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.