Keywords

1 Introduction

The LEAP-2017 project involved 11 numerical simulation teams from different academic institutions and geotechnical engineering firms across the world that participated in modeling of a selection of the performed centrifuge experiments. The simulation exercise consisted of constitutive model calibration, Type-B prediction, and Type-C prediction. This paper presents a summary of the results of the first phase (i.e., calibration) of this exercise. The main purpose of this phase was to provide the numerical simulation teams an opportunity to calibrate the constitutive models (that would be used in Type-B simulations) against the results of monotonic and cyclic triaxial tests conducted on Ottawa F-65 sand during the course of LEAP-2015 and LEAP-2017 projects. Moreover, the calibration phase would allow for a detailed documentation of the model performance against laboratory element tests before the same model is used in numerical simulations of LEAP-2017 centrifuge tests.

In preparation of the (calibration of constitutive models) phase, the following steps were followed:

  • The George Washington University team performed a large number of laboratory tests (80 tests in total) on the selected soil (Ottawa F-65 sand) to obtain:

    • Basic properties of the soil (particle size distribution, specific gravity, hydraulic conductivity)

    • Stress-strain response and liquefaction strength of the soil using stress-controlled cyclic triaxial tests

  • A detailed report on these experimental results (El Ghoraiby et al. 2017, 2018, 2019) was prepared and provided to the participating teams in the simulation exercise.

  • Additional soil characterization and element tests data (monotonic and cyclic strain-controlled triaxial tests) produced during the LEAP (Vasko 2015; Vasko et al. 2018) were also provided to the simulation teams through “datacenterhub.”

  • In addition to the above data, the monotonic and cyclic direct simple shear tests performed by Bastidas (2016) were also made available through “datacenterhub” (Bastidas et al. 2017).

  • The laboratory test data were provided on March 14, 2017, to 20 simulation teams from around the world (9 USA, 5 Japan, 1 China, 1 Germany, 1 Italy, 1 Canada, 1 Colombia, 1 New Zealand) that originally expressed interest in participating in the LEAP-2017 simulation exercise.

  • The deadline for submission of the calibration simulations was set as June 1, 2017.

  • Twelve teams submitted their calibration simulations by or near the deadline. The participating simulation teams submitted 17 different numerical simulations.

The element test results reported in El Ghoraiby et al. (2017, 2018, 2019) are the target of the calibration simulations. Each numerical simulation team submitted a detailed report discussing the process followed in the calibration of their selected constitutive model. The reports provided a description of the constitutive model used by the predictors as well as the method used for calibration. A brief summary of these reports is presented in the papers by each numerical simulation teams in the proceedings of LEAP-UCD-2017 workshop. A summary of the element tests simulations and results is presented in the following sections.

Here it is important to note that triaxial tests were chosen in the present study due to availability of equipment and based on the fact that the boundary conditions are more accurately defined in triaxial tests than in simple shear tests. Majority of the element tests were performed using an initial effective stress of about 100 kPa. This effective stress is larger than the vertical effective stress at mid-depth of the centrifuge model which was about 20 kPa in the middle of the deposit. The density of the sand specimens in the triaxial tests corresponded to relative densities of 71.5%, 87.5%, and 97.5%. The relative densities of the soil specimens in the centrifuge tests ranged from about 40% to 80%. In the following LEAP projects, a new series of direct simple shear and hollow cylinder torsional shear tests are planned so that constitutive models can be calibrated at conditions closer to that in the centrifuge tests.

2 The Numerical Simulation Teams

The numerical simulation teams that submitted their calibration reports and participated in the Type-B simulation exercise are listed in Table 9.1.

Table 9.1 Numerical simulation teams
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The constitutive model and the finite element/difference platform used by each numerical simulation team are also listed in the above table. More detailed information about each constitutive model and the numerical simulation techniques used by each team are provided in separate papers (Wang et al. 2019; Ozutsumi 2019; Fukutake and Kiriyama 2019; Fasano et al. 2019; Chen et al. 2019; Mercado et al. 2017; Qiu and Elgamal 2019; Wada and Ueda 2019; Yang et al. 2019; Tsiaousi et al. 2019; Ichii et al. 2019; Montgomery and Ziotopoulou 2019).

3 Summary of the Element Test Simulations

The numerical simulation teams were requested to present their simulations of the 23 cyclic triaxial tests on Ottawa F-65 sand (see El Ghoraiby et al. 2017, 2018, 2019). Majority of simulation teams simulated cyclic triaxial tests. The UCD-Auburn (Montgomery and Ziotopoulou 2019) and Fugro West teams (Tsiaousi et al. 2019) who worked with a plane strain constitutive model performed their single-element simulations under plane strain conditions and submitted a number of cyclic biaxial simulations for comparison with the experimental results. Hence, to be consistent in comparison of the numerical simulations, instead of the usual p′-q plot for the undrained stress path, the results are plotted in space of deviatoric stress (\( {\sigma}_d={\sigma}_1^{\hbox{'}}-{\sigma}_3^{\hbox{'}} \)) versus minor principal effective stress (\( {\sigma}_3^{\hbox{'}} \)).

Figures 9.1 and 9.2 show detailed comparison of the simulated stress paths and stress-strain curves with two of the cyclic stress-controlled tests with a cyclic stress ratio, CSR = 0.17 and 0.12, performed on specimens with a density of 1666 kg/m3 which, for Gs = 2.65, (ρd)max = 1757 kg/m3, and (ρd)min = 1491 kg/m3, corresponds to a void ratio of 0.585 and Dr = 71.5%. The simulations are labelled simulations 1 to 11. The numbers refer to the order of the simulation teams in the list presented above. The numerical simulation team 6 submitted two different simulations with two different constitutive models but the same finite element platform which are labelled “a” and “b.” It is also noted that a few simulation teams did not submit their simulations for all of the requested cyclic stress ratios. Figures 9.3 and 9.4 show similar comparisons of the numerical simulation with the results of cyclic stress-controlled triaxial tests on denser specimens ρd = 1713 kg/m3 (e = 0.542, Dr = 87.5%) for cyclic stress ratio (CSR) of 0.24 and 0.19, respectively. Figures 9.5 and 9.6 show the numerical simulations of the stress-controlled cyclic triaxial tests for a much denser specimen ρd = 1744 kg/m3 (e = 0.515, Dr = 97.5%) for cyclic stress ratio (CSR) of 0.365 and 0.225, respectively. Numerical simulation team 7 did not submit simulations for these cyclic stress ratios.

Fig. 9.1
figure 1

Comparison of the numerical simulations of a cyclic stress-controlled test on Ottawa F-65 sand for ρd = 1666 kg/m3 (e = 0.585, Dr~71.5%), p′0 = 100 kPa, CSR = 0.17

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Fig. 9.2
figure 2

Comparison of the numerical simulations of a cyclic stress-controlled test on Ottawa F-65 sand for ρd = 1666 kg/m3 (e = 0.585, Dr~71.5%), p′0 = 100 kPa, CSR = 0.12

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Fig. 9.3
figure 3

Comparison of the numerical simulations of a cyclic stress-controlled test on Ottawa F-65 sand for ρd = 1713 kg/m3 (e = 0.542, Dr~87.5%), p′0 = 100 kPa, CSR = 0.24

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Fig. 9.4
figure 4

Comparison of the numerical simulations of a cyclic stress-controlled test on Ottawa F-65 sand for ρd = 1713 kg/m3 (e = 0.542, Dr~87.5%), p′0 = 100 kPa, CSR = 0.19

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Fig. 9.5
figure 5

Comparison of the numerical simulations of a cyclic stress-controlled test on Ottawa F-65 sand for ρd = 1744 kg/m3 (e = 0.515, Dr = 97.5%), p′0 = 100 kPa, CSR = 0.365

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Fig. 9.6
figure 6

Comparison of the numerical simulations of a cyclic stress-controlled test on Ottawa F-65 sand for ρd = 1744 kg/m3 (e = 0.515, Dr = 97.5%), p′0 = 100 kPa, CSR = 0.225

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Figures 9.1, 9.2, 9.3, 9.4, 9.5, and 9.6 present selected examples of the simulations submitted by the numerical simulation teams. A review of Figs. 9.1, 9.2, 9.3, 9.4, 9.5, and 9.6 reveals the following trends:

  1. 1.

    The numerical simulation 1 showed stress-strain responses that are comparable to those observed in the experiments.

  2. 2.

    While the experimental results show ratcheting of the stress-strain curves toward the negative side (extension) of the axial strain, the stress-strain curves simulated by the simulation teams 2, 3, 5, 6b, 7, 10, and 11 are more or less symmetric and do not show a visible bias in the ratcheting response.

  3. 3.

    The numerical simulations 6a show larger ratcheting in the triaxial extension direction compared to the experimental results. Numerical simulations 8 are qualitatively comparable to the numerical simulation of 6a, but show smaller ratcheting and seem to have stabilized at larger effective stresses than those shown in numerical simulation 6a.

  4. 4.

    The stress paths of numerical simulation 4 appear to have stabilized at an effective stresses larger than those observed in the cyclic triaxial experiments.

  5. 5.

    Numerical simulation 9 shows stress-strain responses similar to those observed in the experiments; however, they have reached a larger double amplitude axial strains at a lower number of cycles than those observed in the experiments.

  6. 6.

    In the experiments, the amplitude of the cyclic strains continues to grow with each additional cycle of loading. After some number of cycles, the amplitude of the cyclic strains stops growing in simulations 1, 4, 6a, 6b, and 8. The peak amplitude of cyclic strain is significantly underestimated by simulations 4 and 8.

To gain additional insights into the performance of each model, the experimentally observed and numerically simulated excess pore pressure ratios are plotted against the number of cycles for selected tests (Figs. 9.7, 9.8, and 9.9). All of the models predicted cyclic pore water pressures toward the end of the simulations. It is easy to compare the rate of pore pressure generation in the plots of pore pressure ratio as a function of number of cycles. The rate of pore pressure generation varied significantly from model to model.

Fig. 9.7
figure 7figure 7

(a) Comparisons of the observed versus computed excess pore water pressure ratios with number of cycles for ρd = 1666 kg/m3 (e = 0.585, Dr~71.5%) at CSR = 0.17. (b) Comparisons of the observed versus computed excess pore water pressure ratios with number of cycles for ρd = 1666 kg/m3 (e = 0.585, Dr~71.5%) at CSR = 0.12

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Fig. 9.8
figure 8figure 8

(a) Comparisons of the observed versus computed excess pore water pressure ratios with number of cycles for ρd = 1713 kg/m3 (e = 0.542, Dr~87.5%) at CSR = 0.24. (b) Comparisons of the observed versus computed excess pore water pressure ratios with number of cycles for ρd = 1713 kg/m3 (e = 0.542, Dr~87.5%) at CSR = 0.19

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Fig. 9.9
figure 9figure 9

(a) Comparisons of the observed versus computed excess pore water pressure ratios with number of cycles. ρd = 1744 kg/m3 (e = 0.515, Dr~97.5%) at CSR = 0.365. (b) Comparisons of the observed versus computed excess pore water pressure ratios with number of cycles. ρd = 1744 kg/m3 (e = 0.515, Dr~97.5%) at CSR = 0.225

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4 Liquefaction Strength Curves

The liquefaction strength curves simulated by each team for the three void ratios of 0.585, 0.542, and 0.515 (Dr = 71.5%, 87.5%, and 97.5%) are summarized in Figs. 9.10, 9.11, and 9.12, respectively. The following trends are observed from these curves:

  1. 1.

    For the largest void ratio (e = 0.585), numerical simulations 6a and 9 showed significantly steeper curves than the experimental curves. Numerical simulation 9 showed a reduction in number of cycles for CSRs lower than 0.16 compared to larger CSRs. Numerical simulation 3, while showing a trend consistent with the experimentally observed curve, used different CSRs than those specified in the guidelines for simulations.

  2. 2.

    For the denser specimens with e = 0.542, simulations 6a, 8, and 9 predicted much steeper curves than the experimental curve. For this void ratio, the simulation 11 showed noticeably larger number of cycles than those observed in the experiments.

  3. 3.

    The quality of the match to the experimentally obtained curve for the densest case (e = 0.515) appears to be significantly lower for a large number of models.

Fig. 9.10
figure 10

Comparison of the simulated liquefaction strength curves by different numerical simulations teams with the experimental results reported by El Ghoraiby et al. (2017, 2018, 2019) for ρd = 1666 kg/m3 (e = 0.585, Dr~71.5%)

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Fig. 9.11
figure 11

Comparison of the simulated liquefaction strength curves by different numerical simulations teams with the experimental results reported by El Ghoraiby et al. (2017, 2018, 2019) for ρd = 1714 kg/m3 (e = 0.542, Dr~87.5%)

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Fig. 9.12
figure 12

Comparison of the simulated liquefaction strength curves for ρd = 1744 kg/m3 (e = 0.515, Dr~97.5%) by different numerical simulations teams with the experimental results reported by El Ghoraiby et al. (2017, 2018, 2019)

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5 Conclusions

This article presented a summary of the numerical simulations of cyclic triaxial tests submitted by various numerical simulation teams as part of the calibration phase of LEAP-2017 project. These simulations show that a significant number of the constitutive models used in these simulations are able to capture the overall trends of the stress-strain response of Ottawa F-65 sand at medium dense condition (e = 0.585, Dr~70%). However, capturing the liquefaction strength curves for all the three selected void ratios appeared to be quite challenging.