An analytical model for strength of jointed rock masses

Abstract An analytical model of rock mass with non-persistent joints is utilized to develop linear and nonlinear failure criteria based on intact rock strength, joint shear strength and joint persistence. The analytical model matches the solutions for the strength of fracture-free and fully jointed rocks and provides a reasonable transition of strength for rocks with non-persistent joints. Consistent with empirical evidence, the model predicts that increasing joint intensity and decreasing joint shear strength cause a reduction in the cohesive and frictional components of rock mass strength. Joint persistence in the analytical model has not only a physical definition as the normalized jointed area, but also a mechanical interpretation as the normalized reduction in strength due to the presence of joints. The relationship between the analytical model and the empirical Hoek-Brown failure criterion with Geological Strength Index (GSI) is explored. The analytical model of rock mass is utilized to develop and calibrate a quantitative GSI chart. The analytical model is validated using the results of comprehensive tests on undisturbed samples of naturally jointed Panguna andesite and thermally granulated Carrara marble. Practical application of the analytical model is illustrated by numerical back analysis of displacements around the Nathpa Jhakri powerhouse cavern.