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

Mohr-Coulomb elastoplastic damage constitutive model of rock and implicit return mapping algorithm in principal stress space

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。

An elastoplastic damage model is established based on Mohr-Coulomb(M-C) yield criterion considering the plastic deformation mechanism and stiffness degradation of rock material in the framework of elastoplastic damage theory. The internal variable-equivalent plastic strain is used to characterize the evolution of damage variable of rock material. The M-C yield criterion is a six-pyramid in stress space, stress update exist a 'singularity' problem on the six corners and ridge of a pyramid in the process of the numerical implementation. Angular point smoothing method is used to deal with this problem; but it inevitable lead to approximate results. The implicit return mapping algorithm of elastoplastic damage constitutive equation is deduced on the basis of the M-C constitutive numerical integral algorithm in principal stress space. It includes three main computational steps of elastic trial, plasticity correction and damage correction. Three conditions of flow vector returns to the main plane, ridge and sharp point are discussed in the plastic correction steps respectively. To solve the 'singularity' problem from the angle of principal stress space, the elastoplastic damage constitutive solver(RDM-C) is compiled using C++ language with object-oriented programming method. The uniaxial compression test, the foundation and cavity example are used to analyze and compare the results of calculation. The results show that the established elastoplastic damage constitutive model can well describe the main mechanics and deformation characteristics of quasi-brittle material, plastic zone and damage zone change trend; the program can carry out numerical analysis for geotechnical engineering problems, so as to give certain guidance to the site construction.