基于渐近展开法的脆性岩石双尺度方法初步研究

将渐近展开法与细观统计模型相结合，研究了脆性岩石双尺度计算方法。该方法在细观尺度定义材料属性，假定材料参数符合Weibull分布，采用弹性－理想脆性本构模型，脆断标准采用修正的Mohr-Coulomb准则和最大拉应力准则，通过宏细观尺度耦合计算，得到细观尺度材料损伤演化及其对结构宏观性状的影响。方法包括确定材料统计参数、确定细观尺度代表性体积单元（RVE）及求解边值方程等步骤。数值模型采用商业软件ABAQUS及其内嵌的UMAT用户子程序实现。该方法适用于岩石单轴受压或低围压应力状态，考虑到计算效率，计算时宜采用混合尺度，即模型重点（关键）部位采用双尺度，而其他区域采用单尺度计算。宏观尺度材料软化后未采用正则化方法，此时的计算结果有网格依赖性。

Preliminary study of two-scale model for analyzing brittle rock based on asymptotic expansion method

The asymptotic expansion method was combined with micro-based statistical model to develop a two-scale scheme for analyzing the behavior of brittle rock. The material properties were defined in micro-scale and the elastic-perfect brittle constitutive was adopted, the modified Mohr-Coulomb theory and the maximum tensile strength were selected as the fracture criterion. Through calculating in a global-local coupling way, the damage evolution of material in the micro-scale and its effects on the properties of rock in the macro-scale were derived. The scheme included three steps: determining material statistical parameters, determining representative volume element (RVE) and solving boundary equations. The numerical model was realized by the commercial software ABAQUS and its subroutine UMAT. This scheme can be used in the conditions that the rock is loaded with uniaxial compression or triaxial compression with low confining pressure. The regularization method is not used, so the result is mesh dependent after the rock is localized.