非静水压力下圆形隧洞围岩塑性区分析

Analysis of elastoplastic interface of circle tunnel under non-hydrostatic loading

【目的】针对地下圆形洞室承受非静水初始压力作用下的平面应变问题,分析围岩的塑性区范围,为评价围岩稳定性和洞室支护结构的设计提供依据。【方法】对洞室围岩弹塑性边界两侧分别采用复变函数理论和滑移线场理论得出弹性区和塑性区应力组合表达式,根据弹塑性边界上应力相等得到边界方程;通过有限元算例将本研究方法的结果与卡斯特纳等方法的分析结果进行比较,并分析静水压力的变化情况。【结果】弹塑性边界为近似椭圆形,长轴与最大初始应力方向垂直;本研究方法与有限元分析结果更为接近,能够很好地反映洞室围岩塑性区范围;在静水压力下的分析结果与卡斯特纳公式所得塑性区半径一致。【结论】在非静水压力下塑性区全部包围洞室时,本研究方法能够更好地用于指导支护结构设计以及围岩稳定性评价。

【Objective】This study analysed the plastic zone of surrounding rock to overcome the plane strain problem of elastoplastic interface of underground circle tunnel subject to non-hydrostatic initial stress and to provide basis for evaluating surrounding rock stability and designing supporting structure.【Method】In elastic and plastic regions,the combined stress expressions were derived using complex function theory and slip line field theory,respectively.According to continuous stress condition in elastoplastic boundary,the interface equation was determined.Using FEM numerical result as benchmark,the result of proposed method was compared with methods including Kastner method and the change of hydrostatic loading was analyzed.【Result】The elastoplastic boundary was approximately elliptical,with long axis perpendicular to the maximum initial stress.The proposed method was similar to FEM analysis and the results well showed the plastic zone of surrounding rock.The radius of plastic zone under hydrostatic loading was consistent with Kastner method.【Conclusion】When the circular tunnel was completed covered under nonhydrostatic loading,the proposed method could be used to guide the design of supporting structure and e-valuation of surrounding rock stability.