Discovering Constitutive Models for Clay Through Physical-Guided Symbolic Regression

Abstract

The mechanical properties of soil or other materials are mathematically represented by constitutive models, which employ theoretical derivation, laboratory experiments, and other methods to effectively address diverse engineering challenges. The physical accuracy and practical applicability of constitutive models are inversely related due to the intricate porous characteristic of soil. In this paper, we proposed approach introduces a symbolic learning framework that integrates inherent physical constraints. The finite mathematical operator functions as the fundamental symbolic entity, synthesizing physical information from both the perspectives of physics and mechanics. The aforementioned statement results in a succinct yet resilient portrayal of clay constitutive models. Comparative analyses involving purely data-driven and classical physical models demonstrate that incorporating essential expression forms and considering dimensional balance effectively guides the development of the constitutive model. The proposed model provides a high level of precision with minimal complexity, while also being unaffected by the need for high-resolution. The method presented herein integrates physical exploration and data fitting capabilities, resulting in a model characterized by both high precision and exceptional extrapolation ability.

Keywords: Soil Constitutive, Physical Symbolic Regression, Artificial Intelligence