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PM4Sand & PM4Silt - RS2 vs FLAC vs PLAXIS

Published on: Oct. 27, 2022 Updated on: Jan. 25, 2023

6 minutes read

RS2 has the capability to perform dynamic analysis of geotechnical structures due to earthquake loading or other dynamic loads. The addition of PM4Sand and PM4Silt to RS2’s list of constitutive models has been highly requested by our users recently. With this in mind, both PM4Sand and PM4Silt are now available in RS2.

For regions prone to earthquakes, adequately modeling and performing dynamic analysis of geotechnical structures is critical to effectively identify the potential for earthquake-induced soil liquefaction.

Simulating stress-strain responses of different soil types can be challenging even under static conditions. In dynamic situations, the behavior of soils is even more complex. This highlights the complexities of formulating and selecting the appropriate constitutive model that will accurately represent the behaviour of the materials.

PM4Sand and PM4Silt developed by Ross Boulanger and Katerina Ziotopoulou [1, 2] provide constitutive equations for accurately capturing the behaviour of sands and silts under different loading conditions and specially dynamic scenarios.

RS2's Dynamic Analysis

To verify these two models in RS2, a series of simulations were conducted and the results from RS2 were compared with the results generated in FLAC and PLAXIS. The models are developed by original authors for FLAC as a dll file that can be accessed from their corresponding links above. In PLAXIS, these models are available as user defined soil models [3].

PM4Sand: RS2 vs FLAC vs PLAXIS

The results of verification models for PM4Sand constitutive model in RS2 are compared against results from FLAC and PLAXIS on a series of simulations including Drained Direct Simple Shear Test, Undrained Direct Simple Shear Test and Undrained Cyclic Direct Simple Shear Tests. The PM4Sand primary input parameters are presented in Table 1.

Relative Density (D_R)	Shear Modulus Coefficient (G_o)	Contraction Rate Parameter (h_po)
0.35	476	0.53
0.55	677	0.40
0.75	890	0.63

Table 1: Input parameters for PM4Sand model verifications

The results from the drained monotonic direct simple shear tests in Figure 1 and the undrained monotonic direct simple shear tests in Figure 2 show very good agreement between RS2, FLAC, and PLAXIS. These simulations were all done under strain control loading.

Figure 1a: Monotonic Drained Simple Shear Test loading responses DR = 35%

Figure 1c: Monotonic Drained Simple Shear Test loading responses DR=75% with vertical effective stress of 1 Patm, and Ko=0.5

Figure 2a: Monotonic Undrained Simple Shear Test loading responses for DR = 35%

Undrained Cyclic Direct Simple Shear Test results in Figure 3 show a good agreement between the three tools as well. There are minor differences between the results from the three tools that can be observed in later loading cycles. The main reasons behind this are the difference in application of shear load and the convergence criteria in the different tools. FLAC simulations are strain controlled and the loading direction changes when a certain level of shear stress is reached, whereas RS2 and PLAXIS are stress controlled simulations. Even though the convergence criteria between the three tools are widely accepted between the practitioners, the minor errors at the end of each load stage/step can accumulate when the number of stages/steps is very large. Apart from this, there is good agreement between the results generated in all three programs.

Figure 3a: Cyclic Undrained Simple Shear Test loading responses for DR = 35% under vertical effective stress of 1 Patm, and Ko=0.5 with maximum loading ratio of 0.147*1.6; variation of share stress with shear strain

PM4Silt: RS2 vs FLAC vs PLAXIS

The three main input parameters for PM4Silt model include Shear Strength Ratio (s_u/σ’_vc), Shear Modulus Coefficient (G_o), Contraction Rate Parameter(h_po).

The input parameters used in the verifications of PM4Silt model are listed below in Table 2.

Shear Strength Ratio (s_u/σ’_vc)	Shear Modulus Coefficient (G_o)	Contraction Rate Parameter(h_po)
0.25	588	20
0.50	776	50
0.75	913	60

Table 2: Input parameters for PM4Silt model verifications

As in the simulations using PM4Sand, the drained monotonic direct simple shear tests and undrained monotonic direct simple shear tests are done under strain control loading and the results in Figures 4 and 5 show good agreement between all three software. Figure 6 shows the results of undrained cyclic direct simple shear test. Once again, the simulation in FLAC is strain controlled and the loading direction changes when a certain level of shear stress is reached, whereas RS2 and PLAXIS are stress controlled simulations. There is good agreement of the results between the three programs.

Monotonic Drained Simple Shear Test loading responses for su/'vc = 0.25 — Figure 4a: Monotonic Drained Simple Shear Test loading responses for su/σ'vc = 0.25

Monotonic Drained Simple Shear Test loading responses for su/'vc = 0.50 — Figure 4b: Monotonic Drained Simple Shear Test loading responses for su/σ'vc = 0.50

Monotonic Drained Simple Shear Test loading responses for su/'vc = 0.75 with vertical effective stress of 1 Patm, and Ko=0.5 — Figure 4c: Monotonic Drained Simple Shear Test loading responses for su/σ'vc = 0.75 with vertical effective stress of 1 Patm, and Ko=0.5

Monotonic Undrained Simple Shear Test loading responses for su/'vc = 0.25 — Figure 5a: Monotonic Undrained Simple Shear Test loading responses for su/σ'vc = 0.25

Monotonic Undrained Simple Shear Test loading responses for su/'vc = 0.50 — Figure 5b: Monotonic Undrained Simple Shear Test loading responses for su/σ'vc = 0.50

Monotonic Undrained Simple Shear Test loading responses for su/'vc = 0.75 with vertical effective stress of 2 Patm, and Ko=0.5 — Figure 5c: Monotonic Undrained Simple Shear Test loading responses for su/σ'vc = 0.75 with vertical effective stress of 2 Patm, and Ko=0.5

Cyclic Undrained Simple Shear Test loading responses for ) su/'vc = 0.25 under vertical effective stress of 1 Patm, and Ko=0.5 with maximum loading ratio of τ/ Patm = 0.2; variation of share stress with shear strain — Figure 6a: Cyclic Undrained Simple Shear Test loading responses for ) su/σ'vc = 0.25 under vertical effective stress of 1 Patm, and Ko=0.5 with maximum loading ratio of τ/ Patm = 0.2; variation of share stress with shear strain

Figure 6b: Cyclic Undrained Simple Shear Test loading responses for ) su/σ'vc = 0.25 under vertical effective stress of 1 Patm, and Ko=0.5 with maximum loading ratio of τ/ Patm = 0.2; effective stress path

Using the newly added PM4Sand and PM4Silt constitutive models, RS2 is providing more functionality for better predicting liquefaction potential with dynamic analysis of sandy and silty soils. These models are available in Version 11.017 of RS2. All RS2 users with an active Maintenance+ subscription will have access to these constitutive models.

References

[1] Boulanger, R. W. and Ziotopoulou, K. (2017). “PM4Sand (Version 3.1): a sand plasticity model for earthquake engineering applications.” Report No. UCD/CGM-17/01, Center for Geotechnical Modeling, University of California at Davis.

[2] Boulanger, R. W. and Ziotopoulou, K. (2018). “PM4SILT (Version 1): a silt plasticity model for earthquake engineering applications.” Report No. UCD/CGM-18/01, Center for Geotechnical Modeling, University of California at Davis.

[3] PLAXIS 2D (2018). https://communities.bentley.co...

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Dr. Alireza Azami, Director of Business and Research at Rocscience

1 Authors:

Dr. Alireza Azami, Director of Business and Research at Rocscience

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