考虑峰后应变软化与扩容的圆形巷道围岩弹塑性D-P准则解

Elastoplastic solution for surrounding rock of circular roadway based on D-P criterion by considering post-peak strain softening and dilatancy

将圆形巷道围岩划分为塑性残余区、塑性软化区和弹性区,引入强度参数软化模量和扩容系数及剪胀角,考虑岩石峰后应变软化和扩容特性。基于Drucker-Prager准则和非关联流动法则,建立剪胀角与软化区扩容系数的关系,用洛德参数描述中间主应力大小,计算出弹塑性区应力、位移和塑性区半径的解析表达式。通过算例分析了不同影响因素对巷道围岩塑性区半径和位移的影响。分析结果表明:中间主应力对围岩的塑性区和位移大小具有重要影响且表现出区间性;内聚力和内摩擦角的残余值越大,塑性区半径和位移越小;剪胀角的选取对于分析扩容具有很大影响;降低软化模量和提高支护阻力能不同程度地控制围岩的变形;软化主要影响塑性残余区半径而扩容主要影响围岩的位移。分析结果可以为巷道围岩稳定性评价和支护定量设计提供理论依据。

In this paper, the circular roadway surrounding rock was divided into plastic residual zone, plastic softening zone and elastic zone, and the softening modulus of strength parameters, coefficients of dilatancy and shear dilatancy angle were introduced by considering the rock post-peak strain softening and dilatancy. Meanwhile, based on Drucker-Prager criterion and its generalized non-associated flow rule, the relationship between dilatancy angle and softening zone coefficient of dilatancy was estab-lished. By using Lode parameter to describe intermediate principal stress, the analytical solutions of elastoplastic stress, displacement and plastic zone radius were obtained. In addition, an example was analyzed to study the effect of different factors on plastic zone radius and displacement of surrounding rock. The results show that the intermediate principal stress has significant effect on plastic zone radius and displacement, and presents the interval characteristic. The larger the residual value cohesive force and internal friction angle are, the smaller the plastic zone radius and displacement are. Meanwhile, the selection of dilatancy angle has great influence for analysising dilatancy, and softening modulus de- creasing and supporting resistance increasing can control the surrounding rock deformation in different drgree, while softening mainly has effect on plastic residual zone radius and dilatancy mainly has affect on displacement of surrounding rock.The study in this paper can provide theoretical basis for surround- ing rock stability evaluation and supporting quantitative design.