基于Drucker-Prager准则的深部巷道破裂围岩弹塑性分析

Elastoplastic analysis of cracked surrounding rock in deep roadway based on Drucker-Prager criterion

基于Drucker-Prager屈服准则和非关联流动法则,考虑中间主应力、塑性区弹性应变及岩体剪胀性的影响,推导了深部圆形巷道围岩应力、变形及塑性区半径的封闭解析解。结合工程实例,对比分析了不同屈服准则和围岩参数对围岩状态变化的影响,研究结果表明:中间主应力对围岩破裂范围和表面位移均具有重要影响,且表现出明显的区间效应;剪胀角越大,扩容系数越大,围岩破裂范围与表面位移也就越大;围岩参数(残余黏聚力、残余内摩擦角、初始黏聚力)和支护阻力越大,围岩塑性区及破裂区范围均越小;D-P准则解分别与统一强度准则解、双剪强度准则解和M-C准则解相比,围岩破裂范围及表面位移均偏大,但与M-C准则解最为接近;在满足相同围岩变形条件下,D-P准则解所需支护阻力较其他3种准则解均较大,更偏向于刚性支护形式,分析结果可为巷道围岩稳定性评价与支护设计提供重要理论依据。

Based on Drucker-Prager yield criterion and non-associated flow rule,the closed analytical solution of stress,displacement and plastic zone radius has been deduced by considering the influence of intermediate principal stress,the elastic strain of plastic zone and rock dilatancy. By comparing numerical examples and analyzing the influences of different yield criteria and parameters on surrounding rock＇s stress,displacement and plasticity,the research results show that with a significant interval effect,the intermediate principal stress has a significant influence on the plastic deformation of surrounding rock,the distribution of fracture zone and the surface displacement; the surrounding rock plasticity,the radius of fracture zone and surface displacement become larger as dilatancy angle and dilation coefficient increase; the surrounding rock plasticity and the radius of fracture zone become smaller with the increase of supporting resistance and surrounding rock parameters（ residual cohesion,residual internal friction angle,initial cohe-sion）; comparing the research results with unified strength criterion,twin shear strength criterion and Mohr-Coulomb criterion,the surrounding rock plasticity,the radius of fracture zone and surface displacement are fairly large and they are closest to Mohr-Coulomb; under the same conditions of surrounding rock deformation,the supporting resistance required by Drucker-Prager criterion is larger than that of other three criteria and it is more inclined to take the form of rigid support form. The results can provide an important theoretical basis for roadway surrounding rock＇s stability evaluation and quantitative support design.