岩石摩尔-库仑弹塑性损伤本构模型及其主应力隐式返回映射算法研究

发布时间：2018-08-18 09:00

【摘要】：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。
[Abstract]:Considering the plastic deformation mechanism and stiffness degradation of rock in the framework of elastic-plastic damage theory, an elastic-plastic damage model based on Mohr-Coulomb (M-C) yield criterion is established. The evolution of rock damage variable is characterized by internal variable (equivalent plastic strain). Because the M-C yield criterion is a hexagonal cone in stress space, there is a singularity problem in the stress renewal of the hexagonal corner and prism in the numerical implementation, and the corner smoothing method can deal with this problem. But it inevitably leads to approximate results. Based on the M-C constitutive numerical integral algorithm, the principal stress space implicit return mapping algorithm for elastoplastic damage constitutive equation is derived, which includes three main steps: elastic prediction, plastic correction and damage correction. In the process of plastic modification, the "singularity" problem is solved from the point of view of principal stress space for the flow vector returning to the main plane, the left and right edges and the point of view respectively. The elastoplastic damage constitutive solution program (RDM-C) is developed by using C language and object-oriented programming method. The results of the program are analyzed and verified by uniaxial compression test and numerical examples of foundation and cavern. The results show that the elastoplastic damage constitutive model can well describe the main mechanical and deformation characteristics of rock materials and the trend of plastic and damage zones. The program developed by implicit integral algorithm based on principal stress space can be used for numerical analysis of geotechnical engineering problems and provide guidance and theoretical basis for field construction.
【作者单位】：大连海事大学道路与桥梁研究所;沈阳工业大学建筑与土木工程学院;
【基金】：国家自然科学基金(No.51608332,No.51678101) 辽宁省博士启动基金(No.201601160) 辽宁省教育厅项目(No.201564064)~~
【分类号】：TU45

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