Refined constitutive modelling of widely graded granular soils incorporating fractional particle breakage

Accurate characterization of gradation evolution and its influence on the critical state line (CSL) is essential for modelling the mechanical behaviour of widely graded granular soils. This paper aims to develop a constitutive model capable of depicting the stress–strain relationship and gradation evolution of widely graded granular soils. Firstly, a fractional breakage evolution model is formulated based on the observed breakage of fractional particle groups in artificially dyed granular soils. The model’s capability to accurately reproduce gradation evolution is verified using three representative gradation datasets. Secondly, a gradation-dependent CSL is established to describe the downward shift of the CSL in the ln e -ln p space based on the breakage-packing concept. Then, by incorporating the yield function of the microstructure and fractional-order plasticity theory, a state-dependent dilatancy equation is proposed, achieving a unified description of the loading and plastic flow directions. Finally, these components are integrated into a refined constitutive model for widely graded granular soils incorporating fractional particle breakage. Model predictions showed good agreement with triaxial test data for five granular soils under various loading conditions, demonstrating its robustness and applicability.