基于三轴压缩试验的岩石统计损伤本构模型

基于三轴压缩试验,结合统计强度理论和连续损伤理论建立了一种岩石统计损伤本构模型,并对建立的本构模型的数学意义和物理意义进行了讨论分析。由此可知,统计损伤本构方程实质是用对应于某一屈服准则的等效应力表示的连续损伤演化方程,能较好地描述材料的非线性力学行为,也能逼近材料的弹性应力-应变关系。统计损伤本构模型的统计参数均可以通过单轴或三轴压缩试验得到,在利用三轴压缩试验的轴向实测应力、实测应变时应当对损伤本构模型进行修正。对于单轴压缩试验的压密阶段,还给出了初始损伤的估计方法。引入对数正态分布和Mohr-Coulomb准则,通过理论曲线与若干岩石单轴、三轴压缩试验曲线的对比,验证了所提出的统计损伤本构方程及其参数确定方法以及模型修正的合理性,同时也肯定了对数正态分布和Mohr-Coulomb准则在统计损伤本构研究中的适用性。

Statistical damage constitutive model for rocks based on triaxial compression tests

Based on the triaxial compression tests, a statistical damage constitutive model for rock materials is established using the continuum damage mechanics theory and the statistical strength theory. The mathematical and physical meanings of the model are discussed. It is known from the discussion that the statistical damage constitutive equation in essence is the damage evolution equation in terms of the equivalent stress of a yield criterion. It can describe well the nonlinear mechanical behaviors of rock-like materials and approach their elastic stress-strain relationship. The statistical parameters of the statistical damage constitutive model can be obtained through uniaxial or triaxial compression tests, while the model may be rewritten when using the measured stresses and strains in the compression direction of triaxial tests. An evaluation method for the initial damage variable with the stress-strain curve of uniaxial tests is proposed as well. The model in terms of the log-normally distributed damage and the equivalent stress of the Mohr-Coulomb yield criterion is verified through some uniaxial and triaxial compression tests on rocks. The theoretical fitting curves agree well with the test data, which shows the validity of the statistical damage constitutive equation including the determination method for its parameters and the reasonability of the proposed modification to the model equation. The lognormal distribution and the Mohr-Coulomb yield criterion can be chosen to establish the statistical damage constitutive model for rocks.