类岩石材料微裂纹损伤模型分析

THE DAMAGE MODELS FOR ROCK-LIKEMATERIALS WITH MICROCRACKS

本文建立了压缩荷载作用下类岩石材料的二维和轴对称微裂纹损伤的有效场模型及三维微裂纹损伤的Ｔａｙｌｏｒ模型，分析了微裂纹随外加应力而发生扩展的运动过程，根据扭折型裂纹模型建立了损伤柔度的求解公式，并给出了算例。二维模型和轴对称模型的数值模拟结果表明本文提出的有效场模型的计算结果介于Ｔａｙｌｏｒ模型和自洽模型的计算结果之间，与实验结果具有良好的一致性。三维模型的数值模拟结果则表明中主应力对类岩石材料的损伤本构关系具有显著的影响，表现为随中主应力的增加，最大主应力方向的变形减小，最小主应力方向的变形增大；但当最大主应力较大时，大的中主应力反而使最大主应力方向的变形增加，最小主应力方向的变形减小。

Two-dimensional, axisymmetric effective field damage models and three-dimensionalTaylor damage model are proposed for rock-like materials with microcracks in compression. Kinetic equations are developed to describe the microcrack evolution as a function ofthe applied loads. The microcrack-induced inelastic compliances are derived in terrns ofkinked crack model. In addition, a number of illustrative examples are given. The numerical simulations of two-dimensional and axisymmetric damage models show that the simu-lated curves of the proposed models are betweem that of Taylor model and self-consistentmodel and agree quite well with available experinlental results. The numerical simulationsof three-dimemsional damage model indicate that the intermediate principal stress has astrong influence on the damage constitutive relations of rock-like materials. It is shownthat the intermediate principal stress(σ_(22)= q )makes the strain decrease in maximum principal stress direction and increase in minimum principal stress direction; but when themaximum principal stress is above a certain value, the function of intermediate principalstress ( σ_(22)= q) is to make the strain in the direction of maxinium principal stress (σ_(33)=q)increase and the strain in the direction of minimum principal stress decrease.