The nonlinearity of the constitutive relation for rocks becomes more prominent with a more complex physical-mechanical environment and mechanical behavior. The accurate establishment of the constitutive relation affects the determination of rock deformation and damage state from physical features. In this study, a novel statistical damage constitutive model for rocks is proposed based on quantified energy conversion. The novelty of the model is that the nature of rock damage before and after damage stress is considered. In the constitutive model, the evolution characteristics of energy conversion show a five-stage evolution with a ‘spoon’ form and correspond to the rock deformation and damage process, which can be fitted with the modified GaussAmp function; the damage variable is deduced by the Weibull distribution with energy conversion as the distribution variable, which presents a monotonic decrease caused by initial defects before the σcd and shows a ‘S’ shape caused by nascent cracks after the σcd. Furthermore, triaxial test data of three types of rocks under different confining pressures were used to verify the proposed model, and the results were in good agreement with the test data in most cases. The characteristics of the crack closure stage, peak stress, residual strength, and stress drop process are controlled by the model parameters, which can be determined using experimental data. As these parameters definitely have a physical meaning and a relation to the confining pressure, the proposed model has the potential to be used in rock engineering.

中文翻译：

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基于能量转换的岩石统计损伤本构模型


随着岩石物理力学环境和力学行为的复杂化，岩石本构关系的非线性变得更加突出。本构关系的准确建立影响着从物理特征上判断岩石的变形和损伤状态。在这项研究中，提出了一种基于量化能量转换的新型岩石统计损伤本构模型。该模型的新颖之处在于考虑了损伤应力前后岩石损伤的性质。本构模型中能量转换的演化特征呈现出“勺子”状的五阶段演化特征，对应岩石的变形损伤过程，可以用修正后的GaussAmp函数进行拟合；损伤变量由以能量转换为分布变量的威布尔分布推导出来，呈现出由初始缺陷在σ之前引起的单调递减光盘并显示出由 σ 之后新生裂纹引起的“S”形状光盘。此外，利用三类岩石在不同围压下的三轴试验数据对所提模型进行了验证，大多数情况下结果与试验数据吻合较好。裂纹闭合阶段的特征、峰值应力、残余强度和应力下降过程由模型参数控制，可以使用实验数据确定。由于这些参数确实具有物理意义并且与围压有关，因此所提出的模型具有在岩石工程中使用的潜力。