Keywords

1 Introduction

Soil liquefaction and its consequences on infrastructure continue to be among the most challenging and important subjects of study in geotechnical earthquake engineering. In the last two decades, numerical modeling has started to play a major role in liquefaction hazard assessments, primarily through the use of relatively simple to sophisticated constitutive models, a variety of continuum mechanics-based numerical platforms, and perhaps most importantly, due to the introduction of performance-based design in engineering practice. While constitutive models allow simulating, to some extent, the key characteristics of soil stress-strain response, numerical platforms provide the means to translate such element-scale behavior into engineering demand parameters. It is then paramount to evaluate the capabilities and limitations of numerical platforms and constitutive models against reliable experimental data to properly estimate the consequences of soil liquefaction. Precisely, the LEAP (Liquefaction Experiments and Analysis Projects, Kutter et al., 2018) series of research projects is a collaborative effort with the main objective of providing high-quality laboratory and centrifuge test results to assess the performance of simulating tools and soil constitutive models and understanding their range of applicability and limitations. LEAP works upon the lessons learned in the VELACS project (Verification of Liquefaction Analysis and Centrifuges Studies, Arulanandan, 1994), and has had several installments so far. The first one was held at the University of Kyoto, followed by LEAP-GWU-2015 hosted at George Washington University, LEAP-UCD-2017 at the University of California at Davis, and LEAP-ASIA-2019 hosted at Kansai University, and LEAP-RPI-2020 hosted at the Rensselaer Polytechnic Institute in 2020.

This chapter deals with the numerical simulations conducted at the University of British Columbia (UBC) for LEAP-ASIA-2019. Phase I of this project consisted of constitutive model calibration based on the results of hollow cylinder cyclic torsional shear tests on samples of Ottawa F65 sand, which complemented the monotonic and cyclic triaxial and simple shear tests from earlier projects. For this purpose, a recently developed constitutive model for large post-liquefaction deformation (Barrero et al., 2020), based on the bounding surface plasticity model SANISAND, was used. Then, Phase II consisted of Type-C simulations of eight unidirectional shaking centrifuge tests. Each test followed almost identical specifications as in LEAP-UCD-2017 and consisted of a submerged, gently sloping ground of medium-dense sand subjected to a ramped sine base excitation. The simulations were carried out in a coupled three-dimensional (3D) finite difference numerical platform where the constitutive model was implemented and verified (Barrero, 2019). The following sections describe the simulated centrifuge tests, the constitutive model and its calibration, the numerical modeling approach, and the comparison of experimental and numerical results.

2 Summary of Simulated Centrifuge Experiments

2.1 Description of Centrifuge Tests

The results of eight unidirectional centrifuge tests (Vargas et al., 2023a; Korre et al., 2023; Stone et al., 2023) were timely shared with the UBC team. The prototype target soil deposit of the centrifuge tests was a 4 m deep, 20 m long submerged deposit of Ottawa F65 sand with a ground slope of approximately 5°. This deposit was subjected to a ramped sine wave input motion at its base; further details can be found in Tobita et al. (2023). Five of the centrifuge tests corresponded to the set labeled as Model A: “standard” centrifuge tests with a scaling factor directly related to the centrifugal acceleration η. The other three tests were labeled as Model B, in which the scaling was determined in accordance with the generalized scaling law (Iai et al., 2005), which includes a scaling factor μ for the virtual model, as well as η. The experiments made available to the UBC team were carried out in the centrifuge facilities at Kyoto University (KyU), Rensselaer Polytechnic Institute (RPI), and the University of California at Davis (UCD). The experimental test data included the time histories of acceleration at the base and within the soil deposit, the excess pore water pressures, and the displacements. Table 14.1 summarizes the relevant characteristics of the simulated centrifuge tests.

Table 14.1 Summary of simulated centrifuge tests
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2.2 Base Excitations

Figure 14.1 shows the achieved or recorded base excitations in terms of acceleration time histories of centrifuge tests KyU_A1 and RPI_B1. The Fourier spectra of the recordings, also presented in Fig. 14.1, reveal the presence of low frequency (<0.1 Hz) or long-period waves in the recorded base excitations. The nature of these waves differs significantly from that of the waves with frequencies of 1–3 Hz also present in the excitations, which are consistent with the target input motion (Tobita et al., 2023). The effect of this apparent noise can be further observed in the undesired “waviness” and deviations observed in velocity and displacement time histories, obtained by integration of the acceleration records, also depicted in Fig. 14.1. Similar observations on the recorded base excitations were identified for all of the other centrifuge tests. The nature of these noises is unclear, but they were found to have negative consequences in the numerical simulations. For example, using this “raw” base excitation resulted in an unrealistic pattern of excess pore water pressure built-up, which started much earlier than expected and at a significantly different phase than the base excitation. Consequently, the UBC team decided to process the motions by means of fourth-order highpass digital Butterworth-type filters with bounding frequencies of 0.4–0.8 Hz to 25 Hz. Figure 14.1 shows the filtered base excitations and the corresponding Fourier spectra and velocity and displacement time histories. As can be observed, the filters eliminated the low-frequency waves and the deviations in the velocity and displacement time histories but caused some differences in the phase and peak of acceleration records. Changes in the peak acceleration are summarized in Table 14.2. The filtered motions were used as base input in the Type-C simulations of this study.

Fig. 14.1
8 frequency graphs. Acceleration in gravity versus time in seconds. Fourier amplitude versus frequency in hertz. Velocity in centimeters per second versus time in seconds. Displacement in centimeters versus time in seconds. A recorded and filtered line fluctuates between 20 and negative 20 and drops to zero.

Recorded and filtered acceleration time histories along with their respective Fourier spectra and calculated velocity and displacement records of centrifuge tests: (a) KyU_A1 and (b) RPI_B1

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Table 14.2 Summary of filter used in base excitations
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3 Constitutive Model

This section presents a brief description of the constitutive model used throughout this study along with its calibration against the hollow cylinder cyclic torsional shear tests on Ottawa sand conducted for LEAP-ASIA-2019.

3.1 SANISAND-Sf Model

The material constitutive model used by the UBC team in simulating both the element and centrifuge tests for LEAP-ASIA-2019 is a recently developed extension of the SANISAND model class. SANISAND stands for Simple ANIsotropic SAND constitutive model, a generic name that was introduced in Taiebat and Dafalias (2008) and follows the basic premises of the original two-surface plasticity model developed by Manzari and Dafalias (1997) and its sequel by Dafalias and Manzari (2004). Its constitutive framework is based on bounding surface plasticity with kinematic hardening of the yield surface and critical state soil mechanics concepts, allowing for a unified description of any pressure and density by the same set of model constants. The former studies represent the core of the constitutive model, and a number of subsequent works include different extensions and constitutive features that can be added to the original framework. This study considers a recent extension developed by Barrero et al. (2020), which addresses the progressive development of large post-liquefaction shear strains. By introducing a new state internal variable named Strain Liquefaction Factor, the extended SANISAND model is able to progressively degrade the plastic modulus and dilatancy, when the model enters the so-called semifluidized state. The simultaneous reduction of plastic modulus and dilatancy allows for increasing the plastic deviatoric strain rate while maintaining the same plastic volumetric strain rate. During undrained cyclic loading, the semifluidized state is defined as the state when sand experiences a sudden but temporary loss of stiffness, typically leading to a progressive accumulation of shear strains in each loading cycle. Such a state essentially happens at very low effective stresses. Extending the SANISAND framework with the semifluidized state formulation overcomes the apparent early lock-up of stress-strain loops in the post-liquefaction of the original model.

The SANISAND version of Dafalias and Manzari (2004), together with an overshooting correction scheme as described in Dafalias and Taiebat (2016) and the novel semifluidized state formulation introduced by Barrero et al. (2020), has been considered as the soil constitutive model in this work, and is referred to as SANISAND-Sf hereafter. Table 14.3 summarizes the model constants. An extensive description of the model formulation and role of the parameters can be found in the related foregoing reference and is not repeated here. Model implementation and testing in FLAC3D v5 (Itasca, 2013) was completed by Barrero (2019). This implementation has already been employed and compared against another one in a different numerical platform in the comprehensive study by Ramirez et al. (2018) and was subsequently used in Reyes et al. (2019). The implementation has then been updated for the extended SANISAND and used for this project.

Table 14.3 SANISAND-Sf model parameters for Ottawa F65
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3.2 Model Calibration

As part of Phase I of LEAP-ASIA-2019, the UBC team calibrated SANISAND-Sf against a series of hollow cylinder cyclic torsional shear tests conducted at KyU (Vargas et al., 2023b). The tests selected for this study consisted of saturated samples of Ottawa F65 sand reconstituted to target relative densities (Dr) of 50% and 60% and isotopically compressed to an effective confining pressure of approximately 100 kPa. The samples were then cyclically sheared at cyclic stress ratios (CSR) ranging from 0.10 to 0.20.

Calibration was completed in a single-element configuration in FLAC3D, in which the volume change was prevented during shearing to simulate the undrained conditions of the laboratory test. The elasticity and critical state parameters (see Table 14.3) were inherited from the calibration of the UBC team in LEAP-UCD-2017 (Yang et al., 2022). The parameters controlling the plastic modulus, dilatancy, and fabric dilatancy were updated in light of the new experimental evidence and to accommodate the extended formulation of the model. Details on the recommended calibration procedure for SANISAND-Sf are presented in Barrero et al. (2020). For this study, the calibration aimed first to capture the pre- and post-liquefaction response of the cyclic tests with CSR around 0.15. The pre-liquefaction response, that is, before attaining a mean effective stress close to zero for the first time, was reasonably well captured by tuning the kinematic hardening constants nb and ch, and the dilatancy parameters nd and A0. For the post-liquefaction response, parameters x, cl, and pinr from the semifluidized state formulation were selected so as to simulate the extent and pace of development of shear strains in post-liquefaction. For the remaining tests with different CSR, parameter a was selected in order to capture the CSR resistance curve. With this approach, the obtained liquefaction resistance is controlled by a balance between the pre- and post-liquefaction response of the model. Figure 14.2 summarizes the model performance by comparing the liquefaction resistance from experiments and simulations based on the number of cycles to reach a double amplitude shear strain of 7.5%, showcasing a good match between them. Table 14.3 presents the constitutive model constants, which were used in the Type-C simulations.

Fig. 14.2
A combinational line and scattered graph plots shear stress ratio versus number of cycles to gamma D A =7.5%. 4 lines K Y U G gamma = 50%, K y U D gamma = 60%, U B C D gamma = 50% and U B C D gamma = 60% drops from (10 power 1, 2) to (10 power 3, 0.1). Values are approximated.

Summary of experiments (blue, solid symbols, Vargas et al., 2023b) and simulations (red, hollow symbols) in terms of shear stress ratios and the corresponding number of cycles to reach a double amplitude shear strain of 7.5%. The lines represent the interpolated liquefaction resistance curves for Dr of 50% (dashed) and 60% (continuous)

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4 Numerical Model Specifications

4.1 Numerical Platform

The simulations of the centrifuge tests were conducted in the finite difference program FLAC3D, which uses an explicit time-integration scheme to model the dynamic response of 3D continuous media. In this program, the continuous media is replaced by a discrete-equivalent domain in which forces and displacements involved in the analysis are concentrated at the nodes of the 3D mesh used in representing the domain. Each zone or element of the mesh is comprised by a number of constant strain-rate subzones of tetrahedral shape whose vertices coincide with the ones of the zone. Solid-pore fluid interaction in this platform is based on the well-established coupled formulations of poromechanics originated by Biot (1941) and extended by Detournay and Cheng (1993). The numerical scheme for the coupled formulation in fully saturated media relies on a fluid continuity equation, which relates fluid flow to changes in pore pressure and volumetric strain. Solving this equation requires a series of steps involving fluid flow loops followed by mechanical loops to maintain equilibrium state. The fluid flow loops calculate changes in pore pressure while the mechanical loops address the changes in volumetric strain due to the adjustment of effective stress induced by the fluid flow loops. A built-in isotropic fluid model is used in this study for simulation of the mechanical response of the pore fluid.

4.2 Numerical Model Configuration

The numerical models of the centrifuge tests were completed for the prototype scale model, as the main objective of this study was to verify the performance and limitations of SANISAND-Sf. Validation of the generalized scaling law, which was another purpose of the LEAP-ASIA-2019, would have required complementary simulations at the model scale, and was not included in this chapter.

The numerical models consisted of a 3D finite difference mesh built with 40 zones in the slope dip direction, 8 zones in the height direction, and 1 zone in the slope strike direction, for a total of 320 zones. The zone sizes were 0.5 m in the slope dip direction and 0.39–0.61 m in the height direction. The grid points on the model base were fully constrained along all three directions during the static part of the analysis, while the grid points of the side walls were laterally constrained. This prevented deformation in the slope strike direction, hence working in a similar way as a plain strain condition. During the dynamic stage, the degree of freedom at the model’s base corresponding to the shaking direction, i.e., slope dip direction, was freed. The grid points on the top surface of the slope were allowed full drainage with fixed values of pore pressure in order to model the real submerged conditions of the experiments. Furthermore, during the dynamic stage, Rayleigh damping with a small damping target value of 1% was used to prevent high-frequency artificial noise. The mesh density, boundary conditions, and the location of the instrumentation and displacement markers are presented in Fig. 14.3.

Fig. 14.3
A grid pattern chart illustrates a system with horizontally fixed and impermeable boundaries. It includes dynamic inputs, impermeable boundaries from the bottom, fixed pore pressure, and water pressure applied to the top nodes, showcasing the system's components labeled A H 1 to A H 10 and P 1 to P 8.

Cross-section of the FLAC3D mesh and boundary conditions adopted in the prototype scale numerical model used. Recording locations are also shown for horizontal accelerations (AH), excess pore water pressures (P), and surface displacement markers (M). Note that the centrifuge facility at RPI adopted a different arrangement of surface markers not shown here

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4.3 Soil Properties

The SANISAND-Sf model parameters determined in Sect. 14.3.2 were used in the centrifuge simulations and they were not updated upon examination of the centrifuge experiment results. Taking advantage of the critical state framework of SANISAND, only the initial void ratio was changed in each centrifuge simulation according to the values in Table 14.1.

For the solid-fluid interaction, the isotropic fluid model implemented in FLAC3D was used, with a water bulk modulus of 2.2 × 106 kPa. Soil hydraulic conductivity was first estimated based on the average initial void ratio of the centrifuge tests and the constant head permeability tests conducted by El Ghoraiby et al. (2020) as k = 1.15 × 10−4 m/s. Note that variation of the hydraulic conductivity with the initial void ratio was negligible.

4.4 Simulation Procedure

In order to establish a reasonable initial stress state of the model in the prototype scale, the numerical simulations started with a staged construction of the slope, where the dry soil deposit was constructed in layers and was allowed to establish its stress state under the gravity of 1g. In this process, the mechanical boundary conditions were configured as shown in Fig. 14.3, except for the stress boundary condition on the top surface of the slope. This stage used a simple Mohr-Coulomb material model assigned to the sand layers with a bulk modulus of 6.22 × 105 kPa, shear modulus of 2.38 × 106 kPa, and a friction angle of 33 degrees. After achieving mechanical equilibrium for all layers of the soil deposit, the fluid-mechanical interaction module was activated, and a normal stress gradient representing the target submerged pressures of water was applied on the top surface of the slope, as shown in Fig. 14.3. The pore water pressures at the top surface were fixed to the submerged pressures. Upon reaching mechanical and fluid equilibrium, the constitutive model for the sand was switched to the SANISAND-Sf.

Once the changes of stresses and pore water pressures induced by the change of constitutive model were stabilized, the dynamic analysis feature embedded in the numerical platform was activated. The resulting ratio of effective initial horizontal to vertical stresses (K0) ranged from 0.44 to 0.6 along the model, with an average of 0.49. Furthermore, the initial ratio of static bias, that is, the ratio of shear stress to effective vertical stress (α), ranged from 0.01 to 0.06 for an overall average of 0.04. For the dynamic analysis, the boundary conditions were updated in two stages: first, Rayleigh damping was added to the entire model, followed by mechanical-fluid-dynamic steps to further stabilize the model. Second, the degree of freedom in the x direction at the model’s base was freed to accommodate the base excitation. Also, during the dynamic stage of the analyses, the hydraulic conductivity was doubled to account for the increase of permeability during the liquefaction stage, which has been recognized to occur in different studies (e.g., Manzari & Arulanandan, 1993; Taiebat et al., 2007; Shahir et al., 2012; Yang et al., 2020). The amount of increase was determined following sensitivity analyses which mainly took into consideration the dissipation pattern of pore water pressure. The increased value of hydraulic conductivity, k* = 2.29 × 10−4 m/s, was kept constant throughout the dynamic stage and for all centrifuge models.

Finally, the filtered accelerations records were applied at the base grid points; the duration of the analyses went beyond the significant duration of the base excitation, allowing for the dissipation of excess pore water pressure and displacement stabilization. The total length of the shearing and dissipation process was determined by the duration of the experimental recordings of accelerations and excess pore water pressure.

5 Type-C Simulation Results

The results of the Type-C numerical simulations are presented and compared with the experimental data for the eight centrifuge tests evaluated. The comparison is depicted in terms of acceleration time histories, acceleration response spectra, excess pore water pressure time histories, and displacement time histories at control points and markers at the center of the centrifuge model (see Fig. 14.3). It is important to highlight that although the recorded base accelerations were filtered before their application in the simulations, the experimental recordings of accelerations and others in the soil deposit body were not filtered in the displayed comparison.

5.1 Typical Results

Here, the typical results of the simulations are described with respect to the centrifuge model UCD_A2. Figure 14.4 shows the experimental and simulated acceleration response at the center of the model in terms of time histories and response spectra. It can be observed that the simulations are generally successful in capturing the acceleration response in the time domain: in sensors AH1 and AH2, located at the bottom of the centrifuge and where no signs of severe liquefaction are apparent, the accelerations are closely captured. Similarly, in sensors AH3 and AH4, located at shallower depths and where liquefaction occurrence is evident due to the presence of sharp dilations spikes, the simulations were also able to closely capture the acceleration response in the time domain. The comparison in terms of response spectra further indicates that the simulations captured the acceleration response to a reasonable degree. However, it also shows that the simulated spectral accelerations for the fundamental period of the deposit, approximately 1 s, tend to be progressively underestimated at shallower depths, likely due to the occurrence of liquefaction.

Fig. 14.4
The eight-line graph plots acceleration gravity and spectral acceleration gravity for four components A H 1 to A H 4 comparing experimental and simulated data. The spectral acceleration is depicted over time and period, highlighting base input and component-specific behaviors.

Comparison of experimental and simulated acceleration response in centrifuge test UCD_A2 in terms of time histories and response spectra at the middle of the model

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Figure 14.5 presents the comparison of experimental and simulated excess pore water pressure generation and dissipation. The initial effective overburden pressures, approximately 40, 30, 20, and 10 kPa for piezometers P1, P2, P3, and P4, respectively, are also shown. The time histories show that the numerical results can reasonably capture the peak values of excess pore water pressure, although they also present relatively large spikes absent in the experimental recordings. Moreover, the rate of generation of excess pore water pressure is overestimated in the simulations. This simulated response has been found to be mostly associated with the SANISAND-Sf underestimation of the pre-liquefaction cyclic resistance at low values of CSR. On the other hand, the simulated dissipation rate is relatively close to the experimental evidence. Sensitivity analyses for this particular centrifuge model showed that around a 50% reduction in the constant and already increased hydraulic conductivity used in the simulations can significantly improve the match in the dissipation rate.

Fig. 14.5
4 line graphs plot E P W P in kilopascals versus time in seconds. P 1, P 2, P 3 and P 4 experiment and simulation peak at (10, 10), (10, 20), (10, 30) and (10, 40) in each graph. Values are approximated.

Comparison of experimental and simulated excess pore water pressure response in centrifuge test UCD_A2 in terms of time histories at the middle of the model

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The lateral displacements at the center of the model, both recorded in the experiments and in the simulations, are shown in Fig. 14.6. It can be observed that the simulations tend to overestimate the displacements, in this case, by over 5 cm. This overestimation is thought to be associated, as is the generation of excess pore water pressure, with (a) the stiffness of SANISAND-Sf model for low values of CSR, (b) the presence of initial static shear stresses in the sloped model, and (c) the hydraulic conductivity and its likely variation during and after soil liquefaction.

Fig. 14.6
2 line graph plots displacement x in centimeters versus time in seconds. 2 lines marker 3 experiment and simulation increases from (0, 0) to (20, 15) and (0, 0) to (15, 15) respectively. Values are approximated.

Comparison of experimental and simulated lateral displacement in centrifuge test UCD_A2 in terms of time histories at the middle of the model

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5.2 Summary of Numerical Simulations

To expand the assessment of the constitutive model performance, the comparison presented in the earlier section is extended to the other seven centrifuge tests. For brevity, the experimental and simulated results are illustrated for accelerometers AH1 and AH4, piezometers P1 and P4, and displacement marker M3, all of which are representative of the response of the center of the centrifuge models. In order to maintain consistency in the comparisons, Figs. 14.7, 14.8, 14.9, 14.10, 14.11, 14.12, 14.13 and 14.14 detail the results using the same scales.

Fig. 14.7
The five graphs illustrate the comparison between experimental and simulated data for acceleration in gravity, excess pore water pressure, and spectral acceleration of components A H 1, A H 4, and P 1 over time in seconds and periods, showcasing their dynamic behavior under varying loading conditions.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test KyU_A1

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Fig. 14.8
The five line graphs depict the dynamic responses of components A H 1 and A H 4, point P 1, and excess pore water pressure under experimental and simulated conditions. The graphs display acceleration in gravity, E P W P, displacement, and spectral acceleration over time in seconds and period.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test KyU_A2

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Fig. 14.9
The five line graphs depict the dynamic responses of components A H 1 and A H 4, point P 1, and excess pore water pressure under experimental and simulated conditions. The graphs display acceleration in gravity, E P W P, displacement, and spectral acceleration over time in seconds and period.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test RPI_A1

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Fig. 14.10
The five line graphs depict the dynamic responses of components A H 1 and A H 4, point P 1, and excess pore water pressure under experimental and simulated conditions. The graphs display acceleration in gravity, E P W P, displacement, and spectral acceleration over time in seconds and period.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test UCD_A1

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Fig. 14.11
The five line graphs depict the dynamic responses of components A H 1 and A H 4, point P 1, and excess pore water pressure under experimental and simulated conditions. The graphs display acceleration in gravity, E P W P, displacement, and spectral acceleration over time in seconds and period.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test UCD_A2

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Fig. 14.12
The five line graphs depict the dynamic responses of components A H 1 and A H 4, point P 1, and excess pore water pressure under experimental and simulated conditions. The graphs display acceleration in gravity, E P W P, displacement, and spectral acceleration over time in seconds and period.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test KyU_B1

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Fig. 14.13
The five line graphs depict the dynamic responses of components A H 1 and A H 4, point P 1, and excess pore water pressure under experimental and simulated conditions. The graphs display acceleration in gravity, E P W P, displacement, and spectral acceleration over time in seconds and period.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test KyU_B2

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Fig. 14.14
The five line graphs depict the dynamic responses of components A H 1 and A H 4, point P 1, and excess pore water pressure under experimental and simulated conditions. The graphs display acceleration in gravity, E P W P, displacement, and spectral acceleration over time in seconds and period.

Summary of acceleration, excess pore water pressure, and lateral displacement experimental and simulated response for centrifuge test RPI_B1

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The overall comparison reveals that in the six centrifuge tests where liquefaction occurred (KyU_A1, RPI_A1, UCD_A1, UCD_A2, KyU_B1, RPI_B1), evidenced by the significant dilation spikes in the acceleration records and high values of excess pore water pressure, the simulations were generally successful in capturing the experimental results. However, in most cases, the lateral displacements were overestimated, with the exception of model RPI_B1 where the simulation yielded lower values than the experimental evidence. As detailed earlier, the overestimation of lateral displacements is likely caused by the underestimation of pre-liquefaction resistance for low values of CSR of the constitutive model, the presence of initial static shear stresses in the model, which was not accounted for in Phase I, and the selected value of hydraulic conductivity.

While filtering of base excitations was conducted for all models, an inspection of the acceleration time histories reveals some changes of phase in only a few of the models, particularly UCD_A1 and KyU_B1, which are among the ones with stronger “noise” of the base motion. Additional filtering of the recordings in the deposit body would have probably reduced the changes of phase observed here. Further commentaries on the nature and consequences of this apparent noise are presented in Perez et al. (2023). On the acceleration response spectra, as explained earlier, the simulations tend to underestimate the spectral acceleration for a period of 1 s for the shallower sensor, where evidence of liquefaction was observed in most cases.

As in Sect. 14.5.1, the simulations successfully capture the peak excess pore water pressures recorded in all of the centrifuge tests where liquefaction was triggered. However, the comparisons also reveal that the model overestimated the rate of excess pore water pressure generation, a response largely controlled by the pre-liquefaction stiffness of the extended SANISAND model. Nevertheless, the dissipation rate was surprisingly well captured by the simulations, albeit the use of the same constant value of hydraulic conductivity, k*, doubled from the laboratory results, for all the numerical models. Yet, it is important to mention that even better results could be obtained by using different values of k* for each model, ranging from 0.5 to 3 times to the value of k. In tests KyU_A2 and KyU_B2, where liquefaction did not occur below sensor P4, the excess pore water overestimation caused further differences in the acceleration response and, most importantly, in the lateral displacements.

6 Summary and Outlook

This chapter presents the Type-C numerical simulations conducted at the University of British Columbia for the centrifuge tests of gently sloped liquefiable soil deposits in LEAP-ASIA-2019. For this purpose, the UBC team made use of an extended version of the SANISAND constitutive model, named SANISAND-Sf, which introduces a novel and elegant feature to reduce soil stiffness during undrained cyclic shearing and low values of confining pressure, to allow for the development and accumulation of large post-liquefaction shear deformations.

Phase I of this study consisted of calibrating the new model based on data from undrained hollow cylinder cyclic torsional shear tests. The resulting calibration succeeded in capturing the number of cycles to reach a double amplitude shear strain of 7.5% for different values of cyclic stress ratios. Phase II used such calibration to simulate eight centrifuge models in a finite difference computer program. The simulations revealed that the constitutive model and the adopted numerical modeling approach are reasonably successful in capturing the acceleration and pore water pressure response of the centrifuge tests where liquefaction was evidenced by dilation spikes and high values of excess pore pressure. However, the lateral displacements were overestimated by around 5–15 cm in most of the models.

The results presented here suggest that the performance of the numerical simulations with respect to capturing the experimental results can be improved by increasing the constitutive model stiffness, i.e., its pre-liquefaction resistance, for relatively low values of cyclic shear stress ratios. This can be effectively achieved by considering a new constitutive ingredient in the SANISAND class of models, as was done by Yang et al. (2022). Their latest extension provides the necessary flexibility to capture both pre- and post-liquefaction responses with accuracy. An improved prediction can also be accomplished by evaluating the model predictive capabilities of sand undrained response in the presence of static shear stresses and accounting for their effect. This has been shown to be of major relevance in the recent works of Reyes et al. (2021) and Perez et al. (2023). For this purpose, K0-consolidated cyclic shear tests with initial static shear stress, representative of the initial stress state of the soil in the centrifuge tests, would be excellent data for model validation. The recent experimental works of El Ghoraiby and Manzari (2021) and Lbibb and Manzari (2023) represent major efforts in producing this type of evidence in which more realistic initial stress states, i.e., K0 ≠ 1 with static shear stresses, and cyclic shearing patterns are employed. Furthermore, it was shown that filtering and baseline correction of experimental recordings are important and can cause significant differences in numerical predictions. Ideally, the experimental team should process all records, and the filtering process should be communicated to the numerical simulation team. Finally, hydraulic conductivity and its likely change during and after shaking played a major role in the numerical predictions. Further research is required to determine an efficient procedure to properly model it.