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基于线弹性断裂力学裂隙面张开位移及剪切位移理论公式,考虑裂隙存在常法向和常切向刚度情况,研究了含单个裂隙岩体加载过程中由于裂隙存在而附加的弹性应变能。基于应变能等效方法并假设两种裂隙变形模型——非均匀变形模型和均匀变形模型,研究了二维非贯通裂隙岩体的等效杨氏模量和等效剪切模量解析表达式。研究结果表明,对于贯通裂隙规则分布情况,均匀变形模型得到的解析解与Amadei等的结果一致;对于非贯通裂隙正态分布情况,考虑裂隙相互作用的非均匀变形模型解明显低估裂隙岩体的等效杨氏模量和等效剪切模量,而考虑裂隙相互作用的均匀变形模型解与有限元数值解的偏差在10%以内。得到的解析表达式在一定条件下可以作为裂隙岩体等效弹性模量评价方法之一。
Based on the theoretical formulas of the open displacement and the shear displacement of the cracked surface of the linear elastic fracture mechanics, the elastic normal strain and the normal tangential stiffness of the fractured rock are considered. The elastic strain energy added by the presence of the fractured rock mass during the loading process of a single fractured rock mass is studied. Based on the strain energy equivalent method and assuming two kinds of fracture deformation models-inhomogeneous deformation model and uniform deformation model, the equivalent Young’s modulus and equivalent shear modulus analytical expression of two-dimensional non-through fracture rock mass are studied . The results show that the analytical solution obtained by the uniform deformation model is consistent with that of Amadei et al. For the regular distribution of through fractures. For non-through fractures, the non-uniform deformation model considering the interaction of fractures is obviously underestimated for the normal distribution of fractures. Equivalent Young’s modulus and equivalent shear modulus, while the uniform deformation model considering the interaction of fractures deviates from the finite element numerical solution by less than 10%. The analytical expression obtained under certain conditions can be used as one of the evaluation methods for the equivalent elastic modulus of fractured rock mass.