A Physics-Guided Symbolic Regression Framework for Efficient and Interpretable Sand Constitutive Modeling

Data-driven constitutive modeling for geomaterials encounters significant challenges in achieving a balance among interpretability, physical consistency, and computational efficiency. Traditional symbolic regression often struggles with extensive search spaces, slow convergence rates, and insufficient physical constraints, which limits its applicability to complex granular materials such as sands. In this context, we propose a framework for knowledge-based physically guided symbolic regression (KB-phgSR), which seamlessly integrates classical constitutive models with data-driven optimization techniques. The framework employs a two-stage approach: initially distilling Pareto-optimal equations from established physical models to establish physically consistent solutions; subsequently refining these equations using experimental data while ensuring dimensional balance and adherence to mechanical boundary conditions. Validated against triaxial tests conducted on Toyoura and Ottawa sands under various drainage conditions, KB-phgSR demonstrates enhanced convergence speed and robustness in capturing the intricate behaviors of sand. The optimized equations exhibit both high accuracy and interpretability while conforming to fundamental elastoplastic principles. By effectively combining physics-based priors with data-driven discovery methods, this framework advances constitutive modeling towards improved generalizability and engineering efficacy, positioning it as a paradigm-shifting tool with transformative potential in geomechanics and beyond.