Modelling of granular materials at crushing-dominant stage

Granular crushing significantly changes mechanical behaviours, especially under elevated stress levels. Therefore, this study aims to develop a model to simulate the constitutive behaviours of granular materials at the crushing-dominant stage. Firstly, the contour of elastic potential energy is demonstrated and employed to derive the yield surface or function, acknowledging that the stored elastic energy dominates the breakage yield criterion. The versatility of the proposed yield function in accurately capturing the features of yield surfaces is verified with three cases, including Cam-clay models, test results, and an empirical yield function. Next, a hardening parameter, H, is formulated, considering the extent of crushing, B, and the void ratio, e, to reflect the expansion of the yield surface during hardening. The proposed simple hardening formulation favourably represents compression characteristics under elevated stress levels. Combining the above results of yield and hardening functions, a new elastic-plastic-crushing constitutive model is developed; the model's capability to describe crushable granular material behaviours is validated against experimental counterparts.