Investigating the particle size effect of calcareous sand using a critical state-based model with the covariance matrix adaptation evolutionary strategies algorithm optimization

Abstract

The particle size of natural calcareous sands (CSs) varies significantly. It is of great interest for engineering practice if the mechanical behaviours of coarse-grained CSs can be easily extended from behaviours of fine-grained CSs using a constitutive model, for which the size effect is the key issue. For this purpose, consolidation-drained triaxial shear test results on CSs with five varying particle sizes were first re-interpreted to reveal this effect. The critical state-based constitutive model of sand (SIMSAND model) considering particle breakage effect was adopted for describing the mechanical behaviours of CSs. The optimization theory with the algorithm of covariance matrix adaptation evolutionary strategies (CMA-ES) was integrated with SIMSAND for identifying model parameters of five CSs. The applicability of the SIMSAND model to CS and the rationality of the CMA-ES algorithm in determining model parameters were thus verified. Then, six size-dependent parameters were selected according to the model parameter analysis of five CSs. Six relationships between the size-dependent parameters and the particle size were proposed based on three CSs, together with which the SIMSAND model can consider both particle size and breakage effects. The model’s rationality was further validated by simulating tests of another two CSs (one for interpolation and the other for extrapolation). The findings can lay a foundation for the prediction of mechanical behaviours in CSs with varying particle sizes.