To simulate sand mixed with bentonite under dynamic conditions in PLAXIS 2D, the selection of an appropriate constitutive model depends on the specific material behavior you aim to capture. Here’s a focused breakdown:

Static Case:

• HSsmall is an excellent choice for the static analysis of sand-bentonite mixtures, as it accounts for non-linear stiffness at small strains and stress-dependent stiffness. The given cohesion value (3 kPa) can be directly incorporated in this model.

Dynamic Case:

For dynamic conditions, including liquefaction and cyclic loading:

1. UBC3D-PLM:

• This model is specifically designed for simulating the liquefaction behavior of sands. It effectively captures cyclic mobility and post-liquefaction response.

• However, it is calibrated primarily for clean sands or sandy soils with minimal fines content. The addition of bentonite (which alters soil permeability, cohesion, and plasticity) may not align with the assumptions of this model.

• If the bentonite proportion is low (e.g., less than 10-15% by weight), UBC3D-PLM might still approximate the behavior adequately, but the calibration parameters will need significant adjustments based on laboratory data.

2. Alternative Models:

• Hardening Soil Model with Small Strain (HSsmall):

• If liquefaction is not the primary focus but rather the dynamic stiffness and damping characteristics of the mixture, you can extend the use of HSsmall to dynamic simulations. This model handles dynamic stress-strain behavior well, though it does not account for liquefaction explicitly.

• Mohr-Coulomb Model with Rayleigh Damping:

• For simpler dynamic analyses where liquefaction is not the primary concern, this model can simulate basic dynamic responses, provided cohesion and friction angle are calibrated for the mixture.

3. Customizations and Considerations:

• For a sand-bentonite mixture, you may need to modify input parameters (e.g., shear modulus, damping ratio, and liquefaction parameters) to reflect the influence of bentonite on permeability, stiffness, and cyclic behavior.

• Laboratory or field data (e.g., cyclic triaxial or resonant column tests) are crucial to validate and calibrate the model.

Recommendation:

• Start with UBC3D-PLM if liquefaction is the focus, but ensure parameter calibration reflects the sand-bentonite properties.

• Alternatively, use HSsmall for a more generalized dynamic analysis if you are not targeting liquefaction explicitly.

If bentonite significantly alters the mixture behavior (e.g., cohesion-dominated response), a more tailored approach may require advanced constitutive models beyond PLAXIS defaults, potentially involving user-defined models.

Hasan Altawil First of all, thank you for your detailed and insightful answer. Your breakdown of the suitability of different constitutive models for sand-bentonite mixtures under both static and dynamic conditions is extremely helpful.

Second, I want to clarify the main focus of my study. My primary objective is to evaluate soil liquefaction mitigation, specifically under dynamic conditions. Given that liquefaction is the central aspect of my research, the UBC3D-PLM model appears to be the most suitable choice, as you mentioned.

However, I have some concerns regarding the use of UBC3D-PLM for sand-bentonite mixtures:

Your suggestion to calibrate the UBC3D-PLM parameters based on laboratory data is very useful. I agree that conducting laboratory tests, such as cyclic triaxial or resonant column tests, is necessary. But unfortunately, those tests are not available at my laboratory.