Influence of Terrain Parameters on Tire Forces and Moments Under Multi-Pass Loading

The dynamic response of soft terrain under repeated vehicle passes significantly influences off-road vehicle mobility and performance. The primary innovation of this research is the integration of loading–unloading hysteresis, multi-pass terrain-state evolution, and sensitivity analyses within a unified HSSTM-based framework. Unlike conventional pressure–sinkage models that employ constant terrain parameters and generally neglect terrain deformation, the proposed method identifies the dominant parameters directing sinkage, energy dissipation, rolling resistance, and spindle-level tire forces and moments. As a result, the framework provides a physically interpretable and computationally efficient approach for terrain-parameter prioritization and off-road tire-performance simulation under repeated loading. Two sensitivity analysis methods are employed including one-at-a-time (OAT) local sensitivity analysis which measures the influence of key terrain parameters on soil plastic sinkage, compaction rate, and final peak pressure. Moreover, the global sensitivity methods such as Factor Prioritization by Reduction of Variance (FoR) and Partial Rank Correlation Coefficient (PRCC) determine the dominant terrain variables affecting force and moment on tire spindle. The terrain model is based on the modified Bekker-Wong theory, simulating the loading-unloading behavior, elastic recovery, and plastic deformation. This model considers the rate-dependent terrain response under dynamic loading. A Pearson correlation-based model is developed to simulate rolling resistance using sensitivity-weighted coefficients. It is validated through both synthetic (parameter sweep) and realistic (terrain-operational) scenarios. Moreover, a logarithmic multi-pass influence is employed to simulate terrain behavior through repeated tire passes. The results indicate that parameters such as sinkage exponent n, unloading modulus Au, and friction modulus Kϕ demonstrate strong influence on both rolling resistance and dynamic response. The sinkage exponent n and unloading parameters primarily controlled multi-pass deformation and rolling resistance, whereas n, ϕ, and Cd were important for the spindle forces and moments. In particular, soil damping Cd was the dominant parameter for the vertical force Fz.