83. 4.2.1. Soil-structure Interaction. 83. 4.2.2. Alternative model soils. 84. 4.3 Tests and ..... ratio of water to water plus glycerin by mass β trapezoidal ...... 11 There is 8% change in the small strain dynamic properties of glyben with time during the first 9 .... Shaking table scale model tests of nonlinear soil-pile-sup interaction in ...
THE UNIVERSITY OF WESTERN ONTARIO FACULTY OF GRADUATE STUDIES CERTIFICATE OF EXAMINATION
Chief Advisor
Examining Board
______________________
____________________
Advisory Committee Member
____________________
______________________
____________________ ____________________
The thesis by Alper Turan Entitled Physical modeling of seismic SSI is accepted in partial fulfilment of the Requirement for the degree of Doctor of Philosophy
Date _______________
_____________________ Chair of Examining Board ii
ABSTRACT The understanding of the seismic soil structure interaction (SSI) is still evolving. Numerous analysis tools are developed with different levels of sophistication. However, the number of case histories, response measurements of the instrumented structures during the earthquakes and the reduced scale model tests are limited for the calibration and/or validation of the existing analytical tools. This study aims to experimentally and numerically investigate the seismic soil-structure interaction problem with a particular focus on the buildings with embedded basement stories founded on/in clayey soils. The research involved three major stages, which are the development and characterization of model clays; design, fabrication, commissioning and calibration of laminar soil container and experimental and analytical investigation of SSI problem for the buildings with embedded basement stories. The results of the reduced scale model test and subsequent numerical analyses provide a refreshed insight into the SSI problem in partially embedded buildings. The preceding stages of this study on the model soil development and laminar soil container design are also helpful for the researchers who perform seismic physical model tests using small shaking table with limited base shear capacity and for those who needs an easy to use, well characterized alternative model clay mixture that allows multiple use in physical model tests. Initially, the dynamic characterization of glyben is carried out. Glyben is synthetic clay composed of bentonite mixed with glycerin. A series of laboratory tests including cyclic triaxial, bender element and resonant column tests, are conducted in order to characterize the mechanical properties of glyben and to identify the factors affecting the dynamic behavior of this material. The results of this experimental study show that the iii
modulus reduction ratio of glyben decreases with increasing shear strain amplitude similar to that observed for natural clays. However, there are significant thixotropic changes in the properties of glyben after mixing bentonite with glycerin. In addition, glyben exhibits time-dependent volumetric compression after application of isotropic consolidation pressure, the damping ratio of glyben is higher than that of natural clays and the dynamic properties of glyben are strongly influenced by temperature. Development and testing of a modular neural network (MNN) is conducted in order to predict the influence of various factors affecting the dynamic properties of glyben. The MNN architecture comprised an input layer, two expert modules (neural networks) linked by a gating network, and an output layer. The MNN is trained using 124 data sets obtained from the laboratory tests and tested as part of the current study to evaluate its accuracy. It is shown that the MNN is able to adequately predict the dynamic properties of glyben. The main drawback of glyben, is that it has a damping ratio in the range of 0.15 to 0.22, which is significantly higher than natural soils. Development and characterization of modified glyben, an alternative soil mixture, which has a damping ratio closer to that expected for natural soils, but that retains the favorable characteristic of glyben, is conducted. Modified glyben comprises bentonite mixed with water and glycerin. The viscosity of the pore fluid can be varied by altering the ratio of glycerin-to-water in the pore fluid. The laboratory experiments, including the isotropic consolidation, cyclic triaxial, resonant column, bender elements and x-ray diffraction tests, are carried out in order to characterize modified glyben. The primary objectives of the tests were to characterize the dynamic properties of modified glyben, and to investigate the effect of
iv
temperature, drying and pore-fluid viscosity on the dynamic properties. Overall, the results of this experimental study indicate that the consolidation and dynamic properties of modified glyben are strongly influenced by the pore fluid content and viscosity, which can be varied to achieve soil stiffness and damping ratios similar to that of natural soils. Next, design, fabrication and commissioning of a single axis laminar soil container are carried out in order to simulate vertically propagating shear-waves through a finite thickness model soil deposit on the shaking table. The laminar soil container was designed to overcome the base shear limitations of a small shaking table used in this study. The design details of the box are provided in addition to results of dynamic tests performed to commission the box using the synthetic clay mixture, modified glyben and 1-G similitude theory was employed to maintain model to prototype similarity. A series of shaking table tests and numerical analyses that were performed to study the performance of the laminar box and non-linear seismic behavior of the model clay are described. The laminar container is proven to eliminate significant boundary effects imposed by the container boundaries and is able to maintain 1-D soil column behavior. In addition, the dynamic behavior of the modified glyben during scaled model tests was found to be consistent with the behavior measured during cyclic laboratory tests. Finally, a series of 1-G shaking table tests and analytical solutions are conducted to evaluate the embedment effects on SSI of the buildings with embedded basement stories. A model building with various embedment depths are tested on/in a soil deposit modeled using modified glyben. Testing results are compared to the results obtained from analytical solutions in the literature. The effect of various parameters such as embedment depth, foundation mass and superstructure on the dynamic system parameters of the SSI
v
system is studied. The results showed that the system period decreases with the increasing embedment depth. The damping ratio remained almost unchanged for studied SSI systems. The results of the scaled SSI model tests were observed to follow the trends that existing analytical approaches reveal.
Key words: Soil structure interaction, Synthetic clays, Non-linear soil behavior, Laminar soil container, Modular Neural Networks, Embedded basement stories, Dynamic system parameters, Seismic behavior.
vi
CO-AUTHORSHIP This thesis is prepared in accordance with the regulations for Manuscript format thesis stipulated by the Faculty of Graduate Studies at The University of Western Ontario. Chapters 2, 3 and 5 of this thesis are the current versions of manuscripts accepted for publication as papers. Chapter 4 of this thesis is the current version of a submitted paper. Chapter 6 is a manuscript currently in reviewing. Chapters 2 to 6 inclusive are coauthored by A. Turan, S.D. Hinchberger and M.H. El Naggar. Alper Turan conducted experimental and numerical studies and wrote the draft of the chapters. Dr. Sean Hinchberger and Dr. M. Hesham El Naggar assisted in interpretation of the results and the writing of the chapters of this thesis.
vii
ACKNOWLEDGEMENT In the name of God, the most compassionate and the most merciful. All my praise is to Allah, the Lord of the worlds. He is the Master of the Day of Judgement and keeps us on the right path. We all depend on Him. I would like to place on record my sincere gratitude and appreciations to the individuals who supported me during the course of my PhD studies. This research could not have been possible without their collaboration and support. My supervisors Dr. Sean D. Hinchberger and Dr. M. H. El Naggar supported me with their wise guidance, thoughtful suggestions, continuous support and friendly encouragement, and were always available to discuss. I would particularly like to thank Dr. Hinchberger for his assistance with all aspects of the experimental program. Dr. El Naggar’s mentorship will always be valued. I also thank to Dr. K.Y. Lo, Dr. Tim Newson and other members of UWO Civil Engineering faculty, who lent me their expertise. I would also like to recognize Dr. Adrian Rodriguez-Marek, who shared his knowledge and material on the soil constitutive models. The friendship and collaboration with a number of my fellow gradate students have been invaluable. Special thanks are due to Dr. N. Allotey, Dr. M. Mousavi and Dr. M. Hamidi for their help and advice during the course of this research and to Mr. E. Ertorer for his tremendous help during the model soil compaction. I would like to acknowledge the generous assistance by the staff of the Geotechnical Research Centre (GRC), Boundary Layer Wind Tunnel (BLWTL) and University viii
Machine Services (UMS). I am grateful to M. Richards, W. Logan and T. Stephens for their help in geotechnical laboratory tests. Tireless guidance and exceptionally professional cooperation by G. Dafoe, A. Burggraaf and A. Costache during shaking table testing program made this work come true. Without the dedicated efforts and support of C. Vandelaar and other UMS staff, who helped with the design and commissioning of the laminar soil container, this work could not have been brought to realization. Words are not enough to thank my family. My wife, Neslihan, has always been a memorable journey from my stressful and miserable moments to the pleasant and enjoyable ones. Her patience, encouragement, and love was unbelievable. My children, Sena Suheyla and Huseyin Kiyas, were the sources of a great joy that kept my life in balance. Finally, I want to thank a wise woman, my mother Suheyla, for her love and support. I would like to dedicate this thesis to the memory of father, Kiyas.
ix
TABLE OF CONTENTS
CERTIFICATE OF EXAMINATION
ii
ABSTRACT
iii
CO-AUTHORSHIP
vii
ACKNOWLEDGEMENT
viii
TABLE OF CONTENTS
x
LIST OF TABLES
xvi
LIST OF FIGURES
xviii
NOMENCLATURE
xxvi
CHAPTER 1 INTRODUCTION
1
1.1.
Introduction
1
1.2.
Objectives of the Research
3
1.3.
Scope of Work
4
1.4.
Thesis Layout
5
References
8
CHAPTER 2 MECHANICAL CHARACTERIZATION OF AN ARTIFICIAL CLAY 9 2.1
Introduction
9
2.2
Background
10
2.3
Testing and Methodology
12
2.3.1
Material Preparation
12
2.3.2
Compaction, Vane Shear and Atterberg Limit Tests
13
2.3.3
Cyclic Triaxial Testing
13 x
2.3.4
Bender-Extender Element Tests
15
2.3.5
Resonant Column Tests
17
2.4
Results
18
2.4.1
Compaction, Vane Shear Strength and Gmax/Cu
18
2.4.2
Thixotropic Effects
18
2.4.3
Effect of Shear Strain Amplitude
19
2.4.4
Effect of Confining Stress
21
2.4.5
Influence of the Number of Cycles
22
2.4.6
Temperature Effects
22
2.4.7
Repeatability of Dynamic Properties
24
2.4.8
Consolidation Behavior of Glyben
25
2.5
Summary and Conclusions
28
References
32
CHAPTER 3 PREDICTING THE DYNAMIC PROPERTIES OF GLYBEN USING A MODULAR NEURAL NETWORK (MNN)
55
3.1
Introduction
55
3.2
Background
56
3.2.1 3.3
Artificial Neural Networks
56
Methodology
58
3.3.1
Input and Output Parameters
58
3.3.2
Modular Neural Networks
59
3.3.3
Data Set
61
3.3.4
Training and Testing
61
xi
3.4
Dynamic Glyben Properties
62
3.4.1
Effect of Glycerin Ratio (g/c) and Shear Strain Amplitude (γ)
62
3.4.2
Effect of Frequency (F)
63
3.4.3
Effect of Confining Pressure (σc)
63
3.5
Summary and Conclusions
64
References
66
CHAPTER 4 THE INFLUENCE OF PORE FLUID VISCOSITY ON THE DYNAMIC PROPERTIES OF AN ARTIFICIAL CLAY
82
4.1
Introduction
82
4.2
Background
83
4.2.1
Soil-structure Interaction
83
4.2.2
Alternative model soils
84
4.3
Tests and Methodology
85
4.3.1
Material Preparation
86
4.3.2
Compaction, Atterberg Limits and Vane Shear Tests
86
4.3.3
Cyclic Triaxial Tests
87
4.3.4
Isotropic Consolidation Tests
89
4.3.5
Resonant Column Tests
89
4.3.6
Bender Element Tests
90
4.3.7
X-ray Diffraction Tests
91
4.4
Results of Static and Mineralogy Tests
92
4.4.1
Effects of Glycerin on Bentonite Mineralogy
92
4.4.2
Compaction, Shear Vane Strength and Atterberg Limits
92
xii
4.4.3
Thixotropy
93
4.4.4
Consolidation Behavior
94
Results of Dynamic Tests
96
4.5 4.5.1
The Influence of (gw/c) on G and ξ
96
4.5.2
The Influence of (w/gw) on G and ξ
97
4.5.3
Normalized Dynamic Stiffness, G/Gmax, of Modified Glyben
98
4.5.4
Damping Ratio Versus Pore Fluid Viscosity (w/gw)
99
4.5.5
Effect of Confining Stress on G/Gmax
100
4.5.6
Gmax versus (gw/c), (w/gw) and σc
101
4.6
Evaluation of Beneficial Properties of Modified Glyben
102
4.6.1
Effect of the Number of Cycles
102
4.6.2
Effect of Drying
103
4.6.3
Effect of Temperature
103
Summary and Conclusions
104
4.7
References
108
CHAPTER 5 DESIGN AND COMMISSIONING OF A LAMINAR SOIL CONTAINER FOR USE ON SMALL SHAKING TABLES
138
5.1
Introduction
138
5.2
Background
140
5.3
Methodology
142
5.3.1
Experimental Set-up
142
5.3.1.1
Flexible Soil Container
142
5.3.1.2
Shaking Table
144 xiii
5.3.2
Model Preparation
144
5.3.2.1
Soil Properties and Placement
145
5.3.2.2
Similarity Rule
146
5.3.3
Shaking Table Tests
147
5.3.3.1
Tests Performed and Instrumentation Details
148
5.4
Results and Discussion
151
5.4.1
Performance of Laminar Shear Box
152
5.4.1.1
Bearing Friction and Membrane Effects
152
5.4.1.2
Assessment of Boundary Effects
152
5.4.2
Seismic Free Field Response
153
5.4.2.1
Soil Resonance
153
5.4.2.2
Soil Amplification
154
5.4.2.3
Hysteretic Soil Behavior
155
Summary and Conclusions
156
5.5
References
159
CHAPTER 6 SEISMIC SOIL-STRUCTURE INTERACTION IN BUILDINGS ON STIFF CLAY AND WITH EMBEDDED BASEMENT STORIES
200
6.1
Introduction
200
6.2
Methodology
202
6.2.1
Experimental Set-up
202
6.2.2
Model Description
203
6.2.2.1
Soil Placement and Properties
203
6.2.2.2
Model Building and Instrumentation Details
204
xiv
6.2.2.3
Similarity Rule
205
6.2.3
Shaking Table Tests
206
6.2.4
Interpretation of Shaking Table Test Data
208
6.2.5
Analytical Procedures
209
6.2.5.1
Analytical Method
209
6.2.5.2
Numerical Methods
211
Results and discussion
213
6.3 6.3.1
Verification of Free Field Ground Response
214
6.3.2
Fixed Base Dynamic Response of Superstructure
214
6.3.3
Dynamic Behavior of Structures with Embedded Basement Levels
216
6.3.3.1
Influence of Embedment Depth
216
6.3.3.2
Influence of Foundation Mass
218
6.4
Summary and Conclusions
219
References
221
CHAPTER 7 SUMMARY AND RECOMMENDATIONS FOR FUTURE STUDY 260 7.1
Summary
260
7.2
Recommendations for Future Study
263
APPENDIXES
268
APPENDIX A. SOIL PLACEMENT AND UNIFORMITY
268
APPENDIX B. SOIL STRUCTURE INTERACTION SOLUTIONS OF AVILES AND PEREZ-ROCHA (1998)
271
CIRRICULUM VITAE
275
xv
LIST OF TABLES
Table 2. 1 Summary of dynamic tests
36
Table 2. 2 Variation of Gmax/Cu and bulk density with (g/c) ratio.
37
Table 2. 3 Temperature dependant variation of the viscosity and dielectric constant of glycerin and water (from Dorsey, 1940 and Huck et al., 1988).
38
Table 2. 4 Small strain level reproducibility of dynamic glyben properties (bender element test).
39
Table 2. 5 Changes in dynamic properties due to consolidation (resonant column test).
40
Table 3. 1 Randomized data sets used for training.
70
Table 3. 2 Data sets used in testing of network
73
Table 4. 1 Details of dynamic test specimens
112
Table 4. 2 Temperature dependent properties of glycerin and water (Dorsey, 1940 and Huck et al., 1988).
113
Table 4. 3 Index properties, bulk density and vane shear strength of modified glyben mixtures with (gw/c) = 40 % and varying (w/gw) ratios.
114
Table 4. 4 Changes in vane shear strength of various modified glyben mixtures versus time after mixing. (w/gw = 25%) Table 4. 5 Variation of the pore fluid viscosity with w/gw for (gw/c) = 40 %.
115 116
Table 4. 6 Effect of exposure to air on the dynamic properties of modified glyben with (gw/c) = 42.5% and (w/gw) = 25%. (Specimen RC-5) xvi
117
Table 4. 7 Variation of the viscosities of glycerin-water mixtures with temperature (Dorsey, 1940)
118
Table 5. 1 Summary of available laminar shear box designs.
162
Table 5. 2 Box properties.
163
Table 5. 3 Similitude relationships of parameters between prototype and model (After Meymand, 1998).
164
Table 5. 4 Similitude relationships of clay deposit between prototype and model.
165
Table 5. 5 Summary of tests
166
Table 5. 6 Comparison of dynamic soil properties from cyclic laboratory tests (cyclic triaxial/resonant column) and shaking table tests.
167
Table 6. 1 Similitude relationships of parameters between prototype and model (After Meymand, 1998)
226
Table 6. 2 Similitude relationships of SSI systems between prototype and model (λ=40).
227
Table 6. 3 Summary of Tests
228
Table 6. 4 Parameters of Borja’s model for highly (PI=0) and mildly (PI=100) plastic clays. (After Wong, 2004)
229
Table 6. 5 Dynamic system parameters of SDOF-L for cases with (D/L) values of 0, 0.5, 1 and 2.
230
Table 6. 6 Dynamic system parameters of SDOF-H for cases with (D/L) values of 0, 1 and 2.
231
xvii
LIST OF FIGURES Figure 2. 1 Typical elastic modulus and damping ratio from hysteresis loop.
41
Figure 2. 2 Variation of compacted bulk density and cohesive strength versus glycerin content
42
Figure 2. 3 Variation of the cohesive strength of glyben and bentonite-water mixture vs. time.
43
Figure 2. 4 Variation of shear modulus and damping ratio vs. time.
44
Figure 2. 5 Normalized shear modulus versus shear strain amplitude.
45
Figure 2. 6 Damping ratio versus shear strain amplitude.
46
Figure 2. 7 Variation of shear modulus and damping ratio with confining pressure at high strain levels.
47
Figure 2. 8 Variation of shear modulus and damping ratio with confining pressure at low strain levels.
48
Figure 2. 9 Variation of shear modulus and damping ratio with number of cycles.
49
Figure 2. 10 The effect of temperature on the shear wave velocity of glyben (g/c = 47.5%).
50
Figure 2. 11 The effect of temperature on the dynamic shear modulus and damping ratio of glyben (g/c = 47%).
51
Figure 2. 12 Variation of damping ratio with pore fluid viscosity.
52
Figure 2. 13 Large strain level reproducibility of dynamic glyben properties.
53
Figure 2. 14 Degree of consolidation vs. dimensionless time for glyben and bentonite-water mixture.
54
xviii
Figure 3. 1 General schematics of MNN.
74
Figure 3. 2 The comparison of the estimated (MNN) and measured shear modulus of glyben.
75
Figure 3. 3 The comparison of the estimated (MNN) and measured damping ratio of glyben.
76
Figure 3. 4 Variation of MNN predicted shear modulus with g/c and Figure 3. 5 Variation of MNN predicted damping ratio with g/c and
77 78
Figure 3. 6 Shear modulus degradation curves of glyben at different frequencies.
79
Figure 3. 7 Damping curves of glyben at different frequencies.
80
Figure 3. 8 Variation of MNN predicted dynamic properties with confining pressure.
81
Figure 4. 1 1-D Shear wave propagation model for earthquakes.
119
Figure 4. 2 Scaled model of 1-D shear wave propagation.
120
Figure 4. 3
X-ray diffraction traces (CuKα) obtained on oriented fines of
bentonite: (a) air dried, (b) glycolated and (c) glycolated with diluted glycerin (w/gw) = 25%.
121
Figure 4. 4 Compaction behavior of modified glyben for (w/gw) of 0 and 25 %.
122
Figure 4. 5 Vane shear strength vs. (gw/c) for various (w/gw) of 25 %.
123
Figure 4. 6
Thixotropic changes in Vs and the vane shear strength. (specimen
BE-1).
124
Figure 4. 7 Consolidation response of modified glyben (specimen CTX-14).
xix
125
Figure 4. 8 Effect of (gw/c) on the dynamic shear modulus, G (specimens, CTX10, CTX-11, CTX-12, RC-2, RC-3 and RC-4).
126
Figure 4. 9 Effect of (gw/c) on the damping ratio, ξ (specimens, CTX-10, CTX11, CTX-12, RC-2, RC-3 and RC-4). Figure 4. 10
127
Effect of (w/gw) on G-γ curves – cyclic triaxial and resonant
column tests (specimens CTX-2, CTX-3, CTX-4, CTX-5 and RC-2).
128
Figure 4. 11 Effect of (w/gw) on ξ-γ curves – cyclic triaxial and resonant column tests. (specimens CTX-2, CTX-3, CTX-4, CTX-5 and RC-2).
129
Figure 4. 12 The effect of (gw/c) on the G/Gmax-γ (specimens CTX-6, CTX-7, CTX-8, CTX-9, RC-2, RC-3 and RC-4).
130
Figure 4. 13 G/Gmax-γ curves- modified glyben vs. glyben.
131
Figure 4. 14 The effect of (gw/c) on the ξ−γ (specimens CTX-6, CTX-7, CTX-8, CTX-9, RC-2, RC-3 and RC-4)
132
Figure 4. 15 Variation of low strain shear modulus and damping ratio values with confining stress. (specimen RC-1).
133
Figure 4. 16 Variation of high strain shear modulus and damping ratio values with confining pressures. (specimen CTX-1). Figure 4. 17
134
Variation of Gmax values with confining pressures for various
(gw/c) ratios. (specimens BE-7 to 18) Figure 4. 18 Influence of the number of the load cycles. (specimen CTX-15)
135 136
Figure 4. 19 Variation of Vs of modified glyben with temperature (specimens BE-2, BE-3, BE-4, BE-5, BE-6, BE-12 and BE-13)
xx
137
Figure 5. 1 (a) Laminar box covered with latex membrane and aligned with corner profiles.
168
Figure 5. 1 (b) Isometric view of laminar box.
169
Figure 5. 1 (c) Profile and plan views of the laminar box with vane shear test locations.
170
Figure 5. 2 (a) Stiffness degradation for modified Glyben (after Turan et al. 2008).
171
Figure 5. 2 (b) Damping curves for modified Glyben (after Turan et al. 2008).
172
Figure 5. 3 Schematic of the instrumentation
173
Figure 5. 4 (a) Accelerometer array and soil descritization for use in stress-strain calculations
174
Figure 5. 4 (b) Typical hysteretic loop.
175
Figure 5. 5 Shear strength and shear wave velocity profiles along the depth.
176
Figure 5. 6 Resistance forces against the lateral lamina movement.
177
Figure 5. 7 The influence of the box boundaries on the dynamic response.
178
Figure 5. 8 (a) Acceleration time histories on the soil surface
179
Figure 5. 8 (b) Acceleration time histories on the table.
180
Figure 5. 8 (c) Corresponding power spectra.
181
Figure 5. 9 (a) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.12 g.
182
Figure 5. 9 (b) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.35 g.
183
Figure 5. 9 (c) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.55 g.
xxi
184
Figure 5. 9 (d) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.70 g.
185
Figure 5. 10 (a) Acceleration time histories and Fourier spectra of prototype scale El Centro earthquake
186
Figure 5. 10 (b) Acceleration time histories and Fourier spectra of scaled El Centro earthquake applied to the table
187
Figure 5. 10 (c) Acceleration time histories and Fourier spectra of signal measured on the table.
188
Figure 5. 11 (a) Measured acceleration time histories on the soil surface.
189
Figure 5. 11 (b) Simulated acceleration time histories on the soil surface.
190
Figure 5. 12 (a) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.12 g.
191
Figure 5. 12 (b) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.35 g.
192
Figure 5. 12 (c) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.55 g.
193
Figure 5. 12 (d) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.70 g.
194
Figure 5. 13 Comparison of soil stiffness and damping ratio deduced from laboratory tests and shaking table tests.
195
xxii
Figure 6. 1 Laminar soil container and used in this study.
232
Figure 6. 2 Averaged vane shear strength and shear wave velocity profiles along the depth (Turan et al., 2008b).
233
Figure 6. 3 Stiffness degradation (a) and damping (b) curves for modified glyben (after Turan et al. 2008a).
234
Figure 6. 4 Modular model building used in this study.
235
Figure 6. 5 Instrumentation of the soil-structure system.
236
Figure 6. 6 Schematics of the testing cases.
237
Figure 6. 7 (a) SSI system considered in analytical solutions (after Aviles and Perez-Rocha 1998).
238
Figure 6. 7 (b) SSI system excited by foundation input motion (after Aviles and Perez-Rocha 1998).
239
Figure 6. 7 (c) Replacement oscillator system excited by free field ground motion (after Aviles and Perez-Rocha 1998).
240
Figure 6. 8 Graphical representation of Aviles and Perez-Rocha (1996) and (1998) solutions (after Aviles and Perez-Rocha 1998).
241
Figure 6. 9 (a) Measured free field ground motion at 0.12 g intensity level.
242
Figure 6. 9 (b) Measured free field ground motion at 0.35 g intensity level.
243
Figure 6. 10 (a) Applied acceleration time history on the shaking table.
244
Figure 6. 10 (b) Measured acceleration time history at the mass level of SDOF-L.
245
Figure 6. 10 (c) Fourier spectra of the response measured on SDOF-L.
246
xxiii
Figure 6. 11 (a) Applied acceleration time history on the shaking table.
247
Figure 6. 11 (b) Measured acceleration time history at the mass level of SDOF-H.
248
Figure 6. 11 (c) The corresponding fourier spectra of the response at mass level for SDOF-H.
249
Figure 6. 12 (a) Applied acceleration time history and Fourier spectra of base excitation on the table.
250
Figure 6. 12 (b) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=0.
251
Figure 6. 12 (c) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=0.5.
252
Figure 6. 12 (d) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=1.
253
Figure 6. 12 (e) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=2.
254
Figure 6. 13 (a) Acceleration time history and Fourier spectra of SDOF-H with D/L=0.
255
Figure 6. 13 (b) Acceleration time history and Fourier spectra of SDOF-H with D/L=1.
256
Figure 6. 13 (c) Acceleration time history and Fourier spectra of SDOF-H with D/L=2.
257
Figure 6. 14 (a) Acceleration response spectra at the foundation base for massless and massive foundation cases (D/L=2).
xxiv
258
Figure 6. 14 (b) Acceleration response spectra at the lumped mass level for massless and massive foundation cases (D/L=2).
xxv
259
NOMENCLATURE
c
cohesive strength
cs
shear wave velocity
cu
undrained shear strength
cv
coefficient of consolidation
d
distance between transmitter and receiver tips of bender elements
D
depth of rigid square foundation
D/L
embedment ratio
Eeq
dynamic elastic modulus
f
frequency at which the cyclic testing was performed
G / G max
shear modulus reduction factor
G
dynamic shear modulus
Gmax
maximum shear modulus
g/c
percentage of glycerin in glyben mixture (by mass)
gw/c
ratio of fluids to solids by mass
h
kinematic
hardening
parameter
that
control
the
stiffness
degradation rate (exponential) versus shear strain amplitude curve H
effective height
H0
model parameter defining initial plastic modulus
J0
mass moment of inertia about the centroidal axis of foundation
L
half width of rigid square mat foundation xxvi
LL
liquid limit
m
kinematic hardening parameter that control the shape of the secant modulus versus shear strain amplitude curve
M
effective mass of superstructure
M0
mass of rigid square mat foundation
N
number of cycles
PI
plasticity index
PL
plastic limit
Qh
horizontal component of transfer functions of the foundation input motion
Qr
rocking component of transfer functions of the foundation input motion
R
radius of the bounding surface
t
cure time; duration of consolidation
T
fundamental period of superstructure
T
temperature
Tv
dimensionless time
TP
arrival time for P-waves
TS
arrival time for S-waves
( Tk
fundamental period of soil-structure system considering kinematic interaction
xxvii
( Ti
fundamental period of soil-structure system neglecting kinematic interaction
( T /T
normalized system period
u( zi , t )
absolute displacement at the depth of zi and time t
u&&
acceleration
Vp
compression wave velocity
Vs
shear wave velocity
(Vs)m
shear wave velocities for the prototype
(Vs)m
shear wave velocities for the model
&x&soil (t )
acceleration at soil surface
&x&table (t )
acceleration at the shaking table
w
water content
wi
weighting factors in MNN
w/gw
ratio of water to water plus glycerin by mass
β
trapezoidal integration parameter
β
bias values in MNN
∆z k
soil slice thickness
εa
axial strain
φ
friction angle
γ
shear strain
λ
geometric scaling factor
λε
strain scaling factor xxviii
ν
Poisson’s ratio
µ
learning rate in MNN
ωn
fundamental angular frequency in resonant column test
Ω
fundamental frequency of soil-structure system
ρ
mass density
ρ amp
amplification factor
σa
axial stress
σc
isotropic confining pressure
τ
shear stress
τH
wave parameter (measure of relative stiffness of soil and structure)
ξ
damping ratio
(
ξk
damping ratio of soil-structure system considering kinematic interaction
(
ξi
damping ratio of soil-structure system neglecting kinematic interaction
xxix
2
1
CHAPTER 1 INTRODUCTION
1.1. Introduction Numerous devastating earthquakes causing significant economic loss and fatalities have been reported during history. However, the field of earthquake engineering, which aims to improve the understanding of this complicated phenomenon, is quite new. While the understanding of destructive earthquakes has improved, interest in the dynamic behavior of the soils during earthquakes has also increased since almost all civil engineering structures are either constructed on, in or of soils (buildings, bridges, highways, tunnels, slopes, embankments and earth dams). Therefore, successful design of civil infrastructure is based on accurate knowledge of the strength and stiffness of supporting soil and rock medium. The existence of non-linear plasticity, pore water, heterogeneity of the soil complicates this task and probabilistic nature of seismic loads further magnifies this complexity (Gibson, 1997). It is well known that the free field ground motion is affected by seismic source, wave path and local site effects. The response of structures subjected to dynamic loads is also influenced by interaction between the foundation of the structure and the supporting soils, which is referred to as soil structure interaction (SSI). Proper characterization of the effects of SSI remains as one of the most significant challenges in earthquake geotechnical engineering. SSI can alter the characteristics of ground motion (Finn and Ventura, 1994 and Jakrapiyanun, 2002). In particular, structural accelerations are affected
2 by the flexibility of the foundation support and variations between the foundation and free-field motions. Consequently, an accurate assessment of inertial forces and displacements in structures requires appropriate treatment of SSI effects (Steward et al. 1999). Recent earthquakes and the strong motion data that became available following these earthquakes has resulted in advances in the understanding of local site effects and SSI. These advances were reflected to the updates to code provisions by the Building Seismic Safety Council [BSSC (1997)] and Applied Technology Council [ATC (1984)] codes. The use of empirical procedures to assess SSI effects is started to be replaced by more sophisticated analytical techniques including numerical procedures incorporating nonlinear elastic-plastic constitutive models for the soil. However, the ability to predict soilstructure response during earthquakes still requires improvements despite the availability of a large database of both free-field and structural strong motion recordings from recent earthquakes, and sophisticated SSI analysis procedures including direct and substructure methods.
Therefore, on large, complex and high risk projects, physical modeling
techniques may need to be employed along with empirical, numerical procedures. Reduced scaled models, which are built to represent and study full-scale soil-structure systems, are often used to study seismic SSI. The use of scaling relationships between the model and prototype has made the reasonably accurate quantitative assessment of SSI possible using scaled physical models. The performance of a model is complicated by the stress scaling and constitutive behavior of soil. Stress scaling is linear whereas the constitutive behavior is non-linear. A model made of the same material as the prototype will not behave similarly unless it is built with the same scale. The use of a centrifuge,
3 which is costly to built and operate, helps to avoid this incompatibility by adequately simulating the gravitational stress field in the model soil system to obtain a stress-strain response that is more consistent with that of the full-scale soil deposit. In the cases of cohesive soils, the use of a centrifuge is not as critical as it is for sands since the modeling of overburden stresses does not have a significant impact on the soil stiffness during short-term cyclic loading.
This thesis investigates the seismic behavior of buildings with basement stories situated on and in cohesive soils taking SSI effects into account. The thesis comprises both experimental and analytical components. The experimental work comprises: (i) mechanical characterization of the synthetic clay mixtures called Glyben and Modified Glyben using standard and dynamic geotechnical laboratory tests and (ii) a series of scaled physical model tests performed at 1-G using a shaking table and laminar soil container. The analytical work consists of finite element modeling using the software ABAQUS to interpret the results of physical model tests. This chapter, a short introduction to the dissertation, describes the objectives of the research, scope of the work and the thesis layout.
1.2. Objectives of the Research The main objectives of this thesis are:
•
To characterize the dynamic behavior of a modeling soil called Glyben. Glyben is a synthetic clay mixture consisting of sodium bentonite mixed with glycerin.
4
•
To develop a modified version of glyben with dynamic properties that are closer to those of natural soils.
•
To design, test and commission a 1-D laminar soil container in order to conduct reduced scale SSI tests while maintaining appropriate nonreflecting boundaries.
•
To perform 1-G shaking table tests to investigate the effect of basement embedment on the seismic response of buildings founded on clay.
•
To validate the behavior observed during the model tests using existing analytical solutions and the finite element method.
1.3. Scope of Work The primary focus of this thesis is to identify the seismic behavior of buildings with basement stories embedded in cohesive soils using both reduced scale physical modeling techniques in 1-G environment and analytical techniques. This required the following steps: (i) The mechanical properties of a synthetic clay mixture called glyben were characterized using a series of standard and dynamic laboratory tests. Then, a Modular Neural Network (MNN) simulation was carried out to identify the parameters influencing dynamic behavior of glyben and level of non-linearity between these parameters and dynamic properties of the material; (ii) Then, since the damping ratio of glyben is higher than natural soils, a new synthetic mixture called modified glyben was developed and characterized; (iii) A laminar soil container was designed and manufactured to overcome the base shear limitation of shaking table facility at the University of Western Ontario. Modified glyben was used as the model soil and free field
5 ground response tests were carried out to validate the performance of modified glyben and laminar soil container; (iv) Finally, shaking table tests were conducted to study the SSI problem for buildings with embedded basement stories. The response of a model structure with embedded levels was compared with an existing analytical solution.
1.4. Thesis Layout The current chapter, Chapter 1, summarizes the objectives and scope of work, and presents the format of this thesis. Chapter 2 describes the characterization of a synthetic clay called glyben. Glyben is an artificial soil comprising bentonite mixed with glycerin and it has been used recently in scaled model tests to study seismic soil structure interaction. Chapter 2 presents the results of vane shear tests, cyclic triaxial tests, resonant column tests and bender element tests undertaken to characterize the dynamic properties of glyben. The results show that the modulus ratio of glyben decreases with increasing shear strain amplitude similar to that observed for natural clays. However, there are significant thixotropic changes in the properties of glyben after mixing bentonite with glycerin. In addition, Glyben exhibits time-dependent volumetric compression after the application of isotropic consolidation pressure, the damping ratio of glyben is higher than that of natural clays and the dynamic properties of glyben are strongly influenced by temperature. These factors should be considered when interpreting the results of scaled physical model tests using glyben. Chapter 3 presents a modular neural network that is trained using the data produced in Chapter 2 to predict the dynamic properties of glyben. This chapter describes the development and testing of a modular neural network (MNN) that is suitable for predicting the dynamic properties of glyben. The MNN architecture comprises an input
6 layer, two expert modules (neural networks) linked by a gating network, and an output layer. The MNN is trained using 124 data sets obtained from the literature and Chapter 2 and tested to evaluate its accuracy. It is shown that the developed MNN is able to adequately predict the dynamic properties of glyben. Chapter 4 describes the results of vane shear, laboratory compaction, isotropic consolidation, cyclic triaxial, bender element and resonant column tests that were performed to characterize the dynamic properties of an artificial soil called modified glyben. Modified glyben comprises a mixture of glycerin, water and bentonite, which can be use in scaled-model tests performed at 1-g or N-g in a centrifuge to study seismic soil-structure interaction. Modified glyben was developed by the author to produce a material with a damping ratio lower than glyben and similar to natural soils.
The
laboratory results in Chapter 4 show that the shear strength, coefficient of consolidation, dynamic modulus, and damping ratio are strongly influenced by the viscosity of the pore fluid, which can be varied by altering the ratio of glycerin to water or temperature. In addition, the modified glyben has dynamic properties (including the damping ratio) that are similar to natural soils while maintaining the favorable characteristics of glyben. Chapter 5 describes the design, fabrication and commissioning of a 1-D laminar soil container for use in seismic soil-structure-interaction studies. Design details of the laminar container are provided in addition to the results of preliminary shaking table tests using modified glyben. Chapter 5 describes the 1-g similitude rules used for the tests in addition to the methodologies adopted to place modified glyben into the laminar soil container and to assess the in-situ dynamic properties of the model soil deposit. Finally, a series of shaking table tests and numerical analyses are reported. These tests were
7 performed to evaluate the performance of the laminar box and non-linear seismic behavior of modified glyben. Chapter 6 examines the dynamic soil-structure interaction (SSI) of buildings with basement stories embedded in cohesive soils. This chapter gives details of the scaled physical model (e.g. soil deposit and structure) that was used to study dynamic SSI. The results of shaking table tests are presented and compared with an existing analytical solution for dynamic SSI. In addition, a numerical model is validated using the shaking table test results and then used to extend the laboratory results to more general cases. A summary of the thesis is presented in Chapter 7 and some recommendations for possible complementary research activities are provided.
8
References ABAQUS. 2005. Hibbit, Karlsson and Sorensen., Inc., Version 6.7. Applied Technology Council (ATC). 1984. Tentative provisions for the development of seismic regulation. ATC-3-06, Amended, California. Building Seismic Safety Council (BSSC). 1997. NEHRP recommended provisions for seismic regulations for new buildings, Part 1, Provisions and Part 2, Commentary. Rep. No. FEMA 302 and 303, Federal Emergency Management Agency, Washington, D.C. Finn, W.D.L., and Ventura, C.E. 1994. Ground motions. Preliminary report on the Northridge, California, earthquake of January 17, 1994. Canadian Association for Earthquake Engineering, Vancouver, B. C., pp. 7-71. Gibson A.D. 1997. Physical scale modeling of geotechnical structures at one-g. PhD thesis. Pasadena, CA: California Institute of Technology. Jakrapiyanun, W. 2002. Physical modeling of dynamic soil-foundation-structureinteraction using a laminar container, Ph.D. Thesis, Dept. of Structural Engineering, University of California, San Diego, La Jolla. Stewart, J.P., Fenres, G.L. and Seed, R.B. 1999. Seismic soil–structure interaction in buildings I: Analytical Method. J. Geotech Geoenv. Eng Div., 125(1), 26–37.
9
CHAPTER 2 MECHANICAL CHARACTERIZATION OF AN ARTIFICIAL CLAY
2.1 Introduction Scaled physical modeling is an economic and effective approach to study soilstructure interaction during earthquakes. One of the challenges of such studies is to obtain a model soil that can be scaled to adequately simulate the seismic response of the prototype soil. Several natural and synthetic soil mixtures have been proposed for scaled model tests involving structures founded on or in clay deposits (e.g. Seed and Clough 1963, Seah 1990 and Meymand 1998). Although, most model soils have proven to be useful, their properties can be strongly influenced by stress history, thixotropy and consolidation during spin-up in centrifuge tests. In addition, model soils can be difficult to prepare and place in laminar shear boxes and they can generally be used only once due to drying and consequent desiccation during tests. These characteristics can limit the usefulness of model soils, especially for centrifuge tests. Thus, there is a need for an artificial soil that has fewer limitations compared to conventional model soils. This chapter investigates the effect of time (or thixotropy), temperature, confining pressure and cyclic stress history on the dynamic properties of glyben. Other characteristics such as Atterberg limits, vane shear strength and compaction behavior are also presented. Glyben (see Mayfield 1963, Kenny and Andrawes 1997, Rayhani and El Naggar 2006) is a synthetic clay mixture comprising bentonite and glycerin.
The
stiffness, shear strength and damping of glyben can be varied by altering the percentage of glycerin by mass (g/c) in the mixture. Glyben behaves as a cohesive material, it
10 consolidates but at a very slow rate compared to natural clays, and as such it possesses properties that are favorable for scaled model tests requiring cohesive soil behavior (e.g. where particle size scaling is not required). Although glyben has been used recently for model tests involving cohesive soil response (e.g., Rayhani and El Naggar 2006), factors affecting the dynamic properties of this material are not well established. Consequently, a series of vane shear, cyclic triaxial, resonant column and bender element tests were conducted to characterize the dynamic behavior of glyben. The results of this study are considered to be of interest to researchers designing and conducting scaled physical model tests at 1-G and in a centrifuge.
2.2 Background Several modeling soils have been developed for use in scaled physical modeling applications. In some cases, researchers have used reconstituted soils for scaled model tests (see Nunez and Randolph 1984, Burr et al. 1997 and Moss et al. 1998). When reconstituted soils are used, the soil is normally slurried, placed in a test container and consolidated to obtain the desired strength and stiffness. This process can be performed either prior to or during spin-up in centrifuge tests but it can be impractical for 1-G tests, due to the large quantity of soils required and the length of time needed for consolidation. In addition, reconstituted soils generally cannot satisfy all similitude criteria such as those for the undrained shear strength and dynamic shear modulus. As an alternative to reconstituted soils, a wide variety of artificial and natural soil mixtures have been developed including: supersil, plastellina, aerosil, veegum, silicon gum, plasticine, polyacrylimide, and modified sands, clays and clayey silts. For example,
11 Tavenas et al. (1973) developed an artificial model soil using kaolinite, Portland cement, and bentonite to simulate brittle Champlain clay. Over-consolidated soils have been modeled by Ko et al. (1984) using a kaolinite-water mixture, and by Blaney and Mallow (1987) using fumed silica mixed with bentonite and water. Biscontin and Pestana (2001) studied the influence of torque rate on the vane shear strength of a lightly cemented bentonite-kaolinite mixture. Iskander et al. (2002) created an transparent artificial model clay using amorphous silica. The most extensive studies involving model soils for seismic applications have been conducted at University of California, Berkley (UCB). In 1963, Seed and Clough (1963) developed a kaolinite, bentonite and water mixture (w = 200%) for 1-G shake table studies. The seismic characteristics of the UCB soil can be found in Kovacs (1968). Sultan and Seed (1967), Arango-Greiffenstein (1971), Bray (1990), Lazarte (1996) and Meymand (1998) subsequently used UCB soil with some modifications to study the seismic performance of structures such as clay core dams, and piles and pile groups in clay. Glyben is a mixture of sodium bentonite and glycerin that seems to overcome some of the shortcomings of traditional synthetic modeling soils. Mayfield (1963) conducted a series of triaxial tests on glyben and concluded that it behaved as a cohesive ( φu = 0 o )
material. Sutherland (1988) studied the uplift capacity of piles in cohesive soils using glyben and noted that there was negligible desiccation of glyben at room temperature. Later, Kenny and Andrawes (1997) conducted undrained triaxial tests and vane shear tests and noted that glyben behaved as a purely cohesive material, φu = 0 o , during quick
loading. In addition, Kenny and Andrawes (1997) observed that compacted glyben gave excellent repeatability during testing. Recently, Rayhani and El Naggar (2006)
12 investigated the seismic performance of glyben using resonant column, and in flight T-bar and hammer tests during centrifuge tests. They concluded that glyben exhibited trends of modulus reduction and increased damping that were similar to soft and medium clays. However, Rayhani and El Naggar (2006) found that the damping ratio of glyben at small strain amplitudes was higher than that measured for natural clays. In general, these studies point out a general interest in glyben and a need for further characterization of this material.
2.3 Testing and Methodology A series of compaction tests, vane shear tests, Atterberg limit test, cyclic triaxial, bender element and resonant column tests were performed to investigate the mechanical properties of glyben. Details of these tests and the procedures followed are given in the following sections. Table 2.1 provides a detailed list of each specimen, the type of test performed, and its glycerin or water contents.
2.3.1 Material Preparation Glyben was prepared by mixing bentonite with glycerin in a kneading type geotechnical mixer (Blakeslee, model B-20) for at least 30 minutes. Both bentonite and glycerin were blended very slowly in the mixer over a period of about 15 to 20 minutes to ensure as uniform mixture as possible. After mixing, specimens were then prepared by compacting the glyben into a split mold in four lifts using a drop hammer. The number of lifts and blows with the drop hammer were selected so that the bulk density of each specimen was 95% of the maximum bulk density determined from standard compaction tests. Specimens were subsequently removed from the split mold after compaction,
13 wrapped in plastic and stored at room temperature (22 ±1 ºC) until tested. Unless otherwise stated, specimens were tested at least 5 days after preparation to avoid thixotropic effects.
2.3.2 Compaction, Vane Shear and Atterberg Limit Tests A series of standard geotechnical tests were performed to provide preliminary characterization of glyben. Compaction tests were conducted in accordance with ASTM D-698 on glyben mixtures with glycerin contents (g/c) of 35%, 37.5 %, 40 %, 42.5%, 47.5 % and 50%. In conjunction with the compaction tests, shear vane tests were performed according to ASTM D-2573 to measure the shear strength of glyben. For the vane shear tests, glyben was compacted into a 20cm deep stiff metal container (30 cm× 30 cm) to 95 % of the maximum bulk density. Then vane measurements (Pilcon, 19-01) were taken in the container over a period of time while the glyben cured. In addition, glyben mixtures with different (g/c) ratios were prepared and the liquid limit (LL) and plastic limit (PL) were determined in accordance with ASTM D-4318.
2.3.3 Cyclic Triaxial Testing A Wykeham Farrance cyclic triaxial apparatus was used for the study. The triaxial apparatus is a digitally controlled, servo-pneumatic, closed-loop system, which controls three parameters: axial stress, confining pressure and back pressure. Axial load is applied by a double acting digitally controlled 5 kN pneumatic actuator and a co-axially mounted displacement transducer provides a feed back signal to the control system for precise displacement control and data acquisition. Although the actuator can generate frequencies up to 70 Hz, the testing frequency is dependent on the type of sample tested. In this
14 study, strain controlled testing was used in accordance with ASTM D-3999 (Method B). Tests were performed on glyben specimens with a (g/c), percent glycerin by mass, of 40 %, 42.5 %, 45 % and 47.5 %. During each test, a specimen was placed on the triaxial pedestal with a top cap. A latex membrane was placed over the specimen using o-rings to seal the membrane against the top cap and base pedestal. Finally, the triaxial cell was filled with water, the top cap was connected to the actuator and the cell water was pressurized to the desired cell pressure, σ c . Backpressure was not applied during the tests (i.e. the backpressure valve was open to air). This was considered to be more representative of conditions during scaled physical model tests, where glyben is compacted in a laminar shear box and tested either at 1 G or in a centrifuge without application of back pressure. The cyclic triaxial tests were carried out at cell pressures, σ c , of 50, 100, 200 and 300 kPa using a sinusoidal peak-to-peak strain controlled loading applied to obtain axial strain amplitudes of 0.1%, 0.2%, 0.4%, 1%, 2%, 5% and 10%. Table 2.1 provides a summary of the tests. In total, twenty-one glyben specimens and one bentonite-water specimen were tested and the dynamic properties were measured using three different procedures. For Procedure 1, individual glyben specimens were placed in the triaxial cell and the cell pressure was subsequently ramped from 50 to 300 kPa. At each cell pressure, the dynamic properties were measured at shear strain amplitudes of 0.1%, 0.2%, 0.4%, 1%, 2%, 5% and 10% in accordance with ASTM D3999 (Method B). This procedure, which is referred to as ramped cell pressure and ramped shear strain amplitude in Table 2.1, was used during testing of specimen Ct-1 to study the effect of confining pressure on the dynamic properties of glyben. For Procedure 2, specimens were placed in the cyclic
15 triaxial cell and the cell pressure was held constant while the dynamic properties were measured at shear strain amplitudes of 0.1%, 0.2%, 0.4%, 1%, 2%, 5% and 10% (e.g. Cell pressure held constant and shear strain amplitude ramped). Procedure 2 was used to study the influence of thixotropy on the dynamic response of specimens Tx-1, Tx-2, Tx-3, the effect of shear strain amplitude on the response of specimens St-1, St-2, St-3, St-4, temperature effects on specimens T-1, T-2 and to investigate measurement repeatability using specimens R-1, R-2, R-3 and R-4, respectively. Finally, select specimens were tested individually at constant cell pressure using only one shear strain amplitude. This procedure, which is labeled Procedure 3 in Table 2.1, was performed on specimens V-1, V-2 and V3 to verify the results obtained using Procedures 1 and 2 described above. In addition, Procedure 3 was used during tests conducted on specimens Mv-1 and Mv-2 to study the effects of consolidation on the dynamic properties of glyben (see Table 2.1). For each shear strain level and consequent data point, twenty load cycles were used to measure the shear modulus and damping ratio. Figure 2.1 shows a typical hysteresis loop obtained from the testing. The dynamic shear modulus, G , and damping ratio, ξ , were obtained from each hysteresis loop as illustrated in Figure 2.1. Full details of the data interpretation for these tests can be found in Turan et al. (2006).
2.3.4 Bender-Extender Element Tests Bender elements (see Viggiani and Atkinson 1995, Jovicic et al. 1996, Lee and Santamarina 2005) were used to measure the small-strain dynamic properties of glyben. In this study, however, a bender-extender element system was used (manufactured by IPC Global), which is capable of generating square, sinusoidal and user defined compressionwaves and shear-waves (P-waves and S-waves). In this test program, sinusoidal p-waves
16 and s-waves were generated at frequencies of 0.33, 0.5, 1, 2 and 5 kHz and the corresponding wavelengths were measured. A final measurement was then made using a frequency that produced a wavelength equal to about half the sample thickness. This approach has been reported to minimize near-field effects in bender element test (see Viggiani and Atkinson 1995). For each test, 100mm diameter and 100mm thick cylindrical specimens were prepared by compacting glyben into a split mould to achieve 95% of the maximum bulk density and tests were performed on both unconfined specimens and confined specimens (in a triaxial cell). For each bender element test, a glyben specimen was placed on a triaxial pedestal that had a p-wave and s-wave transmitter embedded in it. A top cap equipped with an embedded receiver was placed on the top of each specimen.
The tips of both the
transmitter and receiver penetrated 3mm into the specimen. For confined tests in the triaxial cell, a latex membrane was placed over the specimen with o-rings on both the top cap and bottom pedestal to seal the specimen and to permit application of cell pressure. Unconfined specimens were tested in the same manner but without applying a membrane or cell pressure. The primary measurement from bender element tests is the peak to peak arrival times of s-waves, TS , and p-waves, TP , and the distance, d , between the transmitter and receiver tips (e.g. Viggiani and Atkinson 1995). From d , TS and TP , the s-wave velocity, VS , and p-wave velocity, VP , can be calculated from which the small-strain dynamic shear modulus, G max , and Poisson’s ratio, ν may be deduced. Turan et al. (2006) gives details of typical p-wave and s-wave traces and their interpretation.
17
2.3.5 Resonant Column Tests The resonant column is widely used to measure the small-strain dynamic properties of soil. A description of the apparatus and applicable procedures can be found in Drnevich et al. (1978) and Morris and Delphia (1992). In this study, resonant column tests were performed on glyben specimens with (g/c) = 45% in accordance with ASTM D-4015 using torsional loading. These tests were performed according to Procedures 1 (ramped cell pressure and ramped shear strain amplitude) and 2 (constant cell pressure and ramped shear strain amplitude) described above for cyclic triaxial tests. Specimen preparation for resonant column tests was identical to that described above for the triaxial tests. First, 70mm diameter and 145mm high specimens were prepared by compacting glyben into a split mould to achieve 95% of the maximum bulk density. Then, the specimen was assembled in the resonant column and a latex membrane was placed over the specimen and sealed to the bottom pedestal and top loading cap using orings.
Procedure 1 was used to test specimen Cr-1 (see Table 2.1) using ramped cell
pressures, σ c , of 100, 200 and 300 kPa and ramped shear strain amplitudes ranging from 0.003 to 0.12 %. The tests performed on Cr-1 were used to study the effect of confining pressure on the dynamic properties of glyben. Specimen Src-1 (see Table 2.1) was tested according to Procedure 2 using a cell pressure of 100 kPa and shear strain amplitudes that were ramped from 0.003 to 0.12 %. The results from tests on Specimen Src-1 were used to study the effect of shear strain amplitude on the shear modulus and damping ratio. From the resonant column test, the fundamental angular frequency, ω n , is measured and the shear wave velocity, Vs , is calculated from ω n (see Turan et al. (2006) for additional details).
18
2.4 Results 2.4.1 Compaction, Vane Shear Strength and Gmax/Cu The results of Standard Proctor compaction and vane shear test are summarized in Figure 2.2. The results summarized in this figure correspond to the maximum bulk densities from each mixture, not the maximum dry density. The maximum bulk density of glyben was 1765 kg/m3 for mixtures with (g/c)=40%. In addition, for the investigated range of (g/c), there is a linear increase in the vane shear strength versus decreasing glycerin content. Natural soils exhibit a similar increase in strength with decreasing water content. The vane shear strength of glyben was found to range from 12 kPa to 64 kPa for glycerin contents (g/c) ranging from 50% to 35%, respectively (see Figure 2.2). Thus, the glycerin content by mass (g/c) may be varied to achieve a wide range of shear strength. Table 2.2 summarizes the small strain shear modulus of glyben versus bulk density. The Gmax values were measured using bender elements. As shown Table 2.2, the Gmax/Cu ratio of Glyben was found to vary from 224 at a bulk density of 1645.4 kg/m3 to 306 at a bulk density of 1676 kg/m3. The Atterberg limits of glyben were also determined. The liquid limit (LL), plastic limit (PL), and plasticity index (PI) were found to be 59, 34 and 25, respectively.
2.4.2 Thixotropic Effects The thixotropic behavior of glyben was investigated using a combination of vane shear and cyclic triaxial tests. Figure 2.3 compares the vane shear strength of glyben, at (g/c) = 47.5 %, with the vane shear strength of bentonite-water prepared with a water content of 65 %. The different pore fluid contents were required to obtain equal vane
19 shear strength (e.g. about 18 kPa after 10 days), which is often a scaled parameter in scaled model tests. As shown in Figure 2.3, glyben reached a steady-state vane shear strength of 18 kPa in 4 days whereas it took 9 days for the vane shear strength of the bentonite-water mixture to equilibrate. The shear strength of glyben increased by 12.5 % after mixing, whereas the strength of the bentonite-water mixture increased by about 10% (Figure 2.3). Consequently, there are significant thixotropic increases in the vane shear strength for both glyben and the bentonite-water mixture. The timeframe over which the thixotropic changes occur is longer for bentonite-water than for glyben. Figure 2.4 shows the results of cyclic triaxial tests performed, 1 day, 5 days and 20 days after mixing bentonite and glycerin. The shear modulus and damping ratio are plotted in Figure 2.4 versus shear strain amplitude for glyben with (g/c) = 47.5 %. The results indicate that there is a time dependent increase in shear modulus of about 32 % over the first 5 days after mixing for a shear strain amplitude, γ , of 0.2%. The damping ratio decreased by about 21% at the same level of shear strain amplitude over the same time period (5 days). However, from 5 days to 20 days, the results in Figure 2.4 show that there are very minor changes in the shear modulus and damping ratio of glyben. These changes, which may potentially be due to some diagenetic process, would introduce some small but tolerable experimental error in scaled model tests.
2.4.3 Effect of Shear Strain Amplitude Figure 2.5 shows variation of the modulus ratio, G / G max , versus shear strain amplitude for the various glyben mixtures studied. Modulus ratio measurements were obtained at both low and high shear strain amplitudes. For comparison purposes, this
20 figure also shows typical curves of G / G max versus shear strain amplitude for natural soils from Vucetic and Dobry (1991) and Ishibashi and Zhang (1993) corresponding to a plasticity index (IP) of 25%.
As discussed above, the tests undertaken in this study were
performed at about 95% of the maximum bulk density of each mixture (see Fig. 2.2) as determined by standard Proctor compaction tests. Figure 2.5 shows four significant trends with respect to the dynamic shear modulus of glyben for tests undertaken at a confining stress, σc , of 100kPa. First, at high shear strain amplitudes (cyclic triaxial tests), the measured modulus ratio, G / G max , is close to that of natural clays with IP=25%. Second, the effect of (g/c) on G / G max is not that significant for glycerin contents between 42.5% and 47.5%. Third, at low shear strain amplitudes (resonant column tests), the modulus ratio, G / G max , plots closest to the curve for natural clay obtained from Ishibashi and Zhang (1993). Fourth, there is a separation or gap in the data from the resonant column and cyclic triaxial measurements. This can be attributed to the difference in mode of loading in resonant column compared with the cyclic triaxial apparatus and the different excitation frequencies (Kim et al.1991, Stokoe et al.1995, D’Onofrio et al. 1999, Matešić and Vucetic 2003). Figure 2.6 summarizes the damping ratio, ξ , versus shear strain amplitude for tests conducted at a confining pressure, σc , of 100 kPa at both low and high shear strain amplitude. In addition, curves from Vucetic and Dobry (1991) and Ishibashi and Zhang (1993) corresponding to IP=25% are also presented for comparison purposes. Referring to Figure 2.6, it can be seen that the damping ratio of glyben is significantly higher than that expected for natural clays. At a shear strain amplitude of 0.02%, the damping ratio is about 0.15 whereas natural soils lie within the range of 0.02 and 0.06. These results, in
21 terms of the high damping ratio, are similar to the findings of Rayhani and El Naggar (2006). In addition, results for bentonite and water are also plotted in Figure 2.6. It can be seen that the damping ratio of bentonite and water mixtures is comparable to that of natural clays at low shear strain amplitudes. Thus, glyben has a damping ratio that is significantly higher than that of natural soils due to the viscosity of glycerin as discussed below in the section on temperature effects.
2.4.4 Effect of Confining Stress Cyclic triaxial tests were also conducted on glyben specimens with (g/c) of 47.5 % to investigate the effect of confining stress on the dynamic properties. Figure 2.7 shows the dynamic shear modulus and damping ratio measured at confining stresses of 50, 100, 200, 300 and 500 kPa and shear strain amplitudes of 0.2 %, 0.4 % and 1 %. It should be noted that these tests were undertaken immediately after application of isotropic confining stress without allowing time for significant consolidation of the glyben. The consequence of this will be discussed later in this chapter. From Figure 2.7, it can be seen that there is a clear increase in the dynamic shear modulus as the confining pressure increases. Conversely, the damping ratio decreases as the confining pressure increases. This type of behavior is commonly encountered in natural soils (e.g. Teachavorasinskun et al. 2002 and Cai and Liang 2004). Similar behavior is evident from the results of resonant column tests shown in Figure 2.8. The resonant column results show a similar effect of confining pressure on the dynamic stiffness and damping properties of glyben for (g/c)=45 % as compared to (g/c)=47.5 % in the cyclic triaxial tests.
22
2.4.5 Influence of the Number of Cycles Figure 2.9 summarizes the effect of the number of loading cycles on the dynamic shear modulus and damping ratio of glyben with a (g/c)=42.5%. The triaxial tests were performed at a confining pressure of 100 kPa, a frequency of 1 Hz and shear strain amplitude of 1%. A relatively high shear strain amplitude was used because it was considered to be a severe test of the impact of cycles on the dynamic properties of glyben. From Figure 2.9, it can be seen that the number of cycles has a relatively small impact on both the dynamic shear modulus and damping ratios for the conditions considered. The dynamic shear modulus was found to vary from 2320 kPa to 2370 kPa and the damping ratio varied from 0.20 to 0.21. These variations are relatively small and in the order of ±1% and ±5% for the shear modulus and damping ratio, respectively. Consequently, the dynamic response of glyben does not appear to be strongly affected by the number of loading cycles for at least up to 500 cycles. Such behavior suggests that glyben is not structured like some natural soils (e.g. Leroueil and Vaughan 1990).
2.4.6 Temperature Effects It has been shown that glyben has a damping ratio that is considerably higher than that of natural soils. This could be attributed to the different physical properties of glycerin compared to water (the normal pore fluid). Table 2.3 summarizes the bulk modulus, viscosity, dielectric constant and unit weight of both glycerin and water. From Table 2.3, it can be seen that the bulk modulus of water and glycerin are comparable. However, the viscosity of glycerin is several orders of magnitude greater than that of water (Dorsey, 1940). In addition, the viscosity of glycerin changes significantly between 20.3°C to
23 37.8°C and as a result, temperature could have a significant effect on the engineering properties of glyben. Cyclic triaxial tests ( σ c = 100 kPa) and unconfined bender element tests were performed to investigate the effect of temperature on the dynamic properties of glyben at low and high strain amplitudes. The results of these tests are summarized in Figures 2.10 and 2.11. For the bender element tests, two different procedures were adopted to measure the influence of temperature on the small-strain dynamic modulus of glyben. The first test procedure involved heating a glyben specimen with (g/c) = 47.5 % to 40°C in an oven for 24 hrs. The specimen was subsequently removed from the oven and bender element tests were performed on the specimen as it cooled in air to 22°C. A thermocouple was inserted into the core of the sample to measure the internal temperature. Based on a finite element analysis of the test (Turan et al., 2006), the thermocouple provides an approximate measurement of the internal temperature of the specimen due to the temperature gradients that develop during sample cooling. In addition to the cooling test, four specimens were heated in an oven to 22°C, 25°C, 30°C and 37°C respectively for 24 hours and tested immediately upon removal from the oven. The results obtained from both of these test procedures are plotted in Figure 2.10. As shown in Figure 2.10, temperature has a significant effect on the small strain dynamic shear modulus of glyben.
At 22°C, the small strain dynamic shear
modulus, G max , is 5159 kPa whereas it decreases significantly to 2632 kPa at 37°C. The decrease in Gmax is greater than 45% over the temperature range from 22°C to 37°C.
24 Figure 2.11 summarizes the results of cyclic triaxial tests undertaken at temperatures of 23°C and 28°C. For this series of tests, the triaxial specimen and cell water were heated to the desired temperature prior to measuring the cyclic properties. Figure 2.11 shows similar trends in behavior as shown in Figure 2.10. For all shear strain amplitudes, there is at least a 10% reduction in the dynamic shear modulus of glyben when the temperature is increased from 23°C to 28°C. Temperature has a similar effect on the damping ratio where the damping ratio is typically 7 to 10% higher at 23°C compared with that measured at 28°C. The results of cyclic triaxial and bender element tests illustrate the significant influence of temperature on the dynamic properties of glyben. Since only the viscosity of glycerin is strongly influenced by temperature (see Table 2.3), it appears that variations in the damping ratio and shear modulus of glyben versus temperature can be attributed to variation of the viscosity of glycerin in the pore space and in the viscous double layer. (glycerin is a polar molecule). Figure 2.12, which shows the damping ratio of glycerin versus pore fluid viscosity, further suggests a correlation between pore fluid viscosity and variations in the damping ratio of glyben.
2.4.7 Repeatability of Dynamic Properties A series of unconfined bender element and confined cyclic triaxial ( σ c =100 kPa ) tests were conducted on glyben specimens with (g/c) = 47.5% to assess the reproducibility of the laboratory results. For each type of test, glyben specimens were prepared from three different batches of bentonite and glycerin. Each test specimen was compacted to 95% of the maximum bulk density (see Table 2.2) and then tested using either bender elements or a cyclic triaxial apparatus. Table 2.4 summarizes the bender
25 element results and Figure 2.13 summarizes the results of cyclic triaxial tests conducted at shear strain amplitudes between 0.1% and 10%. From Table 2.4, it can be seen that measurements of the small strain dynamic properties of glyben were generally reproducible for the limited number of tests performed. The maximum variation was about 3% for tests conducted at a frequency of 0.33 kHz. From Figure 2.13, it can be seen that measurements of the large strain dynamic modulus and damping ratio were also fairly reproducible; although less reproducible than the bender element results. Using the cyclic triaxial apparatus, the measured dynamic modulus tended to vary by not more than ±50 kPa at all levels of shear strain. In addition, the percent variation in the measured parameters tended to increase from about ±3% at a shear strain amplitude of 0.2% to about ±15% at a shear strain amplitude of almost 10%. Such variations are typical of soils.
2.4.8 Consolidation Behavior of Glyben To conclude, the consolidation response of glyben is summarized in this section. Figure 2.14 compares the consolidation response of a typical bentonite-water specimen and glyben specimen during isotropic consolidation. Both specimens were prepared with the same void ratio (see Fig. 2.14), placed in a cyclic triaxial apparatus without lateral strip drains and isotropically consolidated for 10 days at a cell pressure of 200kPa. The axial and radial strains were measured during compression to obtain volumetric strain. Again, backpressure was not applied during the consolidation phase to simulate conditions similar to those in scaled model tests.
The large strain shear modulus
(γ=0.1%) and damping ratio were measured periodically during consolidation and the
26 shear wave velocity was measured before and after consolidation.
Shear modulus
measurements are also presented in Figure 2.14 as described below. Referring to Figure 2.14, the volumetric response of bentonite-water after application of a hydrostatic confining pressure of 200kPa is fairly typical and can be interpreted using conventional consolidation theory.
From the measured response, the coefficient of
consolidation of the bentonite-water specimen is 6.86×10-6 cm2/s. For the glyben specimen, there is also time-dependent volumetric strain after application of isotropic confining stress, which can likewise be interpreted with conventional consolidation theory. Since glycerin is a polar molecule with a dielectric constant comparable to that of water (see Table 2.3), it is expected that glycerin should form a double layer with bentonite and that the resultant glyben mixture would consolidate with time after the application of confining stress. Thus, Figure 2.14 shows the interpreted degree of consolidation of glyben versus dimensionless time, Tv=cvt/d2. To derive the percent consolidation of glyben, it was assumed that the drained bulk moduli of the bentonite-water and glyben specimens are equal at equal void ratio (Note: 100% consolidation of the glyben specimens could not be achieved in a practical time). From this interpretation, it can be seen that the degree of consolidation for glyben after 10 days is approximately 21% (see the symbols in Fig. 2.14).
In addition, the
coefficient of consolidation, cv, for the glyben specimen is approximately 4.96×10-9cm2/s, which is about 1/1382 times the cv of bentonite-water. The ratio of cv for bentonite-water versus cv for glyben is comparable to the ratio of the viscosity of water to glycerin (1/1244 at 23°C). Overall, the consolidation process of glyben appears to be much slower than that of bentonite-water.
Furthermore, the slow rate of consolidation may be
27 attributed primarily to the high viscosity of glycerin noting that there are probably other factors affecting the response such as variations of the glycerin-bentonite double layer thickness, the characteristics of the double layer and differences in the free pore space available for pore fluid flow. Lastly, changes in the dynamic properties of glyben during isotropic consolidation in a triaxial cell are presented in Figure 2.14. Large strain shear modulus, G, values obtained from cyclic triaxial tests at the start of the consolidation (t=0), and at 4 and 9 days after the start of consolidation are denoted by the drop down arrows in this figure. In addition, shear wave velocity measurements made before and after consolidation using bender elements are presented in the lower left corner of Fig. 2.14. Table 2.5 shows additional measurements of G during isotropic consolidation from resonant column tests. From the bender element results in Figure 2.14, it can be seen that the shear wave velocity of glyben changed by about 1.9% due to the time-dependent volume change that occurs during 9 days of consolidation. Similarly, there is a corresponding 8% increase in the large strain (γ=0.1%) dynamic modulus, G, of glyben over the same timeframe. Thus, the time-dependent compression of glyben that occurs after application of confining stresses is expected to introduce some experimental error in scaled model tests. For 1-G model tests, confining stresses are negligible and similarly the volumetric compression of glyben should be negligible as well. Thus, it would be sufficient to account for thixotropy and temperature effects alone in 1G model tests.
For n-G
centrifuge tests, however, confining stresses are significant. Fortunately, the timeframe for most centrifuge tests is less than about 1 hour. In addition, accounting for typical drainage paths in n-G model tests, the degree of consolidation and consequent change in
28 the dynamic properties of glyben would be much less than 8% with proper experimental design. For conventional soils, consolidation effects are more significant as shown in Fig. 2.14, which would require full consolidation of the material before testing to reduce experimental error adding considerable time for both 1-G and centrifuge tests.
2.5 Summary and Conclusions Glyben is an artificial soil comprising glycerin mixed with water and it is suitable for modeling the undrained response of cohesive soils, only, during scaled model tests conducted at 1-G or n-G in a centrifuge. This chapter has presented the results of an experimental investigation into the effect of time (or thixotropy), temperature, strain amplitude and cyclic stress history on the mechanical properties of glyben. The testing program described above comprised vane shear tests, compaction tests, cyclic triaxial tests, bender element tests, resonant column tests and isotropic consolidation tests and the results should be sufficient to assist with experimental design of scaled model tests at 1-G and n-G in a centrifuge. The following is a summary of the results and conclusions arising from this study. 1. The vane shear strength of glyben decreases as the glycerin content (g/c) increases. The vane shear strength of natural clays exhibit a similar decrease with increasing moisture content. 2. The maximum density of glyben in Standard Proctor Compaction tests was 1765 kg/m3 at a glycerin content (g/c) of 40%. 3. There were significant thixotropic changes in the vane shear strength, dynamic shear modulus and damping ratio of glyben during the first five days after mixing
29 bentonite and glycerin. There were small and tolerable changes in these properties beyond five days after mixing. Thus, it is concluded that scaled model tests should ideally be undertaken after allowing sufficient time for thixotropic changes to take place. 4. The modulus ratio, G / G max , of glyben is generally within the normal range for natural clays for shear strain amplitudes between 0.2 and 10%. For strain amplitudes between 0.01% and 0.2%, G / G max is slightly higher than that expected for natural clays. Such behavior is satisfactory for use in scaled model tests simulating cohesive soil response. 5. There is a step or gap in the modulus ratio, G / G max , of glyben at 0.2% shear strain amplitude (see Figure 2.5) which can be attributed to the different modes and frequencies of loading used in resonant column tests (torsion at about 20 Hz) versus cyclic triaxial tests (compression at 1Hz). 6. The damping ratio,
ξ , of glyben is higher than that of natural soils for all levels of
shear strain amplitude investigated. This has to be accounted for when interpreting the results of dynamic tests at small shear strain amplitudes using glyben. 7. The damping ratio and shear modulus of glyben are dependent on the confining stress. As the confining stress increased the damping ratio decreased and the dynamic shear modulus increased. Changes in the damping ratio and dynamic modulus were found to be significant for confining stresses up to 200 kPa and 300 kPa, respectively.
30 8. The dynamic shear modulus, G , and damping ratio,
ξ , of glyben were not
significantly affected by the number of loading cycles (from 1 to 500 cycles) for the high level of shear strain amplitude investigated. This behavior would permit multiple dynamic tests from a single scaled model improving the economics and efficiency of such tests. This is one advantage of glyben over other model soils. 9. Temperature has a significant effect on the dynamic properties of glyben. From Figures 2.10 and 2.11, G max , G and ξ varied by as much as 20% over the temperature range 23°C to 28°C. From this behavior, it is concluded that the temperature effects should be accounted for and/or the temperature controlled during the scaled model tests. 10. Glyben exhibits volume change versus time after application of confining stresses, which can be interpreted with conventional consolidation theory. The coefficient of consolidation of glyben is approximately 4.96×10-9 cm2/s, which is about 1/1382 times that of coefficient of consolidation of bentonite-water. In addition, the ratio of cv is comparable to the ratio of the viscosity of water to the viscosity of glycerin (1/1244 at 23ºC). 11. There is 8% change in the small strain dynamic properties of glyben with time during the first 9 days after application of confining stresses. These changes are due to the time-dependent consolidation of glyben. Although 8% variation of the dynamic properties appears to be significant, it is possible to design and conduct centrifuge tests, which control such changes to tolerable levels by limiting the test duration and controlling the drainage path of the model.
31 12. Finally, glyben has the following advantages over other model soils. First, it can be compacted into place instead of resedimented in a slurry form. This improves the ease of handling.
Second, it consolidates at a very slow rate after the
application of confining stress, which can be used during experimental design to avoid a prolonged consolidation phase during spin up in a centrifuge. Lastly, glyben does not desiccate significantly with time and it can be used multiple times during tests since its dynamic properties do not undergo permanent changes at large strain levels and load cycles. This last advantage permits multiple tests to be performed on a single scaled model, without significant alteration of the dynamic response of the model soil.
32
References Arango-Greiffenstein, I. 1971. Seismic stability of slopes in saturated clay. Ph.D. Dissertation, Univ. of California, Berkeley, CA Biscontin, G., and Pestana, J. M. 2001. Influence of peripheral velocity on vane shear strength of an artificial clay. Geotech. Testing J., ASTM, 24 (4): 423-429. Blaney, G., and Mallow, W. 1987. Synthetic clay soil for dynamic model pile tests in dynamic response of pile foundations – experiment, analysis, and observation. Geotech. Spec. Pub. 11, ASCE, 127-148. Bray, J. 1990. The effects of tectonic movements on stresses and deformations in earth embankments. Ph.D. Dissertation, Univ. of California, Berkeley, CA, USA. Burr, J., Pender, M., and Larkin, T. 1997. Dynamic response of laterally excited pile groups. J. Geotech. And Geoenv. Eng., ASCE, 123(1): 1-8. Cai, Y.Q., and Liang, X. 2004. Dynamic properties of composite cemented clay. Journal of Zhejiang University Science, 5(3): 309-316. D’Onofrio, A., Silvestri, F., and Vinale, F. 1999. Strain rate dependent behavior of a natural stiff clay. Soils Found., 39(2): 69–82. Dorsey, N.E. 1940. Properties of ordinary water-substance. Reinhold Pub. Corp, New York, p. 184. Drnevich, V. P., Hardin, B. O., and Shippy, D. J. 1978. Modulus and damping of soils by resonant-column method. Spec Tech Publ. 654, 91-125, ASTM, Symp on Dyn. Geotech. Test, Denver, CO. Huck, J.R., Noyel, G. A., and Jorat, L. J. 1988. Complex permittivity and relaxation time of
33 supercooled aqueous dielectrics. Proc. in 5th International Conference on Dielectric Materials, Measurements and Applications, Canterbury, UK, 21-24. Iskander, M. G., Liu, J., and Sadek, S. 2002. Transparent amorphous silica to model clay. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 128 (3): 262-273. Ishibashi, I., and Zhang, X. 1993. Unified dynamic shear moduli and damping ratios of sand and clay. Soils and Foundations, 33(1): 182-191. Jovicic, V., Coop, R., and Simic, M. 1996. Objective criteria for determining Gmax from bender element tests. Geotechnique, 46(2): 357–362. Kenny, M. J., and Andrawes, K. Z. 1997. The bearing capacity of footings on a sand layer overlying soft clay. Geotechnique, 47(2): 339–345. Kim, D. S., Stokoe, K. H., and Hudson, W. R. 1991. Deformational characteristics of soils at small to intermediate strains from cyclic tests. Research Rep. No. 1177-3, Center for Transportation Research, Bureau of Engineering Research, Univ. of Texas at Austin, Tex. Ko, H., Atkinson, R., Goble, G., and Ealy, C. 1984. Centrifugal modeling of pile foundations. In Analysis and Design of Pile Foundations, ASCE, 21-40. Kovacs, W. D. 1968. An experimental study of the response of clay embankments to base excitation. Ph.D. Dissertation, Univ. of California, Berkeley, CA. Lazarte, C. 1996. The response of earth structures to surface fault rupture. Ph.D. Dissertation, Univ. of California, Berkeley, CA. Lee, J. S., and Santamarina, J. C. 2005. Bender elements: performance and signal interpretation. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 131(9): 1063–1070.
34 Leroueil, S., and Vaughan, P.R. 1990. The general and congruent effects of structure in natural soils and weak rocks. Geotechnique, 40(3): 467-488. Matešić, L., and Vucetic, M. 2003. Strain-rate effect on soil secant shear modulus at small cyclic strains. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 129(6): 536.
Mayfield, B. 1963. The performance of a rigid wheel moving in a circular path through clay. Ph.D. Dissertation, University of Nottingham, UK. Meymand, P. J. 1998. Shaking table scale model tests of nonlinear soil-pile-superstructure interaction in soft clay. Ph.D. Dissertation, Univ. of California, Berkeley, CA. Morris, D.V., and Delphia, J.C. 1992. Resonant column testing of dynamic rock properties. Proc., 9th Conference on Engineering Mechanics, ASCE, College Station, TX, 1105. Moss, R., Rawlings, M., Caliendo, J., and Anderson, L. 1998. Cyclic lateral loading of model pile groups in clay soil. Proc., 3rd Conf. Geotechnical Earthquake Engineering and Soil Dynamics, ASCE, Seattle, WA, 494-505. Nunez, I., and Randolph, M. 1984. Tension pile behavior in clay – Centrifuge modeling technique. Proc. Symposium on the Application of Centrifuge Modeling to Geotech. Eng., Manchester, UK, 87-102. Rayhani, M. H. T., and El Naggar, M. H. 2006. Characterization of glyben for seismic applications. Report No. GEOT-3-06, The University of Western Ontario, London, ON, Canada. Seah, T.H. 1990. Anisotropy of resedimented boston blue clay. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA Seed, H. B., and Clough, R. 1963. Earthquake resistance of sloping core dams. J. Soil
35 Mechanics and Foundation Div., ASCE, 89(1): 209-242. Stokoe, K. H., Hwang, S. H., Lee, J. N.-K., and Andrus, R. D. 1995. Effects of various parameters on the stiffness and damping of soils at small to medium strains. Proc., 1st Int. Conf. on Pre-Failure Deformation Characteristics of Geomaterials: Pre-failure deformation of Geomaterials, Balkema, Rotterdam, The Netherlands, 785–816. Sultan, H. A., and Seed H. B. 1967. Stability of sloping core earth dams. J. Soil Mechanics and Foundation Div., ASCE, 93(4): 45-67. Sutherland H. B. 1988. Uplift resistance of soils. Geotechnique, 38(4): 493-516. Tavenas, F., Roy, M., and La Rochelle, P. 1973. An artificial material for simulating champlain clays. Can. Geotech. J., 10(3): 489-503. Teachavorasinskun, S., Thongchim, P., and Lukkunaprasit, P. 2002. Shear modulus and damping of soft Bangkok clays. Can. Geotech. J., 39: 1201–1208. Turan, A., Hinchberger, S. D., and El Naggar, M. H. 2006. Mechanical and thermal behavior of glycerin bentonite mixture. Report No. GEOT-2-06, The University of Western Ontario, London, ON, Canada. Viggiani, G., and Atkinson, J. H. 1995. Interpretation of bender element tests. Geotechnique, 45(1): 149–154. Vucetic, M., Dobry, R. 1991. Effect of soil plasticity on cyclic response. Journal of Geotechnical Engineering, ASCE, 117(1): 89-107.
36
Table 2. 1 Summary of dynamic tests Specimen
Test
(g/c)
Parameter Investigated
Tx-1, Tx-2, Tx-3
Cyclic Triaxial2
47.5%
Thixotropic Effects (Fig. 2.4)
St-1, St-2, St-3, St-4
Cyclic Triaxial2
47.5, 45, 42.5 and 40 %
G and ξ (Figs. 2.5 and 2.6)
Src-1
Resonant Column2
45%
G and ξ (Figs. 2.5 and 2.6)
Ct-1
Cyclic Triaxial1
47.5%
G and ξ versus confining pressure (Fig. 2.7)
Cr-1
Resonant Column1
45%
Effect of Confining Pressure (Fig. 2.8)
Nc-1
Cyclic Triaxial3
42.5%
Effect of Loading Cycles (Fig. 2.9)
T-1, T-2
Cyclic Triaxial2 and Bender Elements
47.5%
Temperature Effects (Figs. 2.10 and 2.11)
R-1, R-2, R-3, R-4
Cyclic Triaxial2
47.5%
Repeatability (Fig. 2.13)
V-1, V-2, V3
Cyclic Triaxial3
42.5%
Verification tests for G and ξ (Figs. 2.5 and 2.6)
Mv-1 (Bentonite and water w=45%)
Cyclic Triaxial3
45%
Coefficient of consolidation (Fig. 2.14)
1
40%
Mv-2
Procedure 1: Cell pressure ramped and shear-strain amplitude ramped at each cell pressure. Procedure 2: Cell pressure held constant, shear-strain amplitude ramped. 3 Procedure 3: Cell pressure held constant, shear-strain amplitude constant. 2
37
Table 2. 2 Variation of Gmax/Cu and bulk density with (g/c) ratio. Gmax/cu
Bulk Density (kg/m3)
40
306.3
1676.8
42.5
268.0
1672.0
45
263.6
1662.5
47.5
224.1
1645.4
Glycerin Content g/c
38 Table 2. 3 Temperature dependant variation of the viscosity and dielectric constant of glycerin and water (from Dorsey, 1940 and Huck et al., 1988).
Material
Viscosity, mPa.s
Bulk Modulus, N/m2
Dielectric Constant
Density, kg/m3
(23°C)
Water
0.940
2.15×109
(23°C)
79 (23°C)
1000
73 (37°C)
0.692 (37°C) Diluted
5.460
Glycerin1
3.42×109
(23°C)
53 (23°C)
1132
48 (37°C)
3.450 (37°C) Glycerin
1170
4.52×109
(23°C) 382 (37°C) 1
50% glycerin and 50% water solution
45 (23°C) 39 (37°C)
1264
39
Table 2. 4 Small strain level reproducibility of dynamic glyben properties (bender element test).
Frequency (kHz)
0.33
0.5
1
2
5
Batch Number
s-wave Velocity (m/s)
p-wave Velocity (m/s)
1
48
100.2
2
47.2
101.4
3
48.5
100.5
1
50.4
100.2
2
49.5
101.4
3
50.4
100.5
1
55.6
100.2
2
55
101.4
3
55.6
100.5
1
58.3
100.2
2
58.6
101.4
3
58.7
100.5
1
60.8
100.2
2
60.5
101.4
3
61.1
100.5
Standard Deviation S-wave
0.66
0.52
0.35
0.21
0.30
40
Table 2. 5 Changes in dynamic properties due to consolidation (resonant column test). Confining Stress Strain Level S-wave Velocity (kPa) (%) (m/s) 5 min 350 0.0025 73.7 7 days 350 0.0025 75.08 1 Time after application of confining pressure in the resonant column. Time1
Damping Ratio 0.143 0.139
41
Figure 2. 1 Typical elastic modulus and damping ratio from hysteresis loop.
42
Figure 2. 2 Variation of compacted bulk density and cohesive strength versus glycerin content
43
Figure 2. 3 Variation of the cohesive strength of glyben and bentonite-water mixture vs. time.
44
Figure 2. 4 Variation of shear modulus and damping ratio vs. time.
45
Figure 2. 5 Normalized shear modulus versus shear strain amplitude.
46
Figure 2. 6 Damping ratio versus shear strain amplitude.
47
Figure 2. 7 Variation of shear modulus and damping ratio with confining pressure at high strain levels.
48
Figure 2. 8 Variation of shear modulus and damping ratio with confining pressure at low strain levels.
49
Figure 2. 9 Variation of shear modulus and damping ratio with number of cycles.
50
Figure 2. 10 The effect of temperature on the shear wave velocity of glyben (g/c = 47.5%).
51
Figure 2. 11 The effect of temperature on the dynamic shear modulus and damping ratio of glyben (g/c = 47%).
52
Figure 2. 12 Variation of damping ratio with pore fluid viscosity.
53
Figure 2. 13 Large strain level reproducibility of dynamic glyben properties.
54 Figure 2. 14 Degree of consolidation vs. dimensionless time for glyben and bentonitewater mixture.
55
CHAPTER 3 PREDICTING THE DYNAMIC PROPERTIES OF GLYBEN USING A MODULAR NEURAL NETWORK (MNN)
3.1 Introduction As discussed in Chapter 2, glyben (Mayfield 1963, Kenny and Andrawes 1997, Rayhani and El Naggar 2006, Turan et al. 2006) is a synthetic soil that possesses characteristics that are well suited for scaled physical model tests. The primary advantage of glyben for such tests are: (i) it consolidates at a very slow rate after application of confining stresses, and consequently it can be used in centrifuge tests without a consolidation period after spin up (ii) it develops a Gibson type soil profile instantaneously after application of centrifugal forces (see Turan et al. 2006), (iii) it is resistant to desiccation due to drying, and (iv) its dynamic properties are not significantly degraded by numerous stress cycles. The dynamic properties of glyben can be varied by altering the ratio of glycerin and bentonite (g/c) in the synthetic soil mixture to simulate the response of prototype soils during shaking. Glyben has been used successfully for various scaled physical model studies involving seismic soil-structure interaction (e.g. Rayhani and El Naggar 2006) and model pile studies (e.g. Kenney and Andrawes 1997 and Sutherland 1988). According to results reported in Chapter 2, the dynamic properties of glyben are strongly affected by temperature, glycerin content, excitation frequency, confining stress, strain amplitude and time. With such complex behaviour, there is a need for an empirical approach that relates the dynamic properties of glyben to these parameters.
56 The objective of this chapter is to describe the architecture and testing of a neural network tool that can be used to estimate the dynamic properties of glyben without the need for extensive testing to gain experience with this material. The MNN was trained using results from Chapter 2 and in this chapter the predicted results are compared with the results of cyclic triaxial tests to test the accuracy of the MNN tool. The absence of empirical methods of estimating the dynamic properties of glyben makes the neural network based approach a useful tool for designing glyben mixtures to simulate prototype soils in scaled model tests. Furthermore, the architecture of the network and approach may be of interest to researchers and engineers trying to develop empirical tools to estimating the dynamic properties of other soils.
3.2 Background Numerous artificial soils have been developed and characterized for use in scaled physical model tests (e.g. Seed and Clough 1963, Tavenas et al. 1973, Blaney and Mallow 1987, Meymand 1998, Moss et al. 1998). However, of the modeling soils developed thus far, glyben (sodium bentonite mixed with glycerin) is one of the least intensively researched. As noted above, glyben comprises a mixture of bentonite and glycerin. The glycerin content, g/c, is defined as the percent glycerin by mass in the synthetic soil mixture. The properties of glyben, such as undrained strength, shear modulus and damping ratio, can be varied by changing the glycerin content (g/c) to achieve desirable soil properties for model studies at 1G or N-G on a centrifuge. Detailed mechanical characterization of glyben is described in Chapter 2.
3.2.1 Artificial Neural Networks Artificial neural networks (ANNs) have been studied intensively and applied to a large number of engineering problems. It has been shown that ANNs are capable of mapping non-
57 linear and complex relationships in nature. For example, Ghaboussi et al. (1991), Goh (1995 and 2002), Shi et al. (1998), Juang and Lu (2002), Yang and Rosenbaum (2002) and Shahin et al. (2004) have applied ANN models to geotechnical engineering problems ranging from predicting ground subsidence due to tunneling to soil liquefaction potential.
Since neural network
algorithms appear to be able to handle different types of complex geotechnical problems, this approach was used in the current study to create a predictive tool to estimate the influence of parameters such as shear strain amplitude, confining stress, excitation frequency, and glycerin content on the dynamic properties of glyben. Generally, the architecture of a supervised ANN consists of an input layer, one or more hidden layers and an output layer (e.g. Lee et al. 2003). The input layer to the network comprises the input variables and the output layer contains the target output vector (real results). At least one hidden layer which contains the artificial neurons or processing units is normally used between the input and output layers to assist the network in the learning process (Lee et al. 2003). A supervised ANN typically learns by example through training, where the network is presented with training cases (a database) of input values together with the corresponding output values. A properly trained network can model the unknown function that relates the input variables to the output variables, and it can subsequently be used, by means of testing, to make predictions for a given set of previously unseen input parameters where the output values are unknown (Kurup and Griffin 2006). In training, each input received by the input layer is multiplied by a random weight and these products are summed together. This summation is imposed on neurons in the hidden layer(s) and processed using an activation function (Goh, 2002). Learning occurs by iteratively modifying the connection weights until the difference
58 between the predicted and target output values is minimized to an acceptable error threshold value. Thus, underlying the architecture of an ANN is a learning algorithm (see Patterson 1996, Fausett 1994, Haykin 1994) that permits adjustment of the connection weights without loosing what the ANN has learned by previous experience. The architecture of a feed-forward ANN has a significant impact on its performance and its ability to learn complex behavior (Javadi 2006). A feed-forward neural network that comprises only an input layer and a linear output neuron (e.g. without a hidden layer or hidden neurons) is an affine function of its input (Dreyfus 2005). The addition of hidden layer(s) and neurons on each hidden layer of a feed-forward ANN enhances the ability of neural networks to learn progressively more complex and non-linear relationships (Zealand et al. 1999). In general, the number of hidden layers and neurons required in an ANN increases with increasing non-linearity or complexity of the phenomenon that is to be learned by the network (Hecht-Nielsen 1987). Other than these general characteristics, there is no widely accepted procedure for determining the number of hidden layers and neurons required to learn a particular behaviour. It is, however, generally stated that a feed-forward ANN with a continuous and differential transfer function and one hidden layer can approximate any continuous function and with two hidden layers can approximate any computable function (Cybenko 1988 and Lapedes and Farber 1987).
3.3 Methodology 3.3.1 Input and Output Parameters In this chapter a modular neural network (MNN) algorithm was used (see Fig. 3.1). Since each output parameter exhibits a distinct and complex response to the variation of each input
59 parameter, a MNN was expected to be more suitable for predicting the dynamic properties of glyben. In order to develop and train the MNN, input and output vectors were identified. In accordance with Chapter 2, the following input parameters were used: the ratio of glycerin to bentonite by mass (g/c) in the mixture, the shear strain amplitude (γ), the excitation frequency (F), and the confining stress (σ). Temperature (T) and thixotropy or time after mixing (t) also have a strong impact on the behavior of glyben (Chapter 2); however, there was insufficient data to define an accurate MNN which included these variables. Consequently, temperature (T) and time (t) were omitted from the input layer after some trial and error as described below. The outputs of the MNN are the shear modulus, G, and damping ratio, ξ, of glyben. The data used in the training, validation and testing stages of the MNN can be found in Chapter 2. Figure 3.1 shows a schematic layout (architecture) of the MNN.
3.3.2 Modular Neural Networks The advantages of MNNs over global neural networks like multilayer perceptron neural networks (MLP) or clustering neural networks like radial basis function neural network (RBF) are well documented. MNNs overcome some of the disadvantages of global and clustering networks by allowing for the use of higher order computational units to learn complex behavior and by permitting the problem to be divided into simpler sub-problems. Francesco (2004), Shi et al. (1998) and LeCun (1989) noted that the use of a MNN results in an increase in the performance (speed of learning) of the neural network; while other researchers (e.g. Happel and Murre 1994 and Barna and Kaski 1990) have noted that the use of a MNN results in significant improvement in the predictive capacity (accuracy) of a network. A MNN does not have full interconnectivity between its layers. Therefore, a smaller number of weights are required which
60 increases the speed of the learning process. MNNs allow the use of different neural functions (axons) in different locations of the system increasing the flexibility of the network to learn. A well-modulated neural network will lead to a more accurate and faster simulation; however, it is not clear how to best design the modular topology based on the data. A typical MNN comprises input and output layers, one or more neural networks called expert modules (these contain the hidden layers) and a gating network. The output of each expert module is weighted by a gating network (e.g. Ronco and Gawthrop 1995), which permits training of the MNNs’ expert modules in a competitive manner. The architecture of the MNN developed for glyben comprises two expert modules and a gating network (see Figure 3.1). Each expert module was designed as a multilayer perceptron using a back-propagation algorithm (Patterson, 1996, Fausett, 1994, Haykin, 1994). In the backpropagation algorithm, the learning rate, µ , was chosen as 0.9. As noted above, the MNN architecture was developed by trial and error. Thus, the first MNN comprised 7 input nodes (one for each of T, t, σc, γ, F, g/c and N), two expert modules, 2 hidden layers in each module, and 4 and 6 neurons or processing units in the expert modules 1 and 2, respectively. The network also had 2 output layers (for G and ξ) and a gating network (see Figure 3.1). The initial network was subsequently simplified by excluding (t), (T) and (N) in the final design of the MNN (Figure 3.1) for reasons that have been discussed above. For each neuron, Tanh type axons were used (Figure 3.1). The activation function for a Tanhaxon is n −1
f ( xi , w' ) = tanh[ β * ∑ wi .xi ]
[3.1]
i =1
where β is a bias value (assumed to be 1 in this study), w i is a weighting factor, and x i is input from a preceding neuron.
61
3.3.3 Data Set The data comprised the experimental results of Chapter 2, who studied the effect of shear strain levels, confining stresses, temperature, time and cyclic stress history on the dynamic properties of glyben using bender elements, resonant column and cyclic triaxial tests. The total database contained 136 data sets, which are presented in Table 3.1. The training data set had a uniform distribution on the multi-dimensional space of inputs and outputs. In total, 124 sets of data were allocated for training and the remaining 12 sets (approximately 9% of entire data) were used to test the network based on studies by Shi et al. (1998). In order to allocate the training and testing data sets, all 136 data sets were randomized in Excel and then assigned numbers sequentially. A random number generator was used to select the testing sets and the remaining sets were used for training. Table 3.1 shows randomized input data sets used for training the MNN and Table 3.2 shows the testing data sets. All data used in the training and testing stages were obtained from laboratory tests on glyben at a temperature of 23°C and 5 days after mixing so as to remove the effect of temperature, T, and thixotropy, t, from the database.
3.3.4 Training and Testing Training was carried out using random initial connection weights. The threshold value for mean squared error (MSE) was 0.0005 and the learning procedure finished after the network reached the MSE value at the epoch number of 24800. In the testing stage, test data was provided to the network. Testing of the network performance was carried out using 12 data sets that were not used in training (see Table 3.2). The trained network showed good performance in the testing stage as summarized in Figures 3.2 and 3.3, which show close agreement between real data and predictions using the trained MNN. It should be noted that standard multiple regression
62 analysis could not fit the data well with R2 values of 0.8363 and 0.7538 for G and ξ, respectively. However, R2 values for the MNN were 0.98 and 0.94 for G and ξ, respectively. In the following section, the MNN is used to estimate the dynamic properties of glyben for various test conditions. The following sections provide a detailed description of the MNN’s predictive capabilities.
3.4 Dynamic Glyben Properties In this section, the MNN was used to develop mix proportions for glyben to achieve the desired dynamic properties, G and ξ, for a range of confining stresses, frequencies and shear strain amplitudes expected during seismic tests.
3.4.1 Effect of Glycerin Ratio (g/c) and Shear Strain Amplitude (γ) Figures 3.4 and 3.5 show the effect of (g/c) and shear strain amplitude (γ) on the modulus reduction and damping ratio curves generated using the MNN. As noted above, the curves were developed assuming glyben was tested 5 days after mixing, at 23°C, compacted to 95% of the maximum density and tested at a confining stress of 100 kPa. It is also assumed that the properties are required for scaled-model testing at a frequency of 1 Hz. The glycerin content (g/c) was varied from 38% to 47%. From Figures 3.4, it can be seen that there is a reduction of shear modulus and increase in damping ratio with increasing shear strain amplitude. The trends are very close to those presented in Chapter 2. Referring to Figure 3.5, it is evident that increasing (g/c) values cause a slight increase in the damping ratio and a decrease in shear modulus. The MNN generated data captures the degradation of shear modulus and increase of damping ratio with increasing shear strain amplitude.
63
3.4.2 Effect of Frequency (F) It was noted in Chapter 2 that there was an abrupt change in the G/Gmax ratio for data measured using cyclic triaxial apparatus compared with resonant column apparatus. This abrupt change in behaviour was attributed to the different excitation frequencies in each type of test (e.g. cyclic triaxial test versus resonant column test). In this chapter, the MNN was used to filter out the frequency effect on G and ξ of glyben. Figures 3.6 and 3.7 show the MNN predictions with the original shear modulus and damping ratio values reported by Chapter 2 for glyben with a g/c = 45 %. In this case, the MNN was used to generate modulus degradation and damping curves at different frequencies. From Figure 3.6 it can be seen that there is a significant frequency effect on shear modulus at shear strain amplitudes up to 1 %. At 1 Hz, the MNN predictions show good coherence with the cyclic triaxial test results presented in Chapter 2. MNN predictions at 20 Hz follow the resonant column results presented in Chapter 2. However, since resonant column data between shear strain amplitudes of 0.05-0.15% were obtained at frequencies closer to 18Hz, the shear modulus predictions from the MNN corresponding to 20Hz started to deviate from the resonant column results between γ=0.05-0.15%. As can be seen in Figure 3.7 there is almost negligible frequency effect on MNN predicted damping ratios of glyben, which is consistent with that observed in Chapter 2.
3.4.3 Effect of Confining Pressure (σc) Figure 3.8 shows the effect of confining stress, σ, on the dynamic shear modulus, G, and damping ratio, ξ. The MNN data show a similar trend to that measured in Chapter 2. An increase in shear modulus and decrease in damping ratio is observed with increasing confining
64 pressure (Figure. 3.8). Changes in the dynamic glyben properties are insignificant at confining stresses in excess of 200 kPa, which is captured by the MNN.
3.5 Summary and Conclusions This Chapter has presented the architecture of an MNN and compared predicted dynamic properties using the MNN with measured dynamic properties. The MNN was trained using the experimental results obtained from Chapter 2.
The following summarizes the results and
conclusions drawn from this study: 1. The trained MNN showed good performance in the testing stage. 2. Multiple regression analyses were carried out obtaining comparatively low R2 values of 0.8363 and 0.7538 for shear modulus and damping ratio, respectively. Comparatively, R2 values of 0.98 and 0.94 were obtained using the MNN for shear modulus and damping ratio, respectively. Therefore, the MNN performed with better accuracy than multiple regression analysis providing justification for using this approach. 3. The MNN has been used to develop curves that can be used to design glyben mixtures, which should be useful to researchers who are considering using glyben as a model soil in 1-G or N-G centrifuge tests. 4. The MNN generated data reflects the degradation of shear modulus and increase of damping ratio with increasing shear strain amplitudes. Increasing g/c values resulted in slightly increasing damping ratio and decreasing shear modulus.
65 5. From the MNN predictions, a significant frequency effect on shear modulus at shear strain amplitudes up to 1 % was observed. The damping ratio was seen to be relatively unaffected by the excitation frequency. 6. The effect of confining pressure on the dynamic properties of glyben were learned and then simulated by MNN. An increasing effect of confining stress on the shear modulus and a decreasing effect on damping ratio were observed. The effect of confining stresses in excess of 200 kPa was seen to be insignificant. All of the results are consistent with experimental behaviour. Overall, the MNN showed good performance and it was able to satisfactorily predict the dynamic properties of glyben. The architecture and approach described in this chapter may be of interest to researchers and engineers trying to develop empirical tools for predicting the dynamic properties of other soils and/or rock or other complex behaviour often encountered in geotechnical engineering.
66
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67 Goh, A.T.C. 2002. Probabilistic neural network for evaluating seismic liquefaction potential. Canadian Geotechnical Journal, 39: 219–232. Happel, B., and Murre, J. 1994. Design and evolution of modular neural network architectures. Neural Networks, 7: 985-1004. Haykin, S. 1994. Neural networks: a comprehensive foundation. Maxwell Macmillan International, New York. Hecht-Nielsen, R. 1987. Kolmogorov’s mapping neural network existence theorem. First IEEE International Joint Conference on Neural Networks. Institute of Electrical and Electronic Engineering, San Diego, CA, 1-14. Javadi, A.A. 2006. Estimation of air losses in compressed air tunneling using neural network. Tunneling and Underground Space Technology, 21: 9–20 Juang C. H., and Lu P. C. 2002. Predicting geotechnical parameters of sands from CPT measurements using neural networks. Computer-Aided Civil and Infrastructure Engineering, 17: 31-42. Kenny, M. J., and Andrawes, K. Z. 1997. The bearing capacity of footings on a sand layer overlying soft clay. Geotechnique, 47(2): 339–345. Kurup, P.U., and Griffin, E.P. 2006. Prediction of soil composition from CPT data using general regression neural network. Journal of Computing in Civil Engineering, 20(4): 281-189 Lapedes, A., and Farber, R. 1987. How neural nets work. Neural Information Processing Systems. American Institute of Physics, New-York, 442-456. LeCun., Y. 1989. Generalization and network design strategies. Tech. Rep. CRG-TR-894, Connectionist Research Group, University of Toronto, Toronto, ON, Canada.
68 Lee, S.J., Lee, S.R., and Kim, Y.S. 2003. An approach to estimate unsaturated shear strength using artificial neural network and hyperbolic formulation. Computers and Geotechnics, 30:489–503 Meymand, P. J. 1998. Shaking table scale model tests of nonlinear soil-pilesuperstructure interaction in soft clay. Ph.D. Dissertation, Univ. of California, Berkeley, CA. Mayfield, B. 1963. The performance of a rigid wheel moving in a circular path through clay. Ph.D. Dissertation, University of Nottingham, UK. Moss, R., Rawlings, M., Caliendo, J., and Anderson, L. 1998. Cyclic lateral loading of model pile groups in clay soil. In the Proceedings of the 3rd Conference of Geotechnical Earthquake Engineering and Soil Dynamics, Seattle, WA, 3-6 Aug 1998, ASCE, New-York, 494-505. Patterson, D. W. 1996. Artificial neural networks: Theory and applications, Prentice-Hall, Singapore. Rayhani, M. H. T., and El Naggar, M. H. 2006. Characterization of glyben for seismic applications. Geotechnical Research Centre Report-GEOT-3-06, The University of Western Ontario, London, ON, Canada. Ronco, E., and Gawthrop, P. 1995. Modular neural networks: a state of the art. Technical report - CSC-95026, Centre for System and Control, University of Glasgow, Glasgow, UK. Seed, H. B., and Clough, R. 1963. Earthquake resistance of sloping core dams. J. Soil Mechanics and Foundation Div., ASCE, 89(1): 209-242. Shahin M. A., Maier H. R., Jaksa M. B. 2004. Data division for developing neural
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Sutherland, H.B. 1988. Uplift resistance of soils. Géotechnique, 38(4): 493–516. Tavenas, F., Roy, M., and La Rochelle, P. 1973. An artificial material for simulating champlain clays. Canadian Geotechnical Journal, 10(3): 489-503. Turan, A., Hinchberger, S. D., and El Naggar, M. H. 2006. Mechanical and thermal behavior of glycerin bentonite mixture. Geotechnical Research Centre Report-GEOT2-06, The University of Western Ontario, London, ON, Canada. Yang Y. and Rosenbaum M. S. 2002. The artificial neural network as a tool for assessing geotechnical properties. Geotechnical and Geological Engineering, 20: 149-168. Zealand, C.M., Burn, D.H., Simonovic, S.P. 1999. Short-term stream flow forecasting using artificial neural networks. Journal of Hydrology, 214: 32-48.
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Table 3. 1 Randomized data sets used for training. Data Number
g/c
γ
F
σ
G
ξ
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
47.500 47.500 47.500 47.500 47.500 45.000 40.000 47.500 45.000 45.000 40.000 47.500 42.500 47.500 45.000 45.000 47.500 47.500 47.500 47.500 45.000 47.500 47.500 47.500 47.500 47.500 45.000 47.500 47.500 42.500 40.000 45.000 45.000 47.500 45.000 47.500 40.000 47.500 47.500 45.000 45.000 42.500 40.000 47.500
0.005 0.942 0.194 0.985 0.045 0.009 0.100 0.999 0.956 0.105 0.005 0.059 0.005 0.141 0.015 0.003 0.166 0.005 1.005 4.777 0.023 0.082 0.005 0.005 9.434 1.945 1.000 0.183 0.194 0.005 0.195 0.250 0.123 0.210 1.000 0.189 0.974 0.005 0.404 0.020 0.020 0.005 0.400 1.891
1.000 1.000 1.000 1.000 1.000 20.375 1.000 1.000 1.000 17.000 1.000 1.000 1.000 1.000 18.094 20.940 1.000 1.000 1.000 1.000 19.750 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 16.940 1.000 1.000 1.000 1.000 1.000 1.000 20.312 19.062 1.000 1.000 1.000
90.000 100.000 100.000 100.000 300.000 200.000 300.000 50.000 100.000 200.000 300.000 100.000 300.000 100.000 30.000 300.000 100.000 50.000 100.000 100.000 200.000 100.000 70.000 160.000 100.000 100.000 100.000 50.000 100.000 160.000 100.000 300.000 300.000 300.000 100.000 300.000 100.000 300.000 100.000 300.000 100.000 300.000 300.000 100.000
3000.000 973.992 1888.322 1020.793 3200.000 8263.668 11200.000 866.164 1219.619 5752.749 14900.000 1554.607 8000.000 1061.244 6516.986 8728.326 1263.194 2445.000 978.146 472.446 7764.470 1716.690 2600.000 3300.000 279.630 721.223 2238.722 1351.448 1818.322 7200.000 6324.333 3850.000 5712.213 2600.000 2234.383 2020.723 4384.497 3700.000 1385.909 8212.644 7232.935 8000.000 8800.000 735.284
0.148 0.203 0.191 0.228 0.200 0.153 0.175 0.224 0.237 0.223 0.132 0.135 0.135 0.165 0.016 0.146 0.184 0.149 0.207 0.255 0.168 0.151 0.149 0.144 0.267 0.241 0.238 0.143 0.191 0.140 0.208 0.215 0.230 0.275 0.231 0.123 0.233 0.144 0.212 0.163 0.163 0.138 0.257 0.223
71
Data Number
g/c
γ
F
σ
G
ξ
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
45.000 45.000 42.500 42.500 47.500 45.000 45.000 42.500 47.500 47.500 42.500 47.500 47.500 45.000 47.500 42.500 45.000 42.500 40.000 45.000 42.500 45.000 47.500 40.000 47.500 47.500 45.000 45.000 42.500 47.500 40.000 45.000 47.500 45.000 45.000 47.500 45.000 40.000 47.500 40.000 47.500 47.500 47.500 47.500 40.000 45.000 47.500
0.008 1.000 0.127 0.005 0.365 0.004 1.000 0.080 4.791 4.777 9.137 1.000 0.171 0.104 0.191 0.913 1.911 1.919 0.005 9.351 0.045 0.121 0.404 0.005 4.012 0.985 0.010 4.736 0.005 4.043 1.911 1.000 0.182 0.003 0.001 1.971 0.046 9.072 0.184 0.005 2.019 1.011 0.393 0.005 4.508 0.001 9.397
20.812 1.000 1.000 1.000 1.000 20.562 1.000 1.000 1.000 1.000 1.000 1.000 1.000 15.313 1.000 1.000 1.000 1.000 1.000 1.000 1.000 15.875 1.000 1.000 1.000 1.000 19.562 1.000 1.000 1.000 1.000 1.000 1.000 18.375 20.940 1.000 18.750 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 18.531 1.000
300.000 100.000 100.000 90.000 100.000 200.000 100.000 300.000 100.000 100.000 100.000 100.000 100.000 30.000 100.000 100.000 100.000 100.000 30.000 100.000 300.000 100.000 100.000 70.000 100.000 100.000 100.000 100.000 30.000 100.000 100.000 100.000 100.000 30.000 300.000 100.000 200.000 100.000 200.000 160.000 100.000 200.000 100.000 30.000 100.000 30.000 100.000
8621.945 2269.721 4458.524 6200.000 1271.951 8416.050 2239.337 6400.000 411.535 432.446 668.041 939.548 1421.008 4667.649 1716.690 2254.950 895.734 1592.259 8200.000 380.062 7000.000 5016.549 1355.909 10000.000 216.853 993.793 7617.354 555.225 4600.000 279.630 3341.537 2240.885 1600.007 6720.975 8728.326 677.284 6998.100 1448.054 1841.113 14000.000 316.503 1206.378 715.473 2300.000 2164.462 6835.727 293.375
0.151 0.230 0.208 0.141 0.176 0.149 0.238 0.195 0.260 0.255 0.287 0.242 0.136 0.021 0.215 0.245 0.255 0.265 0.138 0.267 0.175 0.231 0.202 0.137 0.238 0.218 0.151 0.262 0.144 0.266 0.256 0.237 0.131 0.015 0.146 0.250 0.187 0.273 0.126 0.132 0.227 0.207 0.201 0.149 0.272 0.014 0.258
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Data Number
g/c
γ
F
σ
G
ξ
92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124
40.000 47.500 47.500 47.500 40.000 45.000 47.500 45.000 45.000 45.000 45.000 40.000 40.000 47.500 42.500 47.500 45.000 45.000 42.500 47.500 40.000 45.000 47.500 47.500 42.500 45.000 47.500 47.500 47.500 47.500 42.500 45.000 47.500
0.008 0.896 9.415 0.381 0.003 0.003 0.429 0.462 0.002 0.050 0.382 0.035 0.399 1.006 0.005 0.015 0.049 0.041 0.020 0.805 0.017 0.005 0.305 0.007 0.005 1.000 0.100 0.381 2.053 0.845 0.331 0.001 0.388
1.000 1.000 1.000 1.000 1.000 19.812 1.000 11.313 20.500 19.000 1.000 1.000 1.000 1.000 1.000 1.000 17.812 16.969 1.000 1.000 1.000 18.590 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 19.750 1.000
300.000 500.000 100.000 100.000 300.000 100.000 100.000 30.000 200.000 300.000 100.000 300.000 100.000 300.000 70.000 300.000 100.000 30.000 300.000 100.000 300.000 30.000 500.000 300.000 200.000 100.000 300.000 300.000 100.000 100.000 100.000 100.000 200.000
14500.000 1491.882 334.125 1331.611 11490.000 7813.295 939.548 2547.386 8365.373 7185.960 1727.013 13000.000 5465.732 1308.963 5800.000 3450.000 6315.431 5731.788 7800.000 515.375 14000.000 6879.175 2101.764 3500.000 7450.000 2254.950 2800.000 1860.288 411.535 677.284 3306.562 7764.470 1670.168
0.135 0.212 0.264 0.172 0.130 0.144 0.216 0.029 0.146 0.191 0.222 0.150 0.225 0.209 0.144 0.170 0.189 0.018 0.157 0.216 0.140 0.014 0.176 0.145 0.139 0.245 0.242 0.169 0.256 0.242 0.228 0.143 0.171
73 Table 3. 2 Data sets used in testing of network g/c 47.5 40 47.5 40 47.5 45 40 45 47.5 47.5 42.5 47.5
γ (%) 0.3873 0.005 0.3807 0.25 4.7027 0.003 0.1 0.0205 9.4153 1.9447 4.584 0.1679
F (Hz) 1 1 1 1 1 1 1 1 1 1 1 1
σ (kPa) 100 100 50 300 100 300 300 100 100 100 100 500
74
Figure 3. 1 General schematics of MNN. HIDDEN LAYER 1
y
HIDDEN LAYER 2
x
g/c γ
AXIOM
EXPERT MODULE 1 (2 Hidden Layers, 4 Neurons)
Σ
F EXPERT MODULE 2 (2 Hidden Layers, 6 Neurons)
σ
G ζ OUTPUT
INPUT
GATING NETWORK
HIDDEN LAYER 1
HIDDEN LAYER 2
75
Figure 3. 2 The comparison of the estimated (MNN) and measured shear modulus of glyben.
76
Figure 3. 3 The comparison of the estimated (MNN) and measured damping ratio of glyben.
77
Figure 3. 4 Variation of MNN predicted shear modulus with g/c and γ.
78
Figure 3. 5 Variation of MNN predicted damping ratio with g/c and γ.
79 Figure 3. 6 Shear modulus degradation curves of glyben at different frequencies.
80
Figure 3. 7 Damping curves of glyben at different frequencies.
81
Figure 3. 8 Variation of MNN predicted dynamic properties with confining pressure.
82
CHAPTER 4 THE INFLUENCE OF PORE FLUID VISCOSITY ON THE DYNAMIC PROPERTIES OF AN ARTIFICIAL CLAY
4.1
Introduction
In order to design earthquake resistant structures founded on soil, engineers must predict the seismic response of the soil and structure, as well as the interactive forces at the soil-structure interface. Soil profiles influence the seismic response of structures by amplifying or attenuating the bedrock motions during propagation of shear waves through the overlying soil. Accordingly, there has been significant research involving ground response and soil-structure interaction during earthquakes over the past few decades. Several studies focused on characterization of the dynamic properties of soft soils subjected to strong seismic shaking including: Tiers and Seed (1968), Hardin and Drnevich (1972a, b) and Vucetic and Dobry (1991) among others. This chapter describes the results of a laboratory study that was performed to characterize an artificial clay mixture, denoted modified glyben, which has important applications in scaled physical model tests. Modified glyben comprises bentonite mixed with water and glycerin, and can be compacted into a flexible or rigid container as a soil bed for 1-G and n-G scaled model tests on a shake table (see Turan et al. 2008a). The viscosity of the pore fluid in modified glyben can be varied from 0.96 mPa•s to 1170 mPa•s by altering the ratio of glycerin-to-water in the pore fluid. This has a pronounced influence on the stiffness and damping characteristics of the material. In this study, modified glyben has been characterized using a series of laboratory tests including compaction, Atterberg limits, shear vane, isotropic consolidation, cyclic triaxial,
83 resonant column and x-ray diffraction. The primary objective was to characterize the dynamic properties of modified glyben with emphasis on the effect of temperature and pore-fluid viscosity on these properties. The following sections provide some background to the study; describe the tests performed and procedures followed and summarize the results and conclusions arising from the test program.
The results show that the coefficient of consolidation and
dynamic properties of modified glyben are strongly influenced by the pore fluid viscosity, which can be varied to achieve dynamic properties similar to natural soils. The results should be of interest to researchers conducting scaled physical model tests at 1-G using a shaking table and at n-G using a centrifuge.
4.2 Background 4.2.1 Soil-structure Interaction It is common practice to idealize earthquakes as a time-history of horizontal displacement in the bedrock, which induces vertically propagating shear-waves in the overlying soil. Figure 4.1 depicts these conditions. Depending on the properties of the soils overlying bedrock, ground motions may be amplified at the ground surface where structures are typically built. During an earthquake, the overall response of the structure shown in Figure 4.1 may be strongly influenced by soil-structure interaction. The problem depicted in Figure 4.1 can be studied economically using a scaled physical model similar to that shown in Figure 4.2. Referring to Fig. 4.2, an earthquake can be simulated using a shaking table in conjunction with a rigid or flexible container filled with a model soil to create vertical or 1-dimensional shear-wave propagation (Lin and Wang, 2006; Gibson, 1997). Typically, the model soil must be placed into the container so that it possesses scaled properties
84 identical to those of the full-scale soil deposit (Lin and Wang, 2006 and Turan et al., 2008a). In addition, if suitable scaling rules are used (Meymand, 1998), researchers can study the influence of earthquakes on various types of soil-structure systems. Scaled physical model tests such as those shown in Figure 4.2 can be performed at 1-G or at n-G in a centrifuge for problems that require simulation of the in situ stress field. Modified glyben, which is studied here, can be used as the model soil for scaled model tests of structures founded on or in soils that exhibit undrained response during earthquakes, and where particle size scaling is not required (i.e. cohesive soil deposits).
In addition, it can be compacted into rigid and flexible containers instead of
resedimented as slurry.
4.2.2 Alternative model soils Numerous model soils have been developed for use in scaled physical model tests. Based on the available literature, most researchers perform this type of experimentation by (i) reconstituting either natural soil or an artificial soil mixture, (ii) placing the reconstituted material into a rigid or flexible container and consolidating the slurry to achieve the required stiffness and strength (e.g. Nunez and Randolph 1984, Burr et al. 1997, Moss et al. 1998, Tavenas et al. 1973, Blaney and Mallow 1987, Biscontin and Pestana 2001 and Iskander et al. 2002). This approach is difficult and very time consuming. Recently, scaled model tests have been performed using glyben (see Kenny and Andrawes 1997 and Rayhani and El Naggar 2007). Glyben is a mixture of bentonite and glycerin that can be placed and compacted in lifts into rigid or flexible containers to achieve the required soil properties. The dynamic properties of glyben have been reported in Chapter 2 of this thesis, Turan et al. (2008b) and Rayhani and El Naggar (2008 a/b). The dynamic shear modulus, G, vane shear strength and damping ratio, ξ of glyben can be varied by altering the ratio of
85 bentonite and glycerin in glyben. In addition, it was reported that the modulus ratio, G / Gmax , of glyben is within the normal range for natural clays for shear strain amplitudes ranging from 0.001 to 10%. The primary benefits of glyben compared to alternative model soils are: (i) It has a coefficient of consolidation that is 1/1400 times that of bentonite and water mixtures. Consequently, it consolidates at a very slow rate after the application of confining stress, which can be used during experimental design to avoid a prolonged consolidation phase during spin up in a centrifuge; (ii) Glyben does not desiccate significantly with time; and (iii) It can be used multiple times during tests since its dynamic properties do not change after the application of many loading cycles at large strain levels. The main drawback of glyben, however, is that it has a damping ratio in the range of 0.15 to 0.22, which is significantly higher than natural soils (Rayhani and El Naggar, 2008a; Turan et al., 2008b). This study focuses on modifying glyben by adding water into the pore fluid to obtain a damping ratio closer to natural soils, while still retaining the favorable characteristic of glyben.
4.3 Tests and Methodology A series of x-ray diffraction, shear vane, isotropic consolidation, cyclic triaxial, bender element and resonant column tests have been performed to characterize the mechanical behavior of modified glyben. Unless otherwise noted, all of the tests performed in this study were conducted 10 days after preparing the modified glyben specimens in order to avoid the influence of thixotropy. The influence of thixotropy will be addressed below. Table 4.1 summarizes details of the dynamic tests performed including a specimen list, the types of tests performed, the ratio of water to water plus glycerin by mass (w/gw), the ratio of fluids to solids by mass (gw/c) and the purpose of the tests.
86
4.3.1 Material Preparation Modified glyben was prepared in batches by mixing bentonite with glycerin and water for 30 minutes in a Blakeslee Model B-20 kneading type geotechnical mixer. For the mixing, glycerin and water, which are mutually soluble, were combined in a container and mixed by hand for ten minutes. Then, dry bentonite (Halliburton – Quik Gel, High viscosity sodium bentonite) was placed in the Blakeslee mixer and the glycerin-water solution was added slowly to the bentonite while it was being mixed. After combining the bentonite, water and glycerin, the mixing was continued for at least 30 minutes to ensure a uniform blend. Following mixing, specimens were prepared by compacting the modified glyben into a split mold in four lifts using a drop hammer. The number of lifts and blows per lift were selected so that the bulk density of each specimen was 95% of the maximum bulk density determined from standard compaction tests (ASTM D-698). The specimens were subsequently removed from the split mold, wrapped in plastic and stored at room temperature (22 ±1 ºC) for 10 days until testing.
4.3.2 Compaction, Atterberg Limits and Vane Shear Tests Compaction tests were conducted on modified glyben mixtures in accordance with ASTM D698. The compaction tests were performed to determine the maximum bulk density of modified glyben. In addition, the liquid limit (LL), plastic limit (PL) and plasticity index (PI) of modified glyben with (w/gw) ratios of 0, 25, and 100% were determined in accordance with ASTM D4318. A series of shear vane tests were performed according to ASTM D-2573 to measure the variation of vane shear strength versus time for different (gw/c) and (w/gw) ratios. For the vane
87 shear tests, modified glyben was compacted into a stiff 300×300×300 mm3 metal container to 95% of the maximum bulk density. Then shear vane measurements were taken in the container using a Pilcon 19-01 hand vane. The shear vane tests were performed on modified glyben mixtures with (w/gw) ratios of 15, 25, 50 and 100% and (gw/c) ratios of 35, 37.5, 40, 42.5, 45, and 47.5%. The hand vane tests were performed 1, 2, 3, 6, 7 and 9 days after mixing to study the effects of thixotropy.
4.3.3 Cyclic Triaxial Tests A Wykeham Farrance cyclic triaxial apparatus was used to study the dynamic properties of modified glyben at shear strain levels between 0.1 and 2%.
Strain controlled tests were
performed according to ASTM D-3999 (Method B) on specimens with a diameter of 70 mm and height of 140 mm. Tests were performed at (gw/c) ratios of 40, 42.5, 45 and 47.5% and (w/gw) ratios of 15, 25, 50 and 100 % as summarized in Table 4.1. For each triaxial test, specimens were placed on the base pedestal and fitted with a top cap. A latex membrane was placed over the specimen and sealed to the base pedestal and top cap using o-rings. Finally, the triaxial cell was filled with water, the top cap was connected to an 5 kN pneumatic actuator and the cell water was pressurized to achieve the desired cell pressures, σ c . All tests were performed without back pressure since these conditions were considered to be more representative of the conditions during scaled model tests, which are performed without backpressure.
Seventeen cyclic triaxial tests were performed on modified glyben specimens and the dynamic properties were measured in accordance with ASTM D3999 (Method B) using the following Procedures 1-3:
88 1. Procedure 1: Individual glyben specimens were placed in the triaxial cell and the cell pressure was ramped from 37 to 300 kPa. At each cell pressure, the dynamic properties were measured at shear-strain amplitudes ranging from 0.1% to 2%. This testing procedure is referred to as ramped cell pressure and ramped shear strain amplitude and it was performed on specimen CTX-1 in order to study the effect of confining pressure on the dynamic properties. 2. Procedure 2: Most specimens were placed in the cyclic triaxial cell at a constant cell pressure and the dynamic properties were measured at shear-strain amplitudes ranging from 0.1% to 2%. This procedure is referred to as constant cell pressure with ramped shear strain amplitude and it was performed on specimens CTX-2 to CTX-5 to study the influence of varying the water to total fluids ratio (w/gw) ratio. Procedure 2 was also used during the testing of specimens CTX-6 to CTX-9 to investigate the effect of shear strain amplitude on the dynamic shear modulus and damping ratio and on specimens CTX-10 to CTX-13 to investigate the influence of varying the fluid to solid ratio (gw/c). 3. Procedure 3: Select specimens were tested individually at constant cell pressure and using only one shear-strain amplitude. This procedure was performed on specimen CTX-14 to study changes in the dynamic properties of modified glyben during consolidation. It was also used for tests on specimen CTX-15 to investigate the effect of multiple loading cycles and on specimens CTX-16 and -17 to verify results obtained from tests performed using Procedures 1 and 2. Appendix A provides details of how the dynamic shear modulus, G, and damping ratio, ξ, were obtained from test data.
89
4.3.4 Isotropic Consolidation Tests One isotropic consolidation test was carried out in the triaxial apparatus. Specimen No. CTX14 was placed in the triaxial cell without lateral strip drains and consolidated isotropically for 10 days at a cell pressure of 200kPa. Volumetric strain was measured during compression and the isotropic consolidation was carried out in the absence of backpressure to simulate conditions expected during 1-G and n-G scaled model tests. Periodically during consolidation, the large strain shear modulus and damping ratio were measured at a shear strain amplitude of 0.1% to quantify changes in the dynamic properties during consolidation. The results of this test are compared with identical tests performed by Turan et al. (2008b) on bentonite-water and glyben specimens prepared with the same fluid contents.
4.3.5 Resonant Column Tests Resonant column tests were performed according to ASTM D-4015 to augment the cyclic triaxial results. A description of the apparatus and procedures can be found in Drnevich et al. (1978) and Morris and Delphia (1992). The resonant column tests were performed on specimens prepared with a (w/gw) ratio of 25% and (gw/c) ratios of 40 %, 42.5% and 45 % using torsional loading. The resonant column specimens had a diameter of 70mm and height of 145 mm and were prepared and aged exactly as done for the cyclic triaxial tests and described in the Material Preparation section. After aging the specimens for 10 days, each specimen was assembled in the resonant column, a latex membrane was placed over the specimen and sealed to the base pedestal and top loading cap using o-rings.
Next, the cell pressure was applied and held for 5 minutes before
90 commencing the tests. The fundamental angular frequency, ωn , was measured from the resonant column tests and used to calculate the shear wave velocity, Vs . In total, 5 modified glyben specimens were tested in the resonant column apparatus using shear strain amplitudes ranging from 0.001% to 0.2%. Individual glyben specimens were placed in the resonant column cell and the cell pressure was ramped from 37 to 300 kPa. At each cell pressure, the dynamic properties were measured at shear-strain amplitudes ranging from 0.001% to 0.2%, which corresponds to Procedure 1 described above. The ramped cell pressure and ramped shear strain amplitude procedure was performed on Specimen RC-1 to study the effect of confining pressure on the low strain dynamic properties. In addition, Specimens RC-2, RC-3 and RC-4 were placed in the resonant column cell at a constant cell pressure and the dynamic properties were measured at shear-strain amplitudes ranging from 0.001% to 0.2%, corresponding to Procedure 2 (see above). These tests were used to study the variation of shear modulus and damping ratio versus shear strain amplitude. Lastly, Specimen RC-5 was tested using constant cell pressure and a single shear-strain amplitude (0.001%) to study the influence of drying and desiccation on the dynamic properties of modified glyben.
4.3.6 Bender Element Tests Bender element tests (see Viggiani and Atkinson 1995, Jovicic et al. 1996, Lee and Santamarina 2005) were performed to study the effects of thixotropy, temperature and pore-fluid viscosity on the shear wave velocity of modified glyben. A detailed description of the bender elements apparatus, and the procedures followed can be found in Turan et al. (2008b). The following provides a brief summary of the sample preparation and tests performed.
91 Similar to the triaxial and resonant column tests, cylindrical specimens of height 140 mm and diameter 70 mm were prepared as described previously. The modified glyben specimens were then tested under various confining pressures using a bender-extender element system manufactured by GDS Instruments Inc. Sinusoidal p-waves and s-waves were generated at frequencies with corresponding wavelengths equal to about half the sample height to eliminate possible near field effects. From the arrival time of S-waves, TS , and P-waves, TP , and the distance, d , between the transmitter and receiver tips, the S-wave velocity, VS , P-wave velocity, VP , and Poisson’s ratio, ν were determined (e.g. Viggiani and Atkinson 1995).
Referring to Table 4.1, nineteen specimens were tested using the bender element apparatus. The shear wave velocity of specimen BE-1 was measured 1, 2, 3, 6, 7, and 9 days after preparing the specimen to study thixotropic changes in Vs with time. Specimen BE-1 had a (gw/c) of 40% and a (w/gw) of 25 %. Specimens BE-2 to BE-6 (Table 4.1) were prepared with a (gw/c) of 40% and (w/gw) ratios of 0, 15, 25, 50 and 100%, respectively, and tested to study the influence of (w/gw) on Vs. Specimens BE-7 to 21 were prepared with a (gw/c) ratios of 35 %, 40%, 42.5%, 45% and 50% and (w/gw) ratios of 0% (glyben), 25% and 50%, respectively and tested to study the influence of confining pressures on the small strain stiffness. Two specimens, BE-19 and BE-20, were prepared with a (gw/c) of 42.5 % and (w/gw) of 25% and tested at different temperatures to quantify changes in the dynamic properties with temperature.
4.3.7 X-ray Diffraction Tests Lastly, x-ray defraction tests were performed according to ASTM D4452-06 to assess changes in the bentonite structure due to hydration with glycerin and diluted glycerin.
92
4.4
Results of Static and Mineralogy Tests
4.4.1 Effects of Glycerin on Bentonite Mineralogy Referring to Table 4.2, glycerin is a polar molecule with a density of 1264kg/m3 and a dielectric constant that is similar to but slightly less than water (e.g. 45 versus 79). Thus, it is anticipated that glycerin will form a double layer with bentonite particles. In addition, Figure 4.3 shows the results of x-ray diffraction traces (CuKα) on oriented bentonite fines corresponding to (i) air dried at room temperature and humidity, (ii) glycolated with pure glycerin and (iii) glycolated with diluted glycerin (w/gw)=25%. From the resultant x-ray traces, it can be seen that the air dried bentonite gave a broad x-ray peak with a maximum at 13Å and a shoulder at 15Å. After glycolation with pure glycerin, the 13-15Å peak intensified shifting to 17.1 Å and the peak shifted further to 18 Å after glycolation with diluted glycerin, (w/gw)=25%. Thus, in addition to forming a double layer with the bentonite, hydration of the bentonite with glycerin and diluted glycerin increases the basal spacing of the clay minerals, which may have some influence on the material behavior.
4.4.2 Compaction, Shear Vane Strength and Atterberg Limits The compaction behavior and vane shear strength of modified glyben were investigated using standard compaction and shear vane tests. Figure 4.4 compares the variation of bulk density with fluid content, (gw/c) for modified glyben with (w/gw) = 25% and glyben with (w/gw)=0%. Referring to Figure 4.4, the maximum bulk density of modified glyben (w/gw)=25%, was about 1780 kg/m3 occurring at a fluids content (gw/c) of 42.5 %. In comparison, the glyben specimen reached a similar maximum bulk density of 1770 kg/m3 at a fluids content of 40% and the
93 compaction curve obtained for the glyben specimen was much flatter than obtained for modified glyben. Figure 4.5 summarizes variation of the vane shear strength versus fluid content (gw/c) and the (w/gw) ratio. At a given (gw/c) ratio, glyben specimens, (w/gw)=0%, exhibited the highest vane shear strength while the modified glyben with (w/gw) = 50% had the lowest strength. The addition of water to the glycerin causes strength reduction, which can be seen from the curves for (w/gw) = 25% and 50%, respectively. As a result, it can be concluded that (i) The vane shear strength of modified glyben is inversely proportional to the fluids content (gw/c) and the percent of water by mass in the total pore fluid (w/gw). (ii) Since the viscosity of the pore fluid is directly proportional to the (w/gw) ratio as shown below, the strength of this model soil is proportional to the viscosity of the pore fluid. Table 4.3 summarizes additional vane shear strength data versus (w/gw) and Atterberg limits.
4.4.3 Thixotropy Shear vane and bender element tests were used to investigate the influence of thixotropy on the properties of modified glyben. Table 4.4 summarizes the variation of vane shear strength with time after mixing of modified glyben samples ((w/gw) = 25%) prepared with various (gw/c) ratios. For all (gw/c) ratios, the vane shear strength of modified glyben increased with time after mixing.
The maximum increase was 25.62% corresponding to (gw/c)=40%; whereas, the
minimum increase was 12.61% for (gw/c)=45%. Thus, all modified glyben mixtures exhibited significant time-dependent increases in their vane shear strength, which is attributed to thixotropy. To further explore the effects of thixotropy, bender element tests were performed on Specimen BE-1 to measure changes in the shear wave velocity, Vs, and the consequent small
94 strain shear modulus of modified glyben with time after mixing. The measured Vs versus time after mixing is presented in Figure 4.6 and compared with the corresponding increase in vane shear strength from Table 4.4. In this figure, the vane shear strength for each (gw/c) ratio was normalized by the strength after 9 days and the averaged normalized vane shear strength is plotted versus time. From Figure 4.6, it can be seen that there is a 30% increase in the shear wave velocity with time during the first 7 days after mixing. Similar behavior is evident for the vane shear strength, which increased during the first 9 days after mixing. As such, both the vane shear strength and shear wave velocity of modified glyben exhibit significant thixotropy immediately following mixing. The thixotropic changes are however small after 7 to 9 days. Such changes should be accounted for during scaled model tests. In this chapter, all specimens were aged for 10 days to reduce thixotropic effects.
4.4.4 Consolidation Behavior As discussed above, the consolidation behavior of modified glyben was studied using isototropic consolidation tests and the results are reported in Figure 4.7. This figure compares the volumetric response of: (i) glyben, (w/gw)=0%, during 10 days of isotropic consolidation at a confining stress of 200 kPa, (ii) modified glyben, (w/gw) = 25 %, and (iii) a bentonite-water mixture over the same 10 day period.
The glyben, modified glyben and bentonite-water
specimens were prepared so that they had the same initial void ratio. The bentonite-water (w= 45%) and glyben (g/c= 45%) results have been adapted from Turan et al. (2008b). The solid line in Figure 4.7 represents the degree of consolidation versus dimensionless time, Tv=cvt/d2, for bentonite-water, (w/gw) = 100%; the hollow circular symbols summarize the degree of consolidation of the modified glyben specimen, (w/gw) = 25%; and the crosses depict the degree consolidation of the glyben specimen, (w/gw) = 0%. Due to the slow rate of
95 consolidation of both glyben and modified glyben, the degree of consolidation of these specimens was inferred by assuming the drained bulk modulus of all three samples is the same. This was considered to be reasonable since the specimens were prepared at the same initial void ratio. Thus, the volumetric strain of the glyben and modified glyben specimens was divided by the total volumetric strain measured during compression of the bentonite-water specimen. In addition, Figure 4.7 summaries spot measurements of the dynamic shear modulus with time made using the cyclic triaxial equipment and shear strain amplitude of 0.1%. The shear modulus measurements appear as arrows adjacent to the consolidation curve. Referring to Figure 4.7, only the bentonite-water specimen reached 100% consolidation after 10 days. The resultant coefficient of consolidation was 6.86×10-6 m2/s, which is within the normal range for bentonite-water. In contrast, the degree of consolidation of the modified glyben specimen after 10 days was only 66% corresponding to a coefficient of consolidation, cv = 2.19 × 10-7 m2/s. The resultant ratio of cv bentonite-water to cv modified glyben, (w/gw)=25%, is 31. As shown in Table 4.2, the ratio of the pore fluid viscosity is (31.2mPa•s/0.96mPa•s) 33, which is consistent with the principle of intrinsic permeability. Finally, the degree of consolidation for the glyben specimen, (w/gw)=0%, was 22% after 10 days of isotropic consolidation, which corresponds to a coefficient of consolidation of 4.96×10-9m2/s.
Similarly, the ratio of cv
bentonite-water to cv glyben is 1/1344 and the corresponding ratio of the pore fluid viscosities is 1/1244. To conclude, Figure 4.7 shows the variation of dynamic shear modulus, G, and damping ratio, ξ, of glyben, (w/gw)=0%, and modified glyben, (w/gw)=25%, during isotropic consolidation. It can be seen in Figure 4.7 that there is an 8.3% and 8% increase in the large strain (γ=0.1%) dynamic shear modulus of modified glyben, (w/gw)=25%, and glyben,
96 (w/gw)=0%, specimens, respectively, after 10 days of isotropic consolidation. Such changes are small and can be reduced to negligible values during scaled physical model tests provided the drainage path and test duration is controlled by proper experimental design. Thus, from the consolidation response summarized in Figure 4.7, it can be concluded that: (i) Bentonite-water, glyben and modified glyben consolidate with time and at a rate that is proportional to the viscosity of the pore fluid. Accordingly, the concept of intrinsic permeability is satisfied. (ii) There is an 8.3% and 8% increase in the dynamic stiffness of glyben and modified glyben after 10 days of isotropic consolidation. During scaled model tests, however, it is possible to control the drainage path and the test duration to limit the amount of consolidation that occurs and the resultant experimental error due to change in volume and dynamic stiffness. Consequently, it is possible to take advantage of the low cv of both glyben and modified glyben to avoid a prolonged consolidation phase during 1-G and n-G scaled model tests.
4.5 Results of Dynamic Tests 4.5.1 The Influence of (gw/c) on G and ξ Figures 4.8 and 4.9 illustrate the influence of fluid content (gw/c) and shear strain amplitude on the dynamic shear modulus, G, and damping ratio, ξ of modified glyben with (w/gw) = 25%. First, referring to Figure 4.8, increasing the pore fluid content causes a reduction in the dynamic shear modulus of glyben for all shear strain amplitudes. At the upper bound (gw/c) = 40%, the G values vary from 8390 kPa at 0.002% shear strain to 1185 kPa at 2% shear strain. At the lower bound (gw/c) = 45%, the corresponding G values are 5623 kPa and 678 kPa at 0.002 and 2% shear strain amplitude, respectively. In addition to the general reduction of G with shear strain
97 amplitude, there is also a step or offset between the resonant column and cyclic triaxial results, which can be attributed to differences in the frequency and mode of loading in the two tests (Turan et al., 2008b).
For the results presented in Figure 4.8, the fluid content (gw/c) can be
used to vary the stiffness of modified glyben holding the (w/gw) ratio constant at 25%. In contrast, the damping ratio is not affected significantly by the fluids content (gw/c) as shown in Figure 4.9. In this figure, the damping ratio varies from about 0.22 at shear strain amplitude of 2% to 0.06 at 0.002% and all values of ζ fall within a narrow band for (w/gw) of 25%.
In addition, the damping ratio is less sensitive to the mode and frequency of loading as
both resonant column and cyclic triaxial results approximately coincide at a shear strain amplitude of 0.1%.
4.5.2
The Influence of (w/gw) on G and ξ
This section considers the influence of pore fluid viscosity on the dynamic properties of modified glyben. From Dorsey (1940), the viscosity of glycerin-water solutions is inversely proportional to the (w/gw) ratio. Table 4.5 summarizes the viscosity and dielectric constant of glycerin-water solutions with different (w/gw) ratios and Figures 4.10 and 4.11 summarize the results of cyclic triaxial and resonant column tests performed on modified glyben specimens with (w/gw) ratios of 0, 15, 25 and 50%.
These figures focus on only G and ξ values measured in
the cyclic triaxial apparatus for reasons that will become clear in the following sections. Referring to Figure 4.10, there is a decrease in G with increasing shear strain amplitude similar to that seen for natural soils. In addition, G is inversely proportional to the (w/gw) ratio and consequently proportional to the pore fluid viscosity. At 0.1% shear strain amplitude, G is 8100 kPa corresponding to (w/gw) = 0% and a viscosity of 1170mPa•s and G reduces to
98 2050kPa corresponding to (w/gw) = 50% and a pore fluid viscosity of 5.46mPa•s. As a result, the viscosity of the pore fluid can be used to alter the dynamic stiffness of modified glyben similar to that seen above for the (gw/c) ratio. In Figure 4.11, it can be seen that there is an increase in the damping ratio of modified glyben, (w/gw) = 25%, with increasing shear strain amplitude.
Focusing on shear strain
amplitudes between 0.1 and 2%, the damping ratio is inversely proportional to the (w/gw) ratio and proportional to the pore fluid viscosity. At a shear strain amplitude of 0.1%, the damping ratio is 0.175 corresponding to (w/gw)=0% and a pore fluid viscosity of 1170 mPa•s and the damping ratio is 0.13 corresponding to (w/gw) = 50% and a pore fluid viscosity of 5.46mPa•s.
4.5.3 Normalized Dynamic Stiffness, G/Gmax, of Modified Glyben The preceding sections illustrated the influence of (gw/c) and (w/gw) on the dynamic properties of modified glyben.
In this section, the results shown in Figures 4.8-4.11 are
combined in Figure 4.12 to evaluate the influence of (gw/c) and (w/gw) on the variation of G/Gmax with shear strain amplitude, γ. For each of these tests, the dynamic shear modulus has been normalized by Gmax, which was measured using bender elements and occasionally verified by resonant column tests. Referring to Figure 4.12, it can be seen that G/Gmax, values for modified glyben with (w/gw) = 25% fall within a narrow range irrespective of the fluid content (gw/c). As noted above, there is a step or offset between the low and high shear strain amplitude results, which is due to the difference in frequency and mode of loading in resonant column versus cyclic triaxial tests. Notwithstanding the offset between resonant column and cyclic triaxial results, a regression
99 analysis can be performed on the data in Figure 4.12 leading to the following relationship between G/Gmax and γ
G / Gmax = 0.071 + 0.736e (-10.235γ ) + 0.234e (-1.082γ ) ,
[4.1]
which has a coefficient of determination, R2, of 0.99. In Eqn. [4.1], γ is the shear strain amplitude. Eqn. [4.1] is plotted in Figure 4.12 together with the predictions of G/Gmax using equations from Vucetic and Dorby (1991) and Ishibashi and Zhang (1993) for PI=30. Comparing Eqn. [4.1] with Vucetic and Dorby (1991) and Ishibashi and Zhang (1993), the variation of G/Gmax versus shear strain amplitude for modified glyben, (w/gw) = 25%, is similar to that expected for natural soils. However, it is not clear if Eqn. [4.1] is also suitable for other (w/gw) ratios. To investigate the influence of (w/gw) on the normalized shear stiffness, Figure 4.13 compares Eqn. [4.1] with G/Gmax values published by Turan et al. (2008b) for glyben, (w/gw)= 0%. Since the glyben results plot very close to Eqn. [4.1], it is concluded that G/Gmax versus γ for modified glyben is independent of both the (w/gw) and (gw/c) ratios. Further evidence supporting this conclusion will be shown below.
Consequently, the dynamic stiffness of
modified glyben can be fully characterized using Eqn. [4.1] in conjunction with Gmax versus (w/gw) and (gw/c).
4.5.4 Damping Ratio Versus Pore Fluid Viscosity (w/gw) Figure 4.14 summarizes the ξ-γ response of modified glyben from Figures 4.8-4.11 and compares its behavior with (i) the corresponding behavior of glyben as depicted by the dashed
100 line labeled (w/gw) = 0% (from Turan et al. 2008b) and (ii) empirical equations from Vucetic and Dorby (1991) corresponding to PI=30%. From this figure, the damping ratio of modified glyben is clearly dependent on the (w/gw) ratio or pore fluid viscosity. For glyben, (w/gw) = 0%, the damping ratio, ξ, varies from 0.27 at 2% shear strain amplitude to 0.14 at 0.002% shear strain amplitude. In comparison, ξ for modified glyben (w/gw) = 25% decreases from 0.22 at 2% shear strain amplitude to 0.06 at 0.002%. Thus, increasing the (w/gw) ratio and decreasing the pore fluid viscosity from 1344 to 31.2 mPa•s (see Table 4.2) caused the damping ratio to decrease substantially. The solid line in Figure 4.14 is from Vucetic and Dorby (1991) for PI=30 and is assumed to be representative of natural soils. Between 0.2 and 2% shear strain amplitude, the Vucetic and Dorby (1991) curve is reasonably close to the cyclic triaxial results for modified glyben specimens with (w/gw) = 50%, which corresponds to a pore fluid viscosity of 5.46mPa•s. This pore fluid viscosity is close to the viscosity of water. Thus, the Vucetic and Dorby (1991) curve corresponding to a PI of 30% may be taken as the damping ratio of modified glyben mixtures with (w/gw) ratios greater than or equal to 50%. It should be noted however, that the rate of consolidation of modified glyben mixtures with (w/gw) ratios of 50% or greater will be close to that of bentonite-water mixtures, which may lead to excessive consolidation during scaled model tests at n-G in a centrifuge. As such, the favorable characteristics of glyben would be lost.
4.5.5 Effect of Confining Stress on G/Gmax The effect of confining stress on the G/Gmax versus γ response of modified glyben was investigated using a series of resonant column and cyclic triaxial tests performed on specimens CTX-1 and RC-1 (see Table 4.1). The results are summarized in Figures 4.15 and 4.16, which show the confining stress on G/Gmax and ξ versus shear strain amplitude. For the G/Gmax results
101 corresponding to (gw/c) = 40% and (w/gw) = 25%, Gmax was measured using bender elements. Eqn. [4.1] is shown in Figure 4.15 for comparison purposes. Referring to Figures 4.15 and 4.16, it can be seen that the confining stress does not have a significant influence on either G/Gmax or ξ versus shear strain amplitude. In addition, Eqn. [4.1] agrees well with the G/Gmax, values obtained from tests performed at confining stresses ranging from 37 to 300kPa. Although, the dynamic shear modulus, G, of modified glyben is dependent on the confining stress, the results in Figures 4.15 and 4.16 indicate that the dynamic properties of modified glyben can be fully characterized using Eqn. [4.1] and Figure 4.14 and by measuring Gmax or Vs versus (w/gw), (gw/c) and confining pressure.
4.5.6 Gmax versus (gw/c), (w/gw) and σc The results of bender element tests performed to characterize Gmax versus (gw/c), (w/gw) and confining stress are summarized in Figures 4.17 (a) - (c). Figure 4.17 (a) corresponds to glyben, (w/gw) = 0%, and Figures 4.17 (b) and (c) to modified glyben with a (w/gw) ratio of 25 and 50%, respectively. Figures 4.17 in conjunction with Eqn. [4.1] and Figure 4.14 are sufficient to characterize the dynamic stiffness and damping ratio of modified glyben.
The following
summarizes observations that can be drawn from these figures: 1. The Gmax of modified glyben is dependent on the confining pressure. The largest effect was found for mixtures with a (w/gw) ratio of 50% and (gw/c) ratio of 35%. 2. The Gmax of glyben exhibited the lowest sensitivity to confining stress. 3. For all three mixtures, (w/gw) = 0, 25 and 50%, the sensitivity to confining stress was highest for fluid contents (gw/w) less than optimum (see Figure 4.3) and lowest for
102 fluid contents exceeding optimum.
These results suggest that the pressure
dependency for lower (gw/c) ratios is caused by air voids in the compacted specimen, which are not as prevalent wet of optimum as the materials approach the zero air voids line. Thus, there is evidence of a dual porosity effect (e.g. macro and micro pores) in this material.
4.6
Evaluation of Beneficial Properties of Modified Glyben
The preceding sections have characterized the dynamic properties of modified glyben. As noted in the Background section, however, the advantages of glyben were: (i) that it does not desiccate significantly with time; and (ii) that it can be used multiple times during tests since its dynamic properties do not change significantly after the application of many loading cycles at large strain levels. This section explores these factors for modified glyben with (w/gw)=25%.
4.6.1 Effect of the Number of Cycles Figure 4.18 shows the effect of repeated loading cycles on the dynamic shear modulus and damping ratio of modified glyben with a fluids content (gw/c) = 40% and (w/gw) ratio of 25%. The data in Figure 4.18 were obtained from cyclic triaxial tests performed on Specimen CTX-15 at a confining pressure of 350 kPa, using shear strain amplitude of 0.2%, and frequency of 1 Hz. Referring to Figure 4.18, it can be seen that the number of cycles has a minor impact on the dynamic properties of modified glyben for the conditions considered. The G/Gmax ratio varied from 0.56 to 0.6 for 1-500 load cycles representing a variation of 3.4%±. Similarly, the damping ratio varied from 0.12 to 0.125, corresponding to a variation of 2%±. Accordingly, as
103 observed for glyben, it is concluded that the dynamic properties of modified glyben, (w/gw)=25%, are not significantly degraded by the number of loading cycles.
4.6.2 Effect of Drying Specimen RC-5 was left to air dry for 32 days and its dynamic properties were measured using resonant column tests before and after 25 days exposure to air at room temperature and humidity. The specimen mixture comprised (w/gw) = 25% and (gw/c) = 42.5 % and the testing was performed at a confining stress of 37 kPa and 0.00005 shear strain amplitude. The results are presented in Table 4.6. As shown in Table 4.6, the dynamic shear modulus and damping ratio increased by 2.08% and 2.17%, respectively, after 25 days exposure to air at room temperature and humidity. From visual observations, the exposure to air caused a thin veneer of the material to show visible signs of drying. Accordingly, the test results summarized in Table 4.6 confirm that modified glyben remains resistant to drying and significant alteration during exposure to air as reported by Kenny and Adrawes (1997).
4.6.3 Effect of Temperature Finally, the influence of pore fluid viscosity on the dynamic properties of modified glyben has been summarized in Figures 4.10 and 4.11. This section, however, presents the results of a series of unconfined bender element tests conducted on modified glyben specimens at different temperatures to show the effect of temperature induced variations in pore fluid viscosity on the shear wave velocity of modified glyben. Although, the bulk modulus of water and glycerin are comparable
(see Turan et al., 2008b), the viscosity of glycerin changes significantly with varying temperature as reported by Dorsey (1940) and summarized in Table 4.7. As such, the viscosity of the pore
104 fluid can be varied by altering: (i) the temperature and (ii) (w/gw) and it was considered interesting to compare the influence of these two variables on the shear wave velocity and the corresponding Gmax of modified glyben. The testing procedure used to explore temperature effects involved covering two identical modified glyben specimens, BE-19 and BE-20, (gw/c = 42.5 %) with plastic wrap and heating them up to 40°C. Then a thermocouple was inserted into the core of the first specimen to monitor the temperature and shear wave velocity measurements were made from the second specimen. Figure 4.19 shows the measured variation Vs versus pore fluid viscosity. This figure shows the results of tests where the pore fluid viscosity was controlled by (i) altering the temperature or (ii) changing the (w/gw) ratio. From Table 4.7 and Figure 4.19, it can be seen that decreasing the temperature from 35 oC to 12 oC causes the viscosity of the pore fluid to increase from 17.4 to 61.7 mPa.s and the corresponding Vs to increase from 45m/s to 57m/s. The increase in Vs exceeds 30% for the temperature range studied (35 °C - 12°C). In addition, the variation of Vs with viscosity is similar for tests performed by controlling the (w/gw) ratio or temperature. Thus, Figure 4.19 indicates that the dynamic properties of modified glyben are sensitive to the pore fluid viscosity, which can be varied by altering either temperature or the (w/gw) ratio of the pore fluid. It should be noted that, the Vs from the temperature tests are slightly lower than the Vs from varying (w/gw), but within the normal range of variation of this material.
4.7 Summary and Conclusions This chapter has presented the results of an experimental investigation into the effect of time (consolidation and thixotropy), cyclic strain level, confining pressure, fluid content, cyclic stress
105 history, and exposure to air on the dynamic properties of modified glyben. The testing program comprised X-ray diffraction tests, vane shear tests, compaction tests, cyclic triaxial tests, bender element tests, resonant column tests and isotropic consolidation tests. The following is a summary of the results and conclusions arising from this study. 1. The vane shear strength of modified glyben decreases linearly as the fluid content (gw/c) increases. The vane shear strength of natural clays exhibit a similar decrease with increasing moisture content. 2. Increasing the ratio of the water in the pore fluid mixture (w/gw) reduces the pore fluid viscosity causing a reduction in the vane shear strength of modified glyben. 3. The maximum density of modified glyben in Standard Proctor Compaction tests was 1780 kg/m3 at a (gw/c) ratio of 42.5%. 4. There were significant changes in the vane shear strength and Gmax of modified glyben during the first seven to nine days after mixing. There were minor changes in these properties beyond this timeframe. Thus, it is concluded that scaled model tests should ideally be undertaken after allowing sufficient time for thixotropic changes to take place. In this chapter, a period of 10 days was allowed to minimize the effects of thixotropy. 5. Modified glyben exhibits volume change versus time after application of confining stresses that can be interpreted with conventional consolidation theory. From Figure 4.7 it can be seen that the degree of consolidation for modified glyben after 10 days is approximately 66 % and the coefficient of consolidation is approximately 2.19 x 10-7 m2/s, which is about 31 times smaller than that of bentonite-water and 44 times larger that glyben. Overall, the consolidation process of modified glyben appears to be
106 slower than that of bentonite-water and faster than glyben. In addition, the concept of intrinsic permeability applies to the coefficient of consolidation of glyben, modified glyben and bentonite-water mixtures. 6. The dynamic properties of modified glyben have been fully characterized by Figures 4.14 and 4.17, and Eqn. [4.1]. 7. The damping ratio, ξ, of modified glyben with (w/gw) = 25% is comparable to the damping ratio of natural soils at shear strain amplitudes between 0.002 and 2%. Thus, the high damping ratio of glyben can be altered by changing the pore fluid viscosity. 8. Increasing the pore fluid content in modified glyben (gw/c), decreased the shear modulus similar to natural clays. The damping ratio was unaffected by variations in (gw/c). 9. The shear modulus of modified glyben is dependent on the confining stress. The dynamic shear modulus increased as the confining stress increase. However, the normalized shear modulus versus shear strain amplitude is not affected by the confining pressure. 10. Gmax values are influenced by the (gw/c) and (w/gw) ratios of modified glyben. With increasing (w/gw), the sensitivity of Gmax to confining pressure increased.
In
addition, the Gmax of mixtures with (gw/c) ratios less than the optimum fluid content were more sensitive to changing the confining pressure. The damping ratio remained almost unaffected by changes in confining pressure for the range of confining pressures investigated.
107 11. The viscosity of pore fluid influences the shear modulus and the damping ratio of the modified glyben. Both Gmax and ξ reduce with decreasing pore fluid viscosity. 12. Direct air contact for 33 days did not result in significant changes in the dynamic properties of modified glyben. This indicates that modified glyben may be exposed to air for prolonged periods without significant alteration of its dynamic properties. 13. The dynamic shear modulus, G , and damping ratio, ξ, of modified glyben were not significantly affected by the number of loading cycles (from 1 to 500 cycles) under a high level of shear strain amplitude investigated. This behavior would permit multiple dynamic tests from a single scaled model improving the economics and efficiency of such tests. 14. Temperature has a significant effect on the dynamic properties of glyben. From Figure 4.19, Vs varied by as much as 30 % over the temperature range 12°C to 35°C. 15. The pore fluid viscosity appears to be the dominant parameter influencing the dynamic properties of modified glyben since changes in the viscosity caused by altering the temperature or (w/gw) had similar effects on G.
108
References Arango-Greiffenstein, I. 1971. Seismic stability of slopes in saturated clay. Ph.D. Dissertation, Univ. of California, Berkeley, CA Biscontin, G., and Pestana, J. M. 2001. Influence of peripheral velocity on vane shear strength of an artificial clay. Geotech. Testing J., ASTM, 24 (4): 423-429. Blaney, G., and Mallow, W. 1987. Synthetic clay soil for dynamic model pile tests in dynamic response of pile foundations - experiment, analysis, and observation. Geotech. Spec. Pub. 11, ASCE, 127-148. Bray, J. 1990. The effects of tectonic movements on stresses and deformations in earth embankments. Ph.D. Dissertation, Univ. of California, Berkeley, CA, USA. Burr, J., Pender, M., and Larkin, T. 1997. Dynamic response of laterally excited pile groups. J. Geotech. And Geoenv. Eng., ASCE, 123(1): 1-8. Cai, Y.Q., and Liang, X. 2004. Dynamic properties of composite cemented clay. Journal of Zhejiang University Science, 5(3): 309-316. Drnevich, V. P., Hardin, B. O., and Shippy, D. J. 1977. Modulus and damping of soils by resonant-column method. Spec Tech Publ. 654, 91-125, ASTM, Symp on Dyn. Geotech. Test, Denver, CO. Gibson A.D. 1997. Physical scale modeling of geotechnical structures at one-g. PhD thesis. Pasadena, CA: California Institute of Technology. Ishibashi, I., and Zhang, X. 1993. Unified dynamic shear moduli and damping ratios of sand and clay. Soils and Foundations, 33(1): 182-191. Iskander, M. G., Liu, J., and Sadek, S. 2002. Transparent amorphous silica to model clay.
109 Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 128 (3): 262273. Jovicic, V., Coop, R., and Simic, M. 1996. Objective criteria for determining Gmax from bender element tests. Geotechnique, 46(2): 357–362. Kenny, M. J., and Andrawes, K. Z. 1997. The bearing capacity of footings on a sand layer overlying soft clay. Geotechnique, 47(2): 339–345. Ko, H., Atkinson, R., Goble, G., and Ealy, C. 1984. Centrifugal modeling of pile foundations. in analysis and design of pile foundations, ASCE, 21-40. Kovacs, W. D. 1968. An experimental study of the response of clay embankments to base excitation, Ph.D. Dissertation, Univ. of California, Berkeley, CA. Lazarte, C. 1996. The response of earth structures to surface fault rupture. Ph.D. Dissertation, Univ. of California, Berkeley, CA. Lee, J. S., and Santamarina, J. C. 2005, Bender elements: performance and signal interpretation. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 131(9): 1063–1070.
Leroueil, S., and Vaughan, P.R. 1990. The general and congruent effects of structure in natural soils and weak rocks. Geotechnique, 40(3): 467-488. Lin L., and Wang L. 2006. Seismic slope behavior in a large-scale shaking table model test. Engineering Geology, 86:118–133. Meymand, P. J. 1998. Shaking table scale model tests of nonlinear soil-pilesuperstructure interaction in soft clay. Ph.D. Dissertation, Univ. of California, Berkeley, CA. Mayfield, B. 1963. The performance of a rigid wheel moving in a circular path through
110 clay. Ph.D. Dissertation, University of Nottingham, UK. Morris, D.V., and Delphia, J.C. 1992. Resonant column testing of dynamic rock properties. Proc., 9th Conference on Engineering Mechanics, ASCE, College Station, TX, 1105. Moss, R., Rawlings, M., Caliendo, J., and Anderson, L. 1998. Cyclic lateral loading of model pile groups in clay soil. Proc., 3rd Conf. Geotechnical Earthquake Engineering and Soil Dynamics, ASCE, Seattle, WA, 494-505. Nunez, I., and Randolph, M. 1984. Tension pile behavior in clay – centrifuge modelling technique. Proc. Symposium on the Application of Centrifuge Modelling to Geotech. Eng., Manchester, UK, 87-102. Rayhani, M. T., and El Naggar, M.H. 2007. Centrifuge modeling of seismic response of layered soft clay. Bulletin of Earthquake Engineering, 5(4): 571-589. Rayhani, M. H. T., and El Naggar, M. H., 2008a. Characterization of glyben for seismic applications. Geotechnical Testing Journal, ASTM, 31(1): 24-31. Rayhani, M. T. and El Naggar, M.H. 2008b. Dynamic properties of soft clay and loose sand from seismic centrifuge tests. Journal of Geotechnical and Geological Engineering, 26(5): 593-602. Seed, H. B., and Clough, R. 1963. Earthquake resistance of sloping core dams. J. Soil Mechanics and Foundation Div., ASCE, 89(1): 209-242. Seed, H. B., and Sun J. I. 1989 Implications of site effects in the Mexico City earthquake of Sept. 19, 1985 for earthquake-resistant design criteria in the San Francisco Bay Area of California. Report No. EERC 89-03, University of California, Berkeley, CA. Sultan, H. A., and Seed H. B. 1967. Stability of sloping core earth dams. J. Soil
111 Mechanics and Foundation Div., ASCE, 93(4): 45-67. Sutherland H. B. 1988. Uplift resistance of soils. Geotechnique, 38(4): 493-516. Tavenas, F., Roy, M., and La Rochelle, P. 1973. An artificial material for simulating champlain clays. Can. Geotech. J., 10(3): 489-503. Teachavorasinskun, S., Thongchim, P., and Lukkunaprasit, P. 2002. Shear modulus and damping of soft Bangkok clays. Can. Geotech. J., 39: 1201–1208. Tiers, G.R. and Seed, H.B, 1968 Cyclic stress-strain characteristics of clay. Journal of the Soil mechanics and Foundation Engineering Division, ASCE, 94(2): 555- 569. Turan, A., Hinchberger, S. D., and El Naggar, M. H., 2008a. Design and commissioning of a laminar soil container for use on small shaking tables. Soil Dynamics and Earthquake Engineering (accepted for publication). Turan, A., Hinchberger, S. D., and El Naggar, M. H., 2008b. Mechanical characterization of an artificial clay Journal of Geotechnical and Geoenvironmental Engineering, ASCE (accepted for publication). Viggiani, G., and Atkinson, J. H. 1995. Interpretation of bender element tests. Geotechnique, 45(1): 149–154. Vucetic, M., Dobry, R. 1991. Effect of soil plasticity on cyclic response. Journal of Geotechnical Engineering, ASCE, 117(1): 89-107.
112
Table 4. 1 Details of dynamic test specimens Specimen
Type of Test
(gw/c ) ratio
(w/gw) ratio
Parameters Varied
Measured
25 %
Confining pressure, σ c
G and ξ
40 %
0, 15, 25 and 50 %
(w/gw)
G and ξ
Cyclic Triaxial2
40, 42.5, 45, and 47.5 %
25 %
Shear strain amplitude, γ
G and ξ
CTX-10 – CTX-13
Cyclic Triaxial2
40, 42.5, 45, and 47.5 %
25 %
(gw/c)
G and ξ
CTX-14
Cyclic Triaxial3
40 %
25 %
Time
G, ξ and cv
CTX-15
Cyclic Triaxial3
40 %
25 %
Number of cycles, N
G and ξ
CTX-16 -
Cyclic Triaxial3
40 %
25 %
CTX-1
1
Cyclic Triaxial
40 %
CTX-2 – CTX-5
Cyclic Triaxial2
CTX-6 – CTX9
CTX-17
G and ξ
42.5 %
RC-1
Resonant Column1
42.5 %
25 %
Confining pressure, σ c
G and ξ
RC-2 - RC-4
Resonant Column2
40 %, 42.5 % and 45 %
25 %
Shear strain amplitude, γ
G and ξ
RC-5
Resonant Column3
42.5%
25 %
Time
G and ξ
BE-1
Bender Elements
40 %
25 %
Time
Vs
BE-2 – BE-6
Bender Elements
40 %
0, 15, 25, 50, 100 %
(w/gw)
Vs
BE-7 - BE-18
Bender Elements
35, 40, 45, and 50 %
0, 25 and 50 %
Confining pressure, σ c
Vs
BE-19 – BE-20
Bender Elements
42.5%
25 %
Temperature, T
Vs
1
Procedure 1 (Cell pressure ramped, shear strain amplitude ramped at each cell pressure). Procedure 2 (Cell pressure held constant, shear strain amplitude ramped). 3 Procedure 3(Cell pressure held constant, shear strain amplitude held constant). 2
113
Table 4. 2 Temperature dependent properties of glycerin and water (Dorsey, 1940 and Huck et al., 1988). Material
Viscosity, mPa.s
Bulk Modulus, N/m2 (23°C)
Dielectric Constant
Density (Kg/m3)
Water
0.940 (23°C) 0.692 (37°C)
2.15×109
79 (23°C) 73 (37°C)
1000
Diluted Glycerin1
31.22 (23°C) 13.21 (37°C)
3.92×109
46 (23°C) 41 (37°C)
1198
Glycerin
1170 (23°C) 382 (37°C)
4.52×109
45 (23°C) 39 (37°C)
1264
1
75% glycerin and 25% water solution
114
Table 4. 3 Index properties, bulk density and vane shear strength of modified glyben mixtures with (gw/c) = 40 % and varying (w/gw) ratios. w/gw (%)
0 (Glyben) 15 25 50 100 (Bentonite-Water)
wP
wL
Bulk density(kg/m3)
Vane Shear Strength after 10 days (kPa)
34
59
36
66
26
320
1766.12 1712.56 1653.07 1572.85 1470.25
57.00 39.50 35.5 22 20
115
Table 4. 4 Changes in vane shear strength of various modified glyben mixtures versus time after mixing. (w/gw = 25%) Gw/c Total 9 days 7 days 6 days 1 day1 2 days 3 days (%) change (%) (kPa) (kPa) (kPa) (kPa) (kPa) (kPa)
1
40 42.5 45 47.5
30.06 29.42 17.05 13.75
32.33 30.21 18.66 14.66
34.23 31.73 19.33 15.00
Time after mixing the bentonite-water-glycerin.
36.90 34.06 19.16 15.43
37.03 34.33 18.80 15.66
37.76 34.40 19.20 15.55
25.62% 16.93% 12.61% 13.09%
116
Table 4. 5 Variation of the pore fluid viscosity with w/gw for (gw/c) = 40 %.
w/gw (%)
Viscosity (23°C) mPa.s
Dielectric Constant
0 15 25 50 100
1170 93.7 31.2 5.46 0.96
43.12 44.1 45.1 52.92 79
117
Table 4. 6 Effect of exposure to air on the dynamic properties of modified glyben with (gw/c) = 42.5% and (w/gw) = 25%. (Specimen RC-5)
1
Parameter
7 days1 (No air contact)
32 days (Exposed to air contact)
Change (%)
Gmax (KPa) ξ
5101 5.99 %
5207 6.12 %
2.08 2.17
Time after mixing bentonite-glycerin-water.
118
Table 4. 7 Variation of the viscosities of glycerin-water mixtures with temperature (Dorsey, 1940) Glycerin percent weight
10 °C
0 20 25 50 75 100
1.31 2.41 2.95 9.01 65.20 3900.00
20 °C
25 °C 30 °C Viscosity (mPa.s)
1.01 0.90 1.76 1.56 2.13 1.87 6.00 5.11 35.50 28.35 1410.00 1011.00
0.80 1.35 1.61 4.21 21.20 612.00
35 °C
40 °C
0.73 1.21 1.44 3.66 17.40 448.00
0.66 1.07 1.27 3.10 13.60 284.00
119
Figure 4. 1 1-D Shear wave propagation model for earthquakes.
120 Figure 4. 2 Scaled model of 1-D shear wave propagation.
121
Figure 4. 3 X-ray diffraction traces (CuKα) obtained on oriented fines of bentonite: (a) air dried, (b) glycolated and (c) glycolated with diluted glycerin (w/gw) = 25%.
122
Figure 4. 4 Compaction behavior of modified glyben for (w/gw) of 0 and 25 %.
123
Figure 4. 5 Vane shear strength vs. (gw/c) for various (w/gw) of 25 %.
124
Figure 4. 6 Thixotropic changes in Vs and the vane shear strength. (specimen BE-1).
125
Figure 4. 7 Consolidation response of modified glyben (specimen CTX-14).
126
Figure 4. 8 Effect of (gw/c) on the dynamic shear modulus, G (specimens, CTX-10, CTX-11, CTX-12, RC-2, RC-3 and RC-4).
127
Figure 4. 9 Effect of (gw/c) on the damping ratio, ξ (specimens, CTX-10, CTX-11, CTX-12, RC-2, RC-3 and RC-4).
128
Figure 4. 10 Effect of (w/gw) on G-γ curves – cyclic triaxial and resonant column tests (specimens CTX-2, CTX-3, CTX-4, CTX-5 and RC-2).
129
Figure 4. 11 Effect of (w/gw) on ξ-γ curves – cyclic triaxial and resonant column tests. (specimens CTX-2, CTX-3, CTX-4, CTX-5 and RC-2).
130
Figure 4. 12 The effect of (gw/c) on the G/Gmax-γ (specimens CTX-6, CTX-7, CTX-8, CTX-9, RC-2, RC-3 and RC-4).
131
Figure 4. 13 G/Gmax-γ curves- modified glyben vs. glyben.
132
Figure 4. 14 The effect of (gw/c) on the ξ-γ (specimens CTX-6, CTX-7, CTX-8, CTX-9, RC-2, RC-3 and RC-4)
133
Figure 4. 15 Variation of low strain shear modulus and damping ratio values with confining stress. (specimen RC-1).
134
Figure 4. 16 Variation of high strain shear modulus and damping ratio values with confining pressures. (specimen CTX-1).
135
Figure 4. 17 Variation of Gmax values with confining pressures for various (gw/c) ratios. (specimens BE-7 to 18)
136
Figure 4. 18 Influence of the number of the load cycles. (specimen CTX-15)
137
Figure 4. 19 Variation of Vs of modified glyben with temperature (specimens BE-2, BE-3, BE4, BE-5, BE-6, BE-12 and BE-13)
138
CHAPTER 5 DESIGN AND COMMISSIONING OF A LAMINAR SOIL CONTAINER FOR USE ON SMALL SHAKING TABLES
5.1 Introduction Obtaining an improved understanding of phenomenon such as site amplification, dynamic soil behavior and soil-structure-interaction (SSI) continues to be of significant interest in geotechnical earthquake engineering, especially as performance based design is becoming increasingly popular. Research in the field of earthquake geotechnical engineering can involve different methodologies and approaches such as dynamic soil element tests, reduced-scale model tests, numerical and analytical models and full-scale field tests. If done properly, scaled model tests can be advantageous for seismic studies because of their ability to give economic and realistic information about ground amplification, change in pore water pressure, soil nonlinearity, occurrence of failure and soil structure interaction (Turan et al., 2008). Full-scale field tests and reduced-scale model tests are essential to study soil response and soil-structure interaction during earthquakes. These types of tests are usually required to validate analytical models. Full-scale field experiments have the advantage of considering realistic site conditions; whereas, reduced-scale model tests posses the advantage of providing a controlled environment, and they permit economic parametric studies. Typically reduced-scale seismic model tests are performed either at N-G in a centrifuge or at 1-G using a shaking table. The main advantage of centrifuge testing is that a gravitational stress field similar to that expected in situ can be developed in the model simulating the prototype stress state. For many geologic materials,
139 the stress-strain behavior is a function of confining pressure and an appropriate gravitational stress field is required. However, modeling the overburden stresses is not as significant for studying the seismic response of clays, provided the vertical distribution of undrained strength and stiffness corresponding to the initial state can be simulated. Therefore, the use of a centrifuge is not as critical for studying the seismic response of undrained cohesive soils. This chapter describes the design and commissioning of a novel flexible container for use on small shaking tables with limited base shear capacity. This study has two unique aspects that should be of interest to researchers in this field. First, the laminar container comprises laminae that are supported independently on a series of shafts and linear bearings connected to a frame that transfers the weight of each lamina off the shaking table. This arrangement eliminates the mass of the flexible container as an additional mass that must be supported by the shaking table and consequently maximizes the amount of soil that can be placed on the shaking table. Secondly, the box is filled with a synthetic clay comprising bentonite mixed with glycerin and water (see Chapter 4). The synthetic clay, hereafter referred to as modified glyben, is compacted into the flexible container rather than re-sedimented as a slurry and then subsequently consolidated and aged. The design details of the flexible container are provided in the following sections and a methodology for compacting modified glyben into the container is presented. The methodology is shown to achieve a clay layer that possesses increasing stiffness and strength with depth. A series of instrumented scaled model tests were conducted to evaluate the performance of the container and to measure the free field seismic response of a scaled clay deposit. Finally, the response of the model clay deposit was assessed using the computer program SHAKE 91 to gain confidence in the scaled model. Overall, the research presented below should be of interest to
140 researchers that are: (i) considering designing and fabricating a flexible container for seismic studies but have a small shaking table with significant base shear limitations and (ii) that may be looking for an alternative to resedimented clays for use in model tests.
5.2 Background Generally, flexible containers are designed as either passive or active containers for use in shaking table tests at either 1-G or at N-G during centrifuge tests. In the following section, eight different laminar container designs, mostly passive, are reviewed and their characteristics are summarized in Table 5.1.
5.2.1 Flexible Containers Designed for 1-G Tests Prasad et al. (2004) and Gibson (1997) describe single-axis flexible containers for 1-G seismic tests on shaking tables. Single-axis flexible containers permit movement in a single axis only and typically comprise either rigid guide walls that support laminae on bearings or laminae that are stacked on each other separated by bearings. In addition to single-axis containers, Meymand (1998) and Ueng and Chen (2006) provide details of double-axis flexible containers for 1-G tests. Double axis containers permit horizontal movement of laminae in two principal directions. The Meymand (1998) container comprises a ribbed membrane hanging from a top ring supported by a frame connected to the shaking table using universal joints. In contrast, Ueng and Chen (2006) describe a container with laminae supported by inner and outer frames connected to rigid guide walls.
141
5.2.2 Flexible Containers Designed for N-G Tests Flexible containers built for use in a centrifuge include the single-axis rectangular boxes reported by Van Laak et al. (1994) and Pamuk et al. (2007) and the double-axis 12-sided polygonal laminar container described by Shen et al. (1998). These containers have a number of laminae stacked on top of each other and separated by bearings.
5.2.3 Actively Controlled Containers Takahashi et al. (2001) describe an active type flexible container that is suitable for use in a geotechnical centrifuge. The container comprises a number of lamina stacked on top of each other and lamina are connected to horizontal acting actuators, which enforce pre-determined displacement profiles on the soil confined in the container.
5.2.4 General All flexible container designs described thus far in the literature have their mass supported directly on the table causing extra inertia forces and base shear for the shaking table, which must be accounted for to obtain the desired input motions at the table level.
Furthermore, the
additional weight of the box can become an issue for small shaking tables with limited base shear capacity. The following section describes a novel flexible container that has been designed so that the weight of the box is transferred off the table using an external frame. This arrangement allows full utilization of the base shear capacity of small tables.
142
5.3 Methodology 5.3.1 Experimental Set-up 5.3.1.1
Flexible Soil Container
The flexible container described in this section was designed and manufactured at the University of Western Ontario. Figure 5.1(a) shows the flexible container, which consists of 24 horizontal laminae supported individually by linear bearings and steel guide rods connected to an external frame. The soil pressures acting on each of the lamina were estimated in accordance with Veletsos (1984), and the container was designed with the assistance of finite element analyses to ensure that its components are sufficiently rigid during shaking table tests. The laminae comprise solid high strength aluminum alloy box sections (31.65×31.65 mm) bolted together to form rectangular laminae with plan dimensions of 450mm×900mm. Each lamina is supported by two 15mm diameter stainless steel guide rods connected to the outside edge of the lamina using stiff aluminum brackets (Figure 5.1b). The guide rods feed through four low-friction ball bearings per lamina (two per side), which are housed in four vertical bearing brackets. The bearing brackets are in turn connected to the external support frame (Figure 5.1b). The laminar container is formed by assembling the 24 lamina to create a 807 mm high, 900mm long and 450mm wide box with 2 mm of clearance between the laminae to ensure independent movement. The linear bearing system permits single-axis movement parallel to the longitudinal axis of the container (see Figure 5.1c). The external frame is shown in Figure 5.1 (b) and (c). The frame was fabricated using (50 x 50 mm) hollow structural steel sections welded together to create stiff moment resistant
143 connections. The frame is equipped with adjustable legs so that the box can be leveled with 3 mm of clearance between the shaking table and the lowest lamina. Table 5.2 summarizes the physical properties of the flexible container and its components. In order to place soil into the flexible container, L-channels are bolted to the four corners to align the laminae and to prevent shifting of the laminae during placement of the model clay layer. In addition, a 450×900×10 mm thick wooden base plate is bolted to the shaking table. The wooden base plate has coarse sand epoxied to it to prevent sliding at the soil-base plate interface. The interior of the laminar shear box is then lined with thin flexible latex sheets, which prevent soil penetration into the gaps between laminae and provide watertight confinement for cases where saturated soils may be tested. Prior to compaction of modified glyben into the laminar container, the frictional resistance of each lamina was measured using a spring balance connected to the exterior face of each lamina. Two cases were considered while measuring the frictional resistance: (i) without the internal latex membrane and (ii) with the latex membrane. For case (ii), the frictional resistance varied with the amount of deformation of each lamina. As such, the frictional force was recorded after 15mm of relative movement between laminae, which is considered to be well above that expected during testing. Referring to Table 5.2, the laminar box depicted in Figures 5.1 has very low resistance to horizontal movement due to the lightweight and independent arrangement of laminae, the low sliding friction between laminae and the very thin and flexible inner latex membrane. In addition, transferring the mass of the flexible container off the shaking table significantly reduces the base shear and increases the depth of the clay layer that can be accommodated by the shaking table.
144
5.3.1.2
Shaking Table
The shaking table at the University of Western Ontario comprises a 1-D 1.22 m x 1.22 m table that is displaced laterally using either electrical or hydraulic actuators controlled using a digital control module.
The digital control module allows simulation of various types of
dynamic displacement time-histories, including harmonic spectrum, band limited white noise spectrum and pre-stored earthquake records. An amplifier is used to amplify the low voltages generated by the digital control module to high voltage signals suitable for driving the shaking table. As noted above, the table can be excited using either an electrical actuator for high frequency shaking or a hydraulic actuator for low frequency shaking. Due to the similitude requirements, the electrical actuator was used in this study. The shaking table can efficiently run in the range of 1-150 Hz, it has a maximum 12 mm displacement limit in both directions and 3000 N base shear capacity.
5.3.2 Model Preparation The soil used in the shaking table experiments was a synthetic clay mixture termed modified glyben, which consists of bentonite mixed with glycerin and water (Chapter 4). In the soil mixture, the ratio of solids (bentonite) to liquids (glycerin-water) was 57.5% and the ratio of water in the liquid was 25%. The artificial clay was prepared in seven 50 kg batches using a gaspowered concrete mixer (Crown Mortar). First, the glycerin and water were combined in a drum and stirred by hand. Then, the glycerin and water were slowly blended with the bentonite in the concrete mixer. Each 50 kg batch was mixed for half an hour to ensure a homogeneous mixture and then cured for 10 days to avoid thixotrophic changes in the dynamic properties (see Chapter 4).
145
5.3.2.1
Soil Properties and Placement
The dynamic properties of modified glyben including the shear modulus, damping ratio, and stiffness degradation and damping curves are reported in Chapter 4. The methodology used to compact modified glyben into the flexible container and its general dynamic properties are presented in APPENDIX A. The undrained shear strength profile of the soil in the container was determined using hand shear vane (Pilcon). The shear vane tests were performed at locations far enough from the central part of the box to avoid potential disturbance and alteration of the dynamic characteristics of the clay layer. Figure 5.1 (c) shows the locations of the vane shear tests. Shear vane readings were taken at 100, 200, 300 and 400 mm below soil surface and and the following empirical equation (see Appendix A for its development) was used to deduce the shear wave velocity: Vs = 26.52 Ln(cu ) − 33
[5.1]
where, Vs is shear wave velocity and cu is undrained shear strength of modified glyben. Figure 5.2 shows the variation of normalized shear modulus and damping ratio of modified glyben with shear strain, which are given by G / Gmax = 0.071 + 0.736e (-10.235γ ) + 0.234e (-1.082γ )
[5.2]
where, G / Gmax is normalized shear modulus, and γ is the shear strain and
⎡
⎛ 1 + (0.868 × e (-6.284γ ) − 6.284 × e ( −0.868γ ) /(5.598) ⎞⎤ ⎟⎟⎥ [5.3] 6.284 ⎝ ⎠⎦
ξ = 0.058 + 0.923 × ⎢1 - e (-0.868γ ) - 5.128× ⎜⎜ ⎣
where, ξ is damping ratio.
146 The modified glyben was placed and compacted in horizontal lifts into the flexible container. However, prior to setting up the model tests a series of smaller compaction trials was carried out in a rigid container with the dimensions of 340×265×240 mm to determine the thickness of layers required to achieve a uniform continuous soil layer. For the trial tests, modified glyben was compacted in lifts into the trial container using a 5kg free drop compaction hammer with an area of 100 x 100 mm . After compaction, block samples were trimmed from the compacted clay. The uniformity of the clay was assessed using bender element tests and the presence of air voids or layering was examined visually on block samples. After 6 trials, it was determined that 20mm thick lifts were sufficient to produce uniform clay that appeared to be free of air voids or laminations. Full details of the compaction trials can be found in APPENDIX A. Thus, the modified glyben was compacted into the laminar shear box using 20 mm thick layers placed and compacted using a free drop compaction hammer according to the procedures determined in the trial compaction tests described briefly above. After compacting each layer, the top surface of the layer was scarified by hand to enhance adhesion between consecutive layers. The uniformity of the soil bed was then inspected by using hand shear vane readings at four locations.
5.3.2.2
Similarity Rule
The application of similitude rules to reduced-scale 1-G soil models has been described by researchers such as Rocha (1957), Roscoe (1968), Shunzo (1973), Kagawa (1978) and Kana et al. (1986) among others. In this study, similitude relations derived by Iai (1989) and later used by Meymand (1998) and Lin and Wang (2006) were used. Iai (1989) defined the scaling problem in terms of geometric, density and strain scaling factors. If the model soil density is the same as that of the prototype soil, the strain scaling factor is given by;
147
λε =
λ [(Vs ) p /(Vs ) m ] 2
[5.4]
where, (Vs)p and (Vs)m are the shear wave velocities for the prototype and model soils and λ is geometric scaling factor. The model of Iai (1989) assumes a continuous soil medium and only applies to small strain problems where the soil particles do not lose contact. This ensures that the equilibrium equation remains the same before and after the deformation. Since the dynamic properties of modified glyben are not affected by high levels of continuous cyclic strain (see Chapter 4), it is assumed that soil particles remain in contact even under high strains. Therefore, the Iai model is considered to be suitable for the present study. The resultant scaling relationships between prototype and model are given in Table 5.3. The geometric scaling factor λ used in this study is 40. Using this scaling factor resulted in a prototype to model relationships summarized in Table 5.4. The total weight of the model soil placed on the shaking table was 3695 N based on the similitude conversions summarized in Table 5.4.
5.3.3 Shaking Table Tests The methodology of the shaking table tests performed in this study is presented below along with the procedures followed to interpret the generated data. Table 5.5 gives the summary of shaking table tests. A series of shaking table tests were carried out with the following primary objectives: (i) to investigate the performance of the flexible box boundaries, and (ii) to study the non-linear dynamic behavior of the model soil deposit.
148
5.3.3.1
Tests Performed and Instrumentation Details
Figure 5.3 shows a cross-section of the container and the instrumentation layout. Seven accelerometers (ACC1 to ACC7) and one laser displacement transducer (DISP1) were used to monitor the response of the model clay deposit. A large size (Wilcoxon-M731) accelerometer (ACC7) and a laser displacement transducer (Matsushita-KDCL) (DISP1) were used to measure the table motion. Six small size (Analog Devices- ADXL05) accelerometers (ACC1-ACC6) were used to monitor the soil response. Five of the small accelerometers were mounted on the soil surface. Accelerometers ACC1 to ACC4 were situated along the longitudinal axis of the soil layer ranging from the centre of the box to within 50 mm of the boundary. ACC5 was situated on the transverse axis of the clay layer offset 150 mm from the longitudinal axis. ACC6 was embedded at the mid-height of the soil column directly below ACC1. To investigate the effect of the box boundaries, a small amplitude (0.1 g) harmonic excitation was applied to the table and flexible container filled with soil to ensure linear soil behavior (see Test BND-1 in Table 5.5). Since ACC1 – ACC7 inclusive are most accurate at frequencies of 3 Hz and higher, sinusoidal waves were generated at 5 Hz, which is also far enough from the resonance frequency of the soil column (28 Hz), which will be discussed later. The displacement time history measured using DISP1 was compared with the displacement time history calculated from the response of ACC7 for verification purposes. The readings of accelerometers ACC1, ACC2, ACC3 and ACC4 were compared to examine the influence of the box boundaries. All acceleration readings were filtered using 4th order Butterworth filtering procedure with low-pass at 25 Hz. The natural frequency of the soil column was evaluated using a five minute long sinusoidal sweep test, ranging from 0.1 Hz to 50 Hz, which is designated test NF-1 in Table 5.5.
149 Resonance frequencies of the soil and table were deduced from spectral analysis of the response at ACC1 and ACC7. Soil amplification and non-linear soil behavior was studied using sinusoidal displacement time-histories at 10 Hz with various intensities ranging from 0.12g to 0.7g. These tests are denoted AMP-1 to AMP-4, inclusive, in Table 5.5. Interpretation of the results is described below. To conclude, the non-linear response of the model clay deposit was also studied using a more realistic displacement-time history based on the El Centro earthquake (Imp Vall., Irr. Dist. 180). These tests are designated HYS-1 and HYS-2 in Table 5.5.
For the simulated El Centro
earthquake, the shaking table system was not able to exactly replicate the scaled El Centro displacement time-history due to: (i) inertia effects caused by the mass of the table and soil placed on it and (ii) limitations of the actuator and control system. However, an approximate time-history was generated at the table level after taking into account inertia effects, which cause differences between the time history specified in the computer control module compared to that obtained on the table. The resultant approximate time history had similar frequency content and peak ground accelerations compared to that of the scaled El Centro horizontal displacement time-history, however the predominant frequency was lower. Numerical analyses were subsequently carried out for each test case using the equivalent linear analysis procedure implemented in the computer program SHAKE 91. The numerical analyses were performed to verify the model tests and to gain confidence in the scaled-model approach.
150
5.3.3.2
Interpretation of Experimental Data
Interpretation of ground motion amplification of the soil deposit was done using Equation 5.5,
ρ amp =
max( &x&soil (t ) ) max( &x&table (t ) )
[5.5]
where, ρ amp is the amplification factor and &x&soil (t ) and &x&table (t ) are the soil surface and table accelerations, respectively. Hysteretic stress-strain loops were derived from the measured response at ACC-1, ACC-6 and ACC-7 for use in studying the non-linear behavior of modified glyben. The Hysteretic stress-strain loops were derived using the procedure described in Zeghal et al. (1994) and (1995) and summarized here. If the soil is idealized as a one-dimensional shear beam, the shear stresses and shear strains at a particular depth can be calculated utilizing the acceleration measurements at these levels.
By integrating the equation of motion using stress free surface boundary
condition, the shear stress at depth z is;
z
τ ( z , t ) = ∫ ρu&&dz
[5.6]
0
where, τ is shear stress u&& is acceleration and ρ is the mass density. Using linear interpolation between the acceleration measurements at different depths (e.g. ACC-1, ACC-6 and ACC-7), the discrete shear stress value at depth z is; i −1
τ i (t ) = ∑ ρ k =1
u&&k + u&&k +1 ∆zk , i = 2,3,... 2
[5.7]
151 where, subscript i refers to depth zi in Figure 5.4 (a) , τ i = τ ( z i , t ) ; u&&i = u&&( z i , t ) and ∆z k is the soil slice thickness. The corresponding shear strain value γ i can then be calculated in accordance with Pearson (1986) using the displacement values derived from double integration of the acceleration time histories viz.;
γi =
⎡ ∆zi −1 ∆zi ⎤ 1 + (ui − ui −1 ) ⎢(ui +1 − ui ) ⎥ ∆zi −1 + ∆zi ⎣ ∆zi ∆zi −1 ⎦
[5.5]
where, ui = u ( zi , t ) is the absolute displacement at the level of zi . From the above approximations, the shear modulus and damping ratio of the modified glyben were calculated from the shear stress-strain loops. The shear modulus of the modified glyben was calculated using the secant slope and the damping ratio was calculated using the area of the corresponding shear stress-strain loop in accordance with Kramer (1996) (see Figure 5.4b). Shear modulus and damping ratio values calculated form the derived hysteresis loops were compared to those given in Figure 5.2, which shows variation of the normalized shear modulus and damping ratio with shear strain amplitude for modified glyben obtained from cyclic triaxial and resonant column tests (see Chapter 4).
5.4 Results and Discussion Figure 5.5 shows the shear strength profile measured using hand shear vane tests and the corresponding shear wave velocity profile. From Figure 5.5, it can be seen that placement of the modified glyben into the laminar container produced a clay layer that possessed increasing undrained shear strength and shear wave velocity with depth. The increase in shear strength and shear wave velocity with depth can be attributed to the influence of compaction energy of upper
152 layers on the lower layers. The clay deposit has undrained shear strength of 33 kPa at the surface and 46 kPa at 400 mm below surface. Corresponding shear wave velocities for the two locations are calculated as 58 and 67 m/sec, respectively.
5.4.1 Performance of Laminar Shear Box 5.4.1.1
Bearing Friction and Membrane Effects
The friction between laminae is generally a factor that requires calibration in many of the laminar boxes reported in the literature (see Prasad et al., 2004). However, in the current design, laminae are not placed on top of each other. Individual laminae are directly connected to the external frame using low friction linear bearings. Such an arrangement eliminates the sliding resistance introduced in stacked lamina assemblies (e.g. see Prasad et al., 2004). Figure 5.6 plots the measured lateral resistances along the depth of the box for the cases: (i) without and (ii) with the internal membrane. Resisting forces measured for each lamina ranged between 3 and 6 N and 4.5 to 8 N for cases (i) and (ii), respectively. It is noted that the friction and membrane effects are uniform along the depth of the box, and are insignificant compared to the shear resistance of the soil column and the inertial forces generated during shaking.
5.4.1.2
Assessment of Boundary Effects
Figure 5.7 shows the acceleration time histories at ACC1, ACC2, ACC3 and ACC4 for test BND-1 in Table 5.5. Test BND-1 was performed to verify if the laminar container was simulating flexible boundaries or not. The results show that the differences between the responses at ACC1, ACC2 and ACC3 were insignificant. The response of ACC4, which was situated 50 mm away from the box boundary, showed a scattered shape. However, the peak
153 amplitude remained around 0.128 g, which was very close to peak amplitudes measured by other three accelerometers. These results demonstrate that the flexible boundaries of the laminar box functioned appropriately. The scattered shape at ACC4 can be attributed to factors; such as, the local rigid boundary effect within the lamina level (i.e. depth of lamina), and possible compaction imperfections close to the walls of the box. However, the results suggest that the majority of the soil behaves according to the 1-D vertical shear wave propagation model and that there are relatively minor boundary influences within 50mm of the container walls.
5.4.2 Seismic Free Field Response This section presents the results of shaking table tests performed using a sinusoidal sweep (NF-1), harmonic load (AMP-1 to AMP-4) and random earthquake time history (HYS-1 and HYS-2) to study soil resonance, soil amplification and hysteretic soil non-linearity.
5.4.2.1
Soil Resonance
Figures 5.8 (a) and (b) show the acceleration time histories measured on the table (ACC7) and soil surface (ACC1), respectively; whereas Figure 5.8 (c) shows the corresponding power spectra. The root mean square (RMS) of the power spectra reflects the amplification of the input signal. The peaks in the power spectra show the resonance frequencies of the soil and shaking table. According to Figure 5.8 (c), the fundamental frequency of soil column was 28 Hz. The second peak at 50 Hz in the power spectra is due to the dynamic response of the table. Since the mass of the soil placed on the table was larger than the mass of the table, the magnitude of peak power for the soil was predominant and greater than that of the table in both ACC1 and ACC7 spectra.
154
5.4.2.2
Soil Amplification
Figures 5.9 (a)-(d) compare sinusoidal acceleration time histories measured on the shaking table (ACC7) to those measured on the soil surface at ACC1 and predicted using SHAKE 91 for tests AMP-1 to AMP-4 (see Table 5.5). In addition, calculated and measured amplification factors are also presented on Figures 5.9 (a)-(d). It is noted that the calculated amplification factors were obtained using Equation 5.5. The amplitudes of the input time histories were approximately 0.12 g, 0.35 g, 0.55 g and 0.7 g. The duration and frequency of each sine wave were 10 seconds and 10 Hz, respectively. However, only two seconds of the measured response has been shown for a clear visualization. From Figure 5.9, it can be seen that there is good agreement between the experimental and numerical amplification factors for the various acceleration time-histories. The results show that the hysteretic soil behavior played a significant role in the amplification characteristics of the soil deposit. Increasing the shaking intensity resulted in an increase in the amplification factors. The measured amplification factors calculated using Eqn. 5.5 were 1.21 at 0.12g, 1.25 at 0.35g, 1.34 at 0.55g and 1.44 at 0.7g, respectively. The corresponding amplification factors calculated using SHAKE 91 for the model conditions are 1.15, 1.20, 1.27 and 1.32. The maximum difference between calculated and measured amplification factors is 9% at 0.7g, which is considered to be reasonable for such tests. The difference between measured and calculated amplification is about 5% at 0.12g, 0.35g and 0.5g. An approximate version of the scaled horizontal component of the El Centro time history was applied to the shaking table as shown in Figures 5.10 (a)-(c). Figure 5.10 (a) shows the acceleration time history and Fourier spectra of the un-scaled horizontal component of the El Centro earthquake. The scaled horizontal El Centro time-history is shown in Figure 5.10 (b) and
155 Figure 5.10 (c) shows the displacement time-history achieved at the shaking table level. From Figure 5.10 (c), it can be seen that the predominant frequency of the scaled earthquake signal measured on the table is 3.32 Hz as opposed to 9.23Hz (see Figure 5.10 (b)). As discussed in the methodology section, this was due to inertia effects and limitations of the actuator and control system used in the shaking table tests as discussed above in the methodology.
In spite of the
approximate nature of the simulated El Centro time-history, the peak acceleration is accurate, and the frequency content is comparable to that of the scaled earthquake (see Fig. 5.10 (b)). However, the predominant frequency at the peak acceleration is only 3.32Hz compared to 9.23Hz in Figure 5.10 (b). Figures 5.11 (a) and (b) show the measured acceleration time history at ACC1 and the calculated acceleration time-history on the soil surface, respectively. The calculated time-history was obtained using SHAKE 91 for the input motion shown in Figure 5.10 (c). It can be seen in Figure 5.11 that the measured and calculated peak soil surface accelerations were 0.45g and 0.43 g, respectively, and the corresponding measured and calculated (SHAKE 91) amplification factors are 1.32 and 1.26, respectively. The agreement between the experimental and numerical results provides strong evidence that the laminar box and model soil performed well in 1-G conditions.
5.4.2.3
Hysteretic Soil Behavior
A series of hysteretic loops were derived from the measured response of ACC1, ACC6 and ACC7 during the application of harmonic time-histories with the peak amplitudes of 0.12g, 0.35g, 0.5g, and 0.7g. The hysteretic loops are plotted in Figures 5.12 (a)-(d). From the
156 hysteretic loops, a series of modulus reduction factors G / Gmax and damping ratios were estimated and the values are summarized in Table 5.6. Referring to Table 5.6, the hysteretic loops presented in Figures 5.12 (a)-(d) show that the soil stiffness degraded and the damping ratio increased with increasing shear strain amplitudes. The variation of G / Gmax from the shaking table tests is similar to that reported in Chapter 4 from cyclic triaxial and resonant column tests. The modulus reduction factors deduced from Figures 5.12 (a)-(d) are 6% to 39% higher than those measured using cyclic triaxial and resonant column tests. Figure 5.13 compares the modulus reduction and damping ratios from shaking table tests with those obtained from cyclic triaxial tests (see Figure 5.2). From Figure 5.13, it can be seen that the modulus and damping response of the synthetic clay layer during shaking in the flexible container is generally consistent with the results of cyclic laboratory tests on modified glyben. The difference between the behavior deduced from the shaking table tests and those obtained from cyclic laboratory tests can be attributed to: (i) differences in the mode of loading between shaking table tests (pure shear) and laboratory tests (torsion and compression), (ii) the small number of accelerometers on the vertical array, which resulted in giving the average values over a significant depth which is expected to have varying level of strain, and (iii) approximations in the calculation of hysteretic loops for the soil from discrete accelerometer readings.
5.5 Summary and Conclusions This chapter described the design and commissioning of a laminar shear box, which overcame the base shear limitations of a small 1-G shaking table. The performance of the laminar shear box was evaluated using a series of scaled model tests, which are summarized in
157 Table 5.5.
This chapter presented the results of these tests in addition to details of the
methodology used. The following is a summary of the results and conclusions arising from this study. 1. The weight of the laminar box was transferred away from the table using an external frame system. This approach reduced the mass situated on the table permitting full utilization of the base shear capacity of the shaking table for the soil model. 2. The laminae were not stacked on top of each other. Instead, they were directly connected to the external frame using low friction ball bearings. This design reduced frictional forces, which varied between 3 N and 8 N especially in the bottom-most laminae compared to stacked laminae. Measured resisting forces due to bearing friction and membrane effects were found to be linear along the container depth and negligible compared to the shear resistance of the soil placed in the laminar container. 3. The hand vane shear tests showed that a uniform horizontal compaction was achieved. Due to the compaction energy used in the compaction of upper layers, an increase in the stiffness of lower layers was observed. The variation in the shear wave velocity between the top and bottom of the soil column was about 25 %. Since the seismic response of the flexible container and scaled clay layer was consistent with a 1-D soil column, it is concluded that the soil compaction method employed in this study is appropriate. 4. The effect of the boundary on measured accelerations was found to be negligible. The scatter of the reading of the accelerometer closest to the boundary can be attributed to local rigidity at the level of the lamina and possible compaction irregularity near the wall.
158 However, the peak amplitude remained very close to that measured by other accelerometers. 5. The fundamental frequency of soil column was 28 Hz. It was seen in the power spectra that shaking table responds at about 50 Hz. Since the mass of the soil placed on the table was higher than the mass of table, the peak power magnitude for soil degree of freedom was predominant over table degree of freedom in the soils response. 6. The soil non-linearity played an important role in the amplification characteristic of the soil deposit. Increasing the shaking intensity resulted in an increase in the amplification factor. The approximate El Centro time-history applied to the base of the soil column was amplified by an almost identical amount in the shaking table tests and numerical simulations. The good agreement between the experimental and numerical results further proved the performance of laminar shear box and model soil. 7. The variation of stiffness and damping of modified glyben (versus shear strain amplitude) obtained from ACC1, ACC6 and ACC7 during the shaking table test are, in general, consistent with those obtained in laboratory tests at small input motion intensities. It is acknowledged that, in some cases, there was significant difference (ie. up to 38%) between the G and ξ values derived from the response of the model clay layer compared to the laboratory values; however, the differences can be attributed to differences in the mode of loading between the shaking table testes and cyclic laboratory tests and the low number of accelerometer used in vertical array, which resulted in giving the average values over a significant depth that is expected to have varying level of strain.
159
References Gibson, A.D. 1997. Physical scale modeling of geotechnical structures at one-g. PhD thesis. Pasadena, CA, California Institute of Technology. Iai, S 1989. Similitude for shaking table tests on soil-structure-fluid model in 1-g gravitational field. Soils and Foundations, JSSMFE, 29(1): 105-118. Kagawa, T. 1978. On the similitude in model vibration tests of earth structures. Proceedings of Japan Society of Civil Engineering, Tokyo, Japan, 275: 69–77. Kana, D., Boyce, L., Blaney, G. 1986. Development of a scale model for the dynamic interaction of a pile in clay. Journal of Energy Resources Technology. ASME, 108(3):254-261.
Kramer, S.L. 1996. Geotechnical earthquake engineering. Prentice-Hall Inc., Englewood Cliffs, NJ. Lin, L., and Wang, L. 2006. Seismic slope behavior in a large-scale shaking table model test. Engineering Geology, 86:118–133. Meymand, P.J. 1998. Shaking table scale model tests of nonlinear soil-pilesuperstructure interaction in soft clay. PhD thesis, Berkeley, CA, The University of California, Berkeley. Pamuk,_A., Gallagher, P.M., and Zimmie, T.F. 2007. Remediation of piled foundations against lateral spreading by passive site stabilization technique. Soil Dynamics and Earthquake Engineering, 27:864–874.
160 Pearson, E.C. 1986. Numerical methods in engineering and science, Van Nostrand Reinhold Co., New York. Prasad, S.K., Towhata, I., Chandradhara, G.P. and Nanjundaswamy, P. 2004. Shaking table tests in earthquake geotechnical engineering. Current Science 87(10): 13981404. Rocha, M. 1957. The possibility of solving soil mechanics problems by use of models. Proc. 4th Intl. Conf. Soil Mechanics and Foundation Engineering, London, UK, 1: 183-188. Roscoe, K. 1968. Soils and model tests. Journal of Strain Analysis, 3(1): 57-64. Shen, C.K., Li, X.S., Ng, C.W.W., Van Laak, P.A., Kutter, B.L., Cappel, K. and Tauscher, R.C. 1998. Development of a geotechnical centrifuge in Hong Kong. Centrifuge 98, Tokyo, Japan, 1: 13-18. Shunzo, O. 1973. Introduction to earthquake engineering. University of Tokyo Press. Takahashi, A., Takemura, J., Suzuki, A. and Kusakabe, O. 2001. Development and performance of an active type shear box in a centrifuge. International Journal of Physical Modeling in Geotechnics, 1(2): 1-18. Turan, A., Hinchberger, S.D. and El Naggar, M.H. 2008 Investigation of dynamic performance of bentonite-glycerin-water based artificial clay. GRC Research Report, Report No: GEOT-08-01, The University of Western Ontario, London, ON, Canada. Ueng, T.S. and Chen, C.H. 2006. Liquefaction of sand under multidirectional shaking table tests. In: Ng, Zhang and Wang editors, Proceedings of the International Conference on Physical Modeling in Geotechnics, ICPMG ’06, Hong Kong, 481-
161 486. Van Laak, P., Taboada, V., Dobry, R. and Elgamal, A.W. 1994. Earthquake centrifuge modeling using a laminar box. In: Ebelhar, R.J., Drnevich, V. and Kutter, B.L., Dynamic Geotechnical Testing: Second Volume, ASTM STP 1213, American Society for Testing and Materials, Philadelphia, p.370-384. Veletsos, A. 1984. Seismic response and design of liquid storage tanks. Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, ASCE Technical Council on Lifeline Earthquake Engineering, ASCE, NY, p. 255 – 370. Zeghal, M. and Elgamal, A-W. 1994. Analysis of site liquefaction using earthquake records. Journal of Geotechnical Engineering, ASCE, 120(6):996–1017. Zeghal, M., Elgamal, A-W., Tang, H.T. and Stepp, J.C. 1995. Lotung downhole array. II: evaluation of site nonlinear properties. Journal of Geotechnical Engineering, ASCE, 121(4):363–378.
162
Table 5. 1 Summary of available laminar shear box designs. Direction of Operation
Dimensions (WxLxH) mm
Use in
350 x 900 x 470
1-G
1-D
Rectangular
1,4,6
Prasad et al. (2004)
500 x 1000 x 1000
1-G
1-D
Rectangular
1,4,6
Meymand (1998) Ueng and Chen (2006) Van Laak et al. (1994) Pamuk et al. (2007)
2280 x 2130 (D,H)
1-G
2-D
Circular
3,4,6
1888x 1888 x1520
1-G
2-D
Rectangular
2,4,6
254 x 457x 254
n-G
1-D
Rectangular
1,4,6
355 x 710 x 355
n-G
1-D
1,4,6
584 x 500 (D,H)
n-G
2-D
Rectangular 12 sided polygon Rectangular
1,4,5
Reported By Gibson (1997)
Shen et al. (1998)
Takahashi et al. 200 x 450 x 325 n-G (2001) a Notes; 1. A stack of laminae separated by bearings 2. Laminae supported by a frame and move independently 3. Container hanging on the top lamina supported by a frame 4. Entire container placed on shaking table 5. Active 6. Passive
1-D
Shape
Descriptiona
1,4,6
163
Table 5. 2 Box properties. Component Lamina
Property Weight Inside Dimensions Number Bearing Brackets Weight Dimensions Number Guide Rods Weight Length Diameter Number Linear Bearings Number Frictional Force per Lamina* Membrane Material Thickness Total Weight of Container *
Value 26.06N 450mm×900mm 24 75N 25.4 x 31.65 4 7.8N 900mm 15mm 48 96 6.5N (±1.5N)
Latex 0.2 mm 1297N
The frictional force between laminae was measured with the latex membrane in place and by restraining all but one lamina and pulling the unrestrained lamina using a sensitive scale.
164
Table 5. 3 Similitude relationships of parameters between prototype and model (After Meymand, 1998). Mass density
1
Acceleration
1
Length
λ
Force
λ3
λ1/2
Stress
λ
Stiffness
λ2
Shear wave velocity Time
λ1/2
Strain
1
Modulus
λ
Frequency
λ−1/2
EI
λ5
165
Table 5. 4 Similitude relationships of clay deposit between prototype and model. Model
Prototype
Soil depth (m)
0.55
22
Average shear wave velocity (m/s)
53.5
338
0.12, 0.35, 0.55, 0.7
0.12, 0.35, 0.55, 0.7
1
1
Frequency (Hz)
6.32
1
Bulk Density (kg/m3)
1780
1780
Acceleration (g) Strain
166
Table 5. 5 Summary of tests Test No. NF-1 BND1 AMP1 AMP2 AMP3 AMP4 HYS1 HYS2
Purpose To investigate the natural frequency of the soil deposit To investigate the influence of box boundaries To investigate the ground motion amplification To investigate the ground motion amplification To investigate the ground motion amplification To investigate the ground motion amplification To investigate the hysteretic soil behavior To investigate the hysteretic soil behavior
Type of loading
Predominant frequency (Hz)
Peak Amplitude (g)
Sine sweep
0.1 to 50
0 to 0.3
Harmonic
5
0.1
Harmonic
10
0.12
Harmonic
10
0.35
Harmonic
10
0.55
Harmonic
10
0.70
3.32
0.34
3.32
0.34
Random earthquake time history Random earthquake time history
167 Table 5. 6 Comparison of dynamic soil properties from cyclic laboratory tests (cyclic triaxial/resonant column) and shaking table tests.
G/Gmax
Damping Ratio (%)
Shear Strain (%)
Laboratory Tests (Turan et al., 2008)
Shaking Table Tests
Error (%)
0.028 (at 0.12g peak acc.)
0.85
0.908
6.38
0.152 (at 0.35g peak acc.)
0.42
0.487
13.75
0.291 (at 0.55g peak acc.)
0.30
0.437
31.35
0.396 (at 0.70g peak acc.)
0.24
0.393
38.9
0.028 (at 0.12g peak acc.)
7.92
10.75
26.32
0.152 (at 0.35g peak acc.)
13.75
11.07
24.20
0.291 (at 0.55g peak acc.)
17.16
12.44
37.94
0.396 (at 0.70g peak acc.)
18.35
14.95
22.74
* Gmax at the ACC6 level is 7065 KPa.
168
Figure 5. 1 (a) Laminar box covered with latex membrane and aligned with corner profiles.
169
Figure 5. 1 (b) Isometric view of laminar box.
170
Figure 5. 1 (c) Profile and plan views of the laminar box with vane shear test locations.
171
Figure 5. 2 (a) Stiffness degradation for modified Glyben (after Turan et al. 2008).
172
Figure 5. 2 (b) Damping curves for modified Glyben (after Turan et al. 2008).
173
Figure 5. 3 Schematic of the instrumentation
174
Figure 5. 4 (a) Accelerometer array and soil descritization for use in stress-strain calculations
175
Figure 5. 4 (b) Typical hysteretic loop.
176
Figure 5. 5 Shear strength and shear wave velocity profiles along the depth.
177
Figure 5. 6 Resistance forces against the lateral lamina movement.
178
Figure 5. 7 The influence of the box boundaries on the dynamic response.
179
Figure 5. 8 (a) Acceleration time histories on the soil surface
180
Figure 5. 8 (b) Acceleration time histories on the table.
181 Figure 5. 8 (c) Corresponding power spectra.
182
Figure 5. 9 (a) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.12 g.
183
Figure 5. 9 (b) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.35 g.
184
Figure 5. 9 (c) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.55 g.
185
Figure 5. 9 (d) Measured and calculated acceleration time histories and amplification factors at the input motion intensities of 0.70 g.
186
Figure 5. 10 (a) Acceleration time histories and Fourier spectra of prototype scale El Centro earthquake
187
Figure 5. 10 (b) Acceleration time histories and Fourier spectra of scaled El Centro earthquake applied to the table
188
Figure 5. 10 (c) Acceleration time histories and Fourier spectra of signal measured on the table.
189
Figure 5. 11 (a) Measured acceleration time histories on the soil surface.
190
Figure 5. 11 (b) Simulated acceleration time histories on the soil surface.
191
Figure 5. 12 (a) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.12 g.
192
Figure 5. 12 (b) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.35 g.
193
Figure 5. 12 (c) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.55 g.
194
Figure 5. 12 (d) Hysteretic shear stress-strain loops for the input motion intensity levels of 0.70 g.
195
Figure 5. 13 Comparison of soil stiffness and damping ratio deduced from laboratory tests and shaking table tests.
200
CHAPTER 6 SEISMIC SOIL-STRUCTURE INTERACTION IN BUILDINGS ON STIFF CLAY AND WITH EMBEDDED BASEMENT STORIES
6.1 Introduction Seismic forces factor heavily into the design load cases for structures in seismic regions. The magnitude of seismic forces can be strongly influenced by the travel path of seismic shear-waves, the dynamic stiffness of the foundation soil, local site effects and soil structure interaction (SSI). Since the early 1970's, researchers have studied SSI in all types of engineering structures (Veletsos and Vebric, 1973; Bielak, 1975; Luco 1980; Cakmak et al. 1982; Wolf, 1985 and 1988). From these studies, several methods have been developed for estimating SSI forces, and the methods can be classified as either analytical solutions based on the wave equations (Luco, 1976; Pak and Gobert, 1991), or discritization based methods such as finite elements, finite difference or boundary elements (Kaussel and Roesset, 1975; Lysmer et al., 1976), and empirical methods (Gazetas, 1991). The use of full scale observations or reduced scale model tests to confirm analytical methods has however not kept pace. It is recognized that structures founded on or in soils interact through two mechanisms called inertial and kinematic interaction. Inertial interaction occurs as a result of the inertia forces produced by seismic accelerations of the structure. The inertia forces increase the base shear and overturning moments acting on the foundation resulting in relative displacements between the free field and foundation. Kinematic
201 interaction, on the other hand, takes place due to structure interaction of the foundation and soil, which also causes deviation of the foundation motion from the free field motion, due to ground motion incoherence, wave inclination and foundation embedment effects (Steward et al., 1999). Kinematic interaction is governed by the relative stiffness of the foundation and soil. In general, SSI can decrease the base shear, lateral forces, and overturning moments experienced by a structure during earthquakes. However, it increases lateral displacements and the secondary forces associated with P-delta effects (FEMA 450). Therefore, SSI effects should be taken into account during the design process. This chapter presents the results of scaled model tests that were performed on a model building with embedded levels and founded on stiff clay deposit.
In addition, the
response of the model building is compared with an analytical solution for kinematic soilstructure interaction (Aviles and Perez-Rocha, 1996 and 1998) and a nonlinear finite element model. The model structure used in this study comprised a simple 1-degree of freedom structure with a modular box foundation designed to permit the researchers to vary the embedment depth. The model structure was embedded in an artificial stiff clay layer consisting of modified glyben (see Turan et al., 2008a), which was compacted into a laminar shear box on a 1-D shake table. The soil-structure system was subjected to shaking and the response of the system with different embedment depths is compared with analytical solutions by Aviles and Perez-Rocha (1996) and (1998) and a finite element model based on a surface bounding model (Borja 2000). Both the FE model and analytical solution consider inertial and kinematic interaction effects. The primary objectives of this study were (i) to confirm the laminar container and model clay layer
202 and structure for SSI studies and (ii) to gain confidence in two analytical methods that are suitable for studying SSI effects. The following sections describe: (i) the methodology followed for the scaled model tests, (ii) Compares the test results with analytical solutions and (iii) summarizes the work and conclusions. The results presented in this study are considered to be useful for the researchers and practitioners interested in the seismic behavior of partially embedded structures and it is envisioned that the data presented in this study will lead to further studies and an improved understanding of SSI effects on the seismic behavior of the structures with embedded levels.
6.2 Methodology This section provides a brief description of the apparatus used in this study, gives details of the model soil layer and structure used and summarizes the similitude theory used to develop the scaled model.
6.2.1 Experimental Set-up Scaled model tests were carried out at 1-g using a laminar soil container placed on a 1.22 m x 1.22 m 1-D shaking table. Figure 6.1 shows details of the laminar container, which is described in more detail by Turan et al. (2008b). The shaking table can be excited using either a pneumatic or electric actuator controlled by a digital control module, which allows simulation of various types of dynamic displacement timehistories. In this study, an electrical actuator was used since the frequency of the scaled input motion was higher than could be achieved using the pneumatic actuator.
203 The laminar container comprises 24 horizontal lamina supported individually on linear bearings and steel guide rods connected to an external frame (see Fig. 6.1). The inner dimensions of the container are 807 mm, 900 mm and 450 mm corresponding to the height, length and width, respectively. In order to prevent sliding between the model soil layer and the shaking table, a 10 mm thick wooden base plate with sand epoxied to its surface was bolted to shaking table and the interior of the container was lined using thin flexible latex sheets to prevent soil from penetration into the clearances between lamina. The laminar container has been shown to simulate flexible boundary conditions and 1-D vertical shear-wave propagation (Turan et al., 2008b).
6.2.2 Model Description 6.2.2.1
Soil Placement and Properties
The model soil layer comprised modified glyben compacted into the laminar container in 20 mm thick lifts using a free drop compaction hammer in accordance with Turan et al (2008a). The uniformity of the model soil deposit was checked using hand shear vane tests (Pilcon) performed at four points located at 50 mm away from the corners of the box and far enough from the central part of the box to avoid potential disturbance and alteration to the dynamic characteristics of the model soil deposit. At each location, vane measurements were taken at depths of 100, 200, 300 and 400 mm below the soil surface and an undrained shear strength profile was developed by averaging the measurements.
The corresponding shear wave velocity profile was
estimated from the vane strength using the following correlation developed by Turan et al. (2008a),
204 Vs = 26.52 Ln(cu ) − 33
[6.1]
where, Vs is shear wave velocity and cu is undrained shear strength of modified glyben. Figure 6.2 shows the vane shear strength and shear wave velocity profiles measured and calculated in model soil deposit, respectively. Figure 6.3 shows the G/Gmax and damping ratio versus shear strain amplitude for modified glyben (from Turan et al. 2008a).
6.2.2.2
Model Building and Instrumentation Details
The model building used in the shaking table tests was manufactured by University Machine Services (UMS) and is shown in Figure 6.4. The model building comprises a single degree of freedom system (SDOF) representing the superstructure and a rigid box assembly composed of four segments representing embedded basement stories. The SDOF is composed of interchangeable columns that possess a solid square cross-section (25.4 mm x 25.4 mm) and a 6.7 kg cylindrical steel mass rigidly connected to the top. Columns were made of both acrylic and steel to create low frequency and high frequency superstructure behavior, respectively. To simulate embedment, the SDOF system was rigidly connected to a 6.35 mm thick aluminum plate, which was in turn screwed rigidly to the top of the basement assembly. The base assembly was modular. Each module comprised four 50 mm high by 12.7 mm thick acrylic plates that were glued together to make square basement storey assemblies with external dimensions of 200 x 200 mm. The storey assemblies were rigidly connected to each other using six steel pins installed in grooves machined on the walls. A 6.35mm thick acrylic base plate was then glued to the bottom of the basement wall assemblies. The resultant assembly allowed model buildings with various numbers of rigid basement
205 stories in an efficient and economic way. An opening was machined on the top slab to permit installation of instrumentation. Several rectangular brass plates were screwed to the inside of the base walls and distributed evenly on the walls to model the mass of the embedded basement stories where applicable. Figure 6.5 shows the instrumentation plan of the model soil-structure system. Five accelerometers (Analog Devices- ADXL05), ACC1-ACC5 and a laser displacement transducer (Matsushita-KDCL), DISP1, were used to monitor the dynamic behavior of SSI system. ACC1 was mounted to the surface of the shaking table to measure the scaled base excitation generated on the shaking table. The measurements of displacement transducer DISP1 are used for verification of the data measured by ACC1. ACC2 was mounted on the soil surface, 300 mm away from the edge of the embedded model basement. ACC3, ACC4 and ACC5 are mounted on the base plate, top plate and lumped mass of the model building, respectively.
6.2.2.3
Similarity Rule
Similitude relationships derived by Iai (1989) are used in this study. Iai (1989) defined the scaling problem in terms of geometric, density and strain scaling factors. If the model soil density is the same as that of the prototype soil, the strain scaling factor is given by
λε =
λ [(Vs ) p /(Vs ) m ] 2
[6.2]
where, (Vs)p and (Vs)m are the shear wave velocities for the prototype and model soils and λ is the scaling factor for length. The similarity rules derived by Iai (1989) apply to small strain problems only where the soil particles do not lose contact, which assures that
206 the equilibrium equations are valid before and after seismic induced deformation. Turan et al. (2008a) have shown that these assumptions are satisfied by modified glyben. The scaling relationships between prototype and model given by Iai (1989) are shown in Table 6. 1. Using the scaling factor for length, λ=40, prototype-to-model relationships are calculated and are summarized in Table 6. 2 for the model soil deposit and structure.
6.2.3 Shaking Table Tests Shaking table tests were carried out to study the response of structures with embedded stories (see Figure 6.6). A summary of the shaking table tests can be found in Table 6. 3. Prior to testing soil-structure systems, tests were performed to check the dynamic characteristics of the soil deposit and simplified structures separately. First, two harmonic waves with the peak amplitude of 0.12g and 0.35 g were generated on the shaking table with the laminar container and model clay layer fixed to the table. During these tests, which are labeled FFGR-1 and FFGR-2, the free field ground response of the model soil deposit was monitored (FFGR-1 and FFGR-2). Next, the fundamental frequency of the soil layer and structures were determined using a series of sine sweep tests. For these tests, the laminar box and SDOF systems representing (a) tall-slander and (b) short-squat structures (SDOF-L and SDOF-H) were rigidly connected to the shaking table and sine sweep tests were carried out to confirm the dynamic parameters of the structures and to measure the fundamental frequency of the soil deposit. These tests are labeled FB-LF and FB-HF corresponding to test to determine dynamic properties of the low frequency and high frequency structures,
207 respectively. From the results of FB-LF and FB-HF tests, the fundamental frequency and damping ratio of the superstructures were obtained using Fourier analysis and the halfpower method (Clough and Penzien, 1975), respectively. Subsequent to these tests, SDOF-L and SDOF-H were mounted on the surface of the soil deposit and dynamic parameters of the combined SSI system were again determined using a sine sweep test. These tests which correspond to zero embedment are labeled SRF-LF and SRF-HF. In order to model various embedment cases, the model soil (modified glyben) was hand excavated to depths of 50, 100 and 200 mm successively and 1, 2 and 4 levels of basement assemblies were placed in the soil. Gaps around the sides of the embedded basement walls were carefully backfilled with modified glyben that was tamped into place to achieve full soil-structure contact. Soil-structure contact was monitored through the transparent acrylic basement walls during the tamping process. The prefix, EM, is used hereafter to denote shaking table tests performed with embedded basement stories corresponding to D/L of 0.5, 1 and 2 (see Table 6. 3). For each embedment case, tests were carried out using either a sine sweep (SS) or harmonic loading (HL). In total, ten sine sweep tests and 2 harmonic loading tests were performed as outlined in Table 6.3. The test labeled with M was conducted with an additional mass at the foundation level. It is noted that the shear wave velocity of the model clay layer increase with depth and that this is not consistent with analytical solutions which are based on a homogeneous semi-infinite linear elastic medium.
However, the variation of soil
stiffness is considered to be small and the amplitude of excitation applied was small enough to (i) avoid significant non-linearity of the soil and (ii) ensure fully bonded soilstructure interfaces.
208
6.2.4 Interpretation of Shaking Table Test Data The raw data obtained from shaking table tests were filtered using 6th order Butterworth filtering technique in the range of 0.5-50 Hz. The fundamental frequency and damping ratio of the SSI systems were calculated using the filtered experimental data. The fundamental frequency and damping ratio of the interacting system, Ω and ξ , were determined using half-power method in accordance with Clough and Penzien, (1975). The fundamental frequency of the SSI system is defined as the frequency at which the peak of the amplitude spectrum of the transfer function between the relative responses of structural mass and incident wave occur. The damping ratio of the system, ξ , was calculated using the frequencies at which, the response is reduced to ( 1 / 2 ) times of the peak amplitude as shown in Equation [6.3].
ζ =
f 2 − f1 f 2 + f1
[6.3]
where, f1 and f 2 are the frequencies at the left and right of f at which the amplitude is
u=
u peak 2
[6.4]
209
6.2.5 Analytical Procedures The shaking table test results are compared with the analytical solution developed by Aviles and Perez-Rocha (1998) and the results of a non-linear finite element analysis, which are summarized below.
6.2.5.1
Analytical Method
Several analytical solutions have been derived for evaluating SSI. A comprehensive review of static and dynamic SSI studies can be found in Dutta and Roy (2002). SSI effects are taken into account in some building codes by using analytical solutions to modify the dynamic parameters for the soil-structure system followed by calculation of the maximum base shear from standard response spectra representing free field ground motion and the modified dynamic parameters (e.g. FEMA-450, 2003). In current codes, kinematic interaction is neglected and only inertial interaction is considered. A summary of SSI solutions which either neglect kinematic interaction or account for it is given as follows. Dynamic impedance functions for foundations have been derived by Baranov (1967), Veletsos and Wei (1971), Novak and Beredugo (1972), Beredugo and Novak (1972), Veletsos and Vebric (1973), Veletsos and Nair (1975), Luco, (1980), Apsel and Luco, (1987), for rigid circular foundations situated on the surface of a visco-elastic half-space. All of these analytical solutions have simplifying assumptions such as a rigid footing founded on a uniform homogeneous soil layer of infinite depth and lateral extend. In spite of these assumptions, the BSSC (1997) (Building Seismic Safety Council) contains a procedure for evaluating SSI, which has been modified from Veletsos and Nair (1975).
210 Various practical deviations from the underlying simplifying assumptions have been addressed by others. Roesset (1980) derived impedance functions for non-uniform soil profiles. Roesset (1980) and Dobry and Gazetas (1986) analytically derived the effects of foundation shape on impedance functions. Studies considering foundation flexibility were carried out by Iguchi and Luco, (1982), Liou and Huang (1994) and Riggs and Waas (1985). Kuhlemeyer (1969), Kaldjian (1969), Lysmer and Kuhlemeyer (1971), Bielak (1975), Waas (1972), Luco (1976), and Aspel and Luco (1976) studied SSI for embedded foundations. More recently, Aviles and Perez-Rocha (1996) studied the combined effect of foundation embedment, soil thickness and degree of contact between soil and foundation on SSI and Aviles and Perez-Rocha (1998) studied foundation embedment effects by developing impedance functions accounting for both inertial and kinematic interaction for the case of vertically propagating shear-waves. The analytical solution by Aviles and Perez-Rocha (1998) takes kinematic interaction into account. Figure 6.7 shows the simplified SSI system considered by Aviles and Perez-Rocha (1998). The soil-structure system considered in this solution consists of a building embedded in a soil layer as shown in Figure 6.7(a), which can be characterized by the fundamental period, T, damping ratio, ξ , effective mass, M, and effective height, H. The structure depicted in Figure 6.7(a) has been idealized as the SDOF structure depicted in Figure 6.7(b). In this figure, the foundation is idealized as a rigid square mat of half width, L, depth, D, mass, M 0 and mass moment of inertia about the centroidal axis, J 0 , at the base. Both M and M 0 are uniformly distributed. The foundation mass M 0 is assumed to be lumped at a depth D/2. The soil is a uniform linear elastic half-space, which can be idealized by Poisson’s ratio, ν , mass density, ρ , and shear wave velocity,
211 c s and the soil-structure interface is assumed to be fully bonded. The structure illustrated in Figure 6.7(b) can be further simplified to that of a replacement oscillator as shown in Figure 6.7(c). The simplified SSI system subjected to foundation input motion and the replacement oscillator system subjected to free-field ground motion are depicted in Figure 6.7(a) and (b), respectively. Solutions for the system depicted in Figure 6.7(c) have shown that the SSI system period and damping are
( ( Tk = Ti (
ξk =
[6.5] (
ξi Qh + ( H + D).Qr
[6.6]
( ( ( ( where, Tk , Ti , ξ k and ξ i are the effective system period and damping ratio of the SSI
systems, considering the inertial interaction and inertial-kinematic interaction effects, respectively and Qh and Qr are the horizontal and rocking components of transfer functions of the foundation input motion (see APPENDIX B). Figure 6.8 gives the graphical representation of these solutions. The variation of normalized system period and system damping with foundation embedment is given in this figure for a tall-slander and a short-squat structure. The details of these solutions can be found in APPENDIX B.
6.2.5.2
Numerical Methods
The response of the scaled models was also simulated using the finite element software ABAQUS in conjunction with a surface bounding model (Borja, 1994). In addition, the program SHAKE91 was also employed to verify the free field ground
212 response of the model and as a check of Borja (1994) model. The main reason for undertaking this numerical work was to: (i) check the analytical solution using an alternative analytical method, (ii) to give further confidence in the experimental results, and (iii) to verify the accuracy of numerical tools to further extend this study into the non-linear range. For the ABAQUS model, the structure was simplified as a single degree of freedom system in the analyses. The structure and the soil deposit are modeled using a mixture of 8-noded linear hexahedron and tetrahedron solid elements with three degrees of freedom per node. Fully bonded soil-structure interface is chosen (e.g. separation and slippage are not allowed) in order to simulate the experimental cases more realistically (see ABAQUS, 2005). Infinite elements, which are defined over a semi-infinite domain with a suitable decay function, are used to model the soil continuity to the infinity (Lysmer and Kuhlemeyer, 1969). The infinite lateral boundaries were situated 100 m from the centre of the structure. Maximum FE mesh size was used between 1/6th and 1/8th of the minimum Rayleigh wavelength in order to allow the higher frequency components of the input motion to travel within the soil medium (Kramer, 1996). A sensitivity study was performed to determine an adequate mesh density for the FE modeling. The initial step in each FE analysis comprised a static analysis, which was carried out to establish initial geostatic equilibrium. Then, implicit dynamic analyses followed. Seismic loading was simulated by applying acceleration time histories at the base of the model. The soil was modeled as a non-linear elasto-plastic material with constant Rayleigh damping in the dynamic analyses. In order to model non-linear behavior of the soil, a
213 total stress based, multiaxial bounding surface plastic model introduced by Borja and Amies (1994) and implemented in a FE program ABAQUS by Rodriguez-Marek (2000) was used. This non-linear model, which is reported to function effectively for modeling of cyclic behavior of clays (see Borja and Amies 1994, Borja et al. 1999, RodriguezMarek 2000, Wong 2004), will be referred to as Borja’s model hereinafter. Borja’s model requires eight material parameters. The first there parameters are shear wave velocity, Vs , Poisson’s ratio, ν , and density, ρ , of the soil. There are two kinematic hardening parameters, h and m , that control the stiffness degradation rate (exponential) and the shape of the secant modulus versus shear strain amplitude curve, respectively. The bounding surface is circular with radius, R , and a model parameter, H 0 , defines the initial plastic modulus after reaching the bounding surface, and the numerical parameter β is a trapezoidal integration parameter. More details about these parameters can be found in Borja and Amies (1994), Rodriguez-Marek, (2000) and Balendra (2005). Table 6.4 shows the values of model parameters for the soils with different non-linear characteristics. The Rayleigh damping was used along with the hysteretic damping predicted by Borja’s model, in order to model the viscous damping that the soil exhibits at low shear strain levels. In this study, 5 % constant Rayleigh damping was used for this purpose.
6.3 Results and discussion This section presents results obtained from the shaking table tests summarized in Table 6.3 and compares the results with the analytical solutions summarized above.
214
6.3.1 Verification of Free Field Ground Response The free field ground response of the model soil deposit was studied using shaking table tests FFGR-1 and FFGR-2 and the response is compared with numerical simulations using equivalent linear analysis (SHAKE91) and Borja’s cyclic non-linear bounding surface plasticity model (ABAQUS). Figure 6.9 (a) and (b) show the measured (tests FFGR-1 and FFGR-2) and simulated acceleration time histories on the soil surface for the input motion intensities of 0.12 g and 0.35 g. It can be seen in Figure 6.9(a) and (b) that the free field ground response of the model soil deposit exceeds the excitation applied at the table. Thus, there is amplification. In addition, the measured response at the surface of the model soil layer is in good agreement with the numerical simulations for both low and high input motion intensities. At the input motion with 0.12 g peak amplitude, the amplification factors calculated using SHAKE91 and ABAQUS and measured data during the shaking table tests are 1.38, 1.41 and 1.33 respectively. Amplification factors calculated for the input motion with 0.35 g peak amplitude are 1.26, 1.31 and 1.33, for SHAKE91 and ABAQUS analyses and shaking table tests, respectively. Difference between the measured and simulated amplification factors are less than 6 % for both low and high amplitude shaking. The results indicate that both equivalent linear and nonlinear cyclic plastic models are able to predict the dynamic behavior of model soil deposit with a reasonable accuracy.
6.3.2 Fixed Base Dynamic Response of Superstructure The results of shaking table tests performed on fixed base superstructures are presented in this section. Figures 6.10 and 6.11 show the results obtained from tests (FB-
215 LF and FB-HF) performed on the model structures SDOF-L and SDOF-H, which represent low and high frequency superstructures, respectively. Figure 6.10 (a) shows the acceleration time history of sine sweep measured on the shaking table. The acceleration time history and corresponding Fourier spectrum of the time-history measured at the lumped mass of the SDOF-L are shown in Figure 6.10(b) and (c), respectively. From Figure 6.10, it can be seen that the fixed base fundamental frequency ( f ) of the SDOF-L is 10.63 Hz. Thus, the SDOF-L represents a prototype structure with 0.59 sec period. The damping ratio ( ξ ) was calculated to be 0.096 using the amplitude spectrum of the transfer function between the relative responses of the structural mass and incident wave. The amplification factor calculated for SDOF-L was 3.24. Figure 6.11(a)-(c) summarize the dynamic response of SDOF-H. The acceleration time history measured on the table is shown in Figure 6.11 (a). The acceleration time history and corresponding Fourier spectrum of motion measured at the lumped mass of SDOF-H are depicted in Figure 6. 11 (b) and (c), respectively. Figure 6.11 shows that the fixed base fundamental frequency ( f ) and the damping ratio ( ξ ) of SDOF-H are 24.78 Hz and 0.1, respectively. The fundamental period of the prototype structure for SDOF-H is 0.26 sec and the amplification factor of SDOF-H is 7.95. |Even though the SDOF-L represents a superstructure with relatively higher fundamental period compared to SDOF-H, both superstructures have a prototype fundamental period of less than 1 sec. Therefore, both SDOF-L and SDOF-H can practically be considered as low period, short-squat structures. Given the fragile nature of the acrylic used to manufacture the SDOF-H, it was difficult to make longer period models.
216
6.3.3 Dynamic Behavior of Structures with Embedded Basement Levels The results of shaking table test and compared with analytical and numerical solutions in this section for structures with embedded basement levels. The shaking table test data are presented along with the results of confirmatory finite element solutions and analytical solutions.
6.3.3.1
Influence of Embedment Depth
The influence of basement embedment depth on the dynamic system parameters was investigated for superstructures SDOF-L and SDOF-H. The ratios of the structure height to the half width of the foundation, (H/L), were 4.46 and 1.90 for SDOF-L and SDOF-H, respectively. The wave parameter is a measure of relative stiffness of soil and structure and it is expressed mathematically as, τ H = H /(Vs.T ) , where Vs and T are the shear wave velocity of the foundation soil and fixed base period of the superstructure. The value of τ H for SDOF-L and SDOF-H were 0.075. In addition, (D/L) ratios (basement embedment depth to the half-width) of 0, 0.5, 1 and 2 were investigated. Figures 6.12 and 6.13 summarize the measured acceleration time histories and corresponding Fourier spectra of SDOF-L and SDOF-H corresponding to the above D/L ratios. Referring to Figure 6.12(a)-(e), (a) shows the time history and corresponding Fourier spectra of the motion measured on the table surface, and (b)-(e) show the acceleration time history and the corresponding Fourier spectra of the motion at the lumped mass level corresponding to L/D of 0, 0.5, 1 and 2. Comparing Figure 6.10(b) to 6.12(b), it can be seen that the fundamental frequency of the SDOF-L decreases from the fixed base value
217 of 10.63 Hz to 9.36 Hz for D/L = 0 due to the flexibility of the foundation soil layer (tests SRF-LF). This fact indicates the period lengthening effect due to SSI. Full results of the shaking table tests, FE solutions and the analytical solutions of Aviles and Perez-Rocha, (1998) are summarized in Table 6.5 for SDOF-L. Referring to ( this table, the T / T ratios of the SDOF-L structure (H/L=4.46) measured during the
shaking table tests vary from 1.130 to 1.014 for the (D/L) ratios ranging from 0 to 2 (test SRF-LF, EM-SS-1, EM-SS-2, EM-SS-4). Thus, the measured results show that the period decreases with increasing embedment. Similarly, the Aviles and Perez-Rocha ( (1998) solutions for SDOF-L gave T / T ratios of 1.085, 1.060 and 1.055 for (D/L) ratios
of 0, 0.5 and 1, respectively. These results are close to the scaled model test results in that the period decreases with increasing D/L.
( Finally, the FE simulations gave T / T ratios that ranged from 1.11, 1.025, 1.025 and 1.024 for (D/L) ratios of 0, 0.5, 1 and 2. Thus, the experimental behavior and both ( analytical and numerical results show that there is a decrease in T / T for SDOF-L with
increasing embedment depth. The damping ratios ( ξ ), however, remained unaffected from the depth of embedment for all solutions. It is worth pointing out that the
( embedment effects on T / T and ξ for this particular τ H value (0.075) is very small. The results of shaking table tests on SDOF-H (H/L=1.9) for three different embedment cases with (D/L) ratios of 0, 1 and 2 are shown in Figure 6.13 (test SRF-HF, EM-SS-3, EM-SS-5). These results were obtained by exciting the SSI system with a sine sweep that had a peak acceleration of 0.1 g as depicted in Figure 6.12(a). Comparing Figures 6.11(c) and 6.13(b), the fundamental frequency of SDOF-H decreased from 24.78 Hz for the fixed base condition to 22.97 Hz for D/L = 0 due to the SSI.
218 Table 6.6 summarizes the results of shaking table tests corresponding to D/L of 0, 1 and 2 for SDOF-H with Aviles and Perez-Rocha (1998) and the FE calculations. From ( this figure, the T / T ratios of SDOF-H (H/L=1.90), measured in the shaking table tests,
( increased from 1.078 to 1.130 for (D/L) ratios increasing from 0 to 2. T / T ratios calculated using analytical solutions of Aviles and Perez-Rocha, (1998) were 1.045 and 1.060 for (D/L) ratios of 0 and 1, respectively and from the Finite element simulations,
( the T / T ratios were 1.07, 1.098 and 1.120 for (D/L) ratios of 0, 1 and 2. Both ( experimental and analytical results show that there is a slight increase in the T / T ratio of
SDOF-H with increasing embedment depth. The damping ratios ( ξ ) also slightly increased with increasing embedment depth for the given value of τ H . Based on the above discussions and results, the shaking table tests, numerical simulations and analytical solutions showed similar trends for SDOF-L and SDOF-H.
6.3.3.2
Influence of Foundation Mass
As discussed in the methodology section, the influence of foundation mass on the dynamic behavior of the SSI system was studied for deeply embedded basements (D/L=2). Figure 6.14 summarizes shaking table test results for SDOF-L supported on a basement with the (D/L) ratio of 2 and having negligible mass and significant mass (see EM-SS-4 and M-EM-SS-6 in Table 6.3). The SSI system was excited using the sine sweep with a peak acceleration of 0.1 g as depicted in Figure 6.12 (a). Figures 6.14 (a) and (b) show the acceleration response spectra measured at the foundation base (ACC3) and at the lumped mass for SDOF-L (ACC5) with a massless foundation and foundation with significant mass, respectively. Referring to Figure 6.14, the mass of the embedded
219 levels of the structure (including the foundation slab) had a very small effect on the motion at the level of foundation base and superstructure. There was no alteration of the period due to the foundation mass at the level of superstructure and foundation base for this particular case of deeply embedded structure in stiff clay.
6.4 Summary and Conclusions This chapter described the results of scaled physical modeling and numerical modeling of soil structure interaction in buildings with embedded basement stories. Shaking table tests were conducted using two superstructure systems representing a tallslender structure and a short-squat structure supported on stiff clay with embedded basement stories. Embedment ratios between (D/L) of 0 and 2 were considered. The results of the shaking table tests for various embedment depths were compared with a closed-form analytical solution (Aviles and Perez-Rocha 1998) and results from FE analyses.
The following is a summary of the results and conclusions arising from this study. 1. The dynamic response of the model soil deposit comprising modified glyben was seen to be in a good agreement with numerical simulations performed using equivalent linear and non-linear plastic soil behavior assumptions. 2. It was seen that for both shaking table test cases, where SDOF-L and SDOF-H were supported on the surface of the model soil deposit, the fixed base fundamental frequencies of SDOF-L and SDOF-H decrease due to the flexibility of the supporting model soil deposit.
220 ( 3. Both experimental and numerical results showed that T / T ratios of SDOF-L
decreased with increasing (D/L) ratios. The damping ratio remained almost unaffected. These variations agree with the Aviles and Perez-Rocha (1998) solution and non-linear FE results although it is acknowledged that ( embedment effects on T / T and ξ for this particular τ H value (0.075) are
small.
( 4. Contrary to the SDOF-L cases, T / T ratios of SDOF-H increased for the increasing (D/L) ratios as can be seen from the experimental, analytical and numerical results. The damping ratios also slightly increased with increasing embedment depth for the given value ofτ H . These variations also agreed well with the findings of Aviles and Perez-Rocha (1998). 5. The shaking table test results showed that the influence of foundation mass on the dynamic response of the structure is negligible for the buildings with deep basements embedded in stiff clayey soils.
221
References ABAQUS. 2005. Hibbit, Karlsson and Sorensen., Inc., Version 6.7. Applied Technology Council (ATC). 1984. Tentative provisions for the development of seismic regulation. ATC-3-06, Amended, California. Apsel, R.J and Luco, J.E. 1976 Torsional response of rigid embedded foundations. Jour. of Eng. Mech. Div., ASCE, 102(EM6), 957-970. Apsel, R. J. and Luco, J. E. 1987. Impedance functions for foundations embedded in a layered medium: An integral equation approach. J. Earthquake Engrg. Struct. Dyn., 15(2), 213–231.
Aviles, J. and Perez-Rocha, L. E. 1996. Evaluation of interaction effects on the system period and the system damping due to foundation embedment and layer depth. Soil Dyn. Earthquake Eng., 15, 11-27. Aviles, J. and Perez-Rocha, L. E. 1998. Effect of foundation embedment during buildingsoil interaction. Earthquake Eng and Structural Dyn., 27, 1523-1540. Balendra, S. 2005. Numerical modeling of dynamic soil-pile-structure interaction. M.Sc. thesis. Pullman, WA., Washington State University. Baranov, V.A. 1967. On the calculation of excited vibrations of an embedded foundation. Voprosy Dynamiki, Prochnocti, No: 14, Polytechnical Institute of Riga, 195-209. Beredugo, Y. O. and Novak, M. 1972. Coupled horizontal and rotational vibration of embedded footings. Canadian Geotechnical Journal, 9(4), 477-497.
222 Bielak, J. 1975. Dynamic behavior of structures with embedded foundations. Earthquake Eng. Structural. Dyn. 3, 259-274. Borja, R.I. and Amies, A.P. 1994. Multiaxial cyclic plasticity model for clays. Journal of Geotechnical Eng., ASCE, 120(6), 1051-1070. Borja, R.I., Chao, H.Y., Montans, F.J., and Lin, C.H. 1999. Nonlinear ground response at Lotung LSST site. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125, 187-197. Building Seismic Safety Council (BSSC). 1997. NEHRP recommended provisions for seismic regulations for new buildings, Part 1, Provisions and Part 2, Commentary. Rep. No. FEMA 302 and 303, Federal Emergency Management Agency, Washington, D.C. Cakmak, A.S., Abdel-Ghaffar, A.M. and Brebbia, C.A. 1982. Soil dynamics and earthquake engineering. Proceedings of the Conference on Soil Dynamics and Earthquake Engineering, vol. I, II, Rotterdam, A.A., Balkema. Clough, R. W. & Penzien, J. 1975. Dynamics of structures. McGraw-Hill, New York. Dobry, R., and Gazetas, G. 1986. Dynamic response of arbitrarily shaped foundations. J. Geotech. Eng., ASCE, 112(2), 109–135. Dutta, S.C. and Roy, R. 2002. A critical review on idealization and modeling for interaction among soil–foundation–structure system. Computers and Structures, 80, 1579-1594. FEMA-450, 2003. NEHRP recommended provisions for seismic regulations for new buildings and other structures.
223 Gazetas, G. 1991. Formulas and charts for impedances of surface and embedded foundations. Journal of Geotechnical Engineering, 117(9), 1363-1381 Iai, S. 1989. Similitude for shaking table tests on soil-structure-fluid model in 1g gravitational field. Soils and Foundations, JSSMFE, 29(1), 105-118. Iguchi, M., and Luco, J. E. 1982. Vibration of flexible plate on viscoelastic medium. J. Eng. Mech., ASCE, 108(6), 1103–1120. Jennings, P.C. and Bielak, J. 1973. Dynamics of building-soil interaction. Bull. Seism. Soc. Am., 63, 9-48. Kaldjian, J.M. 1969. Discussions of design procedures for dynamically loaded foundation. By R.V. Whitman and F.E. Richard, Jour. Of Soil Mech. Found. Div., ASCE, 97, 969-980. Kaussel, E. and Roesset, J.M. 1974. Soil structure interaction for nuclear containment structures. Proc., ASCE, Power Division Specialty Conference, Boulder, Colorado. Kramer, S.L. 1996. Geotechnical earthquake engineering. Prentice-Hall Inc., Englewood Cliffs, NJ. Kuhlemeyer, R.L. 1969. Vertical vibrations of footings embedded in layered media. PhD. Thesis, University of California, Berkeley, CA. Liou, G.S., and Huang, P.H. 1994. Effect of flexibility on impedance functions for circular foundations. J. Engrg. Mech., ASCE, 120(7), 1429–1446. Luco, J. E. 1980. Linear soil-structure interaction. Soil-structure interaction: The status of current analysis methods and research, J. J. Johnson, ed., Rep. No. NUREG/CR-1780 and UCRL-53011, U.S. Nuclear Regulatory Commission, Washington, D.C. and
224 Lawrence Livermore Laboratory, Livermore, CA. Lysmer, J., and Kuhlemeyer, R.L. 1969. Finite dynamic model for infinite media. Journal of the Engineering Mechanics Division, ASCE, 95(EM 4), 859-877. Mita, A. and Luco, J. E. 1989. Impedance functions and input motions for embedded square foundations. J Geotech. Engng., ASCE, 115, 491-503. National Earthquake Hazard Reduction Program (NEHRP). 2000. Recommended provisions for the development of seismic regulations for new buildings. FEMABSSC, Washington. Novak, M. and Beredugo, Y.O. 1972. Vertical vibration of embedded footings. Journal of the Soil Mechanics and Foundations Division, 98(12), 1291-1310. Pak, R.Y.S. and Gobert, A.T. 1991. Forced vertical vibration of rigid discs with arbitrary embedment. Journal of Engineering Mechanics, 117(11), 2527-2548. Riggs, H. R., and Waas, G. 1985. Influence of foundation flexibility on soil-structure interaction. J. Earthquake Eng. Structural Dyn., 13(5), 597–615. Rodriguez-Marek, A. 2000. Near-fault seismic site response. Ph.D. Dissertation, University of California, Berkeley. Roesset, J. M. 1980. A review of soil-structure interaction. Soil-Structure Interaction: The Status of Current Analysis Methods and Research. J. J. Johnson, ed., Rep. No. NUREG/CR-1780 and UCRL- 53011, U.S. Nuclear Regulatory Commission, Washington, D.C. and Lawrence Livermore Laboratory, Washington, D.C. Stewart, J.P., Fenres, G.L. and Seed, R.B. 1999. Seismic soil–structure interaction in buildings I: Analytical Method. J. Geotech Geoenv. Eng Div., 125(1), 26–37.
225
Todorovska, M.I. and Trifunac, M.D. 1992. The system damping, the system frequency and the system response peak amplitudes during in-plane building-soil interaction. Earthquake Engng. Structural Dyn. 21, 127-144. Turan, A., Hinchberger, S.D. and El Naggar, M.H. 2008a. Investigation of dynamic performance of bentonite-glycerin-water based artificial clay. GRC Research Report, Report No: GEOT-08-01, The University of Western Ontario, London, ON, Canada. Turan, A., Hinchberger, S.D. and El Naggar, M.H. 2008b. Design and commissioning of a laminar soil container for use on small shaking tables. Soil Dynamics and Earthquake Engineering, Accepted (April, 2008). Veletsos, A.S. and Nair, V.V.D. 1975. Seismic interaction of structures on hysteretic foundations. J. Struct. Div. ASCE 101, 109-129. Veletsos, A. S., and Verbic, B. 1973. Vibration of viscoelastic foundations. J. Earthquake Engrg. Struct. Dyn., 2(1), 87–102. Veletsos, A. S., and Wei, Y. T. 1971. Lateral and rocking vibrations of footings. J. Soil Mech. and Found. Div., ASCE, 97(9), 1227–1248. Waas, G. 1972. Earth vibration effects and embedment for military facilities. Technical Report, S-71-14, Report 3, U.S. Army Engineers Waterways exper. Station, 182. Wolf, J.P. 1985. Dynamic soil–structure interaction. Englewood Cliffs, NJ, Prentice-Hall. Wolf, J.P. 1988. Soil–structure interaction analysis in time domain. Englewood Cliffs, NJ, Prentice-Hall. Wong, J.C. 2004. Seismic behavior of micropiles. M.Sc. thesis. Pullman, WA., Washington State University.
226
Table 6. 1 Similitude relationships of parameters between prototype and model (After Meymand, 1998) Mass density Force
1 3
λ
2
Acceleration Shear wave velocity
Stiffness
λ
Time
Modulus
λ
Frequency
Length
λ
1/2
Stress
1/2
Strain
λ 1
EI
λ5
1 λ
λ
λ−1/2
227 Table 6. 2 Similitude relationships of SSI systems between prototype and model (λ=40). Tall and slander structure (SDOF-L)
Short and squat structure (SDOF-H)
Model
Prototype
Model
Prototype
Soil depth (m)
0.55
22
0.55
22
Average shear wave velocity (m/s)
63.4
401
53.5
338
Acceleration (g)
Variable
Variable
Variable
Variable
Strain
1
1
1
1
Frequency (Hz)
1-60
0.16-9.48
1-60
0.16-9.48
Bulk density of soil (kg/m3)
1780
1780
1780
1780
Embedded storey height (m)
0.05
2
0.05
2
Fixed base fundamental frequency of superstructure (Hz)
10.63
1.68
24.78
3.92
228 Table 6. 3 Summary of Tests
2
Peak Amplitude (g) 0.12 and 0.35
1 to 60
2
0.1
Sine sweep
1 to 60
2
0.1
Sine sweep
1 to 60
1
0.1
Sine sweep
1 to 60
2
0.1
Sine sweep
1 to 60
2
0.1
Sine sweep
1 to 60
1
0.1
FFGR-1 FFGR-2
To identify dynamic behavior of model soil deposit.
Harmonic
Predominant frequency (Hz) 10
FB-LF FB-HF
To identify fixed base dynamic system parameters (DSP’s) of superstructures. To identify DSP’s of superstructures supported on a surface foundation. (D/L=0), SDOF-L and SDOF-H To obtain DSP’s of soil-structure system. (D/L=0.5), SDOF-L
Sine sweep
To obtain DSP’s of soil-structure system. (D/L=1), SDOF-L and SDOF-H To obtain DSP’s of soil-structure system. (D/L=2), SDOF-L and SDOF-H To obtain DSP’s of soil-structure system. (D/L=2), SDOF-L with massive foundation
Test No.
SRF-LF SRF-HF EM-SS-1 EM-SS-2 EM-SS-3 EM-SS-4 EM-SS-5 M-EM-SS-6
Objective
Type of loading
Number of test
229 Table 6. 4 Parameters of Borja’s model for highly (PI=0) and mildly (PI=100) plastic clays. (After Wong, 2004)
Vs Mildly plastic soil PI=100 Highly plastic soil PI=0
(m/sec) 100 to 401 100 to 401
ν
ρ 3
h
m
β
R
H0
(kg/m ) 0.35
1780
4
0.8
0.5
0.0043
0.0001
0.35
1780
0.585
1.082
0.5
0.0007
0.0001
230 Table 6. 5 Dynamic system parameters of SDOF-L for cases with (D/L) values of 0, 0.5, 1 and 2. Normalized system period 1
Damping Ratio2
( (T /T )
(D/L) ratio
(ξ )
0
0.5
1
2
0
0.5
1
2
Shaking Table Tests
1.130
1.031
1.030
1.014
0.095
0.098
0.094
0.096
FE Simulation
1.110
1.025
1.025
1.024
0.05
0.05
0.05
0.05
1.085
1.060
1.055
N/A
0.05
0.05
0.05
N/A
Analytical Solution Aviles and Perez-Rocha (1996) and (1998)
1 The values are interpolated between (D/L) ratios of 0.5 and 1.5 for analytical solutions (Aviles and Perez-Rocha, 1998) 2 The damping ratio of fixed base SDOF-L is 0.096 whereas this ratio is assumed as 0.05 for numerical and analytical solutions (Aviles and Perez-Rocha, 1998)
231 Table 6. 6 Dynamic system parameters of SDOF-H for cases with (D/L) values of 0, 1 and 2. Damping Ratio2
Normalized system period
( ( T / T )1
(D/L) ratio
(ξ )
0
1
2
0
1
2
Shaking Table Tests
1.078
1.100
1.130
0.108
0.110
0.114
FE Simulation
1.070
1.098
1.120
0.100
0.105
0.105
1.045
1.050
N/A
0.1
0.1
N/A
Analytical Solution Aviles and Perez-Rocha (1996) and (1998) (
1 The T / T values are interpolated between (D/L) ratios of 0.5 and 1.5 for (D/L)=1 (Aviles and Perez-Rocha, 1998) 2 The damping ratio of fixed base SDOF-L is 0.1 whereas this ratio is assumed as 0.05 for numerical and analytical solutions (Aviles and Perez-Rocha, 1998)
232
Figure 6. 1 Laminar soil container and used in this study.
233
Figure 6. 2 Averaged vane shear strength and shear wave velocity profiles along the depth (Turan et al., 2008b).
234 Figure 6. 3 Stiffness degradation (a) and damping (b) curves for modified glyben (after Turan et al. 2008a).
235
Figure 6. 4 Modular model building used in this study.
236
Figure 6. 5 Instrumentation of the soil-structure system.
237 Figure 6. 6 Schematics of the testing cases.
238
Figure 6. 7 (a) SSI system considered in analytical solutions (after Aviles and PerezRocha 1998).
239
Figure 6. 7(b) SSI system excited by foundation input motion (after Aviles and PerezRocha 1998)
240
Figure 6. 7 (c) Replacement oscillator system excited by free field ground motion (after Aviles and Perez-Rocha 1998).
241
Figure 6. 8 Graphical representation of Aviles and Perez-Rocha (1996) and (1998) solutions (after Aviles and Perez-Rocha 1998).
242
Figure 6. 9 (a) Measured free field ground motion at 0.12 g intensity level.
243
Figure 6. 9 (b) Measured free field ground motion at 0.35 g intensity level.
244
Figure 6. 10 (a) Applied acceleration time history on the shaking table.
245
Figure 6. 10 (b) Measured acceleration time history at the mass level of SDOF-L.
246
Figure 6. 10 (c) Fourier spectra of the response measured on SDOF-L.
247
Figure 6. 11 (a) Applied acceleration time history on the shaking table.
248
Figure 6. 11 (b) Measured acceleration time history at the mass level of SDOF-H.
249
Figure 6. 11 (c) The corresponding fourier spectra of the response at mass level for SDOF-H.
250
Figure 6. 12 (a) Applied acceleration time history and Fourier spectra of base excitation on the table.
(
251
Figure 6. 12 (b) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=0.
252
Figure 6. 12 (c) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=0.5.
253
Figure 6. 12 (d) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=1.
254
Figure 6. 12 (e) Acceleration time history and Fourier spectra of the excitation on the SDOF-L with D/L=2.
255
Figure 6. 13 (a) Acceleration time history and Fourier spectra of SDOF-H with D/L=0.
256
Figure 6. 13 (b) Acceleration time history and Fourier spectra of SDOF-H with D/L=1.
257
Figure 6. 13 (c) Acceleration time history and Fourier spectra of SDOF-H with D/L=2.
258
Figure 6. 14 (a) Acceleration response spectra at the foundation base for massless and massive foundation cases (D/L=2).
259
Figure 6. 14 (b) Acceleration response spectra at the lumped mass level for massless and massive foundation cases (D/L=2).
260
CHAPTER 7 SUMMARY AND RECOMMENDATIONS FOR FUTURE STUDY
This chapter summarizes the research conducted in this thesis and the conclusions arising from the research. In addition, recommendations for future research are also provided.
Summary The primary objective of this thesis was to develop the research infrastructure required to conduct scaled-model studies of buildings with embedded basement stories. The research undertaken can be divided into three main stages;
•
Development and characterization of a model clay for scaled-model tests,
•
Design, fabrication and calibration of laminar soil container,
•
Experimental and analytical study of soil-structure interaction
The first stage of this study focused on synthetic model soils. Glyben, which is a synthetic clay composed of bentonite mixed with glycerin, was initially considered for use as the model clay in shaking table tests. Consequently, a series of laboratory tests including cyclic triaxial, bender element and resonant column tests, were performed to characterize the dynamic properties of glyben. The influence of temperature, thixotropy, shear strain amplitude, confining stress and the number of load cycles was studied using
261 predominantly bender elements, cyclic traixial tests and resonant column tests. The results indicated that the variation of dynamic stiffness and damping ratio of glyben with increasing shear strain amplitude showed a similar trend to those observed for natural clays. However, glyben exhibited significantly high damping ratios compared to natural clays at all shear strain amplitudes. In addition, this study showed that there are significant thixotropic changes in the properties of glyben after mixing bentonite with glycerin. The isotropic consolidation tests conducted on glyben specimens showed that the consolidation of glyben occurs in a significantly slower rate compared to that in natural clays. The sensitivity of the dynamic properties of glyben to the changes in temperature is another significant result that needs to be taken into consideration when using glyben in model tests. This study is described in Chapter 2. Next, a modular neural network (MNN) was developed, trained and tested in order to identify the influence of various factors such as shear strain amplitude, glycerin content, excitation frequency and confining pressure on dynamic properties of glyben. Details of the MNN are described in Chapter 3. The MNN architecture comprised an input layer, two expert modules (neural networks) linked by a gating network, and an output layer. The MNN was trained using 124 data sets obtained from the laboratory tests and tested as part of the current study to evaluate its accuracy. It was shown that the MNN is able to adequately predict the dynamic properties of glyben. Chapters 2 and 3 showed that a significant drawback of glyben is that it has a damping ratio in the range of 0.15 to 0.22, which is significantly higher compared to that observed in natural clays. Thus, an alternative soil called modified glyben was developed and its properties are reported in Chapter 4. Modified glyben comprises bentonite mixed with water and glycerin. Laboratory experiments including isotropic consolidation, cyclic
262 triaxial, resonant column, bender elements and x-ray diffraction tests were carried out in order to characterize modified glyben. The primary objectives of these tests were to characterize the dynamic properties of modified glyben, and to investigate the effect of temperature, drying and pore-fluid viscosity on the dynamic properties of modified glyben. Overall, the results of this experimental study (see Chapter 4) indicate that the consolidation and dynamic properties of modified glyben are strongly influenced by the pore fluid viscosity, which can be varied by controlling the temperature or glycerin-water ratio to achieve soil stiffness and damping ratios similar to that of natural soils. The dynamic properties of modified glyben were found to be insensitive to drying and the large amplitude cyclic strains experienced during the model tests. Despite the increased rate of consolidation compared to glyben, modified glyben has a consolidation rate that is considered to be sufficiently low to maintain stable material properties during the 1-G and n-G scaled physical tests. All these features make the modified glyben a useful model soil mixture that allows multiple uses in scaled physical model tests. The second stage of this thesis comprises the design details of a laminar soil container. The laminar soil container was designed using a novel approach to overcome the base shear limitations of a small shaking table used in this study. This work is described in Chapter 5, which gives design details of the box in addition to the results of dynamic tests performed to commission the box. In Chapter 5, a series of shaking table tests and numerical analyses that were performed to study the performance of the laminar box and non-linear seismic behavior of the model clay are described. The laminar container is shown to have insignificant boundary effects and able to maintain 1-D soil column behavior. In addition, the dynamic behavior of the modified glyben during scaled
263 model tests was found to be consistent with the element scale dynamic behavior presented in the first stage of this study. In the final stage of this study (Chapter 6), a series of 1-G shaking table tests were conducted and compared with an analytical solution and FE model to study soil-structure interaction (SSI) of the buildings with embedded basement stories. A model building with various embedment depths was fabricated and embedded in a model soil deposit comprising modified glyben placed in a laminar container situated on a shake table. The model was subject to various levels of shaking and the behavior was compared to an analytical solution and FE calculations. The effects of various parameters such as embedment depth, foundation mass and period of the superstructure were studied for a stiff clay layer. The results showed that the system frequency and system damping ratio increases with the increasing embedment depth. The behavior of the reduced-scale SSI model tests, was found to be similar to that predicted by the closed-form analytical solution and the non-linear elasto-plastic FE solutions.
Recommendations for Future Study This section provides a list of recommendations based on the research that has been undertaken and described in this thesis. The recommendations on organized under the headings (a) model soils, (b) shaking table and soil container and (c) reduced scale model SSI studies are given as follows;
264
a.
Model Soils •
A gap between the stiffness values measured using the resonant column test and cyclic triaxial test was reported in this study for glyben and modified glyben. This gap was attributed to the mode of loading and excitation frequency used in the respective apparatus. The dynamic stiffness of modified glyben should be measured using an alternative testing procedure such as cyclic hollow cylinder test, to identify the relative importance of frequency and mode of loading.
•
A more detailed investigation on the microstructure of glyben and modified glyben should be carried out in order to gain a deeper insight into the material behavior. It would be worth conducting an electron microscopy and mercury porosimetry study on synthetic clay mixtures with various (gw/c) and (w/gw) values. Such a study may help to explain phenomenon such as thixotrophy, high damping ratio at low strain levels and insensitivity of dynamic properties to drying and cyclic stress history.
•
Class C fly ash, which is reported to cause the shrinkage of the double layer around clay minerals as a result of the cation exchange, can be added to the modified glyben mixtures to adjust the stiffness and strength properties of this mixture.
•
Nanotechnology may be used to further improve the modified glyben mixture. The effects of the nano-particles seeded in the soil mixture, on the consolidation rate and dynamic properties are potentially worth studying.
265
•
The modified glyben should be used in centrifuge tests and the dynamic properties along with the consolidation behavior observed under a realistic nG gravitational stress field should be compared to those simulated in laboratory tests.
•
A neural network tool similar to the one developed for glyben may be developed in order to predict the dynamic properties of modified glyben and the parameters affecting these properties.
b.
Shaking Table and Soil Container •
The shaking table should be upgraded using a better feed-back real time control system in order to eliminate the discrepancies between the signal applied to the table and measured on the table.
•
The laminar soil container developed in this study allows only 1-D shaking. The same design approach, which moves the mass of the soil container away from the shaking table, can be employed to develop a 2-D laminar container. Also centrifuge type containers, which work on the same principle, can be designed and fabricated.
•
The current laminar soil container configuration can easily be transformed from passive to active type using a number of lateral actuators connected to the exterior of the lamina. Such an arrangement, which allows pre-determined displacement profiles enforced on the soil confined in the container, may be desirable since it eliminates the requirement of a shaking table and is appropriate for the cases where kinematic effects are predominant.
266
c.
Model SSI Studies •
The model SSI studied should be conducted using other scaling factors in order to evaluate the validity of the similarity rules and performance of the testing setup.
•
Denser instrumentation arrays, comprising higher quality devices, may be used in order to improve the accuracy of the stiffness and damping values back calculated form the system response.
•
Soil-structure interface pressure measurements could be conducted. A pressure measurement technique called pressure sensitive painting could be implemented into the model SSI model tests.
•
The determination of the model soil profile in the laminar soil container is carried out by correlating the measured vane shear strength profiles to the shear wave velocity profiles. This approach is validated by comparing the response measured on the model soil surface and results of free field ground response analyses. However, further validations using surface hammer blow shear wave velocity tests should be performed.
•
More shaking table tests may be conducted using structural configurations including the flexible basement walls. Considering the soil mixtures with different consistencies, softer soil mixtures may be useful since this type of soils magnify rocking components of the seismic motions experienced by the
267 foundation of the structure. A dramatically different seismic response of soilstructure system should be expected in this case due to a more predominant kinematic component in the interplay of soil and structure.
•
The SSI models studies on the buildings with embedded basement stories should also be carried out in a realistic gravitational stress field in centrifuge.
•
The seismic SSI in the buildings with embedded basement stories, should be parametrically studied using an advanced numerical model calibrated using the model test results presented herein. The various aspects of the problem, which could not be considered experimentally, can be studied numerically. The soil and structure nonlinearity, non-linear behavior of soil structure interface, various combinations of geometrical parameters can be simulated using various soil profiles.
268
APPENDIXES APPENDIX A SOIL PLACEMENT AND UNIFORMITY
In order to standardize the compaction of the modified glyben into the soil container, a number of compaction trials were performed in a rigid container. Then, bender element tests were carried out on the specimens extruded from the rigid container. The compaction trials are summarized in Table A1. As can be seen in trials T-1 to 3, the number of drops beyond 20 does not change the level of compaction and consequently the shear wave velocity. The comparison of trials T-2, T-4, T-5 and T-6 shows that the lift thicknesses under 20 mm do not result in a better compaction. It can be seen in Table A1 that decreasing lift thicknesses resulted in increasing shear wave velocities. The modified glyben compacted in 40, 30 and 20 mm lifts using 20 hammer drops gave the shear wave velocities of 54, 55.4 and 60.1 m/sec, respectively. The use of a 10 mm layer thickness resulted in negligible change in the shear wave velocities. The shear wave velocity of the compacted glyben obtained using 20 mm lift thickness and 20 hammer drops is considered to be sufficiently accurate and practically applicable. When using modified glyben in scaled physical model tests, it is practical to obtain in-situ shear wave velocity profile in the soil container and to use these values along with the stiffness degradation and damping curves depicted in Figure 4.12 and 4.14, respectively. Equation A1 is derived from laboratory tests and relates the vane shear strength and shear wave velocity of the modified glyben.
269
Vs = 26.52 Ln(cu ) − 33
[A1]
where, Vs is shear wave velocity and cu is undrained shear strength of modified glyben. The compaction of modified glyben into a laminar soil container in accordance with the procedure summarized in this study and shaking table tests conducted for verification can be found in Chapter 5.
270
Table A1.
Compaction trials on modified glyben.
Trial Number
Thickness of Lifts (mm)
Number of Drops
Measured Vs (m/s)
T-1 T-2 T-3 T-4 T-5 T-6
20 20 20 10 30 40
10 20 25 20 20 20
54.3 60.3 60.6 60.6 55.4 54.0
271
APPENDIX B SOIL STRUCTURE INTERACTION SOLUTIONS OF AVILES AND PEREZ-ROCHA (1998)
The following describes the procedure for calculating the dynamic system parameters taking inertial and kinematic interaction effects into account and neglecting the influence of foundation mass, M 0 , mass moment of inertia J 0 and coupled stiffness and damping of the soil K hr and C hr . Step 1
First, the fundamental frequency of the fixed base structure, Ω e , and the natural frequencies of the interacting system corresponding to translation, Ω h , and rocking, Ω r are calculated where
Ωh =
Kh , M
[B1]
Ωr =
Kr , M ( H + D) 2
[B2]
and K h and K r are translational and rocking components of static soil stiffness. Step 2
Next, the damping ratios of the interacting system corresponding to translation, ξ h , and rocking, ξ r are calculated viz.
272
ξh =
Ch 2ω h M
[B3]
ξr =
Cr 2ω r M ( H + D) 2
[B4]
while, ξ ′ = (ω / Ω)ζ , ξ h′ = (ω / Ω h )ξ h and ξ r′ = (ω / Ω r )ξ r , and normalized pseudoacceleration of the interacting system results in
⎛ ω2 ω2 ω2 ⎛ ⎞⎞ ω2 ω2 ⎜1− − ⎜ ⎟⎟ ′ ′ ′ ′ ′ = + + − + − − − − ( Q ( H D ) Q ). i 2 . ξ .( ξ ξ ) .( ξ ξ ) h r h r 2 2 ⎜ ⎟⎟ ⎜ Ω2 Ω 2 Ω 2 ω 2 .X g Ω Ω h r h r ⎝ ⎠⎠ ⎝ Ω2 .X e
−1
[B5] where, Qh = X 0 / X g and Qr = Φ 0 / X g are the ratios that relate the amplitude of translational and rocking components of the input motion to the amplitude of free-field ground motion (see Mita ans Luco, 1989). It should be noted that the kinematic interaction is excluded when Qh and Qr are taken as 1 and 0, respectively. Step 3
( ( Finally, the effective system frequency, Ω and damping ratio, ξ , are calculated (
corresponding to the resonance condition ( ω = Ω ). An iterative procedure is needed for ( ( the calculation of Ω and ξ , since these values are unknown in the beginning. 1 1 1 (2 = 2 + 2 Ω Ω Ωh
⎛ 1 + 4ξ ′ξ h′ ⎞ 1 ⎜ ⎟ ⎜ 1 + 4ξ ′ 2 ⎟ + Ω 2 h ⎠ r ⎝
( Ω 2 ⎛⎜ ξ h′ − ξ ′ ξ = ξ′+ 2 ⎜ 2 Ω h ⎝ 1 + 4ξ h′ (
( ⎞ Ω2 ⎟+ ⎟ Ω 2 r ⎠
⎛ 1 + 4ξ ′ξ r′ ⎞ ⎜ ⎟ ⎜ 1 + 4ξ ′ 2 ⎟ r ⎝ ⎠
⎛ ξ r′ − ξ ′ ⎜ ⎜ 1 + 4ξ ′ 2 r ⎝
⎞ ⎟ ⎟ ⎠
[B6]
[B7]
273 The kinematic interaction effects are taken into account in accordance with the procedures provided by Aviles and Perez-Rocha (1998) viz.
( ( Tk = Ti (
ξk =
[B8] (
ξi Qh + ( H + D).Qr
[B9]
( ( ( ( where, Tk , Ti , ξ k and ξ i are the effective system period and damping ratio of SSI
systems, considering the inertial interaction and inertial-kinematic interaction effects, respectively. The ratios Qh = X 0 / X g and Qr = Φ 0 / X g represent the transfer functions of the components of the foundation input motion. They relate the amplitudes of the translational and rocking input motions, respectively, to the amplitude of the free-field motion at the ground surface. The values of Qh and Qr can be determined from Figure B1. From the Equation B8 and B9, it can be seen that the system period is insensitive to the kinematic interaction; however, the damping ratio may vary based on the variations of the translational and rocking components of the input motion.
274 Figure B1. Real (dashed line) and imaginary (dotted line) parts and amplitude (solid line) of the translational and rocking components of the foundation input motion (adapted from Mita and Luco)
275
CIRRICULUM VITAE Name:
Alper Turan
Place of birth:
Igdir, TURKEY
Year of birth:
1977
EDUCATION •
Ph.D., Engineering Science, Civil and Environmental Engineering, 2005-2008,
The University of Western Ontario •
MSc., Engineering Science, Civil and Environmental Engineering, 1999-2002,
Karadeniz Technical University, Trabzon, Turkey •
Bachelors of Engineering, Civil and Environmental Engineering, 1995-1999,
Karadeniz Technical University, Trabzon, Turkey
HONORS AND AWARDS •
Milos Novak Memorial Award, 2007
•
Graduate Scholarship (The University of Western Ontario), 2005
•
NATO Research Scholarship (Von Karman Institute), 2004
•
Deans’ Honors List (Karadeniz Tech Uni.), 1997-1998
276
EXPERIENCE •
Geotechnical/Structural Analyst, Hatch Renewable Power, Niagara Falls, ON.
Sept 2008 – Present, Supervisor: Robert Dawson, Ph.D., P.Eng. •
Research/Teaching Assistant, The University of Western Ontario, London, ON.
Jan 2005 – Aug 2008, Supervisors: Sean Hinchberger, Ph.D., P.Eng. & M. Hesham El Naggar, Ph.D., P.Eng. •
Research Assistant, Von Karman Institute for Fluid Dynamics
,
Brussels,
Belgium. May 2004 – Jan 2005, Supervisor: Jeroen Van Beeck, Ph.D. •
Structural Engineer, State’s Hydraulic Works, Trabzon, Turkey. Dec 1999 – May
2004, Supervisor: Bahri Ege, Ing.
PUBLICATIONS T
Journal Publications;
• Turan, A., Hinchberger, S., El Naggar, M.H. 2006. Predicting the dynamic properties of glyben using a modular neural network (MNN). Canadian Geotechnical Journal. (Accepted) • Turan, A., Hinchberger, S., El Naggar, M.H. 2006, Mechanical characterization of an artificial clay. The Journal of Geotechnical and Geo-environmental Engineering, ASCE. (Accepted).
277 • Turan, A., Hinchberger, S., El Naggar, M.H. 2008. Design and commissioning of a laminar soil container for use on small shaking tables. Soil Dynamics and Earthquake Engineering. (Accepted) • Turan, A., Hinchberger, S., El Naggar, M.H. 2008. Influence of pore fluid viscosity on the dynamic properties of an artificial clay. The Journal of Geotechnical and Geoenvironmental Engineering, ASCE. (In Review) • Turan, A., El Naggar, M.H., Hinchberger, S., 2008. Dynamic behavior of buildings with embedded stories. Soil Dynamics and Earthquake Engineering. (In Review)
Conference Publications;
• Turan, A., Hinchberger, S., El Naggar, M.H. 2008. Design and performance assessment of a laminar shear box. 61th Canadian Geotechnical Conference, Edmonton. • Turan, A., Hinchberger, S., El Naggar, M.H. 2008. Lateral behaviour of micropile groups under static and dynamic loads. Geohazard IV, Quebec City. • Turan, A., Hinchberger, S., El Naggar, M.H. 2007. Seismic performance of micro-pile foundations in layered soils. 8th International Symposium on Micro-piles, Toronto. • Turan, A., Hinchberger, S., El Naggar, M.H. 2007. Performance of inclined sheets of micro-piles as active vibration barriers. 60th Canadian Geotechnical Conference, Ottawa. • Turan, A., Hinchberger, S., El Naggar, M.H. 2006. Dynamic properties of modified glyben as an artificial clay for seismic applications. 4th ICEGE, Thessaloniki, Greece. • Turan, A., Ikizler, B. 200 Determination of slope stability numbers using ANN. First National Dams and Hydroelectricity Symposium, Ankara, Turkey. •
