An analytical solution for stresses induced by a post-tensioned anchor in rocks containing two perpendicular joint sets

A new analytical approach for the analysis of stress around a post-tensioned anchor in rock with two perpendicular joint sets is presented. The solution considers nonlinear shear stresses developed along the anchor bond length as well as debonding at the tendon–grout interface. The bearing plate effects are also considered in the analyses. The following assumptions are made: (1) homogeneous and orthotropic elastic rock; (2) half-space rock mass with plane strain conditions; (3) trilinear bond-slip model for the behavior of the tendon–grout interface; (4) an elastic anchor. The employed methodology is to decompose the anchor problem into two problems of simpler loadings: stresses produced under a rigid bearing plate and stresses induced by interfacial shear stresses mobilized along the bond length. Based on the proposed solution, an illustrative example is given and the results show that a large compressive region is formed around the anchor free length. Tensile stress concentrations are also observed around the bond length and near the rock surface outside the bearing plate. A parametric study is also conducted to investigate the effects of joint properties on the induced stresses. The results show that as the number of joints intersecting the anchor axis increases, the magnitude of compressive stresses in the free zone decreases, while the size of compression zone around the anchor increases. To verify the results of the analytical approach, a comparison is made with numerical results obtained by using the finite element method. The analytical solutions compare very well with the results obtained by numerical method.