深部围岩变形与破坏模型及数值方法研究

STUDY OF DEFORMATION AND FAILURE MODEL FOR DEEP ROCK MASS AND ITS NUMERICAL METHOD

为很好地描述岩石的剪切变形局部化现象,给出一个非连续平面应变弹塑性模型。这个模型以经典滑移线理论为框架,采用光滑函数组合描述位移场在滑移线上的间断;其控制方程是在局部正交曲线坐标系下由物理定律推导得出。材料的变形被划分为3个阶段:弹性、塑性及峰后局部剪切阶段。材料在滑移线上服从库仑强度准则。峰后在滑移线上出现断裂,材料初始黏聚力线性减小并最终消失。对模型进行有限元离散,并用Newmark法求解。采用Fortran语言编写代码并做一个简单算例。与传统连续介质模型比较,该模型中材料的应变、应力均不对称,材料的塑性行为、能量耗散与间断界面的变形运动密切相关。非连续模型能够深刻地描述深部围岩峰后剪切变形局部化现象。

A discontinuous elastoplastic model for plane strain was presented to depict rock shear strain localization phenomenon;and the classical slip line field theory is used as a frame in the model.The discontinuities of displacement field on slip lines are described with an assemblage of continuous functions;and control equations in the model are deduced from physical law in local orthogonal curvilinear coordinates.The deformation process is divided into three phases：elastic,plastic and post-peak shear localization phases.The materials on slip lines obey the Coulomb criterion and break on slip lines appeared after peak strength,while initial cohesion decreases linearly and finally disappears.The model is dispersed with finite element method（FEM） and solved with the Newmark method,which is actualized with Fortran code.A simple case is given to validate the model by comparing with the analytical solutions of traditional continuous model.Both strain and stress tensors of materials are asymmetric in the model;and plastic behavior and energy dissipation of materials depend on deformation motion at discontinuous interface.The discontinuous model can profoundly describe the post-peak shear localization phenomenon of deep rock mass.