含空洞缺陷的圆形硐室围岩应力弹性解析解

基于复变函数理论，建立真实平面上含空洞缺陷硐室外域和复平面上单位圆外域之间的映射关系，得到了在远场应力作用下含空洞缺陷圆形硐室围岩弹性应力解析解，分析了围岩应力分布规律以及缺陷位置、缺陷凸出程度和场地应力比对孔口应力分布的影响。结果表明：硐室缺陷部位应力分布与无缺陷情况具有明显区别，在缺陷中部应力集中效应明显，但在硐室孔壁与缺陷相交部位应力明显较小，甚至会出现环向应力为拉应力的情况；较轻微的缺陷便可引起较大的应力集中现象，且随缺陷凸出程度的增加，缺陷中部应力集中现象明显加剧；随着缺陷凸出方向与最小主应力方向夹角的减小，缺陷中部的应力集中现象加剧；当缺陷凸出方向与最小主应力方向平行时，随围压应力比的减小缺陷处的应力集中程度增大，而两者处于垂直状态时，随围岩应力比的减小缺陷处的应力集中现象逐渐降低。因此，在实际工程应用中应充分考虑空洞缺陷所引起的应力集中现象的影响。

ELASTIC ANALYTIC SOLUTION OF CIRCULAR CHAMBER SURROUNDING ROCK WITH VOID DEFECTS

Based on the complex variable function theory, the mapping relationship between the outer space of a chamber with defects and the outer space of a unit circle is established. The elastic analytic solution of the stress of the surrounding rock with defects under the action of far-field stresses is obtained. The stress distribution and the influence of the defect location, defect protrusion degree and stress ratio are analyzed. It is shown that the stress distribution in the defective part of the chamber is different from that in a non-defective chamber. The stress concentration is obvious in the middle of the defect, but the stress at the junction of the chamber and the defect is small and the circumferential stress may even become tensile stress. A slight defect can cause a significant stress concentration. The extent of stress concentration in the middle of the defect increases with the increase of the protrusion degree of the defect. It also increases with the decrease of the angle between protruding direction of defect and the minimum principal stress direction. If the protruding direction of the defect is parallel to the minimum principal stress direction, the stress concentration increases with the decrease of the stress ratio, while the relationship reverses if protruding direction is vertical to the minimum principal stress direction. Therefore, the effect of stress concentration caused by cavity defects should be fully considered in engineering applications.