Abstract Underground rock engineering projects are often subjected to cyclic loading such as earthquake, rock blasting. A suitable constitutive model for rock materials modeling the deformation failure characteristics of rock materials subjected to triaxial cyclic loading is significant when evaluating the long-term stability of the engineering. To date, however, there have been notably few studies on proposing constitutive models for rock materials under triaxial cyclic loading. The paper presents and validates the formulation of a new constitutive model able to reproduce the cyclic behavior of rock materials under triaxial cyclic loading. The constitutive model is based on the subloading surface theory and the modified cohesion weakening and frictional strengthening (CWFS) model. It contains kinematic hardening of the subloading surface, isotropic softening on the cohesion and isotropic hardening on the friction angle, and the effect of confining stress. Further, the model is numerically implemented in a self-developed finite element program using elastic prediction-plasticity correction method. In addition, the model is validated against two different rock materials (T2b marble and crystalline marble) under triaxial damage-controlled and constant amplitude cyclic compression loading. A reasonable consistency is observed between the numerical and experimental results for the stress-strain curves, the evolution of residual strain with number of cycles, degradation of strength and the effect of confining stress. It shows that the model can effectively reproduce the cumulative plastic deformation, hysteretic loop, damage and the effect of confining stress of rock materials under triaxial cyclic loading. Therefore, the proposed model can provide a helpful method to describe the main deformation and strength properties of rock materials under triaxial cyclic loading, and lays a foundation for the accurate analysis of the response of underground rock engineering under cyclic loading.

中文翻译：

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三轴循环压缩岩石材料的本构模型

摘要 地下岩石工程经常受到地震、岩石爆破等循环荷载的影响。在评估工程的长期稳定性时，一个合适的岩石材料本构模型对岩石材料在三轴循环载荷下的变形破坏特征进行建模具有重要意义。然而，迄今为止，关于在三轴循环载荷下提出岩石材料本构模型的研究非常少。本文提出并验证了一种新的本构模型的公式，该模型能够重现岩石材料在三轴循环载荷下的循环行为。本构模型基于子加载表面理论和修正的凝聚力减弱和摩擦强化 (CWFS) 模型。它包含子加载表面的运动硬化，各向同性软化对内聚力的影响，各向同性硬化对摩擦角的影响，以及围压的影响。此外，该模型是在自行开发的有限元程序中使用弹性预测-塑性校正方法进行数值实现的。此外，该模型在三轴损伤控制和恒幅循环压缩载荷下针对两种不同的岩石材料（T2b 大理岩和结晶大理岩）进行了验证。观察到应力-应变曲线的数值和实验结果、残余应变随循环次数的演变、强度退化和围压效应的合理一致性。表明该模型能有效再现累积塑性变形、滞回环、三轴循环荷载作用下岩石材料的损伤及围压效应[J]. 因此，该模型可为描述三轴循环荷载作用下岩石材料的主要变形和强度特性提供有用的方法，为准确分析循环荷载作用下地下岩石工程的响应奠定基础。