损伤岩石受拉变形模量的理论计算方法

Theoretical Calculation Method of Tensile Deformation Modulus of Damaged Rock

岩石受拉破坏过程本质是微裂纹扩展过程,假设均匀损伤的岩样由很多单裂纹岩石单元组成,受拉条件下含裂纹岩石单元的应变包括裂纹张开引起的岩石弹性应变,非弹性应变,岩石基质的弹性应变。采用COD理论计算裂纹尖端的最大张开位移,根据裂纹张开位移计算单裂纹单元的应变增量,计算出岩样受拉破坏时的应变与初始裂纹密度和裂纹最小间距的关系,最后建立了受拉条件下损伤岩样的体积变形模量计算方法。本方法能同时有效描述初始裂纹数量和裂纹长度对岩石变形的影响,更符合实际情况。结合算例分析显示:岩石裂纹张开引起的应变(包括弹性部分和塑性部分)是损伤岩石变形的重要组成部分,与初始损伤系数和内在抗拉强度成正比,与岩石基质弹性模量成反比。岩石的变形模量随着岩石的初始损伤增加而减小,随着裂纹长度损伤因子的增大而减小。并且初始损伤系数与初始裂纹密度以及裂纹最大半长的平方均成正比。

The essence of tensile rock failure is the propagation of micro cracks. Assuming that the uniform damage of rock sample consists of many single cracked rock units,the strain of crack in rock unit under the condition of tensile including elastic strain and inelastic strain caused by crack opening,elastic strain caused by rock matrix. Calculating crack opening displacement with COD theory,and by which we can calculate the strain increment of rock element. The relationship between rock tensile failure strain and the initial crack density and crack spacing was calculated,and the calculation method of damage rock specimen's bulk modulus of deformation under the condition of tensile was finally established. The method can effectively describe the influence of the initial crack number and the crack length on the rock deformation,which is more accordant with the actual conditions. Combined with example analysis shows that: the strain caused by the crack opening ( including elastic and plastic parts) is an important part of the deformation of damage rock,and the initial damage coefficient and internal tensile strength is directly proportional to the strain,and elastic modulus of rock matrix is inversely proportional to the strain. The deformation modulus of rock decreases with the increase of initial damage of rock,and decreases with the increase of crack length damage factor. And the initial damage coefficient is proportional to the initial crack density and the square of the maximum half length of the crack.