An elastic–plastic model considering the dilatancy behavior of granular materials under proportional stress paths

Granular materials exhibit complex stress–strain behavior that varies significantly under different stress states and loading paths. Even when loaded under the same initial and final stress conditions, the experienced stress path can profoundly influence their mechanical response and deformation behavior. In this study, conventional triaxial compression experiments and proportional loading experiments were conducted on Fujian sands to investigate the dilatancy behavior and hardening law of granular materials. It is found that in both kinds of experiments the dilatancy ratio decreases nonlinearly when the stress ratio increases, and the positive dilatancy ratio during proportional loading is considerably higher than that during triaxial compression under the same stress state. A new dilatancy parameter was introduced to the stress dilatancy equation to describe the incremental plastic strain direction during both triaxial compression and proportional loading paths. Additionally, a stress-path-independent hardening parameter was introduced to unify the description of hardening behavior during different stress paths. On this basis, an elastic–plastic constitutive model that takes into account the dilatancy behavior of granular materials under proportional stress paths was proposed. The model parameters can be calibrated by routine experiments. Specifically, the dilatancy parameter k can be determined from proportional loading tests when available or set to a recommended default value of 0.5 otherwise. The model is verified using existing experimental data and is found to be capable of capturing important behavior of coarse granular materials, including pressure-dependent shear strength, volumetric contraction during initial shearing, and subsequent dilation at larger strains. This model offers an alternative theoretical reference for predicting the behavior of granular materials under complex field loading conditions.