多孔隙岩石加卸载力学特性及本构模型研究

为了研究岩石在加载-卸载过程中的应力-应变关系,以砂岩为例,对其进行常规三轴加卸载试验。分析了峰后卸载阶段岩石的非线性特性,对岩石的损伤变量进行定义,给出了峰后卸载过程中用于描述应力-应变关系的弹性模量模型。通过分析加载-卸载过程中的轴向应变与径向应变的关系,得到了卸载过程中泊松比模型。引入D-P塑性模型,针对砂岩的塑性硬化特性,对硬化函数进行修正,建立了与等效塑性应变相关联的损伤模型。将计算模型矩阵化后进行数值计算。在此过程中得到如下结论:多孔隙岩石在加载过程中表现出明显的非线性特征,随着体应力的增大,岩石的弹性模量逐渐增大。岩石峰后卸载过程中,当轴向应力大于围压时,应力-应变可以利用峰前弹性阶段的弹性模量模型乘以连续性因子进行描述。随着等效塑性应变的增大,泊松比先增大后减小,最终趋于稳定。峰后卸载过程中,等效塑性应变不发生变化,此时泊松比保持不变。利用提出的本构模型进行了数值计算,数值计算结果与试验结果进行对比,结果表明,提出的模型能够反映出岩石在峰后卸载过程中的应力-应变规律。

Mechanical properties and constitutive model of porous rock under loading and unloading

The conventional triaxial tests were carried out on sandstone to study the stress-strain relationship of rock during the loading-unloading process. The nonlinear characteristics of rock in the post-peak unloading process were analyzed, and the damage variable of rock was defined. Meanwhile, the elastic modulus model was established to describe the stress-strain relationship in the post-peak unloading process. The Poisson's ratio model under unloading was obtained by analyzing the relationship between the axial strain and radial strain in the loading-unloading process. The D-P plasticity model was introduced to modify the hardening function according to the plastic-hardening characteristics of sandstone, and a damage model associated with the equivalent plastic strain was established. At last, the established model was matrixed and numerically calculated. In this study, the following conclusions are obtained. During the loading process, the porous rock exhibits obviously nonlinear characteristics, and the elastic modulus of the rock increases with the increase of the body stress. During the post-peak unloading process, when the axial stress is greater than the confining pressure, the stress-strain can be described by the elastic modulus in the pre-peak elastic phase multiplying by the continuity factor. With the increase of equivalent plastic strain, Poisson's ratio increases first and then decreases until reaching a stable value. During the unloading process, the equivalent plastic strain maintains stable, and Poisson's ratio remains constant. The numerical calculation is conducted by the proposed constitutive model. Compared the numerical results with the experimental results, the proposed model can reflect the stress-strain relationship of rock in the post-peak unloading process.