Symmetric wedge in the roof of a tunnel excavated in an inclined stress field

An analytical method is presented for the calculation of the stability of a two-dimensional symmetric rock wedge which is formed in the roof of an underground circular opening within an inclined biaxial stress field. The stability of the wedge is evaluated using a two-stage relaxation procedure. In the first stage, the forces acting on the joint faces of the wedge are calculated analytically from the elastic stress distribution around the opening. Thus, formulae are provided that calculate the horizontal and vertical force components on the wedge faces exerted by the surrounding rock mass. In the second stage, a steadily increasing pull out force is applied to the wedge which strains its joints. Failure is assumed to occur due to simultaneous yield along the face of one of the joints. The stability of the wedge, which is expressed by its pull out resistance, is calculated from limit equilibrium equations at failure. Finally, analytically calculated values of the pull out resistance of the wedge are compared with numerically obtained ones using a discrete element code.