 55 Figure 5.1 Transitions in behavior of unsaturated, compacted soils during compression to high stresses under drained conditions.......................................................................................... 59 Figure 5.2 Procedures for application of hydro-mechanical stresses for the drained compression tests under constant matric suction ....................................................................................... 64 Figure 5.3 Volume change versus net stress during drained compression of Boulder clay specimens under different rates of axial strain: (a) 1 %/hr (Volumetric strain rate = 3%/hour); (b) 0.1 %/hr (Volumetric strain rate = 0.3%/hour) ........................................................................... 65 Figure 5.4 (a) Comparison of water outflow and volume change; (b) Degree of saturation with net mean stress ............................................................................................................................ 66 Figure 5.5 Comparison of the constant rate of strain test with an incremental consolidation test 66 Figure 5.6 (a) Comparison of water outflow and volume change; (b) Degree of saturation with net mean stress ............................................................................................................................ 67
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Figure 5.7 Time series of mean effective stress and water outflow from Boulder clay specimens with different initial degrees of saturation during drained compression: (a) Sr,0 = 1.00; (b) Sr,0 = 0.92; (c) Sr,0 = 0.84; (d) Sr,0 = 0.72; (e) Sr,0 = 0.62 .................................................. 69 Figure 5.8 Volume change versus mean effective stress during drained compression of Boulder clay specimens having different initial degrees of saturation: (a) Sr,0 = 1.00; (b) Sr,0 = 0.92; (c) Sr,0 = 0.84; (d) Sr,0 = 0.72; (e) Sr,0 = 0.62 ............................................................................... 70 Figure 5.9 Change of degree of saturation during drained compression of unsaturated Boulder clay specimens with different initial degrees of saturation .......................................................... 71 Figure 5.10 Compression behavior of clay specimens with different Sr: (a) e-logpʹ compression curves; (b) e-pʹ compression curves under low mean effective stresses; (c) e-pʹ compression curves under high mean effective stresses ............................................................................ 72 Figure 5.11 Drained compression response of soils with different Sr,0: (a) Comparison of water outflow and specimen volume change; (b) Volume change at p'ps versus initial volume of air Va; (c) Water outflow at maximum applied stress versus initial volume of water Vw ......... 74 Figure 5.12 (a) Compression curves for Boulder clay specimens having different initial degrees of saturation and different drainage conditions (e-logp); (b) Compression curves for Boulder clay specimens having different initial degrees of saturation and different drainage conditions (e-p); (c) Change of outflow rate during compression of a saturated Boulder clay specimen ............................................................................................................................................... 76 Figure 5.13 The role of drainage conditions on the compression characteristics of unsaturated clay: (a) Change of yield stress with the initial degree of saturation; (b) Change of compressibility with the initial degree of saturation; (c) Stresses at the point of pressurized saturation as a function of the initial degree of saturation ............................................................................ 77 Figure 5.14 Calibration of fitting parameter a1: (a) Data points obtained from compression test (Se of 0.89); (b) The comparison between compressibility parameter (Se) and experimental data; (c) Isotropic compression tests data of Boulder clay with calibrated curves ........................ 79 Figure 5.15 Data predictions: (a) Yield surface in the plane of effective saturation as a function of mean effective stress; (b) the prediction of the unsaturated compression curves ................. 81 Figure 5.16 Prediction of the hydraulic behavior of unsaturated soil: (a) Effects of the a2 parameter (Zhou et al. 2012); (b) Predictions of the changes in the effective saturation; (c) Predictions of the point of pressurized saturation .................................................................................... 83 Figure 5.17 Relationships between the structure parameters affecting the transition to void closure for specimens compacted at different initial effective saturations ........................................ 84
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Figure 5.18 Model Prediction: (a) Comparison of the model calibration (dashed lines) with the experimental data (solid lines) for drained compression of clay under different Se (e-logp); (b) Comparison of the model predictions (dashed lines) with the experimental data (solid lines) for drained compression of clay under different Se (e-p); (c) Model predictions under different Se (e-logp); (d) Model predictions under different Se (e-p) ................................... 86 Figure 6.1 Properties of Mason sand - Boulder clay mixtures: (a) Compaction curves (b) Grain size distribution; (c) Comparison of SWRC ......................................................................... 90 Figure 6.2 (a) The specimen of sand-clay mixtures (20% clay) and oedometer cell (b) hydraulic loading system ...................................................................................................................... 91 Figure 6.3 Compression behaviors of sand-clay mixtures in oedometer under different initial degrees of saturation: (a) Sr = 1.00 (b) Sr = 0.46 .................................................................. 93 Figure 6.4 Compression characteristics of sand-clay mixtures in oedometer under different initial degrees of saturation: (a) Sr = 1.00 (b) Sr = 0.46 .................................................................. 94 Figure 6.5 Volume change versus mean effective stress during drained compression of Mason sand - Boulder clay mixtures specimens having portion of clay: (a) 20%; (b) 10%; (c) 5% ........ 95 Figure 6.6 Drained compression response of soils with portion of clay ....................................... 96 Figure 6.7 Compression behavior of mixtures specimens with portion of clay: (a) e-logpʹ compression curves; (b) e-pʹ compression curves ................................................................ 96 Figure 6.8 Comparison of compression behaviors: (a) mixtures vs. sand; (b) mixtures vs. clay; (c) the role of portion of clay in mixtures behavior ................................................................... 97 Figure A.1 (a) The equilibrium of an air bubble; (b) Volumetric composition of the pore fluid in an unsaturated soil (Fredlund and Rahardjo 1993) ............................................................. 117
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LIST OF TABLES Table 2.1: Details of the high pressure syringe pump .................................................................. 10 Table 3.1: Index properties of Mason sand ................................................................................... 22 Table 3.2: Summary of changes in the grain size distribution of Mason sand during isotropic compression to different mean effective stresses.................................................................. 28 Table 3.3: Comparison of compression responses with different initial relative densities .......... 29 Table 3.4: Coefficients of the empirical model for the compression response of dry sand under different initial relative densities and drainage conditions ................................................... 33 Table 4.1: Geotechnical properties of Boulder clay ..................................................................... 44 Table 4.2: Summary of results from the isotropic undrained compression tests .......................... 45 Table 4.3: Undrained compression model parameters for Boulder clay ...................................... 55 Table 5.1: Historically suggested rates of strain for CRS compression test by ASTM (1982) .... 61 Table 5.2: Summary of results from the isotropic compression tests ........................................... 63 Table 5.3: Drained compression model parameters for Boulder clay having e0 = 0.51 ............... 85 Table 6.1: Results from a standard Proctor compaction tests for sand-clay mixtures .................. 90 Table A.1: Influence of the temperature on the coefficient of Solubility (Gibbs et al. 1960) .... 118
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1. INTRODUCTION MOTIVATION The rapid release of energy from a shallowly-buried explosive in soil will exert an upward pressure that depends on the compression characteristics of the underlying soil layer. Surface loading imposed by the overburden pressure can be anticipated in an element of soil at some distance from the blast, as shown in Figure 1.1. The reaction provided by the underlying soil is influenced by a variety of factors including the depth of burial, soil type, soil density, and soil degree of saturation (Akers 2001) as well as the geometry of explosive (larger geometry, higher output). Furthermore, the deformation characteristics of soils may depend on the drainage conditions, which are typically considered sensitive to the rate of loading. As the excess pore water pressure is dissipated, the applied stress is transferred from pore water pressure to effective stress. Although the rate of water outflow depends on the permeability of soil, fast loading is typically considered to lead to undrained conditions, as time is not available for water to drain from the soil pores. Therefore, it is crucial to characterize different drainage conditions for comparisons regarding transient fluid flow processes in the blast simulations.
Figure 1.1: Shallowly-buried explosion in unsaturated soil Although a buried explosion involves high loading rates, the equilibrium compression curve defined by using the quasi-static compression testing is commonly used in the analyses of these problems, such as in the Hybrid-Elastic-Plastic (HEP) model developed (Zimmerman et al. 1987; Akers et al. 1995). Although the HEP model has been calibrated using 1-D compression tests on dry soils to mean stresses up to 1000 MPa, it is not capable of regarding the fact that soil is considered a three-phase medium, consisting of solid particles, pore-water, and pore-air. As the detonation explosive is largely contingent upon the initial and drainage conditions of soils, comprehensive research is required to focus on unravelling and reducing the uncertainties
1
associated with the dependence of soil conditions. Especially, it is essential to understand the role of initial conditions and drainage conditions on compression responses of soils over a wide range of stresses so that the all possible conditions that can be encountered in the field may properly be accounted for the blast simulations. PROBLEM STATEMENT According to previous studies, particle breakage is one of the factors that governs the stressstrain behavior and friction angle of a granular material by altering the grain size distribution (Lee and Seed 1967; Vesić and Clough 1968; Yamamuro and Lade 1996; Vilhar et al. 2013). Based on their observations, more particle breakage occurs during shearing with increasing confining pressure and the particle size distribution shifts toward a more well-graded condition after shearing. Variables that play a role in particle breakage include the initial grain size distribution, particle shape, particle strength, and degree of saturation (Akers 2001). Lee and Seed (1967) noted that particle mineralogy plays an important role in particle breakage during compression and shearing, and noted that sands with greater amounts of feldspar or mica may have greater amount of particle breakage than pure silica sands. Although the particle breakages have not yet been widely investigated, it can be clearly concluded that the breakages occur due to high stresses. Many studies have characterized the drained compression curve of sands to high stresses using onedimensional and isotropic loading devices (Murphy 1971; Coop and Lee 1993; Akers 2001; Ehrgott et al. 2010), however; only a few have considered particle breakage trends (Yamamuro et al. 1996). A hypothetical representation of the isotropic compression response of sand under different drainage conditions over a wide range of stress levels is illustrated in Figure 1.2.
Figure 1.2: Isotropic compression response of sand under different drainage conditions (inspired by Whitman 1970 and Veyera 1994)
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One crucial mechanism that contributes to soils reaching void closure at high stresses is the less particle crushing that is observed during compression rather than during shear. From these observations, it is clear that the compression curve is highly nonlinear compared to the behavior at lower stresses. Although the compression behavior of sands is well accepted to be nonlinear over the entire stress range of the experiments, an important gap in these previous studies is that the roles of drainage conditions and particle breakage in this nonlinearity have not been carefully evaluated for dry and saturated sand. Compression of unsaturated soils can occur due to rearrangement of the soil skeleton, compression of the pore fluids, or compression and crushing of the particles themselves (Vesić & Clough 1968; Akers 2001; Wang & Lu 2003). The primary hypothesis of the study of unsaturated clay is that the mechanisms of compression are expected to change at different stages during the loading process and different drainage conditions. The initial compression of an unsaturated soil in undrained conditions (no drainage path for air or water) will occur due to compression of the air-filled voids until reaching the point of pressure saturation where the air dissolves into the pore water. Beyond this point, deformation of the undrained soil may only occur due to elastic compression of the water and potentially soil skeleton. Hypothetical isotropic compression curves for unsaturated, compacted clay under undrained conditions are shown in Figure 1.3.
Figure 1.3: Transitions in behavior of unsaturated, compacted soils during compression to high stresses under undrained conditions In order to evaluate the compression response of soils in undrained conditions, some models involve the use of total stress analysis (e.g., Zimmerman et al. 1987). However, a model that is based on total stress analysis alone is not capable of capturing the fundamental mechanisms governing the compression response of unsaturated soils, where the magnitude of pore water
3
pressure generation and compressibility of the soil skeleton during undrained loading depend on the initial degree of saturation. To address these issues, the concepts from effective stress analyses can be used to obtain an undrained compression model in terms of total stress that can be applied to both saturated and unsaturated soils compressed to high stresses. The hypothetical representations of the drained, isotropic compression curves of unsaturated clay under different initial conditions are shown in Figure 1.4. Initial compression of an unsaturated soil in drained conditions near the ground surface will typically follow a recompression line (RCL) having a slope , until reaching the mean apparent preconsolidation stress pc. Several studies have noted that the preconsolidation stress increases with suction magnitude (Maatouk et al. 1995; Lloret et al. 2003; Jotisankasa et al. 2007). These studies also observed that the slope of the virgin compression line (s) becomes steeper with increasing suction magnitude when plotted in terms of mean net stress. Along these lines, Uchaipichat (2010) performed a series of suction controlled shear tests using triaxial testing equipment. Different from the trends observed when plotting the compression data as a function of the mean net stress, Uchaipichat (2010) observed that the slopes of the virgin compression lines (VCL) and the recompression lines were independent of matric suction and preconsolidation stress when plotted in terms of mean effective stress. However, they did not perform their tests to sufficiently high compression levels to fully evaluate the transition points.
Figure 1.4: Transitions in behavior of unsaturated, compacted soils during compression to high stresses under drained conditions When soils are compressed to higher stresses, it is expected that the virgin compression lines for different suction values will collapse to a single virgin compression line at the point of pressure saturation. Pressure saturation can occur due to either expulsion of the air during drained loading,
4
or dissolution of the pore air into the pore water following Boyle’s and Henry’s laws. During drained compression to extremely high pressures, the particles will begin to crush and rearrange until reaching the point of void closure. Only a limited number of experiments has been performed to study soil behaviors under extremely high pressures (Akers 2001; Ehrgott et al. 2010), with the studies primarily restricted to dry soils. One issue with these studies and the corresponding constitutive relationships is that they assume that the mean net stress and suction have independent effects on the compression behavior of soils. Loret and Khalili (2001) observed that the use of a single-value effective stress parameter is more fundamentally correct, and can be used to unify the behavior of saturated and unsaturated soils. Although the current hydro-mechanical models are capable of reproducing essential features of the behavior of unsaturated soils such as suction hardening, they do not consider phenomena encountered at high stresses such as pressure saturation and void closure. It is difficult to extend these models to high stresses using the available data in the literature, as only a few studies have considered changes in the degree of saturation during drained compression under constant suction conditions (Lloret et al. 2003; Jotisankasa et al. 2007) and the soil behavior has only been evaluated up to mean stresses of 10 MPa. Many of natural soils (e.g., residual soils) are composed of mixtures of clay mineral and granular material even though previous experimental research has tended to focus on clearly pure soil type. In geotechnical applications, sand-clay mixtures are commonly used as a liner/barrier material (e.g., soil-bentonite mixtures for the construction of hydraulic and waste containments) so that the permeability, compressibility and strength of mixtures are the important properties for the design of the liner/barrier of the containments. Nonetheless, the behavior of sand-clay mixtures has not received significant attention in geotechnical engineering. Several experimental investigations involving the determination of the stress-strain-strength properties have been conducted (Georgiannou 1988; Georgiannou et al. 1990; Vallejo and Mawby 2000; Wood and Kumar 2000). However, the compression behavior of sand-clay mixtures has only been evaluated under mean stresses up to 3 MPa (D’Appolonia 1980; Baxter 2000; Ghazi 2015). The sand-clay mixtures are the combination of two different materials in terms of particle size distribution and chemical activity so that the mechanical behavior is expected to combine aspects of the behavior of each of the soil components. Therefore, the research should focus on characterizing the compression responses of mixtures with different portion of materials over a wide range of stresses in an effort to identify the factors that influence the behavior of such mixtures.
5
OBJECTIVES AND APPROACH The primary objective of this study is to understand the compression behaviors of several types of soils (unsaturated clays, sand, and sand-clay mixtures) under different initial moisture content and drainage conditions over a wide range of hydrostatic stresses. To achieve the objective of this research, the behaviors of soils are evaluated under isotropic stresses up to 160 MPa using highpressure isotropic loading apparatus. This stress range is suitable to identify the role of high stress states such as the pressurized saturation, void closure, and particle crushing. Based on the results observed in the experimental data, a secondary objective of this study is to establish and modify available constitutive relationships for the compression behaviors of soils. Irrespective of testing variables, the specific research objectives of this study are as follows: i.
Assess the key parameters affecting the compression responses of soils in the literature in order to formulate the hypothetical compression curves of soils under different drainage conditions.
ii.
Develop a high pressure isotropic loading apparatus in order to test soil specimen up to high stresses under different drainage conditions using the high-pressure syringe pump and the suction control system to evaluate the role of unsaturated conditions using the axis translation technique.
iii.
Evaluate the response of the isotropic loading apparatus to mechanical loading schemes (e.g., system calibration due to increased cell pressure).
iv.
Perform a series of compression tests to characterize the compression response of different types of soils (Mason sand, Boulder clay, and sand-clay mixtures) under different initial degrees of saturation and drainage conditions.
v.
Utilize the experimental results to evaluate the relative testing conditions on the overall volume change of soils.
vi.
Utilize the experimental findings to verify the hypothetical compression curves of soils.
vii.
Formulate the constitutive relationships to describe the isotropic compression responses of soils regarding the key factors affecting soil responses based on the experimental observations.
6
SCOPE OF DISSERTATION This dissertation is organized into seven chapters. Each of chapter has a separate and distinct subject for different soil types and drainage conditions that has its own background, the relevant geotechnical soil properties, experimental procedures, results, and analysis. This document is organized in the following manner. Chapter 2 includes a description of the new high pressure isotropic cell developed for this study along with the system calibration. Chapter 3 discusses the effect of drainage conditions on the compression response of sand to high stresses, which was evaluated by comparing results of undrained and drained isotropic compression tests on dry and saturated specimens. Constitutive relationships were proposed to match the experimentally-derived compression curves to high stresses for drained and undrained conditions that incorporated the relationship between the breakage factor and mean stress. Chapter 4 proposes a constitutive model to describe the isotropic compression response of unsaturated, compacted clay under undrained conditions over a wide range of mean stresses. The model was calibrated using results from a series of compression tests on compacted clay specimens having various initial degrees of saturation and the same initial void ratio. Chapter 5 presents a constitutive model to represent the isotropic compression behavior of unsaturated, compacted clay under drained conditions over a wide range of mean effective stresses. The results from drained, isotropic compression tests on compacted clay specimens having different initial degrees of saturation were used for calibration of the model. Chapter 6 includes a summary of the results from drained, isotropic compression tests on sandclay mixtures specimens having different portion of clay. The results from this study provides insight into how existing constitutive models for sand-clay mixtures can be extended to high stress conditions. The conclusions of each of chapter are summarized in Chapter 7.
7
PUBLICATIONS BASED ON THE PRESENT WORK 1. Mun, W. and McCartney, J.S. (2016). “Impact of drainage on the compression response of sand to high pressures.” Journal of Geotechnical and Geoenvironmental Engineering. In review. 2. Mun, W. and McCartney, J.S. (2015). “Compression mechanisms of unsaturated clay under high stress levels.” Canadian Geotechnical Journal. 10.1139/cgj-2014-0438. 3. Mun, W. and McCartney, J.S. (2016). “Constitutive model for the undrained compression of unsaturated clay.” Journal of Geotechnical and Geoenvironmental Engineering. In review. 4. Mun, W. and McCartney, J.S. (2016). “Constitutive model for the drained compression of unsaturated clay.” Journal of Geotechnical and Geoenvironmental Engineering. In review. 5. Mun, W. and McCartney, J.S. (2015). “Rate effects in constant rate of strain compression tests on unsaturated soils to high pressures.” 15th Pan-American Conf. on Soil Mechanics and Geotechnical Engineering (XV PCSMGE). Buenos Aires. Nov. 16-18. 1-8. 6. Mun, W. and McCartney, J.S. (2014). “Compression behavior of unsaturated clay under high stresses.” Proceedings of GeoCongress 2014 (GSP 234), ASCE. 1443-1452. 7. Mun, W., Svoboda, J., Teixeira, T., Balci, M.C., and McCartney, J.S. (2016). “Shearing rate effect mechanisms in unsaturated compacted soils.” Soils and Foundations. 8. Mun, W., Balci, M.C., Valente, F., and McCartney, J.S. “Shearing and compression behavior of sand-clay mixtures.” In preparation, to be submitted to Geotechnical and Geological Engineering. 9. McCartney, J.S. and Mun, W. “Effective stress evaluation of undrained compression of unsaturated soils.” In preparation, to be submitted to 8th International Conference on Porous Media & Annual Meeting.
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2. DEVELOPMENT OF THE EXPERIMENTAL SETUP AND TESTING APPROACH EXPERIMENTAL SETUP Isotropic loading test cell has been developed to investigate the compression behavior of unsaturated soil under high stresses up to 160 MPa and different drainage conditions. A picture and sketch of the components of the experimental setup are shown in Figure 2.1 and Figure 2.2, respectively. The setup incorporates an isotropic pressure cell used to contain the soil specimen, a high-pressure syringe pump (model 65HP from Teledyne Isco) used to apply the cell pressure and track changes in volume of the soil specimen, and a pressure control panel used to control the pore air and water pressures. The picture of high-pressure syringe pump and pressure control panel is shown in Figure 2.3(a) and Figure 2.3(b), respectively. By using a pressure control panel, matric suction is controlled using the axis-translation technique (Hilf 1956), and the change of degree of saturation is tracked with water outflow from the soil specimen during compression in the case of the unsaturated testing conditions. When provided a target cell pressure, the system controller in the pump will direct a piston into or out of the pump reservoir until the target pressure is met in accordance with a set of input variables defining the tolerance of the system. Details of the syringe pump are summarized in Table 2.1. Pressures are delivered from the syringe pump to the test cell using hydraulic oil through steel tubing which has the strength of 240 MPa. Automotive brake fluid was selected for the cell fluid due to its high bulk modulus (2.068 GPa) and because it is easy to remove from the equipment after testing.
Figure 2.1: View of the overall experimental setup
9
Figure 2.2: Schematic of the pressure control system and connections to the isotropic pressure cell
(a) (b) Figure 2.3: (a) View of the high pressure syringe pump; (b) View of the pressure control panel Table 2.1: Details of the high pressure syringe pump Pressure range (MPa)
0.07 ~ 165
Cylinder capacity (ml)
68
Flow rate (ml/min)
0.00001 ~ 25
Flow accuracy
±0.3% of set point
Dimensions (H×W×D, cm)
103×27×45
10
The pressure cell consists of a hollow stainless steel cylinder sandwiched between two 50.8 mm-thick plates. A 38.1 mm-thick, 71.1 mm-diameter bottom platen used for mounting of the specimen is integrated into the bottom plate. A schematic view of the pressure cell is shown in Figure 2.4(a), and a picture of the assembled cell is shown in Figure 2.4(b). A stainless steel load frame with 76.2 mm-thick plates held together with six steel alloy rods is used to resist the pressure within the cell. Before pressurizing the cell, the rods of the load frame are pre-stressed to a torque of 2,983 N·m. The inside of the top plate is slightly tapered toward a flush valve so that air can be evacuated from the cell as it is filled with hydraulic fluid. The cell has five ports in the bottom plate. Two ports are used to supply and flush water to the bottom platen, two port are used to supply and flush air to the bottom platen, and one port is used to supply the hydraulic fluid to the cell. Dual rubber membranes, each with a thickness of 0.64 mm, are used to confine the soil specimen.
(a) (b) Figure 2.4: Isotropic pressure cell: (a) Schematic; (b) Picture A schematic view and photos of the bottom platen of the cell are shown in Figure 2.5. The pore air pressure in the specimen is applied via a porous sintered stainless ring in the bottom platen of the pressure cell. The pore water pressure in the specimen is applied via a ceramic disk also in the bottom platen of the pressure cell having a high air-entry (HAE) suction which only permits water
11
to pass until reaching a suction of 300 kPa. The recess in the bottom platen that houses the HAE ceramic disk includes a grooved flushing path that allows for uniform distribution of water pressure underneath the disk. Water was supplied from and drained to the exterior via one hole located at both ends of the grooved channel. Air was also supplied from the exterior via 1.59 mmdiameter holes located at both ends of the circular grooved channel underneath the sintered ring.
(a)
(b) (c) Figure 2.5: Bottom platen for suction control: (a) Schematic; (b) Picture of the platen having HAE ceramic disk and sintered porous ring; (c) Picture of the platen with pressure inlet/outlet Pore air pressure (ua) and pore water pressure (uw) are applied to the specimen through two independent burettes that are included in a pressure control panel (Figure 2.3(b)). Each burette allows for the unique application of air/water pressure, vacuum pressure, or venting. In addition, the applied pressure in each burette is controlled and monitored by calibrated pressure gauge. During compression, the change of degree of saturation of the soil specimen is monitored by tracking the outflow or inflow of water from the specimen using a differential pressure transducer (DPT) connected to the pore water pressure burette. As the compressibility of air is relatively high, dissolved air inside the water could negatively impact the accuracy of mechanical response for high pressure testing, so it is important to ensure that all water is de-aired prior to testing. The
12
pressure control panel also includes a third burette to apply a seating cell pressure at the beginning of testing, which facilitates the flushing of air from the system. The cell pressure burette is also used to flush air from the high-pressure syringe pump and can be controlled by an independent pressure gauge to permit the application of the net stress easily before compression testing. When the syringe pump is activated, the supply line from cell pressure control burette is closed using a high pressure valve so that operation of the pump leads to inflow or outflow from the cell. A saturation cap was constructed to initially saturate the HAE ceramic disk before testing. After placement of the saturation cap over the bottom platen as shown in Figure 2.6, the entire system was placed under a vacuum of -75 kPa to fully de-air the system. Next, de-aired water was passed through the flushing paths above and below the HAE ceramic. While maintaining the water beneath the porous stone at a vacuum of -75 kPa, water was permitted to flush downward through the HAE disk for several hours. Because of this saturation procedure and because the axis translation tests on soils reported later in this study were all performed under backpressure, cavitation or dissolution of air were not observed in the water flowing from the base of the HAE ceramic disk.
(a)
(b) (c) Figure 2.6: Saturation system for the high air entry porous disk: (a) Schematic; (b) Saturation cap; (c) Placement of the saturation cap over the bottom platen
13
SYSTEM CALIBRATION Before testing of the soil specimens, the machine deflection of experimental setup was evaluated using an aluminum specimen with known elastic properties (Young’s modulus of 69 GPa and Poisson’s ratio of 0.334). The aluminum specimen with a diameter and height of 71.1 mm was first placed into the pressure cell and covered with the membrane. The cell was then filled with hydraulic fluid and pressurized. Using the high-pressure syringe pump, the aluminum specimen was subjected to an isotropic loading and unloading cycle from 0 to 160 MPa and back under a volumetric strain of 2 %/min. The rate of the syringe pump is controlled to ensure that the level of over-estimated pressure is marginalized. Pressure and total volume change provided by the high-pressure syringe pump including refilling process and pressure and cumulative total volume change with operation time are shown in Figure 2.7(a) and (b), respectively. The slight initial non-linear shape reflects the pre-stress of the bolts of the loading frame. It is important to maintain the pressure inside the chamber when testing materials under high pressures so that the precise pressure-deformation relationship can be obtained. In order to verify that the cell held pressure with minimal creep relaxation, the operation of the syringe pump was stopped for some time. The results show that constant pressure was maintained for an hour while the pump was stopped. The pressure effect can be observed from the subtraction of the measured data with the displacement of the aluminum specimen, shown in Figure 2.8. The equation fitted to the experimental machine deflection data is shown in this figure, which facilitated application of the machine deflection of the cell to interpret deformation results of soil specimens.
(a) (b) Figure 2.7: Example of typical pressure and total volume change with time provided by the highpressure syringe pump for the isotropic pressure cell: (a) Raw data; (b) Cumulative data
14
Figure 2.8: Machine response curve of the isotropic pressure cell INSTRUMENTATION CALIBRATION All data generated during testing are recorded and instantaneously displayed by a data acquisition (NI SCXI-1001/NI SCXI-1320 DAQ package) system developed for the experimental setup. Pore air and water pressures on the bottom of the specimen were controlled independently through burette pressurized with air regulated by type 70 manual pneumatic pressure regulators, manufactured by Bellofram Co., having ranges of 13 to 1035 kPa. An independent gauge pressure transducer (GPT) is used to monitor the water pressure during suction control and the cell pressure within the system and communicates back to the syringe pump via a LabView system controller program. The GPT currently used for the research is a 690 kPa Geotac© Pressure Sensor (Model PS-1072) manufactured by Geotac©. The GPT was calibrated to determine the water pressure corresponding to the measured voltage signal obtained by the data acquisition system during testing. This was accomplished by applying a known pressure to the GPT using the Trautwein pressure control panel. For each pressure increment, an applied pressure was correlated with a corresponding voltage output measured by the DAQ. Pressure increments from 0 to 414 kPa then back to 0 kPa were used during calibration testing to analyze the repeatability of the voltage output measurements under a loading/unloading cycle. Applied pressures were plotted against the voltage outputs and the calibration coefficients were established. A strong linear relationship was observed for the GPT as shown in Figure 2.9.
15
Figure 2.9: GPT calibration results During compression, the change of degree of saturation of the soil specimen is monitored by tracking the outflow or inflow of water from the specimen using a differential pressure transducer (DPT) connected to the pore water pressure burette. The DPT used for the research is a Validyne (Model P300D) differential pressure transducer with an operating capacity of 55 kPa using a 3-34 diaphragm. The DPT was calibrated to determine the correlation between the volume of water (hw × Aburette) and the voltage outputs. An air pressure of 345 kPa was applied to the air chamber of the DPT and an initial water pressure of 345 kPa was applied to the water chamber of the DPT at the same time by using a burette, which is incorporated with pressure panel (Figure 2.3(b)). The initial pressure was selected to simulate the pressure conditions utilized for suction control. Then, the level of water in burette was increased with small increments (1inch, 25.4mm). It was found that the volume of burette is 790.4mm3/mm. For each water level increment in burette, the applied air/water pressure was correlated with a corresponding voltage output measured by the DAQ. The water volume difference was plotted against the DPT voltage outputs and the calibration coefficients were established. A strong linear relationship was observed for the DPT as shown in Figure 2.10.
16
Figure 2.10: DPT calibration results As one of the goals of this study is to evaluate the role of the initial suction on the compression behavior, the initial suction values in several of the compacted specimens having different initial degrees of saturation were assessed using a de-aired UMS T5 tensiometer. The tensiometer was calibrated to determine the water pressure corresponding to the measured voltage signal obtained by the data acquisition system during suction measurement. In a similar manner with the calibration procedure of GPT, a known pressure was applied to the tensiometer. For each pressure increment, an applied pressure was correlated with a corresponding voltage output measured by the DAQ. Pressure increments from 6.9 to 69 kPa then back to 6.9 kPa were used during calibration. Applied pressures were plotted against the voltage outputs and the calibration coefficients were established. A strong linear relationship was observed for the tensiometer as shown in Figure 2.11.
Figure 2.11: Tensiometer calibration results
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3. COMPRESSION BEHAVIOR OF SANDS TO HIGH STRESSES INTRODUCTION It is well known that granular materials sheared under high confining stresses above those experienced in typical geotechnical applications (i.e., greater than 10 MPa) exhibit considerable particle breakage (Hall and Gordon 1963; Hirschfield and Poulos 1963; Bishop et al. 1965; Bishop 1966; Lee and Seed 1967; Vesić and Clough 1968; Marachi et al. 1969; Tai 1970; Murphy 1970; Murphy 1971; Lo and Roy 1973; Colliat-Dangus et al. 1988; Lade and Yamamuro 1996; Yamamuro and Lade 1996; Akers 2001; Salim et al. 2004; Vilhar et al. 2013). Based on their observations, more particle breakage occurs with increasing confining pressure and the particle size distribution shifts toward a more well-graded condition after shearing. These studies found that particle breakage is one of the factors that governs the stress-strain behavior and friction angle of a granular material by altering the grain size distribution. Variables that play a role in particle breakage include the initial grain size distribution, particle shape, particle strength, and degree of saturation (Akers 2001). The stress path is also important, with greater particle breakage occurring in specimens with lower degrees of freedom, like in plane-strain conditions (Becker et al. 1972). Further, shearing in drained or undrained conditions also affects particle breakage due to the constraint on volume change during shearing. Particle breakage also occurs during compression to high stresses, although this subject has not been as widely investigated as in the case of shearing. Several studies have characterized the drained compression curve of sands to high stresses using one-dimensional and isotropic loading devices (Hendron 1963; Murphy 1971; Akers et al. 1986; Coop and Lee 1993; Hagerty et al. 1993; Yamamuro et al. 1996; Akers 2001; Ehrgott et al. 2010). Only a few have considered particle breakage trends (Yamamuro et al. 1996). Although less particle crushing is observed during compression than during shear, it is an important mechanism that contributes to soils reaching void closure at high stresses. These studies observed that the compression curve is highly nonlinear compared to the behavior at lower stresses. However, the role of particle breakage in contributing to this nonlinearity has not been thoroughly investigated. Further, the behavior in other drainage cases has not been fully assessed, for example preventing drainage of air in dry sand specimens, or preventing drainage of water in saturated sand specimens. Several studies have used devices such as the Split-Hopkinson pressure bar to evaluate the compression curve under extremely high stresses as well as high rates (Whitman 1970; Charlie et
18
al. 1990; Veyera 1994; Field et al. 2004; Martin et al. 2009; Kabir et al. 2010; Omidvar et al. 2012; Luo et al. 2015). Although these tests may reach high stresses where particle breakage may occur, the stress state is not well defined due to potential lateral expansion of the confining cell. Furthermore, there may be rate effects that prevent characterization of important transition points in the compression curve, which can be affected by particle rearrangement, particle breakage, or fusing of particles together under extremely high contact stresses. Although the compression behavior of sands is well accepted to be nonlinear over the entire stress range of the experiments, an important gap in these previous studies is that the roles of drainage conditions and particle breakage in this nonlinearity have not been carefully evaluated for dry and saturated sand. Drainage conditions may be important to consider when evaluating the compression response of soils under high speed loading, as many blast simulation models use the parameters of the quasi-static compression curve as important constitutive inputs for soil behavior (Zimmerman et al. 1987; Akers et al. 1995; Moral et al. 2010). To address this gap, this study presents the results from isotropic compression tests to different mean stresses on saturated and dry sands to quantify the role of different drainage conditions on the shape of the compression curve and the amount of particle breakage. With these results, the breakage factor of Marsal (1967) is used to develop new constitutive relationships for the isotropic compression response of sand specimens with different drainage conditions. BACKGROUND 3.2.1. High Pressure Behavior of Sand under Quasi-Static Loading A hypothetical representation of the isotropic compression response of sand under different drainage conditions over a wide range of stress levels is illustrated in Figure 3.1, based on the observations of previous studies. During drained compression of dry or saturated sand, changes in behavior are expected at different threshold stress levels. The initial stress-strain response is associated with elastic deformation of the skeleton and soil particles. Then the response becomes inelastic during yielding of the frictional connections between individual sand particles comprising the soil skeleton, after which the particles slide into the voids (A-C). Particle breakage occurs predominately in this phase, with a greater amount of breakage at higher stresses. The rearrangement of sand particles along with particle breakage results in a denser arrangement, which leads to an increase in the number and area of contact points between the particles. Finally,
19
a hardening response is observed as particle rearrangement becomes more difficult and the voids begin to close (C-D). The undrained compression response of dry sand is likely similar to that of the drained response of dry sand due to the high compressibility of air, but this hasn’t been thoroughly characterized. The undrained compression response of saturated sand is much stiffer than those of dry or saturated sand under drained conditions, dominated by the compressibility of water (A-B). However, it is possible that some soil particle rearrangement and particle breakage may occur during isotropic compression meaning that the soil skeleton may still have a slight effect on the undrained compression response.
Figure 3.1: Isotropic compression response of sand under different drainage conditions (inspired by Whitman 1970 and Veyera 1994) Although some studies have used conventional bilinear model using the log-linear slope to capture the virgin compression response of sands within the critical state framework (Been et al. 1991; Pestana et al. 1995; Vilhar et al. 2013), many sands show a smooth, highly nonlinear compression curve when loaded to high stresses. The bilinear approach is not suited for considering the role of particle breakage or the tendency toward void closure at high stresses. Nonetheless, during unloading, sands often show an elastic response similar to that of an overconsolidated clay with a log-linear slope . High pressure may lead to interesting stress-strain behavior since it tends to destroy the initial fabric and structure of the specimen and can result in completely different soil properties and characteristics. Zimmerman et al. (1987) and Akers et al. (1995) devised the Hybrid-Elastic-Plastic (HEP) constitutive model to simulate the shear and compression behavior of geologic material during blasting. The HEP model does not account for the situation that soil withstands more compressive loading than tensile loading even though tension and compression of the soil follow different stress paths (Moral et al. 2010).
20
3.2.2. Particle Breakage Factors Several studies have proposed empirical indices or parameters to reflect the amount of particle breakage during shearing or compression (Lee and Farhoomand 1967; Marsal 1967; Miura and O’Hara 1979; Hardin 1985). These indices involve the change in individual particle sizes between the particle size distributions before and after loading. Lee and Farhoomand (1967) proposed a breakage indicator expressing the change in a single particle size from their investigation of earth dam filter materials. Miura and O’Hara (1979) introduced a method to compute the changes in particle surface area as an indicator of particle breakage, which was taken into account new surfaces possibly generated due to particle breakage. The specific surface area of particle size can be estimated by assuming all particles are perfectly spherical. Hardin (1985) suggested the relative breakage index Br (Bt/Bp) as an indicator of particle degradation by using two different quantities the breakage potential (Bp) and total breakage (Bt). Marsal (1967) defined a breakage factor BM in order to quantify the amount of particle breakage during large scale triaxial tests on rock fill materials The value of BM is calculated as the sum of the percent increases in soil retained on each sieve, as follows: BM = % Increase in retained on all sieves
(3.1)
A graphical interpretation of the calculation of BM proposed by Vankov and Sassa (1998) is shown in Figure 3.2 for a sand specimen compressed isotropically to 160 MPa.
Figure 3.2: Graphical example of the calculation procedure for Marsal’s breakage factor BM for Mason sand isotropically compressed to 160 MPa Theoretically, the percent decrease in the amount retained on the larger sieves (shown as small b’s Figure 3.2) should be equal to the percent increase in the amount retained on the smaller sieves (shown as large B’s in Figure 3.2). Marsal (1967) showed that BM increases with confining stress
21
for triaxial compression shear tests performed on different granular soils. Marsal’s breakage factor BM was adopted in this study due to its simplicity in calculation and its success in reflecting the role of particle breakage with confining stress. MATERIAL (MASON SAND) Mason sand, purchased from a local quarry in Longmont, Colorado, was used in this study. The index properties of the sand are summarized in Table 3.1. This sand is classified as poorly graded sand (SP) according to the Unified Soil Classification System (USCS), which indicates that the material has a narrow range of particle sizes. The specific gravity Gs was measured to be 2.62. The minimum void ratio of 0.50 corresponds to a maximum dry density of 1.74 kg/m 3, while the maximum void ratio of 0.78 corresponds to minimum dry density of 1.47 kg/m3. Most tests in this study were performed at a relative density of 75%, which corresponds to a void ratio of 0.57. The shear strength properties of this sand under a void ratio of 0.54 were reported by Svoboda and McCartney (2013). Mason sand contains a mixture of approximately 95% silica and 5% feldspar particles. Lee and Seed (1967) noted that particle mineralogy plays an important role in particle breakage during compression and shearing, and noted that sands with greater amounts of feldspar or mica may have greater amount of particle breakage than pure silica sands. Detail information of Mason sand along with standard testing procedure is described in Svoboda (2013). Table 3.1: Index properties of Mason sand Property
Value
Units
D10
0.15
mm
D30
0.28
mm
D50
0.50
mm
Cu
3.33
-
Cc
1.05
Gs
2.62
-
emin
0.50
-
max
1.74
kg/m3
emax
0.78
-
min
1.47
kg/m3
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EXPERIMENTAL APPROACH A series of isotropic tests for sand were performed in this study, with the compression tests under different mean stresses from 10 to 160 MPa. Tests were performed with different drainage conditions (drained and undrained) for two different degrees of saturation (air dry conditions, S r,0 = 0.0 and saturated conditions, Sr,0 = 1.0). It is assumed that the behavior of dry sand is similar to the drained behavior of saturated sand, so compression tests were conducted under both drained and undrained conditions for dry sand but only under undrained conditions for saturated sand. The soil specimens were prepared by tamping dry sand into a neoprene membrane held in place with a metal mold and attached to the bottom pedestal of the cell. This tamping procedure was used to reach a target void ratio of 0.57, and the specimen dimensions were 76.2 mm in both diameter and height (1:1 ratio). A void ratio of 0.57 corresponds to a target relative density of 0.75. Additional tests were performed on specimens having initial relative densities of 0.60 and 0.96 to assess the role of initial conditions on the compression response. For the tests on dry specimens, after the sand was tamped into place a rigid top cap without drainage ports was placed on top of the specimen. The lack of drainage ports ensures that the compression response of the cell is relatively stiff. For the tests on saturated specimens, the specimens were prepared using the same approach as the dry specimens but were saturated before placing the rigid top cap. After placement within the membrane, a temporary top cap with drainage ports was placed on the specimen. Next, a vacuum of -75 kPa was applied to the top of the specimen. After waiting approximately 20 minutes, de-aired water was permitted to flush upwards through the specimen under a low flow rate while vacuum was maintained on the top of the specimen. After flushing several pore volumes of water through the specimen, the vacuum was shut off and the temporary top cap was carefully removed. A rigid top cap that does not have drainage ports was placed on top of the sand layer and the membrane was carefully pulled up around this cap while avoiding air inclusions. After the specimen was prepared and the cell was assembled, a syringe pump was used to increase the mean stress at a constant rate of strain of 10%/hr. In each of the tests, the system deformation was monitored by the high-pressure syringe pump. For dry sands, specimens were tested with both free drainage of air (drained) and without drainage of air (undrained). For saturated sands, specimens were only tested without drainage of water (undrained) as the behavior under drained conditions was assumed to be similar to that in dry conditions. After loading to different
23
mean stresses, the specimen was unloaded and Marsal’s breakage factor BM was calculated to assess the impact of drainage conditions on soil particle breakage under different stress states. In the tests on dry specimens compressed to stresses greater than 80 MPa, cementation was observed, potentially caused by fusion at the particle contacts under the high local stresses (Figure 3.3). These specimens were carefully broken apart using a rubber mortar and pestle to ensure that all particle agglomerations were separated.
Figure 3.3: Photo of Mason sand specimen after high pressure compression test under 80MPa EXPERIMENTAL RESULTS 3.5.1. Role of Drainage in the Compression of Sand to High Pressures The compression curves for dry and saturated Mason sand specimens under different drainage conditions are shown in Figure 3.4. The void ratio of the soil specimens is plotted both as a function of mean stress on both logarithmic (e-logp′ or e-logp) and natural scales (e-p). The shape of the curves on a natural scale indicates that the drained compression curves for dry sand (Sr,0=0.00) are starting to decay asymptotically toward a certain void ratio, reflecting that the sand is transitioning toward void closure for stresses greater than approximately 30 MPa (Figure 3.4(a) and Figure 3.4(b)). The undrained compression curves for dry sand (Sr,0=0.0), the results seems very comparable to the drained compression curves, due to the much lower compressibility of air than that of water (Figure 3.4(c) and Figure 3.4(d)). The unloading curves for the drained and undrained tests on dry sand tend to become more and more nonlinear with increasing mean stress. Similar behavior was noted by Yamamuro et al. (1996) following unloading after compression to 850 MPa. This may have been due to interlocking between the particles that could not be recovered, as well as plastic fusion at particle contacts. The undrained compression curves of saturated sand are stiffer than those tested under drained conditions (Figure 3.4(e)), following a linear behavior with mean stress on a natural scale (e-p) as shown in and Figure 3.4(f). Different from the tests on the dry 24
sand, the unloading curves were observed to be linear and follow the same trend as the compression curve for the undrained tests. Total 5 tests were conducted in each different drainage condition (drained or undrained) and initial degree of saturation (Sr,0=0.0 or 1.0).
(a)
(b)
(c)
(d)
(e) (f) Figure 3.4: Compression behavior of Mason sand specimens with different drainage conditions: (a) e-logpʹ (drained, dry sand); (b) e-pʹ (drained, dry sand); (c) e-logp (undrained, dry sand); (d) ep (undrained, dry sand); (e) e-logp (undrained, saturated sand); (f) e-p (undrained, saturated sand)
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In order to consider the impact of drainage conditions, a comparison of compression curves of Mason sand for different testing conditions over the same stress range (160 MPa) is shown in Figure 3.5(a) and Figure 3.5(b). The drained compression curves for Sr,0 of 0.0 and 1.0 are shown in terms of mean effective stress while the undrained compression curves for Sr,0 of 1.0 are shown in terms of the mean total stress for ease of comparison as it was not possible to estimate the mean effective stress in the undrained compression tests. For dry sand specimens, the undrained compression curve shows a slightly stiffer response than the one that has been drained at higher level of stress. This may be due to the finite compressibility of air, which although large may provide some resistance to particle rearrangement. It is assumed that the drained compression curve for dry sand is similar to the drained compression curve for saturated sand. Also the void ratio of dry sand for the drained compression curve shows slightly greater slope than that of undrained compression curve at the stress of 160 MPa. It indicates that the undrained compression response for dry sand has not been affected by drainage condition due to the much less compressibility of air. However, the undrained compression curve for saturated sand is controlled by the less compressible pore water and particles potentially with a steeper slope than that observed in drained conditions.
(a) (b) Figure 3.5: Comparison of compression curves for specimens with different drainage conditions: (a) e-logpʹ or e-logp; (b) e-pʹ or e-p Grain size distributions for the Mason sand specimens were determined before and after testing, and are shown in Figure 3.6(a), Figure 3.6(b), and Figure 3.6(c). The changes in the key parameters of the grain size distributions are summarized in Table 3.2. As expected, a significant amount of particle breakage is observed in the dry sands, with an increase in the amount of fines with increasing mean stress. This was the case for both drained and undrained conditions, although 26
slightly lower fines generation was noted for the undrained, dry sand. The grain size distributions for undrained, saturated sand specimen did not change as significantly with compression as they did for dry sand. However, the slight upward shift with increasing mean stress indicates that the soil skeleton may also have a slight effect on the undrained compression response, and that compression leads to a rearrangement of the skeleton and corresponding particle breakage. The higher coefficients of uniformity (CU) and of curvature (CC) shown in Table 3.2 reflect a larger range of particle sizes after compression.
(a)
(b)
(c) Figure 3.6: Grain size distributions of Mason sand before and after compression to different mean stresses: (a) Drained, dry sand; (b) Undrained, dry sand (c) Undrained, saturated sand
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Table 3.2: Summary of changes in the grain size distribution of Mason sand during isotropic compression to different mean effective stresses
Property
Drainage and specimen conditions
D10
Drained, Dry (D,D) Undrained, Dry (U,D) Undrained, Wet (U,W)
D30
D60
Cu
Cc
Drained, Dry (D,D) Undrained, Dry (U,D) Undrained, Wet (U,W) Drained, Dry (D,D) Undrained, Dry (U,D) Undrained, Wet (U,W) Drained, Dry (D,D) Undrained, Dry (U,D) Undrained, Wet (U,W) Drained, Dry (D,D) Undrained, Dry (U,D) Undrained, Wet (U,W)
Particle size [mm] After compression to different mean stresses (MPa) 10 20 40 80 160
Before testing -
0.15
0.28
0.50
3.33
1.05
0.12
0.12
0.09
0.12
0.12
0.09
0.15
0.15
0.27
