Modelling the evolving critical state of crushable soils and parameter optimization with an improved genetic algorithm (AIS–RCGA)

The critical state line (CSL) plays an essential role in the constitutive modelling of granular soils. It serves as a reference line for the measurement of the state parameter. The critical state of crushable soils cannot accurately be determined from experimental data because of the ever-changing soil properties due to particle breakage. In this study, two new parameters e B and e b are introduced, which account for the final position and the evolution of CSL of crushable soils during shearing, respectively. To identify the optimal CSL-related parameters from experimental data, a hybrid genetic algorithm combining artificial immune system (AIS) and real-coded genetic algorithm (RCGA), namely AIS–RCGA is adopted. The fitness is defined to minimize the prediction error of both void ratio (or pore water pressure) and deviatoric stress. We have refined the tuning methods for several hyperparameters of AIS–RCGA and proposed a novel method to assess the similarity of individuals within AIS–RCGA. Results show that the new method is more efficient in finding the global optimal for our problem. With optimized model parameters, the new constitutive model can accurately predict the response of crushable soil, outperforming other constitutive model reported in the literature.