> For the complete documentation index, see [llms.txt](https://2025.istvs.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://2025.istvs.org/submissions/papers/8140.md).

# 8140 - NUMERICAL MODELING OF PLATE SINKAGE AND IN SITU BEVAMETER SHEAR TESTING USING FEM AND THE DENSITY-DEPENDENT NORSAND CRITICAL STATE CONSTITUTIVE SOIL MODEL

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Paper presented at ISTVS 2025 | 55th Conference of the International Society for Terrain-Vehicle Systems <https://doi.org/10.56884/RD0R8NHU>
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**Authors:** *Ray Kruger, Petrus Arnoldus Crous, Yuderka Trinidad Gonzalez, Mehari Tekeste*

**Keywords:** Plate Sinkage; In Situ Shear Tests; Bevameter; Critical State Soil Mechanics (CSSM); Finite Element Method (FEM); NorSand Constitutive model

**Abstract:**

The Bekker-Wong terramechanics model remains a cornerstone for predicting wheel–soil interactions, relying on Bevameter tests to characterize soil behavior via plate sinkage and in situ shear tests. However, accurately modeling these tests, and the underlying physics, remains challenging. Physics-based methods like the Discrete Element Method (DEM) lack key critical state soil mechanics features such as density dependence, yield functions, and pore pressure effects. This study employs an implicit, large-strain Finite Element Method (FEM) formulation and the NorSand critical state model to simulate plate sinkage and shear testing in partially saturated Cullinan sand. NorSand captures soil behavior through evolving yield surfaces and stress–dilatancy relationships linked to effective stress, void ratio, and density-dependent strength. Density-dependent shear resistance is captured by linking state parameters to increased mobilized friction ratios. Parameters were calibrated using 18 CU and CD triaxial tests via an automated Bayesian optimization scheme. Validation against field Bevameter experiments was performed in a forward-only modeling approach. The model shows good agreement with in situ shear tests, capturing peak shear strength and post-peak softening behavior across a range of densities. Plate sinkage predictions match early-stage stiffness but diverge at large settlements due to numerical instability. Numerical results demonstrate good agreement with experimental data, successfully capturing the soil density trends and deformations up to the pre-failure region.


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