考虑残余强度和阈值影响的岩石弹性损伤统计模型

基于统计学理论和损伤理论,考虑岩石的残余强度和损伤阈值影响,建立了三轴压缩条件下岩石损伤统计模型。以损伤模型为基础,利用岩石在低围压作用下应力应变的极值特性,导出了模型参数的统一求解方法。通过与试验数据的对比和验证发现:以Drucker-Prager准则和Mohr-Coulomb准则计算岩石微元强度比以轴向应变函数计算岩石微元强度能更好地反映岩石的力学特性,说明了岩石的破坏进程与其应力状态密切相关;为考虑残余强度,引入损伤变量修正系数,在此基础上提出一种求解该修正系数的新方法,从而使得模型得出的理论曲线能很好地接近试验数据;以屈服点的微元强度为损伤阈值点,避免了损伤系数在低荷载下不在0,1]之间的情况。最后通过分析岩石损伤变量的变化过程,证明了该模型可以很好地反映三轴受压状态下岩石的应力-应变关系。

Statistical Constitutive Model of Elastic Damage for Rock Considering Residual Strength and Threshold

Based on the statistical theory and damage theory, we establish a statistical damage model under triaxial compression in consideration of residual strength and damage threshold of rock. On the basis of the damage model presented, as well as extreme characteristics of stress?strain relationship at low confining pressure, we derive a uni?fied solution of mechanical parameters of the model. In comparison with the experimental data, we discover that mi?cro?unit strength of rock based on Drucker?Prager criterion or Mohr?Coulomb criterion is better than axial strain in reflecting rock mechanical properties, which shows that the failure and extension of rock is closely relevant with stress state. Then, in light of residual strength of rock, we introduce correction factor of damage variable and pro?pose a new method for solving the factor. The results show that, data from theoretical curve in the damage model is in correspondence with experimental data;by using stress yield point as damage threshold point, we can avoid the situation that value of damage factor is not in the interval from 0 to 1 at low loading. Finally, through analyzing the changing process of rock damage variable, we conclude that the damage model can well reflect the stress?strain rela?tionship of rock under triaxial compression.