Abstract: The damage parameter is a variable used to describe the transition of geomaterials from a bonded state to an unbonded state. The correct expression of the damage evolution of structured soil is crucial in establishing constitutive models for structured soils. Currently, research on damage laws typically involves assuming expressions for damage parameters and then fitting these parameters using experimental results to establish the damage law. The rationality and applicability of these damage laws are yet to be validated. To derive a unified expression for the damage law of structured sands incorporating microscopic mechanisms, a prediction model based on symbolic regression is proposed. Firstly, using the definitions of damage parameters with microscopic physical significance, various damage databases are constructed using the distinct element method (DEM). Secondly, preliminary parameter screening is conducted on isotropic compression and constant p true triaxial compression stress paths using a method that combines input variables. p is the average effective stress. Combined with the genetic programming-based symbolic regression (GPSR), damage expressions with different complexities are derived. Finally, the best-performing expression is selected as the damage law for structured sand, namely the GPSR damage law, based on an analysis of prediction and generalization errors. The applicability of different expressions is compared using various DEM damage databases. The results show that the GPSR damage law represents damage parameters as functions of plastic deviatoric strain ε_s, normalized mean effective stress p/py and coefficient of intermediate principal stress b. It effectively reflects the transition from structured soil to remolded soil. The outstanding prediction ability of the GPSR damage law on different damage databases further demonstrates its applicability to various geomaterials. The research findings are valuable to establish constitutive models for structured sands.

Key words: structured sand, distinct element method (DEM), machine learning, symbolic regression, damage law