Crushing of grains can greatly influence the strength, dilatancy, and stress-strain relationship of rockfill materials. The critical state line (CSL) in the void ratio versus mean effective stress plane was extended to the breakage critical state plane (BCSP). A state void-ratio-pressure index that incorporated the effect of grain crushing was proposed according to the BCSP. Rowe’s stress-dilatancy equation was modified by adding the breakage void-ratio-pressure index, which was also incorporated into the formulations of the bounding stress ratio and plastic modulus. A BCSP-based bounding surface plasticity model was proposed to describe the state-dependent stress-strain behaviors and the evolution of grain crushing during shearing process of rockfill materials, and was shown to sufficiently capture the breakage phenomenon.

颗粒的破碎会极大地影响堆石料的强度，膨胀率和应力-应变关系。空隙率相对于平均有效应力平面的临界状态线（CSL）延伸至断裂临界状态平面（BCSP）。根据BCSP，提出了一种兼有晶粒破碎作用的状态空压比指数。通过添加破损空隙率-压力指数修改了Rowe的应力-膨胀方程，该指数也被纳入边界应力比和塑性模量的公式中。提出了一种基于BCSP的边界表面可塑性模型，用于描述堆石料剪切过程中状态相关的应力应变行为和晶粒破碎的演变过程，并表明该模型可以充分捕捉碎裂现象。