A gradation-density-dependent hypoplastic model for calcareous sand with particle crushing

The impact of particle crushing and relative density on calcareous sand is substantial; however, relevant studies, particularly in constitutive modelling, remain limited. To address this gap, a gradation-density-dependent hypoplastic model has been developed to predict the behaviour of calcareous sand under crushing conditions. First, particle crushing is quantified and represented through a proposed gradation evolution law. The reduction in void ratio on normal consolidation lines (NCLs) and critical state lines (CSLs) is then decomposed into two components: particle rearranging and crushing. By integrating the developed grain size distribution evolution and the void ratio reduction, the model effectively captures the gradation-density-dependent features of NCLs and CSLs. These features are subsequently incorporated into a hypoplastic framework, resulting in a gradation-density-dependent hypoplastic model for calcareous sands. The proposed model demonstrates a strong agreement with a series of experimental results for calcareous sands with varying relative densities.