基于摩尔-库仑准则的断续节理岩体复合损伤本构模型

针对工程实际中断续节理裂隙岩体的损伤本构模型，假设岩石微元强度服从Weibull随机分布，以摩尔-库仑破坏准则作为描述微元强度的表示方法，推导出细观损伤变量。利用能量和断裂力学理论，综合考虑节理几何特征及力学特性，推导宏观损伤变量计算公式。基于Lemaitre应变等效假设，考虑宏细观缺陷耦合作用，推导出复合损伤变量，建立了基于摩尔-库仑准则的宏细观缺陷耦合作用的断续裂隙岩体损伤本构模型。研究结果表明：（1）采用摩尔-库仑准则作为描述微元强度的统计分布变量建立的损伤模型能够较好地反映岩石内部缺陷分布和变形特征，该模型真实地反映岩石微元强度受应力状态的影响。（2）该模型建立的理论曲线与断续节理岩体的试验曲线吻合较好。（3）节理裂隙岩体宏观损伤变量及峰值强度随节理倾角的变化规律与综合考虑宏细观耦合作用下的损伤变量及裂隙岩体峰值强度随节理倾角的变化规律基本一致。（4）宏细观耦合作用下的等效弹性模量与节理贯通率呈非线性负相关；在节理倾角一定的情况下，损伤变量与节理长度呈非线性正相关；在贯通率较小时，岩体的宏观损伤变量与内摩擦角的关系呈线性负相关变化，贯通率达到一定程度，线性关系变成非线性关系。

Composite damage constitutive model of rock mass with intermittent joints based on Mohr-Coulomb criterion

To investigate damage constitutive model of rock mass with intermittent joints in engineering practice with the assumption that the rock microscopic element strength obeys the Weibull random distribution function, the Mohr-Coulomb failure criterion is used to describe the strength of the microscopic element and the microscopic damage variable is deduced. A formula for macroscopic damage variable is deduced using energy and fracture mechanics theory and considering geometrical features and mechanical properties of the joint. Finally, based on the Lemaitre strain equivalence hypothesis, considering the macro-meso defect coupling effect, the composite damage variable is derived. A damage constitutive model of rock mass with intermittent joints under the action of macro-meso defect coupling is established based on the Mohr-Coulomb criterion. The results show that: (1) The damage model established by the Mohr-Coulomb criterion as the statistical distribution variable describing the strength of the micro-element can well reflect the characteristics of rock deformation and distribution of internal defects, which reflects that the micro-element strength of rock is influenced by the stress state. (2) The theoretical curve established by this model is in good agreement with the test curve of intermittent jointed rock mass. (3) The change of the macro damage variable and peak strength of jointed rock mass with the joint tilt angle and the change of damage variable considering the macro-meso coupling action and the peak strength of jointed rock mass with the joint tilt angle are generally consistent. (4) The relationship between the equivalent elastic moduli of macro-meso coupling and the crack connectivity rate exhibits nonlinear negative correlation. When the joint angle is constant, the relationship between the damage variable and joint length exhibits nonlinear positive correlation. When the connectivity rate is small, the relationship between the macroscopic damage variable and the internal friction angle of jointed rock mass shows a linear negative correlation, and the linear relations become nonlinear relations when the connectivity rate reaches a certain extent.