基于均匀化理论的岩石细观力学损伤模型及其应用研究

RESEARCH ON HOMOGENIZATION-BASED MESOMECHANICAL DAMAGE MODEL AND ITS APPLICATION

基于均匀化理论构建细观力学损伤模型的热动力学框架,提出运用Eshelby夹杂问题解的岩石损伤摩擦耦合模型。其中,岩石被认为是由弹性固体基质和裂纹构成的非均匀材料。在细观力学分析的基础上,首先导出裂隙岩体宏观自由能的一般表达式及相应的热力学力,进而采用库仑型滑动摩擦准则和非关联流动法则来确定非弹性应变的变化率;损伤的演化用修正的Mazars损伤准则来描述。该模型能够考虑岩石及岩石类材料在外力作用下的主要力学现象如非线性应力–应变关系、材料损伤的各项异性、裂纹面内损伤和滑移的耦合、静水压力对力学响应的影响、体积膨胀以及裂纹闭合效应等。用提出的细观损伤模型模拟大理岩的常规三轴试验。研究结果表明,模拟值和试验值之间有较好的一致性,从而验证了模型的合理性和有效性。

The present study aims to establish a homogenization-based constitutive thermodynamic framework for the description of anisotropic damage by mesocracking.With the help of the basic solution to Eshelby′s matrix-inclusion problem,a new micromechanics-based damage-friction coupled model is developed for rock materials,which are considered here as heterogeneous solids composed of elastic solid matrix and imbedded penny-shaped microcracks.From mesomechanical analysis,the general form of the macroscopic free energy is obtained,from which the conjugated thermodynamic forces are derived within the standard thermodynamic framework.Further,similar to classic plasticity theory,a Coulomb-typed interfacially frictional sliding criterion at mesoscopic scale is used as loading function and as commonly;a non-associated flow rule is adopted in determination of the evolution rate of friction-induced inelastic deformation.The proposed model has the ability of taking into account the main phenomena due to microcracking such as nonlinear stress-strain relations,damage induced anisotropic behaviours,coupling between damage and friction on cracks surfaces,sensitivity of mechanical responses to confining pressures,volumetric dilation as well as unilateral effects due to total or partial closure of microcracks,etc..In order to illustrate the predictive ability of the proposed model,comparisons are performed between the model predictions with experimental data from conventional triaxial compression tests on a marble.The results show a generally good agreement;and the validation of the proposed mesomechanics-based damage model is checked.