LEAP-UCD-2017 Simulation Team Fugro
Abstract
Fugro participated in the Liquefaction Experiment and Analysis Projects (LEAP) by performing numerical simulations using two different constitutive models implemented in the software FLAC. Fugro developed a calibration framework based on soil-specific laboratory test data considering multiple elements of dynamic response such as liquefaction triggering criteria (i.e., number of cycles to a specified strain and pore pressure ratio threshold) as well as post-triggering strain accumulation rate. The calibrated model parameters were subsequently used to obtain “Type B (blind)” predictions of the centrifuge experiments with the opportunity to refine after the centrifuge results were provided (Type C simulations). Overall, Fugro’s blind predictions captured the centrifuge test responses well with small refinements needed during Type C simulations. Estimated deformations were within a factor of about two compared to the observed. The overall good comparison provides confidence in the proposed calibration framework, which can be implemented and used for different sand types and project conditions.
Keywords
Liquefaction Numerical modeling Centrifuge Lateral spreading Dynamic27.1 Introduction
The LEAP 2017 simulation exercise consisted of the following four stages: (1) constitutive model calibration, (2) Type-B (blind) predictions, (3) Type-C simulations, and (4) sensitivity analyses. A series of stress-controlled cyclic triaxial laboratory tests were available (El Ghoraiby et al. 2017, 2019) and used in the calibration process. Next, the model parameters obtained during model calibration were used to analyze the centrifuge experiments, providing the base excitation and the soil density without any knowledge of the actual results (Type-B predictions). The simulation teams were subsequently provided with the centrifuge experiment results and simulations were refined, if necessary, to obtain better agreement (Type-C simulations). Last, a series of sensitivity analyses were performed to assess the influence of soil relative density (D_{R}), motion intensity, and motion high frequency content on the simulation results.
27.2 Constitutive Model Calibration
27.2.1 Introduction
Fugro calibrated two constitutive models, PM4SAND and UBCSAND, to the available cyclic stress-controlled triaxial laboratory tests on Ottawa F65 sand (El Ghoraiby et al. 2017, 2019). The cyclic triaxial tests were performed for three different soil densities. The three groups of specimens tested had void ratios of approximately 0.585, 0.542, and 0.515 corresponding to relative densities of about 65%, 80%, and 90%, respectively, based on a maximum void ratio (e_{max}) of 0.74 and a minimum void ratio (e_{min}) of 0.49 per Vasko as tabulated in Table 6 of the El Ghoraiby et al. (2017) report. At the time of this calibration process, no other test data was available.
Constitutive model calibration was performed considering multiple elements of response such as number of cycles to specified strain and pore pressure ratio thresholds as well as post-triggering strain accumulation rate.
27.2.2 Model Description, Parameters, and Implementation
PM4SAND Constitutive Model
PM4SAND Version 3 constitutive model developed by Boulanger and Ziotopoulou (2015) was initially calibrated. Stress-controlled plane strain compression (PSC) test simulations were performed using PM4SAND and calibrated against the available stress-controlled triaxial test data. The soil elements were initially confined with vertical and horizontal stresses of one atmosphere, considering coefficient of earth pressures at rest of one (K_{o} = 1). Plane strain compression loading conditions were stress controlled by imposing a velocity until a specific stress ratio was reached and then the sign of velocity was changed.
PM4SAND calibrated model parameters
Parameter | Function | Values |
---|---|---|
D_{R} | Relative density | 65%, 80%, and 90% for e_{o} of 0.585, 0.542, and 0.515, respectively based on e_{max} ~ 0.74 and e_{min} ~ 0.49 |
G_{o} | Shear modulus coefficient | 625, 1321, and 2001 for void ratio e_{o} of 0.585, 0.542, and 0.515, respectively based on the equation: G_{o} = 167 × (N_{1,60} + 2.5)^{0.5} and using multiplier of 0.8, 1.4, and 1.9 for e_{o} of 0.585, 0.542, and 0.515, respectively |
h_{po} | Contraction rate parameter | 0.07, 0.038, and 0.03 for void ratio e_{o} of 0.585, 0.542, and 0.515, respectively |
e_{max} and e_{min} | Maximum and minimum void ratios | e_{max} ~ 0.74 and e_{min} ~ 0.49 based on lab test data per Table 6 of the El Ghoraiby et al. (2017) report |
Plane strain compression tests were simulated for the relative densities of 65%, 80%, and 90% for various cyclic stress ratios (CSR) in order to compare the plane strain simulation results with the triaxial test results. Each plane strain compression simulation was compared to a triaxial test of a soil sample with similar relative density and stress ratio (CSR) in terms of liquefaction triggering and strain accumulation rate. Liquefaction strength curves were plotted for both the actual triaxial tests and the simulated plane strain compression tests in terms of numbers of cycles to 98% excess pore pressure ratio, and 2 and 5% double amplitude axial strain.
UBCSAND Constitutive Model
The UBCSAND constitutive model, which has been modified from the commonly available 904ar version by Fugro and Peter Burn, was also used in this study. This model has been modified, subsequently calibrated and validated by Fugro (Giannakou et al. 2011), and used in major projects such as the BART Offshore Transbay Tube Seismic Retrofit (Travasarou et al. 2011). The primary modification consists of introducing one additional model parameter (hfac4), which controls the rate of shear strain accumulation after liquefaction triggering. Detailed description of the model can be found in Beaty and Byrne (1998) and Byrne et al. (2004).
UBCSAND calibrated model parameters
Parameter | Function | Values |
---|---|---|
N_{1,60} | Normalized and corrected SPT Blowcount | 19, 29, and 37 for D_{R} of 65%, 80%, and 90%, respectively |
KGE | Elastic shear modulus multiplier | 1166, 1339, and 1448 for D_{R} of 65%, 80%, and 90%, respectively based on the equation: KGE = 21.7 × 20 × (N_{1,60})^{0.333} |
me | Elastic shear exponent | 0.5 |
KB | Elastic bulk modulus multiplier | 816, 937, and 1013 for D_{R} of 65%, 80%, and 90%, respectively based on the equation: KB = KGE × 0.7 |
ne | Elastic bulk exponent | 0.5 |
KGP | Plastic bulk modulus multiplier | 1421, 3581, and 6130 for D_{R} of 65%, 80%, and 90%, respectively based on the equation: KGP = KGE × (N_{1,60})^{2} × 0.003 + 100.0 |
np | Plastic bulk exponent | 0.4 |
ϕ_{cs} (degrees) | Critical state friction angle | 33 |
ϕ_{peak} (degrees) | Peak friction angle | 36.9, 38.9, and 40.5 for D_{R} of 65%, 80%, and 90%, respectively |
R_{f} | Failure ratio | 0.81, 0.71, and 0.63 for D_{R} of 65%, 80%, and 90%, respectively |
hfac1 | Controls liquefaction triggering | 0.45 |
hfac2 | Controls liquefaction triggering | 0.5 |
hfac3 | Controls liquefaction triggering | 1.0 |
hfac4 | Controls post-trigger response | 2.2, 2.0, and 1.8 for D_{R} of 65%, 80%, and 90%, respectively |
For calibration of the UBCSAND constitutive model, undrained cyclic direct simple shear (DSS) single element tests were simulated and compared against the DSS simulations using the PM4SAND calibrated properties. The UBCSAND model was not directly calibrated against the triaxial tests due to time limitations.
Overall, the liquefaction strength curves implied by UBCSAND are generally steeper than those implied by PM4SAND and the laboratory tests. Hence, the UBCSAND model may need to be calibrated with a tighter target CSR range, corresponding to that induced by the input motions.
27.3 Type B Simulations (Blind Predictions)
27.3.1 Introduction
During this phase of the project, the model parameters obtained as part of the calibration process were used to simulate the centrifuge experiments. The numerical simulations were conducted without any knowledge of the actual results. The simulation teams were only given information about the main characteristics of the centrifuge experiments, including the geometry of the centrifuge model, the centrifugal acceleration, the viscosity of the pore fluid (μ), the base excitation (horizontal and vertical components) and the achieved soil density.
Summary of centrifuge experiments selected for LEAP-2017 Type-B simulations
Experiment | Cent. Acc. (g) | μ/g | ρ_{d} (kg/m^{3}) | D_{R} (%) |
---|---|---|---|---|
CU-2 | 40 | 1.175 | 1605.8 | 46 |
Ehime-2^{a} | 40 | 1 | 1656.55 | 64 |
KAIST-1^{a} | 40 | 0.897 | 1701.2 | 78 |
KAIST-2 | 40 | 0.936 | 1592.5 | 42 |
KyU-3 | 44.4 | 0.991 | 1637 | 57 |
NCU-3^{a} | 26 | 1 | 1652 | 62 |
UCD-1^{a} | 43 | 1 | 1665 | 67 |
UCD-3^{a} | 43 | 1 | 1658 | 64 |
ZJU-2^{a} | 30 | 1 | 1606 | 46 |
27.3.2 Analysis Platform
The analysis platform used for the numerical simulation of the centrifuge experiments is FLAC2D, Version 7.0 for PM4Sand and Version 8.0 for UBCSAND, respectively (Itasca 2011, 2017). FLAC is a two-dimensional explicit finite difference program for engineering mechanics computation, following a “mixed discretization” scheme (Marti and Cundall 1982).
27.3.3 Numerical Modeling
A triangular pressure was applied at the soil surface simulating the load due to the water mass. Initially, during the gravity loading, Mohr-Coulomb properties were assigned to soil. A gravitational field with a vertical acceleration equal to 9.81 m/s^{2} was applied and once equilibrium was reached, PM4SAND or UBCSAND constitutive models were assigned to soil elements and equilibrium was reached again. In the next step, the groundwater flow mode was set on and equilibrium was reached once more. During this process of gravity loading, the error tolerance was on the order of 10^{−4}. The pore pressure was fixed at the soil surface. The horizontal displacement was also fixed at the vertical boundaries of the model. Last, the base of the model was constrained to move neither horizontally nor vertically.
After the end of the gravity loading phase, horizontal and vertical mean input motions, obtained from recorders AH11–12 and AV1–2, respectively, were applied at the base and the vertical boundaries of the model. Rayleigh damping (stiffness- and mass-proportional) with a minimum value of 0.5% at 3.3 Hz was assigned to the soil elements. After the end of shaking, the analyses continued until the excess pore water pressures dissipated fully. This procedure was followed for each of the simulated centrifuge tests. For each simulation, the corresponding input motions were baseline corrected and then applied to the model.
27.3.4 Material Properties and Constitutive Model Parameters
Material properties used for numerical simulations
Centrifuge test | Permeability (cm/s) | Water bulk modulus (kPa) | D_{R} (%) | ρ_{d} (kg/m^{3}) |
---|---|---|---|---|
Ehime-2 | 0.0118 | 480,000 | 65 | 1657 |
NCU-3 | 1652 | |||
UCD-1 | 1665 | |||
UCD-3 | 1658 | |||
KAIST-1 | 80 | 1701 | ||
ZJU-2 | 50 | 1606 |
After shaking, the model was allowed to reconsolidate until excess pore pressures dissipated and initial effective stresses were re-established. After end of shaking, permeability was scaled by ten to reduce calculation time, and the time was also scaled in the post-processing phase to ensure that the results are not affected compared to the solutions that would have been obtained by not scaling the permeability.
As aforementioned, the gravity loading was applied in two stages. In the first stage, Mohr-Coulomb properties were assigned to the soil elements. Basically, the gravity loading was initially applied elastically since no failure occurred.
In the second stage of gravity loading, as well as the dynamic part of the numerical analyses, advanced constitutive models were assigned to the soil elements, such as PM4SAND and UBCSAND models. Constitutive models PM4SAND and UBCSAND were calibrated for soil relative densities of 65%, 80%, and 90%. For the Type-B simulations of centrifuge tests with D_{R} of about 65% (Ehime-2, NCU-3, UCD-1, and UCD-3) and 80% (KAIST-1), the initial calibrated parameters for a D_{R} of 65% and 80% were used, respectively. There was no calibration performed for a D_{R} of 50%; hence, for Type-B simulation of ZJU-2 with a D_{R} of about 50%, the calibrated parameters corresponding to a D_{R} of 65% were used while a D_{R} of 50% was used as input to the simulation. For PM4SAND and UBCSAND constitutive models, the calibrated model parameters presented in Tables 27.1 and 27.2, respectively, were used based on the idealized relative density of each centrifuge test per Table 27.4.
27.3.5 Simulation Results
27.4 Type-C Simulations
27.4.1 Introduction and Constitutive Model Parameters
27.4.2 Simulation Results
27.5 Sensitivity Study
27.5.1 Introduction
Sensitivity analyses: inputs and results
Simulation # | NS-1 | NS-2 | NS-3 | NS-4 | NS-5 | NS-6 | NS-7 | |
---|---|---|---|---|---|---|---|---|
Dry density (kg/m^{3}) | 1651 | 1608 | 1683 | 1651 | 1651 | 1651 | 1651 | |
Soil | Ottawa F65 | Ottawa F65 | Ottawa F65 | Ottawa F65 | Ottawa F65 | Ottawa F65 | Ottawa F65 | |
D_{R} (assuming p_{max} = 1765 & p_{min} = 1476 kg/m^{3}) | 65% | 50% | 75% | 65% | 65% | 65% | 65% | |
Motion to be used for simulation provided in Excel sheet | Achieved RPI-1, Motion 1 | Anticipated RPI-3 Motion 1 | Achieved RPI-1, Motion 1 | Achieved RPI-1, Motion 1 scaled up | Achieved RPI-1, Motion 1 scaled down | Achieved RPI-2 Motion 1 | Achieved RPI-2 Motion 1 scaled up | |
PGA (g) | 0.15 | 0.15 | 0.15 | 0.25 | 0.11 | 0.14 | 0.2 | |
PGA of 1 Hz component (g) | 0.135 | 0.135 | 0.135 | 0.27 | 0.099 | 0.11 | 0.16 | |
PGA of the high frequency component (g) | 0.021 | 0.021 | 0.021 | 0.035 | 0.015 | 0.08 | 0.11 | |
Simulation result: X-displacement at middle point on the specimen surface (cm) | PM4SAND | 0.7 | 48 | 0 | 28.9 | 0.2 | 10.6 | 32.6 |
UBCSAND | 4.9 | 63.6 | 0.2 | 13.9 | 0.2 | 12.4 | 25.1 | |
Simulation result: Duration of liquefaction at P4 after end of shaking (cm) | PM4SAND | 0 | 130 | 0 | 80 | 0 | 20 | 60 |
UBCSAND | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
27.5.2 Sensitivity Analyses Results
Sensitivity analyses NS-1 to NS-3 were used to explore the sensitivity of simulations to relative density. Sensitivity analyses NS-1, 4, and 5 were used to explore the sensitivity of simulations to motion intensity. Sensitivity analyses NS-6 and NS-7 were used to assess the influence of superimposed ground motion high frequencies on simulation results. Table 27.5 presents the resulting horizontal displacement at the middle of the model surface and the duration of liquefaction at point P4 (P4 location: middle at 1-m depth) after the end of shaking.
The sensitivity analyses also show that soil relative density has a significant impact on the model behavior.
27.6 Conclusions
We used two different constitutive models (PM4SAND and UBCSAND), implemented in the software FLAC, to simulate liquefaction-induced slope instability from six centrifuge tests.
The methodology adopted for the constitutive model calibration process considered both liquefaction triggering and post-liquefaction accumulation of shear strains. Firstly, constitutive models, PM4SAND and UBCSAND, were calibrated against laboratory tests to comply with liquefaction triggering criteria such as the number of cycles required to reach specific strain and pore pressure ratio thresholds. Secondly, the strain accumulation rate (SAR) following liquefaction triggering was used as a target for model parameter calibration.
Overall, the blind predictions captured the centrifuge tests behavior well and bounded the centrifuge response in most cases, indicating the benefits of using more than one constitutive model when performing numerical modeling. The predicted permanent displacements based on both constitutive models were generally within a factor of 2 from the actual measurements. The liquefaction strength curves implied by the UBCSAND model are steeper than the ones implied by PM4SAND and the laboratory test data. Hence, during the Type-C simulations, the UBCSAND model calibration was adjusted considering a CSR range corresponding to the CSR induced by the input motions. This should be considered when model calibrations are performed in practice, especially when multiple hazard levels are involved.
Differences between the predicted and measured responses are partially associated with limitations in the laboratory test data available, which affect the results of the numerical model calibration. For example, direct simple shear tests rather than triaxial tests, tests with static bias in addition to the no-bias conditions as well as tests at different CSR levels, representative of the CSR induced by the input motions, would be more relevant and are recommended. Differences between observed and computed responses are also attributed to simplifications in the prototype-scale numerical model (e.g., simulating possibly heterogeneous actual conditions with an idealized uniform relative density), accuracy of measurements and conversions from model to prototype scale, and differences between the input motions in the simulations (“average” of recorded at the centrifuge base) and the actual recorded input motions in the centrifuge which may vary across its base.
The sensitivity analyses suggest that horizontal displacements increase when high frequencies are introduced in the ground motion and for smaller soil relative density and higher ground motion intensity.
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