Thermal damage constitutive model for rock considering damage threshold and residual strength

Abstract

With the gradual depletion of mineral resources in the shallow part of the earth, resource exploitation continues to move deeper into the earth, it becomes a hot topic to simulate the whole process of rock strain softening, deformation and failure in deep environment, especially under high temperature and high pressure. On the basis of Lemaitre’s strain-equivalent principle, combined with statistics and damage theory, a statistical constitutive model of rock thermal damage under triaxial compression condition is established. At the same time, taking into account the existing damage model is difficult to reflect residual strength after rock failure, the residual strength is considered in this paper by introducing correction factor of damage variable, the model rationality is also verified by experiments. Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure, initiation, expansion, penetration, and the formation of macro-cracks under coupled effect of temperature and confining pressure. Rock thermal damage shows logistic growth function with the increase of temperature. Under the same strain condition, rock total damage decreases with the rise of confining pressure. By studying the electron microscope images (SEM) of rock fracture, it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite. The model parameter F reflects the average strength of rock, and M reflects the morphological characteristics of rock stress–strain curves. The physical meanings of model parameters are clear and the model is suitable for complex stress states, which provides valuable references for the study of rock deformation and stability in deep engineering.

摘要

随着地球浅部矿物资源逐渐枯竭, 资源开采不断走向地球深部, 模拟深部高温高压条件下岩石应变软化变形破坏行为是岩石力学研究的重要内容。 本文基于 Lemaitre 应变等价性理论, 结合统计学和损伤力学, 同时引入损伤变量修正系数考虑岩石残余强度对峰后曲线的影响, 建立了三轴压缩条件下岩石热力耦合统计损伤本构方程, 并通过试验验证模型的合理性。 研究结果表明: 温度–荷载总损伤演化曲线反映了岩石内部微裂纹闭合、 萌生、 扩展、 贯通、 直至出现宏观裂纹的全过程; 岩石的热损伤变量随温度的升高呈 logistic 函数增长; 同等应变情况下, 损伤变量随围压的升高而减小, 通过研究岩石破裂后 SEM 电镜图片, 推断出 35.40 MPa 是花岗岩的脆塑性转换临界围压; 模型分布参数 F 反映了岩石的平均强度, m 反映了岩石应力–应变曲线的形态特征。 该模型不仅能反映温度、围压对岩石损伤的影响, 而且能较好地反映岩石峰后残余强度阶段变形特征, 模型参数物理意义明确, 适用于复杂应力状态情况, 这对于研究深部岩石损伤软化问题具有重要的意义。