An iterative method for the linearization of nonlinear failure criteria

Linearization of a nonlinear failure criterion may be required if a software incorporating the nonlinear failure criterion is not readily available or if an additional computational difficulty is encountered due to the nonlinearity of the failure criterion. In this paper, a novel method is proposed for the linearization of nonlinear failure criteria. The proposed method is based on an iterative procedure and the least-squares regression is used for the linearization. The material is assumed to be elastic-perfectly plastic. By conducting analytical and finite element analyses of stresses and displacements around underground openings in rock mass governed by the generalized Hoek-Brown failure criterion, it is shown that the proposed method is convergent, efficient and effective.