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在弹塑性损伤理论框架内考虑岩石的塑性变形机制和刚度退化,建立基于Mohr-Coulomb(M-C)屈服准则的弹塑性损伤模型,采用内变量即等效塑性应变表征岩石损伤变量的演化。由于M-C屈服准则在应力空间为一个六棱锥,在数值实施过程中六棱锥角点和棱线上的应力更新存在“奇异性”问题,角点光滑化方法可以处理该问题,但其不可避免的导致近似的计算结果。在M-C本构数值积分算法的基础上,推导弹塑性损伤本构方程的主应力空间隐式返回映射算法,包括弹性预测、塑性修正和损伤修正3个主要计算步骤。在塑性修正过程中,针对流动向量返回到主平面、左右棱线和尖点3种情况分别进行讨论,从主应力空间的角度出发解决“奇异性”问题。采用面向对象的编程方法,使用C++语言开发弹塑性损伤本构求解程序(RDM-C),并采用单轴压缩试验、地基和洞室算例对程序计算的结果进行分析和验证。研究结果表明,所建立的弹塑性损伤本构模型能够较好地描述岩石材料主要的力学和变形特性、塑性区和损伤区变化趋势。基于主应力空间的隐式积分算法所开发的程序可以进行岩土工程问题的数值分析,对现场施工提供指导和理论依据。
In the framework of elasto-plastic damage theory, the plastic deformation mechanism and stiffness degradation of rock are considered. The elastoplastic damage model based on the Mohr-Coulomb (M-C) yield criterion is established and the evolution of rock damage variables is characterized by the internal variable, ie equivalent plastic strain. Because the MC yield criterion is a hexagonal pyramid in the stress space, the problem of “singularity ” exists in the stress update at the hexagonal pyramid corner and ridge during the numerical implementation. The corner smoothing method can handle this problem, but it can not Avoid approximating the result of the calculation. Based on the M-C constitutive numerical integration algorithm, the implicit return mapping algorithm for the principal stress space of elastoplastic damage constitutive equations is derived, which includes three main steps of elastic prediction, plasticity correction and damage correction. In the process of plasticity correction, three cases of the return of the flow vector to the main plane, the left and right ridges and the cusp are respectively discussed, and the problem of “singularity ” is solved from the viewpoint of the main stress space. The object-oriented programming method was used to develop elasto-plastic damage constitutive program (RDM-C) using C ++ language. The results of program calculation were analyzed and verified by uniaxial compression test, foundation and cavern case study. The results show that the established elastic-plastic damage constitutive model can describe the main mechanical and deformation characteristics of rock materials, and the trend of plastic zone and damage zone. The program developed by the implicit integration algorithm based on the principal stress space can carry out numerical analysis of geotechnical engineering problems and provide guidance and theoretical basis for on-site construction.