University of Nevada Reno. Evaluation of Site Response Analysis Programs in. Predicting Nonlinear Soil Response Using

Transcription

1 University of Nevada Reno Evaluation of Site Response Analysis Programs in Predicting Nonlinear Soil Response Using Geotechnical Downhole Array Data A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil and Environmental Engineering by Seyed Farshid Ghazavi Dr. Ramin Motamed/ Thesis Advisor May, 2015

2 UNIVERSITY OF NEVADA RENO THE GRADUATE SCHOOL We recommend that the thesis prepared under our supervision by Seyed Farshid Ghazavi entitled Evaluation of Site Response Analysis Programs in Predicting Nonlinear Soil Response Using Geotechnical Downhole Array Data be accepted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Ramin Motamed, Ph.D., Advisor Raj Siddharthan, Ph.D., Committee Member Raj R. Kallu, Ph.D., Graduate School Representative David W. Zeh, Ph.D., Dean, Graduate School May, 2015

3 i Abstract Liquefaction is a state of soil in which soil starts to behave as a fluid. This happens when the pore pressure rises up and it can t get dissipated as fast as it is rising up during the earthquake. Trying to predict the soil dynamic response and taking into account the effects of this phenomena is one of the geotechnical engineering design challenges. A variety of available software have been used to carry out the above prediction. Important point here is the reliability of these software in terms of degree of accuracy. An evaluation between two most commonly used software packages, DEEPSOIL and OPENSEES, in estimating the seismic response of the soil has been conducted. OPENSEES is a finite element based program which is capable of 3D modeling meanwhile DEEPSOIL is a finite different based software which can only perform one dimensional modelling. This evaluation has been carried out by modeling a well instrumented geotechnical vertical array located by UC Santa Barbara using both computer programs. Analyzing the results, it can be seen that OPENSEES predicts the soil behavior more accurately. On the other hand, DEEPSOIL results are not satisfying. Moreover, a review of available methods for estimating the liquefaction induced lateral ground displacement has been carried out. As indicated, empirical methods such as Shamoto 1998 and Valsamis 2010 methods can provide fairly reasonable estimates in terms of lateral displacement estimations. Keywords: Liquefaction, OPENSEES, DEEPSOIL, Site Response Analysis.

4 ii Acknowledgements I would like to express my appreciation to Prof. Motamed, my advisor, who has guided me through my research work here in University of Nevada Reno. Much gratitude is also given to my committee members, Prof. Raj Siddharthan and Prof. Raj R. Kallu for their comments and guidance. I would like to thank my family, specially my mother, for their ineffable love and supports, my girlfriend Hila for sticking by my side during the difficult moments, and my friends for their help and supports.

5 iii Table of Contents 1 Introduction General Introduction Problem Description Scope Literature review Characterization of the Wildlife Liquefaction Array (WLA) Location Instrumentation In Situ Testing Selected Earthquake Event for the Modeling Soil Properties Site Response Analysis Modeling DEEPSOIL OPENSEES Model Results and Analysis DEEPSOIL Equivalent Linear_ East West Direction Equivalent Linear_ North South Direction Non-linear_ East West Direction Non-linear_ North South Direction OPENSEES... 61

6 iv Applied Motion in East West Direction Applied Motion in North South Direction Applied Motion in 2 Directions Excess Pore Water Pressure Liquefaction Induced Lateral Soil Displacement Estimation Methods Background Empirical Methods Hamada et al and Youd et al Faris et al Zhang et al. 2004, Faris Shamoto et al Valsamis et al Bardet et al Theoretical method Investigated cases using the empirical and theoretical methods Taboada-Urtuzuastegui et al (Tests number 1 to 7) Abdoun et al (Tests number 8 to 9) Feigel et al (Tests number 10 to 11) Caltrans Guidelines on Foundation Loading and Deformation Due to Liquefaction Induced Lateral Spreading 2012 (Tests number 12 to 13) UC Davis Report: #UCD/CGM- 03/01 (Tests number 14 to 15)

7 v Cetin et al (Tests number 16 to 24) Results and Discussion Conclusion Conclusions and Recommendations References

8 vi List of Tables Table 1. Site Classification (ASCE Chapter 7-05 Chapter 20) Table 2. Selected Earthquake Properties (NEES Santa Barbara Website) Table 3. Relative Density of Sand versus Qc (EPRI 1990) Table 4. Consistency Index of Clay versus N and Qc (EPRI 1990) Table 5. Consistency of Permeability (EPRI 1990) Table 6. MulitiYieldIndepend Material Properties Table 7. Permeability Values of each Type of Soil in cm/s (OPENSEES wiki website). 21 Table 8. MultiYieldDepend Material Properties (OPENSEES wiki website) Table 9. Equivalent Linear Analysis in DEEPSOIL Tabular Data Table 10. Non-linear Analysis in DEEPSOIL without Pore Water Pressure Tabulated Data Table 11. Summary of Each Layer Properties Table 12. Continued Summary of Each Layer Properties Table 13. Testing Program Table 14. Key Measured Parameters in Centrifuge Tests Table 15. Soil Testing Parameters in the Liquefaction Large Scale and Centrifuge Tests at 25g Simulating a 5-6 m Thick Saturated Sand Deposit Table 16. Shaking and Measured Parameters in Large Scale and Centrifuge Tests Table 17.Test M2-2: Observed Displacement 0.47 m Table 18. M2-4: Obserrved displacement of 0.61 m Table 19. M2-5: Observed displacement: 0.68 m Table 20. M2a-3: Observed displacement: m

9 vii Table 21. M2a-4: Observed displacement: m Table 22. M2b-5: Observed displacement: 0.3 m Table 23. M2c-6: Observed displacement: m Table 24. FF-P2: Observed displacement: m Table 25. FF-V1: Observed displacement: 0. 0 m Table 26. Test1: Observed displacement: 0. 8 m Table 27. Test2: Observed displacement: 0. 8 m Table 28. Worked Example 1: Observed displacement: 1.0 m Table 29. Worked Example 2: Observed displacement: 1.32 m Table 30. PDS03: Observed displacement: 2.0 m Table 31. SJB01: Observed displacement: 2.0 m Table 32. SPT-PS2: Observed displacement: 2.4 m Table 33. SPT-PS3: Observed displacement: 0.1 m Table 34. SPT-PS34: Observed displacement: 0.9 m Table 35. SPT-SF5: Observed displacement: 0.3 m Table 36. SPT-SF6: Observed displacement: 1.2 m Table 37. SPT-DN1: Observed displacement: 0.9 m Table 38. SPT-YH1: Observed displacement: 0.2 m Table 39. SPT-YH2: Observed displacement: 0.15 m Table 40. SPT-YH3: Observed displacement: 0.05 m

10 viii List of Figures Figure 1. Schematic Presentation of Multi Degree of Freedom Layered System (Hashash et al. 2010)... 7 Figure 2. Extended Masing Rules (Vucetic et al. 1990)... 9 Figure 3. Accelerometers and Pressure Transducers Location (NEES Santa Barbara Website) Figure 4. Shear Wave Velocity Log (NEES Santa Barbara Website) Figure 5. CPT Boring Log Data Collection (NEES Santa Barbara Website) Figure 6. Measured Data Based on NEES Website for M4.9 Event (Steidl 2013) Figure 7. Acceleration Time History in East West Direction (NEES Santa Barbara Website) Figure 8. Acceleration Time History in North South Direction (NEES Santa Barbara Website) Figure 9. Degradation Curve and Damping Ratio Curve (Vocetic and Dobry 1991) Figure 10. Degradation Curve and Damping Ratio Curve (Seed and Idriss, 1991) Figure 11. Soil Profile and Frequency Content for Each Layer in DEESPOIL Model and the WLA Soil Profile Figure 12.3D Soil Column Modeled in OPENSEES Figure 13. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Equivalent Linear Analysis, East- West Direction Figure 14. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, Equivalent Linear Analysis, East- West Direction... 35

11 ix Figure 15. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, Equivalent Linear Analysis, East- West Direction Figure 16. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, Equivalent Linear Analysis, East- West Direction Figure 17. Acceleration Response Spectra at Surface Figure 18. Acceleration Response Spectra at Depth of 2.5m Figure 19. Acceleration Response Spectra at Depth of 4.65m Figure 20. Acceleration Response Spectra at Depth of 8.2m Figure 21. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Equivalent Linear Analysis, North- South Direction. 41 Figure 22. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, Equivalent Linear Analysis, North- South Direction Figure 23. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, Equivalent Linear Analysis, North- South Direction.. 43 Figure 24. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, Equivalent Linear Analysis, North- South Direction Figure 25. Acceleration Response Spectra at Surface Figure 26. Acceleration Response Spectra at Depth of 2.5m Figure 27. Acceleration Response Spectra at Depth of 4.65m Figure 28. Acceleration Response Spectra at Depth of 8.2m Figure 29. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Non-Linear Analysis, East- West Direction... 48

12 x Figure 30. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, Non-Linear Analysis, East- West Direction Figure 31. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, Non-Linear Analysis, East- West Direction Figure 32. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, Non-Linear Analysis, East- West Direction Figure 33. Acceleration Response Spectra at Surface Figure 34. Acceleration Response Spectra at Depth of 2.5m Figure 35. Acceleration Response Spectra at Depth of 4.65m Figure 36. Acceleration Response Spectra at Depth of 8.2m Figure 37. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Non-Linear Analysis, North- South Direction Figure 38. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m Figure 39. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m Figure 40. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m Figure 41. Acceleration Response Spectra at Surface Figure 42. Acceleration Response Spectra at Depth of 2.5m Figure 43. Acceleration Response Spectra at Depth of 4.65m Figure 44. Acceleration Response Spectra at Depth of 8.2m... 60

13 xi Figure 45. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, East- West Direction Figure 46. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, East- West Direction Figure 47. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, East- West Direction Figure 48. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, East- West Direction Figure 49. Acceleration Response Spectra at Surface Figure 50. Acceleration Response Spectra at Depth of 2.5m Figure 51. Acceleration Response Spectra at Depth of 4.65m Figure 52. Acceleration Response Spectra at Depth of 8.2m Figure 53. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, North- South Direction Figure 54. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, North- South Direction Figure 55. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, North- South Direction Figure 56. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, North- South Direction Figure 57. Acceleration Response Spectra at Surface Figure 58. Acceleration Response Spectra at Depth of 2.5m Figure 59. Acceleration Response Spectra at Depth of 4.65m... 74

14 xii Figure 60. Acceleration Response Spectra at Depth of 8.2m Figure 61. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, East- West Direction Figure 62. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, East- West Direction Figure 63. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, East- West Direction Figure 64. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, East- West Direction Figure 65. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, North- South Direction Figure 66. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, North- South Direction Figure 67. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, North- South Direction Figure 68. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, North- South Direction Figure 69. Acceleration Response Spectra at Surface, East- West Direction Figure 70. Acceleration Response Spectra at Depth of 2.5m, East- West Direction Figure 71. Acceleration Response Spectra at Depth of 4.65m, East- West Direction Figure 72. Acceleration Response Spectra at Depth of 8.2m, East- West Direction Figure 73. Response Spectra at Surface, North- South Direction Figure 74. Response Spectra at Depth of 2.5m, North- South Direction... 86

15 xiii Figure 75. Response Spectra at Depth of 4.65m, North- South Direction Figure 76. Response Spectra at Depth of 8.2m, North- South Direction Figure 77. Predicted and Measured Excess Pore Pressure at Depth of 2.64m Figure 78. Predicted and Measured Excess Pore Pressure Ratio (ru) at Depth of 2.64m. 89 Figure 79. Predicted and Measured Excess Pore Pressure at Depth of 2.64m Figure 80. Predicted and Measured Excess Pore Pressure Ratio (ru) at Depth of 2.64m. 90 Figure 81. Side View of Laminar Box with Instrumentation Used In Test M2-4 (Not in Scale) Figure 82. Setup and Instrumentation of Centrifuge Model Tests Simulating Large Scale Tests SG-1 (Gonzalez 2008) Figure 83. Model Configuration for Test 1: (a) Side View (b) Section A-A' Figure 84. Model Configuration for Test 2: (a) Side View (b) Section A-A' Figure 85. Soil Profile and Properties Figure 86. Abutment Configuration and Soil Properties Figure 87. Schematic Model Layout of the Third Centrifuge Test, PDS Figure 88. Schematic Model Layout of the Fourth Centrifuge Test, SJB Figure 89. Summary of Lateral Displacement Calculations for Police Station Site Figure 90. Summary of Lateral Displacement Calculations for Degirmendere Nose Site Figure 91. Summary of Lateral Displacement Calculations for Yalova Harbor Figure 92. Comaprison between Predicted and Measured Displacements Figure 93. Comparison between Predicted and Measured Displacements limited to 2 m 135 Figure 94. Average and Deviation from Average for Each Method

16 xiv Figure 95. Average and Deviation from Average for Each Method except Hamada

17 1 1 Introduction 1.1 General Introduction Liquefaction is a state of soil in which soil starts to behave as a fluid. This happens when the pore pressure rises up and it can t get dissipated as fast as it is rising up during the earthquake. As the pore pressure goes up, the effective stress decreases to a limit that it becomes zero or even negative values. Susceptible soils to liquefaction are the ones with loose and uniform grading conditions such as sands. So, particle properties such as size, shape and gradation play an important role. Characteristics of the soil that can provide resistance to liquefaction are density, stress condition, prior seismic straining, over consolidation ratio, soil fabric, period of the time soil is under pressure, and also lateral pressure coefficient (Kramer 1996). In order to predict the possibility of liquefaction, there are three different approaches: energy dissipation approach, effective stress based response analysis approach and probabilistic approach (Kramer 1996). This phenomenon has caused lots of hazards in the past such as Niigata-Chuetsu earthquake in 2004, Kobe earthquake in 1995, and Loma Prieta earthquake in That event showed that not only slope stability considerations should be taken in to account but also an understanding of the dynamic behavior of the soil such as liquefaction which makes large soil displacements should be considered. (Towhata 2005). Therefore, trying to predict the possibility of occurrence of this event and also mitigating it in the desired construction field is one of the interesting research areas. Predicting this event can be done by studying the type of existing soil, investigating the water table conditions, running physical and numerical models based on the gathered information.

18 2 In order to gather information about the soil and water table in the desired construction location, a variety of site investigations methods such as SPT, CPT, Seismic Refraction and so on can be done. By recognizing the type of soil, depth of water table and soil resistance parameters liquefiable layers can be distinguished. Having determined the type of soil, modeling, physical or numerical, can begin. Physical modeling is one of the great ways to study the behavior of the soil and the soil structures under seismic and non-seismic events. Physical modeling is done through using a centrifuge or a shake table test. The target is to model soil conditions, soil profile, and also simulate the earthquake and ground shaking in small scales. Using a centrifuge gives us the opportunity of applying accelerations of g and greater. Since the centrifuge machine can apply the same amount of in situ stress, existing effective stresses can be applied on the soil though this option is really expensive. Shake table test is another physical modeling option which has the disadvantage of not being able to replicate insitu stress conditions meanwhile it is more doable in terms of being easier to build the model since bigger models can be built and also it is more affordable. Numerical modeling along with vertical downhole arrays can be really effective in terms of time and cost reduction meanwhile they can make disastrous consequences. The key point here is to have a good engineering judgment. Since in case of modeling geomatrials, there are not that much of available data. This problem is worse when it comes to excavation and tunneling projects. Numerical modeling can be an uncoupled where there s only one main variable or coupled meaning more than one parameter plays the main role. Moreover, Vertical downhole arrays are typically used to evaluate the existing methods of estimating the dynamic soil behavior. In order to do so, a series of

19 3 1D, 2D or 3D modeling time domain analyses have been conducted to simulate the soil response using a variety of available software packages. Other issues in terms of choosing the type of analysis are personal experience; special features each software present in terms doing the analysis; and also the availability of each software in the work environment or the research institute. Current popular software is OpenSees, Shake, Abaqus, Deepsoil and LSDYNA. 1.2 Problem Description There are two approaches for performing seismic hazard analysis: deterministic and probabilistic seismic hazard analysis. Deterministic approach includes characterization of the seismic sources, recognition of the effective factors for each source, choosing the attenuation equations and finally ground motion computation. Major drawbacks for this approach are conservatism level of the design; the design will be based on the result of a single source, or single magnitude or even single distance to the fault. Meanwhile the probabilistic approach covers all the deterministic approach s drawbacks (CEE 745). Ground motion prediction equations (GMPEs) are used in the probabilistic approach in order to measure the characteristics of the ground motion such as magnitude, intensity, damping ratio and so on. Site conditions based on the shear wave velocity in the upper 100 feet (Vs30) is implemented in the modern GMPEs. Basin effects such as reflection of the body waves and generation of the surface waves at the edges of the basin are the physical processes contributing to so called site effects. Site effects can be modeled under numerical or empirical models. Numerical models are based on wave propagation analyses whereas empirical ones are based on the statistical

20 4 analyses and quantification of different ground motions at different locations. One of the key factors in the numerical models is the type of the material simulation which can be linear, equivalent linear or non-linear. Also, another factor is the analysis type which can be total or effective stress analysis. Equivalent linear modeling is the most common one in terms of practice due to more well- known input parameters such as shear wave velocity, unit weight of the soil and so on. Since soil has a non-linear behavior, a non-linear modeling can result in better and more accurate analysis. However, Non-linear modeling is less famous despite of its more accurate results. The reason for it is less investigation about the non-linear characterization and soil parameters. Total stress analysis is often used for cohesive materials and also investigating the short term behavior of the soil. On the other hand, effective stress analysis gives the effective shear strength of the soil which is used for long term design purposes. Two of most commonly used software for predicting the soil response are OpenSees and Deepsoil which are a finite element and finite difference based programs respectively. In OpenSees, soil profile is modeled based on the non-linear behavior of the soil meanwhile in Deepsoil soil can be modeled in three different modes such as linear, equivalent linear and non-linear. OpenSees is capable of running 1D, 2D and 3D analyses meanwhile Deepsoil is only capable of performing 1D analysis. These two software packages are being used widely for site response analysis, generation of pore water pressure but the accuracy of them is questionable. The fact that designs are being done based on output results of these programs can raise some concerns. The problem rises up when the results that are being used in the design calculations are not

21 5 the in the safe side. Also, if the numbers are in the safe side, what is the level of the conservatism? 1.3 Scope In order to evaluate the mentioned computer programs for site response analysis, a geotechnical downhole array called wildlife liquefaction array, located in Santa Barbara was selected for the sake of comparison. For DEEPSOIL modeling, since it is only capable of performing one dimensional analysis, different methods such as equivalent linear, and non-linear were used for the predictions. On the other hand, OPENSEES which can do the calculations in 1D, 2D and 3D was used to model a soil column using three dimensional elements with application of one directional and two directional motions. Moreover, OPENSEES is capable of conducting total and effective stress analyses where DEEPSOIL can only perform the total stress analysis type. As indicated, OPENSEES modeling with two different motions applying at the base was able to predict the soil behavior much better than application of one motion and also the DEEPSOIL modeling. All the predictions were underestimating soil response at short periods except the OPENSEES with two direction motion at the base.

22 6 2 Literature review Numerical modeling is one of the most common ways for predicting the soil seismic response. This is achieved through linear, equivalent linear, and non-linear modeling. Since geo-material behavior is non-linear, the linear modeling can not provide accurate results. Therefore, equivalent linear and nonlinear modeling have more credibility in terms of predicting the behavior of the geo-material. Among these two, equivalent linear modeling has been used more due to its more accessible required data (Kramer and Paulsen 2004). One of the most common software in equivalent linear modeling is SHAKE (Schnabel et al. 1972). This type of analysis is based on parameters such as G (equivalent shear modulus) and (equivalent viscous damping ratio). The equivalent shear modulus can be derived from the reduction curve based on the small strain shear modulus ( ). can be calculated from a number of equations such as where is the density of the. soil and is the shear wave velocity and also, 1000, (Seed and. Idriss et al. 1975) where, is a constant relied on Dr and is the mean effective stress. Also is affected by parameters such as mean effective stress, void ratio, over consolidated ratio (OCR), cyclic shear strain and strain rate. Equivalent linear analysis is a repetitive type of process which starts with an initial value for and. Linear dynamic analyses are performed in order to gain the effective shear strains. These effective shear strains are used to appraise proper values for and. This procedure goes on till the final calculated value is typically the same as its previous calculated value.

23 7 Nonlinear modeling is based on the either frequency domain analysis or time domain analysis. In both methods, the soil profile layer is broken into multiple layers as a system with concentrated mass or a continuous system with distributed mass same as structural analysis (Clough and Penzien et al. 1993; Chopra et al. 2000). Figure 1 shows a schematic view of multi degree of freedom system for a layered soil profile. Figure 1. Schematic Presentation of Multi Degree of Freedom Layered System (Hashash et al. 2010) Having those said, the frequency domain analysis is done by solving the wave equation meanwhile the time domain method can be derived from the solution of motion equation of the above defined systems.

24 8 The big difference between nonlinear and equivalent linear modeling is the ability of the nonlinear modeling in performing effective stress analysis. This feature provides the opportunity to calculate the generated pore water pressure, and its dissipation after the earthquake. Soil material models employed range from relatively simple cyclic stress strain relationships (e.g., Ramberg and Osgood et al. 1943; Kondner and Zelasko et al. 1963; Finn et al. 1977; Pyke et al. 1979; Vucetic et al. 1990) to advanced constitutive models incorporating yield surfaces, hardening laws, and flow rules (e.g., Roscoe and Schofield 1963; Roscoe and Burland 1968; Mroz 1967; Prevost 1997; Dafalias amd Popov 1979). (PEER 2008/ ). Cyclic nonlinear models are governed by back bone curve and loading-unloading, pore water generation, and stiffness degradation behavior rules. Along with the backbone curve, Masing rules (Masing 1926) and extended Masing rules (Pyke 1979; Wang et al. 1980; Vucetic 1990) are taken into account in order to model the dynamic soil behavior better. Masing rules and its extended ones are as follows: 1. For the first round of loading, backbone curve and stress strain one are the same. 2. Reloading phase is two times the first loading curve but identical in shape. 3. In case of curve exceeding the maximum previous strain and having an intersection with the backbone curve, it follows the backbone curve. 4. Stress strain curve follows the previous curve in case it crosses another loading unloading curve (Figure 2).

25 9 Figure 2. Extended Masing Rules (Vucetic et al. 1990) Advanced constitutive models can mimic the soil behavior effectively due to their reliance on plasticity effect. Key parameters here are yield surface, flow rules and hardening laws. Yield function is the state that the behavior of the material turns into plastic from elastic. Flow rules are the connection between plastic strain and stress. Hardening laws are defined when plastic deformation takes place. These laws address the difference in yield surface size and shape. In order to avoid the inaccurate responses in models containing small strains, taking advantage of viscous damping term is mandatory. Viscous damping fills the gap where

26 10 nonlinear model can t capture damping at small strains. This problem with nonlinear modeling is due to the fact of backbone curve becoming linear in those strains (Vucetic and Dobry 1986). A series of codes in modeling the nonlinear behavior of the soil are as follows: DEEPSOIL (Hashash and Park 2001, 2002; Park and Hashash 2004; OPENSEES (Ragheb 1994; Parra 1996; Yang 2000; McKenna and Fenves 2001; opensees.berekely.edu), D-MOD_2 (Matasovic 2006), SUMDES (Li et al. 1992) and TESS (Pyke 2000). A brief description of each one is indicated in the following. DEEPSOIL is a finite difference based analysis method which is capable of performing linear, equivalent linear and non-linear analysis modes with no restrictions on input motion length, number of layers and properties of the material. It can calculate the pore water pressure generation only through non-linear method. Input parameters for DEEPSOIL are such as shear stress at reference, curve fitting constants, initial tangent shear modulus of soil, soil properties including thickness, saturated unit weight, shear wave velocity, and viscous damping ratios and frequencies for Raleigh damping equations (PEER 2008/ ). OPENSEES is a finite element based method which able to perform non-linear calculations in 1, 2 and 3 directions. Due to its non-linear calculation capability, OPENSEES is a good means of predicting of pore water pressure generation. Required parameters in OPENSEES for conducting analysis are the ones related to yield surfaces definition, controlling variables for dilatancy and contraction response, soil layers

27 11 properties such as thickness, saturated unit weight, bulk modulus, shear wave velocity and also Rayleigh damping formulation frequencies (PEER 2008/ ). D-MOD_2 is more advanced type of D-MOD which is also capable of reproducing seismically induced slips. In case of wave propagation problems, D-MOD_2 assumes that waves propagate vertically through the layers. Input parameters required for D-MOD_2 to do the modeling are as follow: MKZ backbone curve, initial tangent shear modulus, sear stress reference strain, degradation parameters, pore water pressure generation and dissipation parameters, each layer properties and Rayleigh damping coefficients. SUMDES is a finite element based non-linear method which is able to perform three directional analysis. It can also calculate the pore water pressure generation too. SUMDES relies on bounding surface hypoplasticity model (Wang 1990; Wang et al. 1990). SUMDES parameters for running a test are such as plastic shear modulus controlling parameters, contraction dilation controlling parameters, soil layers properties including thickness, saturated unit weight, and Rayleigh damping formulation parameters (PEER 2008/ ). TESS is similar to DEEPSOIL and D-MOD_2 in terms of hyperbolic function. TESS is a finite difference analysis method which is capable of performing one directional analysis. Mandatory parameters for modeling using TESS are initial backbone curve parameters, degradation curve variable, pore water pressure generation and dissipation controlling parameters, each soil layer properties and also controlling low strain damping parameters (PEER 2008/ ).

28 12 3 Characterization of the Wildlife Liquefaction Array (WLA) Vertical arrays such as WLA are typically used to evaluate the existing methods of estimating the dynamic soil behavior. In order to do so, a series of 1D, 2D or 3D modeling time domain analyses are conducted to simulate the soil response using a variety of available software packages. 3.1 Location Wildlife Liquefaction Array (WLA) is a geotechnical downhole array which is used for liquefaction related research, the array used to be in the Imperial Wildlife area of California State game refuge. It was located in 60 km from east of San Diego, and 13 km from the Brawley, California. During the past 75 years, liquefaction has been observed within the instrumental array in six earthquake events. Since the site has been affected by investigators from the beginning of the instrumentation in 1982 and failure of the piezometers, reestablishing WLA in new location, in 65 m northward from its old location was decided (NEES website). As it can be seen in Figure 3, the soil profile consists of a silty clay to clayey silt with thickness of 2.5m at the top which is underlain by 4.3m of silty sand to sandy silt, 5.2m of silty clay to clay and 18m of slit at the bottom. Additionally, the ground water table is at the depth of 1.2m. 3.2 Instrumentation New infrastructure at this site includes cased drill holes for (1) five downhole strong ground motion accelerometers at depths of 2.4 m, 4.8 m, 7.2 m, 30 m and 97 m; (2) eight electrical piezometers at depths ranging from 2.7 m to 6.3 m; (3) two standpipe piezometers to depths of 4.5 m; (4) five slope inclinometer casings to depths of 10 m; and

29 13 (5) three flexible casings set at depths of 10 m for measurement of permanent lateral ground displacement (NEES website). As indicated, this site is pretty well instrumented in terms of accelerometers and pore water pressure transducers so a good comparison for each depth can be performed. A section of the soil including the accelerometers, pressure transducers and soil profile can be seen in Figure 3. Figure 3. Accelerometers and Pressure Transducers Location (NEES Santa Barbara Website) For the current study, recorded data from accelerometers 00, 01, 02, 03, 04 and 05 have been used. Moreover, recorded pore water pressure from pressure transducer 60 which is located at the top of the liquefiable layer, has been used.

30 In Situ Testing For the purpose of in situ testing, one seismic CPT based on ASTM D and one SPT using Longyear auto safety hammer were used (NEES geotechnical report 2004). Based on the shear wave velocity acquired from the seismic CPT, Figure 4, the Vs30 of the soil profile is m/s and natural period of the site would come to 0.61s. According to Table 1, chapter 20 of ASCE manual s table: site classification procedure for seismic design, it can be said that the mentioned location classification is site class D. Figure 4. Shear Wave Velocity Log (NEES Santa Barbara Website)

31 15 Table 1. Site Classification (ASCE Chapter 7-05 Chapter 20) The CPT boring log containing friction ratio, tip resistance, local friction, soil behavior type and inclination can be seen in Figure 5. Based on Figure 5, it can be seen that CPT equipment had a maximum inclination of 7 at the depth of 31m. This inclination has been ignored in modeling since it is too small and is not going to affect the results that much. In terms of SPT, a modification in the drop height of the hammer has been done. Since the hammer used in this method had an average energy ratio of about 90 percent which is way bigger than usual 60 percent, a decrease of drop height to 25 inches was done. This reduction was also done for higher accuracy in low blow count layers. Energy measurement data acquisition was done for different depths such as 9, 12, 15 and 18. It should be noted that gained data at depths 25 to 27m and also 96m is not fully reliable. The reason of this unreliability is the way this data has been collected. This data is based on cuttings mixed with the drilling mud and there is fairly a good chance of bentonite contamination (NEES geotechnical report 2004).

32 Figure 5. CPT Boring Log Data Collection (NEES Santa Barbara Website) 16

33 Selected Earthquake Event for the Modeling In order to do the modeling and applying motion to the base of the model, a recorded earthquake event with magnitude of 4.9 has been selected. Table 2 indicates the earthquake properties. Table 2. Selected Earthquake Properties (NEES Santa Barbara Website) Distance Depth Date Magnitude (km) (km) 8/27/ The reason for this selection is pore water pressure generation can be observed in this event based on measured data. Although liquefaction has not been fully generated in this event, a pore water pressure ratio (ru) of greater than 50 percent was observed as an indication of liquefaction initiation. A sample of recorded data based on NEES website can be seen in Figure 6.

34 18 Figure 6. Measured Data Based on NEES Website for M4.9 Event (Steidl 2013) 3.5 Soil Properties Based on the CPT boring log, Figure 4, and available tables in different references, required data for modeling the soil profile in DEEPSOIL and OPENSEES have been obtained. Considering the fact that no pore water pressure data was provided data for in the CPT boring log, no correction was applied for the tip resistance. Therefore in current work, Qc is assumed to be equal to Qt. According to EPRI information provided in Table 3 and Table 4, relative density of each soil layer was determined. Using the mentioned values for relative density and also taking OPENSEES wiki website tables for PressureDependMultiYield02 material and PressureIndependMultiYield material, soil

35 19 properties such as shear modulus, bulk modulus, void ratio, unit weight of the soil were selected. The OPENSEES suggested properties are shown in Table 6 and Table 8. In order to double check the obtained values for soil unit weights, Dr. Robertson table based on CPT data was used. Important parameter here in calculation of pore water pressure is permeability coefficient. First estimations were done using the available figures in Advanced Soil Mechanics book by Das. This estimation relied on void ratio values. Comparing the achieved results with provided permeability values table by OPENSEES wiki website which can be seen in Table 7 and EPRI table in Table 5, some of the permeability values were out of range and needed to be revised. Even attempt of taking into account Dr. Robertson s equation for calculating the permeability values did not turn out great. Therefore for the sake of this thesis, values provided in Table 7 have been used for the modeling in OPENSEES modeling. Table 3. Relative Density of Sand versus Qc (EPRI 1990)

36 20 Table 4. Consistency Index of Clay versus N and Qc (EPRI 1990) Table 5. Consistency of Permeability (EPRI 1990)

37 21 Table 6. MulitiYieldIndepend Material Properties Table 7. Permeability Values of each Type of Soil in cm/s (OPENSEES wiki website)

38 Table 8. MultiYieldDepend Material Properties (OPENSEES wiki website) 22

39 23 4 Site Response Analysis Modeling 4.1 DEEPSOIL DEEPSOIL analysis has been done using two different methods: equivalent linear and non-linear method. In order to do so, a layered soil profile is needed to be employed. The layering should be in a way that it satisfies the maximum frequency fitting within the 25 to 50 Hz for each layer. Maximum frequency can be calculated from 4 where is the shear wave velocity and H is the thickness of the layer. Having the soil profile layered in the above mentioned way, it looks like Figure 11. For the purpose of equivalent linear method, two different motions, one in the East- West direction and the other one in North- South direction have been applied to the base of the model one at a time. Acceleration time history of each motion is plotted in Figure 7and Figure 8. Tabulated data about each layer is shown in Table 9. Results in terms of time history acceleration and time response spectra can be found in the model results and analysis part of this thesis. Acceleration (g) Time (s) Figure 7. Acceleration Time History in East West Direction (NEES Santa Barbara Website)

40 24 Acceleration (g) Time (s) Figure 8. Acceleration Time History in North South Direction (NEES Santa Barbara Website) In order to conduct the non-linear modeling, more parameters were involved. To do so, an appropriate degradation curve is chosen according to the type of soil. Silty clay layers at the top and the bottom of the liquefiable layer have been modeled as clayey layer so that Vucetic and Dobry (1991) curve has been picked with different plasticity indices. For the top layer based on the provided data by NEES website, a plasticity index of 21 and for the bottom silty clay, the ones beneath the liquefiable layer, a plasticity index of 19 has been picked. Silty layers below the silty clay layer have been modeled as a clayey layer with plasticity index of 15 and for the degradation curve, same degradation curve, Vucetic and Dobry (1991), Figure 9, has been selected. For liquefiable layer, sandy silt, degradation curve of Seed and Idriss (1991, mean limit), Figure 10, has been picked. By using the fitting procedure of MRDF-UIUC method implemented in DEEPSOIL software, the required parameters get calculated and filled in their place. Tabulated data about each layer is shown in Table 9 and Table 10. In case of pore water pressure generation, it is only applicable in non-linear method. However, scarcity of data and also vague guidance provided by the DEEPSOIL manual

41 25 prevented pore water pressure calculations. So in the analysis chapter of current thesis, non-linear method without pore water pressure generation result are included. Figure 9. Degradation Curve and Damping Ratio Curve (Vocetic and Dobry 1991)

42 Figure 10. Degradation Curve and Damping Ratio Curve (Seed and Idriss, 1991) 26

43 Figure 11. Soil Profile and Frequency Content for Each Layer in DEESPOIL Model and the WLA Soil Profile 27

44 28 Table 9. Equivalent Linear Analysis in DEEPSOIL Tabular Data Layer Layer Thickness # Name (m) Unit weight (kn/m3) Shear Velocity (m/s) 1 Silty Clay Silty Clay Sandy Slit Sandy Slit Silty clay Silty clay Silty clay Silty Clay Silt Silt Silt Silt Silt Silt Silt Silt Silt Silt Silt Silt Silt

45 29 Table 10. Non-linear Analysis in DEEPSOIL without Pore Water Pressure Tabulated Data 4.2 OPENSEES Soil model in OPENSEES includes a 3D soil column which is 30 meters tall, and a square base of 2 by 2 meters. This column has been discretized into a number of elements for each layer. Figure 12 shows the 3D soil column modeled in OPENSEES.

46 30 Figure 12.3D Soil Column Modeled in OPENSEES This discretization has been done by assuming a constant maximum frequency of 25 Hz for the entire soil column. Size of each element has been calculated based on where, is the size of element and is lowest velocity (Zerwer et al. 2002). In the mentioned equation, x should be less than 0.5. Doing so the number of elements comes down to 66 in total. Using the mentioned tables Chapter 3: Characterization of the Wildlife Liquefaction Array (WLA), all the required input data has been estimated and implemented into the model. For the sake of this study, three different types of analysis has been run. One is applying an East-West motion to the base of the soil column, one North-South motion and one analysis including the application of

47 31 both North-South and East-West motions at the same time to the base of the soil column. The latest analysis applied is bi- directional shaking to the soil column. Boundary conditions that have been used for this model include a fixed base in three different direction (x, y, z) and a degree of freedom for pore water pressure. Type of element used in this analysis is a SSPbrickUp which is an eight node element based on OPENSEES wiki website. This model is exclusively for dynamic analysis, and that degrees of freedom for pore water pressure is implemented in it. In order to apply the input motion to the base of the model, the UniformExcitation code has been used which applies the motion in terms of acceleration time history. Using this specific code, gives the results in terms of relative acceleration to the base motion. Running a number of tests, it appeared that the model is so sensitive to permeability and bulk modulus. In order to get better results and make the model more accurate, bulk modulus for each layer was recalculated with a poisson s ratio of 0.5. Table 11 and Table 12 show the summary of each layer properties which were used in modeling the soil column in the OPENSEES.

48 32 Table 11. Summary of Each Layer Properties Table 12. Continued Summary of Each Layer Properties

49 33 5 Model Results and Analysis The results of the analyses using each software are included in terms of time histories of acceleration, velocity, displacement and acceleration response spectra. First, DEEPSOIL results are presented based on type of analysis and the direction of applied motion. Secondly, OPENSEES results are presented regarding the direction of applied motions. For case of OPENSEES, pore water pressure generation results have been presented too since it was capable of calculating and predicting that part of soil behavior. 5.1 DEEPSOIL Equivalent Linear_ East West Direction Time History Following figures represent time history in different depths such as surface, 2.5m, 4.65m, and 8.2m. It should be noted that depth of measured and predicted data are not exactly the same at some depths. This is due to different thicknesses of model soil profile layers.

50 Figure 13. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Equivalent Linear Analysis, East- West Direction 34

51 Figure 14. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, Equivalent Linear Analysis, East- West Direction 35

52 Figure 15. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, Equivalent Linear Analysis, East- West Direction 36

53 Figure 16. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, Equivalent Linear Analysis, East- West Direction 37

54 Acceleration Response Spectra Figures below represent time history in different depths such as surface, 2.5m, 4.65m, and 8.2m. Same reason applies to the fact that measured data and predicted ones are not at the same depths. Figure 17. Acceleration Response Spectra at Surface Figure 18. Acceleration Response Spectra at Depth of 2.5m

55 39 Figure 19. Acceleration Response Spectra at Depth of 4.65m Figure 20. Acceleration Response Spectra at Depth of 8.2m

56 Equivalent Linear_ North South Direction Time History Following figures represent time histories at different depths such as surface, 2.5m, 4.65m, and 8.2m. It should be noted that depth of measured and predicted data are not exactly the same at some depths. This is due to different thicknesses of model soil profile layers in DEEPSOIL.

57 Figure 21. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Equivalent Linear Analysis, North- South Direction 41

58 Figure 22. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, Equivalent Linear Analysis, North- South Direction 42

59 Figure 23. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, Equivalent Linear Analysis, North- South Direction 43

60 Figure 24. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, Equivalent Linear Analysis, North- South Direction 44

61 Acceleration Response Spectra Figures below represent time history in different depths such as surface, 2.5m, 4.65m, and 8.2m. Same reason applies to the fact that measured data and predicted ones are not at the same depths. Figure 25. Acceleration Response Spectra at Surface Figure 26. Acceleration Response Spectra at Depth of 2.5m

62 46 Figure 27. Acceleration Response Spectra at Depth of 4.65m Figure 28. Acceleration Response Spectra at Depth of 8.2m

63 Non-linear_ East West Direction Time History Results of the no-linear analysis without calculations for generation of pore water pressure are indicated in the following figures. The applied input motion is in the East West direction. It should be noted that depth of measured and predicted data are not exactly the same at some depths. This is due to different thicknesses of model soil profile layers.

64 Figure 29. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Non- Linear Analysis, East- West Direction 48

65 Figure 30. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, Non- Linear Analysis, East- West Direction 49

66 Figure 31. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, Non- Linear Analysis, East- West Direction 50

67 Figure 32. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, Non- Linear Analysis, East- West Direction 51

68 Acceleration Response Spectra Figures below represent time history in different depths such as surface, 2.5m, 4.65m, and 8.2m. Same reason applies to the fact that measured data and predicted ones are not at the same depths. Figure 33. Acceleration Response Spectra at Surface Figure 34. Acceleration Response Spectra at Depth of 2.5m

69 53 Figure 35. Acceleration Response Spectra at Depth of 4.65m Figure 36. Acceleration Response Spectra at Depth of 8.2m

70 Non-linear_ North South Direction Time History Results of the no-linear analysis without calculations for generation of pore water pressure are indicated in the following figures. The applied input motion is in the North South direction. It should be noted that depth of measured and predicted data are not exactly the same at some depths. This is due to different thicknesses of model soil profile layers.

71 Figure 37. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, Non- Linear Analysis, North- South Direction 55

72 Figure 38. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, Non-Linear Analysis, North- South Direction 56

73 Figure 39. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, Non-Linear Analysis, North- South Direction 57

74 Figure 40. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, Non-Linear Analysis, North- South Direction 58

75 Time Response Spectra Figures below represent time history in different depths such as surface, 2.5m, 4.65m, and 8.2m. Same reason applies to the fact that measured data and predicted ones are not at the same depths. Figure 41. Acceleration Response Spectra at Surface Figure 42. Acceleration Response Spectra at Depth of 2.5m

76 60 Figure 43. Acceleration Response Spectra at Depth of 4.65m Figure 44. Acceleration Response Spectra at Depth of 8.2m

77 OPENSEES Applied Motion in East West Direction Time History Measured and predicted acceleration, velocity, and displacement at surface, depth of 2.5m, 4.65m and 8.2m and plotted in the following. It should be noted that due to layered nature of the soil in the model and also fixed depth of each accelerometer in the ground, measured and predicted depths are not exactly the same. It s been tried so that closest depths get selected.

78 Figure 45. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, East- West Direction 62

79 Figure 46. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, East- West Direction 63

80 Figure 47. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, East- West Direction 64

81 Figure 48. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, East- West Direction 65

82 Acceleration Response Spectra For each depth, predicted and measured time response spectra in logarithmic scale have been plotted. Same reasoning for different depth of measured and predicted results is true here. Figure 49. Acceleration Response Spectra at Surface

83 67 Figure 50. Acceleration Response Spectra at Depth of 2.5m Figure 51. Acceleration Response Spectra at Depth of 4.65m

84 68 Figure 52. Acceleration Response Spectra at Depth of 8.2m Applied Motion in North South Direction Time History Measured and predicted acceleration, velocity, and displacement at surface, depth of 2.5m, 4.65m and 8.2m are plotted in the following. It should be noted that due to layered nature of the soil in the model and also fixed depth of each accelerometer in the ground, measured and predicted depths are not exactly the same. It s been tried so that closest depths get selected.

85 Figure 53. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, North- South Direction 69

86 Figure 54. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, North- South Direction 70

87 Figure 55. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, North- South Direction 71

88 Figure 56. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, North- South Direction 72

89 Acceleration Response Spectra For each depth, predicted and measured time response spectra in logarithmic scale have been plotted. Same reasoning for different depth of measured and predicted results is true here. Figure 57. Acceleration Response Spectra at Surface Figure 58. Acceleration Response Spectra at Depth of 2.5m

90 74 Figure 59. Acceleration Response Spectra at Depth of 4.65m Figure 60. Acceleration Response Spectra at Depth of 8.2m

91 Applied Motion in 2 Directions Time History Measured and predicted acceleration, velocity, and displacement at surface, depth of 2.5m, 4.65m and 8.2m are plotted in the following. It should be noted that due to layered nature of the soil in the model and also fixed depth of each accelerometer in the ground, measured and predicted depths are not exactly the same. It s been tried so that closest depths get selected.

92 Figure 61. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, East- West Direction 76

93 Figure 62. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, East- West Direction 77

94 Figure 63. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, East- West Direction 78

95 Figure 64. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, East- West Direction 79

96 Figure 65. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Ground Surface, North- South Direction 80

97 Figure 66. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 2.5m, North- South Direction 81

98 Figure 67. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 4.65m, North- South Direction 82

99 Figure 68. Predicted and Measured Time Histories Acceleration, Velocity and Displacement at Depth of 8.2m, North- South Direction 83

100 84 Figure 69. Acceleration Response Spectra at Surface, East- West Direction Figure 70. Acceleration Response Spectra at Depth of 2.5m, East- West Direction

101 85 Figure 71. Acceleration Response Spectra at Depth of 4.65m, East- West Direction Figure 72. Acceleration Response Spectra at Depth of 8.2m, East- West Direction

102 86 Figure 73. Response Spectra at Surface, North- South Direction Figure 74. Response Spectra at Depth of 2.5m, North- South Direction

103 87 Figure 75. Response Spectra at Depth of 4.65m, North- South Direction Figure 76. Response Spectra at Depth of 8.2m, North- South Direction

104 Excess Pore Water Pressure One Direction Generation Using East West Motion As it is indicated, measured and predicted excess pore water pressure at depth of 2.64m have been plotted. It can be seen that the generated pore water pressure is not getting dissipated. Figure 77. Predicted and Measured Excess Pore Pressure at Depth of 2.64m

105 89 Figure 78. Predicted and Measured Excess Pore Pressure Ratio (ru) at Depth of 2.64m Two Direction Generation As it is indicated, measured and predicted excess pore water pressure in addition to excess pore water pressure ratio at depth of 2.64m have been plotted. Again, It can be seen that the generated pore water pressure is not getting dissipated.

106 90 Figure 79. Predicted and Measured Excess Pore Pressure at Depth of 2.64m Figure 80. Predicted and Measured Excess Pore Pressure Ratio (ru) at Depth of 2.64m

107 91 6 Liquefaction Induced Lateral Soil Displacement Estimation Methods 6.1 Background Ground shakings which lead to liquefaction in saturated cohesionless soil can result in sand boils, lateral soil displacement, flow slides, settlement in the soil and ground oscillations. These phenomena can cause notable damage to available structures and foundations (Zhang et al. 2004). Lateral spreading which happens in mild slopes to near level grounds is the most catastrophic type of liquefaction induced ground failure (Taboada et al. 1998). As indicated by, this phenomenon happens due to residual shear strain distribution in liquefied layers of the soil profile (Abdoun et al. 2013, Taboada et al. 1998, Sasaki et al. 1991, Yasuda et al. 1992). These residual shear strains depend on two factors: Maximum cyclic shear strains and biased in situ static shear stresses. The latter one is a function of ground conditions such as the ground slope. Also, it should be noted that liquefied layer thickness affects the amount of lateral displacement. The thicker the layer, the greater the lateral displacement will be (Zhang et al. 2004). Events such as San Francisco earthquake in 1906, Alaska earthquake in 1964, Niigata earthquake in 1964 are examples where lateral displacement of the soil has played an important in the occurred damages. Therefore, predicting the liquefaction induced lateral ground displacement through numerical, experimental and also field test based analyses can help mitigate those catastrophic events (Zhang et al. 2004). In terms of numerical modeling, empirical and theoretical methods are available. Empirical methods can be categorized in three different groups according to their input parameters (Motamed et al. 2013):

108 92 1. Methods developed from case history data of past lateral spreading. Earthquake magnitude and site to source distance are the input parameters in these methods. Youd et al method falls under this category. 2. Methods based on geometry and other characteristics of the ground such as the liquefied layer s thickness. Hamada et al method is in this category. 3. Methods consisting both mentioned parameters as their input. Recent developed methods fall under this group. Following is the applied methods for estimating the liquefaction induced lateral ground displacement based on the 24 lab experiments. A brief explanation about each method has been mentioned. After that, the properties and geometry of each lab test and achieved results have been indicated. At the end, comparison between the measured and estimated results is provided. 6.2 Empirical Methods Seven different empirical methods has been used to estimate the liquefaction induced lateral ground displacement of 24 different experimental tests. Below is a brief definition of each one of them Hamada et al and 1999 This method is based on the geometric properties of the ground such as the slope of the ground surface and the thickness of the liquefiable layer. Since this method is not dependent on the magnitude of the earthquake or other ground shaking variable, it can be highly conservative in areas with low earthquake s magnitudes. Moreover, this method can t be used for liquefaction evaluation since high chance liquefaction happening is one

109 93 of its assumptions. Hamada has developed the first equation in 1986 based on Niigata 1964, San Fernando 1971, and Nihonkai- Chubu 1983 earthquakes. He upgraded this version by taking into account earthquake intensity and soil density. The new method requires the following variable in addition to the previous one in old version: average corrected SPT blow count for liquefied layer, mean horizontal acceleration time history, and acceleration time history time length Youd et al Bartlett and Youd developed two different empirical equations to estimate the liquefaction induced lateral ground displacement. One of them does the estimation for a locations close to steep banks and the second one does the estimation for a gently sloping ground. Both of these two equations are based on case histories including Western United States and Japan with earthquakes magnitudes ranging from 6.4 to 9.2 and source to site distance of smaller than 90 km. In case the estimated displacement based in this method is more than six, it can be implied of possibility of large displacements. However, the estimated number is not reliable. Required parameters for this method are as follow: earthquake magnitude, horizontal distance to nearest seismic source or to nearest fault rupture, gradient of surface topography or ground slope, thickness of saturated layers with, smaller than 15, average fine content (particles smaller than mm), average D50, and ratio between height of free face over distance from the base of free face.

110 Faris et al This method is a semi-empirical one based on the principle of strain potential index, SPT results, cyclic shear simple shear laboratory and back analyzing the case histories. In order to make the most out of the available data and mitigate the case histories uncertainties back analyses, a Bayesian probabilistic approach has been employed. Input parameters in this method are: static load, magnitude of the earthquake, thickness of the liquefiable layer and strain potential index Zhang et al. 2004, Faris 2004 This semi-empirical method is based on SPT and CPT data. Laboratory test results, SPT and CPT based methods together are used to estimate the lateral displacement index. This index can be calculated by integration of maximum cyclic shear strain with depth. Using Faris method, the relation between lateral displacement index and actual lateral displacement is made. Input parameters include maximum cyclic shear strain and liquefiable layer thickness Shamoto et al This method is based on taking into account laboratory test results and empirical adjustment factor. This semi-empirical lateral ground displacement estimation uses residual shear strain potential and liquefiable layer thickness to conduct the calculation. In case of more than one liquefiable layer, an empirical factor of 1.0 or 0.16 gets multiplied by the answer for each layer. Residual shear strain potential values can be obtained from provided graphs in the paper.

111 95 Moreover, this method has been verified with the observed displacement in Kobe earthquake in Valsamis et al This method estimates the lateral ground displacement using a numerical approach which relies on fully coupled and effective stress dynamic analysis. Current method is also based on free face ground conditions parametric study for lateral ground displacement. Major parameters here are: 1. Seismic shaking variables including peak base acceleration, number of cycles required for initiation of liquefaction, and predominant period of input motion. 2. Soil liquefied properties such as relative density, corrected SPT blow counts, fine contents. 3. Geometry variables such as free-face height and ratio, and total liquefiable soil layer thicknesses. This method has been verified with the 19 centrifuge experimental test Bardet et al Current method is based on a multi-linear regression which is based on parameters such as ground shaking magnitude, horizontal distance to nearest seismic source or to nearest fault rupture, gradient of surface topography or ground slope, and thickness of saturated layers with, smaller than 15. Based on obtained results, the estimated displacements fall in the conservatism range.

112 Theoretical method This method is developed using theory of Lagrangean equation of motion along with Hamiltonian principle, and also principle of minimum potential energy. Different boundary conditions and their effects can be analyzed using this method. Using a scalar function of time has made it possible to calculate the displacement increase prediction (Towhata et al. 1999). The predicted displacement in this method abides with the observed results from the shaking table test such as sinusoidal variation of the lateral displacement in the vertical direction (Sasaki et al. 1992). Moreover, one of the notable points about this method is that its input parameters can be obtained from an existing field or laboratory test framework. 6.4 Investigated cases using the empirical and theoretical methods 24 different experimental cases have been used in order to figure out the accuracy of each of the above mentioned methods. Detailed information about each case has been provided with each test s layout. Not all of the previously mentioned methods can be used to calculate the lateral displacement due to different sort of information each method requires. However, it s been tried to pick those cases which are the most inclusive in terms of existing information and detail. Having these said, following is the case histories used for the comparison Taboada-Urtuzuastegui et al (Tests number 1 to 7) 11 centrifuge and laminar box tests have been described in this paper. Tests are conducted on saturated homogenous coarse sand with relative density of 40-45%, peak acceleration of 0.17 to 0.46g, a frequency of 1-2 Hz, duration of 22 cycles and sloe angle

113 97 of 0 to 10. Due to availability of data for the mentioned methods, only seven tests have been selected to perform the estimation using the methods. Following is the experiment laminar box condition and also tables containing the tests data. Figure 81. Side View of Laminar Box with Instrumentation Used In Test M2-4 (Not in Scale) Table 13. Testing Program Test amax (g) f (Hz) α N αfield M M M M M M M M2a M2a M2b M2c

114 98 Table 14. Key Note: In all tests D, = 40-45% and H = 10 m. α, model slope angle; αfield, prototype slope angle in the field; amax (g), peak input acceleration at model base in prototype units; H (m), thickness of sand deposit in prototype units; D, (%), relative density of sand; f (Hz), frequency of input motion in prototype units; N, number of cycles of shaking. Parameters in Centrifuge Tests Measured Test ID Thickness of Liquedfied Soil H1 (m) Lateral Ground Displacement DH (cm) Depth of Maximum Shear Strain (m) Value of Maximum Shear Strain (%) M M M2a M2a M M M (at 6s) - M M M2b-5 (3 s) M2b-5 (end of Shaking) M2c Abdoun et al (Tests number 8 to 9) In this paper, two large scale and four smaller scale centrifuge tests were analyzed. Each test configuration is shown in the following tables. Among them, only two tests has been chosen to compare its results to previously mentioned liquefaction induced lateral ground displacement estimation methods.

115 99 Figure 82. Setup and Instrumentation of Centrifuge Model Tests Simulating Large Scale Tests SG-1 (Gonzalez 2008) Table 15. Soil Testing Parameters in the Liquefaction Large Scale and Centrifuge Tests at 25g Simulating a 5-6 m Thick Saturated Sand Deposit Test SG- 1 FF- P1 FF- P2 FF- V1 FF- V3 LG- 0 Test Type Prototype Deposit Thickness (m) Test Inclination Sand Total Saturated Unit Weight (kn/m3) Void Ratio, e Pore Fluid Viscosity Prototype Permeability k (cm/s) Normaliazed Shear Wave Velocity V (m/s) LS 5.6 SG Ottawa E C 6 SG Sealed E C 6 SG Sealed E C 6 SG Ottawa E C 6 SG Ottawa E LS 4.85 LG Ottawa E Note:LS = large-scale test; C = centrifuge test; SG = sloping ground (2 test angle); LG = level ground; Vs1 = shearwave velocity, Vs, at a vertical effective overburden pressure; and = 1 atm = kpa.

116 100 Table 16. Shaking and Measured Parameters in Large Scale and Centrifuge Tests Test Sand Vs1 (m/s) Input amax (g) Maximum Pore Pressure Ratio, (ru)max Permanent Ground Surface Lateral Displacement (cm) SG-1 Ottawa FF-P1 Sealed FF-P2 Sealed FF-V1 Ottawa FF-V3 Ottawa LG-0 Ottawa Feigel et al (Tests number 10 to 11) In this paper, two centrifuge tests has been studied. The first one models a uniform saturated sand layer and the second one models the behavior of an impermeable nonplastic silty layer underlain by a sand layer. Both tests model the behavior with a slope angle of 2.6. Tests configurations can be found in Figure 83 and Figure 84.

117 Figure 83. Model Configuration for Test 1: (a) Side View (b) Section A-A' 101

118 Figure 84. Model Configuration for Test 2: (a) Side View (b) Section A-A' 102

119 Caltrans Guidelines on Foundation Loading and Deformation Due to Liquefaction Induced Lateral Spreading 2012 (Tests number 12 to 13) Two worked examples from Caltrans guideline has been selected. First example is a soil profile containing pile foundations. It s got a slope of 2%, peak acceleration of 0.5g and the magnitude of the possible earthquake is 7.5. The rest of this example configuration is in Figure 85. Second example is about a bridge abutment, where peak acceleration and earthquake magnitude are 0.5g and 7.5, respectively. Other detailed information are implemented in the Figure 86. Figure 85. Soil Profile and Properties

120 104 Figure 86. Abutment Configuration and Soil Properties UC Davis Report: #UCD/CGM- 03/01 (Tests number 14 to 15) A series of large scale dynamic centrifuge model tests have been conducted to analyze the behavior of single pile and pile groups under liquefaction effect. Out of these number of tests, two of them have been selected to do the estimation with the above mentioned methods. The layout of these two tests is in Figure 87 and Figure 88.