A Thermodynamically Consistent Hyperelastic Potential for Unbound Granular Materials: Critical-State Formulation, Machine-Learning Benchmarking, and Finite Element Application

Abstract

Two paradigms dominate the literature on resilient strain behaviour of unbound granular materials (UGMs): empirical formulations, often lacking theoretical grounding, and machine learning (ML) models, operating as black boxes. This study proposes a hyperelastic strain energy potential—the KHP (Karasahin Hyperelastic Potential) model—deriving its volumetric component from the logarithmic compression relationship of critical-state soil mechanics and its shear component from a power-law distortional term. Analytical differentiation yields strains that inherently satisfy Maxwell’s symmetry, guaranteeing thermodynamic consistency. The model was calibrated to repeated-load triaxial data from sand-and-gravel and crushed limestone specimens and evaluated using Leave-One-Out Cross-Validation against three empirical models and two ML algorithms (Gaussian Process Regression, GPR, and a Neural Network). For axial strain, KHP ranked second only to GPR; for radial strain, it achieved the highest accuracy across both materials, outperforming all ML models. Its practical value was shown through a nonlinear finite element analysis of a flexible pavement section, reproducing the stress-dependent resilient behaviour of the base layer as a numerical demonstration of engineering usability, rather than a validation against measured field response. These findings show that a physical hyperelastic framework can match or exceed machine learning accuracy while preserving thermodynamic consistency, interpretability, and generalisability.