复杂应力下脆性岩石材料的微裂纹损伤特性

Investigation of the damage for microcracks weakened brittle rocks subjected to arbitrary three-dimensional stress

基于无限大体深埋平片状椭圆形裂纹的变形场及其扩展条件,分别推导了脆性岩石材料内部具有任意空间取向的单个张开型或闭合型椭圆形微裂纹及其扩展引起的附加柔度张量;考虑微裂纹系统对材料变形的影响,引入了概率密度函数,得到了任意应力状态下脆性岩石材料的宏细观损伤模型;分析了椭圆形微裂纹的短长轴比率对材料损伤的影响。计算结果显示:材料损伤随着短长轴比率的增大而增大,短长轴比率对材料损伤的影响会随着载荷的增大而提高。将本文模型应用于混凝土的单轴拉伸和花岗岩的单轴压缩,结果表明本文模型能够对实验现象给予很好地解释。

Based on the analysis of the deformation field caused by elliptic crack embedded in infinite isotropic elastic matrix,the additional compliance tensor induced by a single opening/closed elliptic microcrack in a representative volume element and its growth is deduced,respectively.Considering the deformation of microcracks system,a macro-micro damage model for brittle rocks under arbitrary loadings is obtained by making use of statistical mechanics and a probability density function.The effect of elliptic ratio on material damage is investigated,and it is shown that the material damage increases with elliptic ratio,and the dependence of material damage on elliptic ratio increases with loading force.The tests of uniaxial tension for concrete and uniaxial compression for granite are simulated by this model,and good agreement is achieved between the calculated and experimental results.