北山花岗岩细观损伤力学本构模型研究

 甘肃北山花岗岩是一种典型的准脆性材料，与裂纹有关的非弹性变形和损伤发展是其材料劣化和结构破坏的基本力学机制。基于均质化方法和热动力学理论，提出模拟北山花岗岩非线性力学行为的损伤–摩擦耦合本构模型。把花岗岩看成是由基质和大量分布的微裂纹构成的非均质材料，并以固体基质和币型微裂纹构成的特征单元体为研究对象。通过均质化方法确定特征单元体的自由能表达式，推导出与非弹性应变和损伤变量相关联的热动力学力，分别采用关联的广义库仑摩擦准则和基于应变能释放率的损伤准则来描述非弹性应变和损伤的演化。通过损伤–摩擦耦合分析进行强度研究，获得岩石强度的解析表达式，并明确损伤抗力函数的基本特征。运用所提出的细观力学损伤模型对北山花岗岩的三轴压缩力学特性进行模拟。数值模拟结果和试验数据具有较好的一致性，可验证模型的准确性，显示多尺度本构模型的突出优点。

A MICROMECHANICAL CONSTITUTIVE DAMAGE MODEL FOR BEISHAN GRANITE

Beishan granite is a typical quasi-brittle rock and its material degradation and structure failure is mainly attributed to the inelastic deformation and the damage development due to microcracks. This paper is devoted to modeling the nonlinear mechanical behaviors of Beishan granite. A damage-friction coupled model was developed based on the method of linear homogenization and the irreversible thermodynamics. The granite was viewed as a heterogeneous material composed of the matrix and a large number of randomly distributed microcracks，and thus our studies started with a representative elementary volume(REV)，i.e. the matrix-cracks system. The free energy of the REV was determined with Mori-Tanaka method and the thermodynamic forces associated with the inelastic strain and the damage variable were derived. The development of the inelastic strain and the damage were determined with the criterion of associated general Coulomb friction and the damage criterion of rate-based strain energy release respectively. An explicit function of the rock strength was derived during the damage-friction coupled analyses. The essential feature of the damage resistance function was described. The proposed multiscale model was finally applied to simulate a series of triaxial compression tests on Beishan granite. The comparison between the numerical predictions and the experimental data validated the model and showed outstanding advantages of the multiscale constitutive formulations over the phenomenological models.