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本文运用复变函数方法给出了带有一个裂隙的圆孔周围的应力分布,特别在单轴或双轴应力场中,对任意方位的单一裂隙的解答都可用该方法获得。在该方法中,使用施瓦茨(Schwartz)积分推导出了从带有任意方位单一裂隙的圆孔到单位圆的映象函数。 根据这个理论结果,完成了对五种不同裂隙方位和四种不同裂隙长度的数值计算,获得了相应的圆孔周围的应力相位移分布。运用岩石的脆性断裂理论,分析了这些裂隙对圆形隧道周围应力和位移分布及围岩断裂的影响。分析结果表明裂隙的方向和位置对围岩断裂的影响是显著的。
In this paper, the stress distribution around a circular hole with a crack is given by the method of complex variable function. Especially in the uniaxial or biaxial stress field, the solution to a single crack of arbitrary orientation can be obtained by this method. In this method, the Schwartz integral is used to derive the mapping function from a circular hole with a single flaw in any orientation to a unit circle. Based on this theoretical result, the numerical calculation of five different fracture orientations and four different fracture lengths was completed, and the corresponding phase displacement distribution around the circular hole was obtained. The brittle fracture theory of rock is used to analyze the influence of these fractures on the stress and displacement distribution around the circular tunnel and the surrounding rock fracture. The analysis results show that the influence of the direction and position of the fracture on the fracture of the surrounding rock is significant.