Elasto-plastic solution of tunnel problems using the generalized form of the Hoek-Brown failure criterion

The Hoek-Brown failure criterion is a semi-empirical method widely used in the estimation of shear strength of rock. Among other parameters involved in this criterion, the coefficient a dictates whether the criterion applies to intact rock or rock masses (a = 0.5 for intact rock and a > 0.5 for rock masses). Most of the existing elasto-plastic solutions for tunnel problems in Hoek-Brown media consider an intact rock (i.e., a = 0.5). This is not only due to historical reasons (the failure criterion was originally developed for intact rock), but also due to the mathematical difficulties of deriving neat, closed-form expressions for the general case in which a ≥ 0.5. This paper presents a rigorous, elasto-plastic solution for the axi-symmetrical problem of excavating a circular tunnel in generalized Hoek-Brown material (a ≥ 0.5). The solution is obtained by re-writing the generalized Hoek-Brown failure criterion in terms of transformed stress quantities. Application of the transformation rule described in this paper to elasto-plastic problems of excavations in generalized Hoek-Brown materials is shown to bring significant advantages in the interpretation and extrapolation of results obtained with analytical and numerical methods.