Solution of Minor Principal Stress for Generalized Hoek–Brown Rock Material in Two Dimension Using Newton–Raphson Method

Two dimensional generalized Hoek et al. (2002) criteria is very popular for determining the strength of rock materials worldwide. While using this criterion, it is usually required to determine the minor principal stress first. Since, GHB criteria is a nonlinear function of minor principal stress, its solution is not very straightforward and simple. Few analytical and numerical solution to find out the value of minor principal stress already exist. Some solutions are unable to give acceptable value of minor principal stress for whole range of geological strength index (GSI) values of rocks. In the present paper, a solution strategy based on Newton–Raphson method to determine the value of minor principal stress from GHB criteria in two dimensions is presented. The obtained solution of minor principal stress for few problems are compared with the solutions from existing literature. The proposed solution strategy can determine the value of minor principal stress for whole range of GSI (0–100) very accurately with very less computational effort. Finally, the variation of various rock strength parameters such as angle of internal friction, cohesion and shear stress are investigated for different values of GSI and disturbance factor (D).