一种基于弹性应变能的裂隙岩体等效弹性模量评价方法

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。

A method for estimating equivalent elastic moduli of fractured rock masses based on elastic strain energy

Based on the formulae of normal displacement and shear displacement of crack faces from linear elastic fracture mechanics, this paper aims to investigate the stored excessive elastic strain energy during the fracturing process of a rock with a single crack by applying external loading. The normal stiffness and shear stiffness of the crack are assumed be constant rather than traction-free. Two deformation models, i.e. the non-uniform deformation mode and the uniform deformation mode, are applied to calculate normal and shear displacements. In addition, based on equivalence of elastic strain energy, the analytical expressions of equivalent Young’s modulus and shear modulus of 2D fractured rock mass containing regularly distributed non-persistent cracks are studied. The comparison between the analytical expression and a closed-form solution derived by Amadei and Goodman (1981) shows that the uniform deformation mode provides the same result. The comparison of normally distributed cracks between the analytical expressions and FEM shows that the non-uniform deformation mode considering crack interactions obviously underestimates the elastic moduli, while the uniform deformation mode predicts directional moduli within 10% deviation of FEM results. The obtained analytical expression can be used as one of effective methods to estimate the equivalent elastic modulus of rock mass under specific conditions.