基于应变能密度的非均质岩石损伤本构模型研究

Research on damage constitutive model of inhomogeneous rocks based on strain energy density

基于岩石细观单元弹性模量近似服从Weibull分布的假设,结合应变能密度理论,建立岩石损伤本构模型,借助声发射事件能量信号和岩石纵波波速提出岩石均质度系数m和弹性模量折减系数K0确定方法,并对参数进行修正。利用建立的损伤本构模型进行单轴加载模拟,将模拟结果曲线与已有模型理论曲线以及单轴加载实验曲线进行对比,该模型能很好地描述试件应力、应变关系与声发射情况。在此基础上,利用该模型进行石膏试件反复加载模拟,分析其应力–应变及声发射特征,并与室内实验结果进行对比分析。研究结果表明:试件均质度越高,脆性破坏特征越明显;借助声发射信号和岩石纵波波速确定的均质度m以及弹性模量折减系数K0的计算结果与试验结果吻合。基于应变能密度的岩石损伤本构模型的构建为综合考虑岩石的均质度及反复加载过程对岩石试件影响提供了新的理论依据。

Adopting the assumption that the elastic modulus of the rock mesoscopic unit approximately conforms to the Weibull distribution,a rock damage constitutive model was established based on the strain energy density theory.A method for determining the rock homogeneous degree coefficient m and the reduction factor of the elastic modulus K0 was proposed using the AE(acoustic emission)energy signal and the rock longitudinal wave velocity,and the parameters were corrected as well.The uniaxial loading simulation was carried out by using the established damage constitutive model,and the simulation results were compared with the existing theoretical model and the uniaxial loading experimental results.It is shown that the proposed model can well describe the stress-strain relationship and acoustic emission conditions of specimens.The model was further used to simulate the repeated loading of plaster specimens and then to analyze stress,strain and acoustic emission characteristics,and comparison with the laboratory results was conducted.The research shows that the higher the homogeneous degree of the specimen is,the more obvious the characteristics of the brittle failure,and that the calculated results of m and K0,which are determined based on the AE signal and the rock longitudinal wave velocity,agree with the experimental results.The established model provides a new theoretical basis for comprehensively considering the effects of rock homogeneous degree and repeated loading on rock specimens.