考虑应变软化和扩容的圆形巷道围岩强度准则效应

Effect of strength criteria on surrounding rock of circular roadway considering strain softening and dilatancy

为了研究强度准则效应对圆形巷道围岩稳定性的影响,首先对Mohr-Coulomb(MC)准则、Drucker-Prager(DP)准则、统一强度理论和Mogi-Coulomb(MO)准则等4种岩石材料常用的强度准则进行归纳总结,得到了平面应变条件下统一形式的屈服方程;然后将巷道围岩划分为破碎区、塑性软化区和弹性区,同时引入强度参数软化模量和扩容系数,考虑中间主应力效应、岩石峰后应变软化和扩容特性,推导了巷道围岩应力、位移和塑性区半径统一解,并对新解的各影响因素进行了对比分析。分析结果表明:本文所提出的新解不仅形式简洁,而且可以灵活匹配不同的岩石强度准则;不考虑中间主应力效应的强度准则相对偏于保守,考虑中间主应力效应时,MO准则和权系数<0. 5的统一强度理论计算得到的塑性区半径和位移处于中间水平,而外接圆DP准则和权系数>0. 5的统一强度理论对中间主应力效应考虑较多,选用时需谨慎;应变软化会使塑性区内围岩的性质得到进一步劣化,出现更大范围的破碎区,提高破碎区残余强度是一种有效的支护方法;巷道围岩的扩容特性不仅与剪胀角有关,而且还与塑性势函数有关,不考虑扩容将会低估围岩的真实变形。研究结果可为巷道围岩稳定性评价和支护设计提供重要理论参考依据。

In order to study the effect of strength criteria on the surrounding rock stability of circular roadway,under the plane strain condition,a unified yield equation was firstly summarized for four commonly used strength criteria of rock materials,such as Mohr-Coulomb(MC)criterion,Drucker-Prager(DP)criterion,uniform strength theory and Mogi-Coulomb(MO)criterion.Then,the circular roadway surrounding rock was divided into fracture zone,plastic softening zone and elastic zone,and the softening modulus of strength parameters and coefficients of dilatancy were introduced by considering the intermediate principal stress effect,post-peak strain softening and dilatancy.Furthermore,the new unified solutions for stress,displacement and plastic zone radius of surrounding rock had been deduced,and the comparative analyses were conducted on the various influence factors of the new solutions.It was found that the new solutions proposed in this paper not only have the form of conciseness,but also can flexibly match different rock strength criteria.The strength criteria without considering the effect of the intermediate principal stress are relatively conservative.When considering the effect of intermediate principal stress,the radius and displacement of the plastic zone calculated by the MO criterion and the unified strength theory with weight coefficient less than 0.5 are in the middle level.The circumcircle DP criterion and the unified strength theory with weight coefficient greater than 0.5 have more considerations for the effect of the intermediate principal stress,which should be selected carefully.The strain softening causes the properties of the surrounding rock in the plastic zone to be further degraded,resulting in a wider range of fracture zone.Increasing the residual strength of the fracture zone is an effective support method.The dilatancy is not only related to the dilatancy angle,but also related to the plastic potential function,in addition,the actual deformation of surrounding rock will be underestimated without the consideration of dilatancy.The results can provide an important theoretical basis for roadway surrounding rock’s stability evaluation and quantitative support design.