Stress Distribution Around Rock Bolts: Elastic Stresses

Rock bolts are commonly used to support and stabilize the rock around excavated openings. The assumption is made that the less competent rock near the surface can be supported by bolting it to more competent rock away from the surface. Naturally, a rock bolt can be no more effective than its anchoring mechanism which induces a stress field into the surrounding rock. Details of various types of bolts have been described e1sewhere.l The purpose of the present investigation is to study the stress distribution around an expansion-type rock bolt anchor, using the theory of elasticity. The elastic stress distribution provides some insight into the behavior of rock bolt anchors which may eventually lead to improved designs. Very little information is available on the induced stress field which is rather complex; consequently, photoelastic techniques have been used to obtain a qualitative picture of the stress ditribution.2 The present work provides quantitative information on the stress field induced by an idealized distribution of surface tractions, provided that the assumptions of the linear theory of elasticity are approximately satisfied. FORMULATION OF THE PROBLEM Consider an elastic region which extends to infinity and contains a circular cylindrical hole as shown in Fig. 1. The hole is assumed to be the bolt hole and the surface tractions shown are assumed to be caused by an idealized rock bolt anchor. The relationship between the idealized