基于复变函数不同形状的巷道围岩应力分析

Stress analysis of roadway surrounding rock with different shapes based on complex function

深埋巷道开挖后围岩应力重新分布,影响巷道稳定。因此分析巷道围岩二次应力分布状态对于评估围岩稳定性或设计支护参数具有重要意义。目前岩石力学相关理论中讨论了圆形巷道、椭圆形巷道和矩形巷道二次应力弹性分布特征,缺乏对六边形巷道的分析。本文从弹性力学的孔口问题为切入点,基于复变函数理论,通过保角变换将矩形、六边形巷道转化为单位圆,结合弹性力学理论建立了矩形、六边形巷道围岩分析的力学模型,并分析得到巷道围岩应力分布的解析解。将解析结果与数模拟分析结果对比可知,相同结构巷道围岩二次应力分布一致且大小基本相同,就应力集中情况而言,六边形巷道优于矩形巷道。

The stress of surrounding rock is redistributed after deep roadway excavation,which affects the stability of the roadway.Therefore,the analysis of the secondary stress distribution of roadway surrounding rock is of great significance for evaluating the stability of surrounding rock or designing support parameters.At present,the characteristics of secondary stress elastic distribution of circular roadways,oval roadways,and rectangular roadways are discussed in the relevant theories of rock mechanics,but there is a lack of analysis of hexagonal roadways.In this paper,starting from the orifice problem of elasticity and based on the theory of complex function,rectangular and hexagonal roadways are transformed into unit circles by conformal transformation.Combined with the theory of elasticity,the mechanical model of surrounding rock analysis of rectangular and hexagonal roadways is established,and the analytical solution of stress distribution in the surrounding rock of the roadway is obtained.The comparison between the analytical results and the numerical simulation results shows that the secondary stress distribution of the surrounding rock of the roadway with the same structure is the same and the magnitude is basically the same.In terms of stress concentration,the hexagonal roadway is better than the rectangular roadway.