Keywords: Hoek-Brown failure criterion, plasticity, elastic-brittle-plastic rock, finite element analysis, underground openings, dilatancy.

The conventionally used linear Mohr-Coulomb (M-C) failure criterion may not be suitable for jointed or many other types of rock mass. For such rock masses, the Hoek-Brown (H-B) failure criterion [1] is considered to be more appropriate. However, since the H-B failure criterion is non-linear and recently developed, this criterion has not yet been incorporated in most of the existing computational tools. A few specialized software packages such as the finite element code Phase2 have incorporated this failure criterion in the material model. However, due to the nonlinearity of the failure criterion, a computational difficulty arises in the analysis of stresses and displacements around underground openings in rock masses governed by this failure criterion. In some cases, the results may not converge to the analytical solutions, particularly for dilatant rock masses [2,3].

To circumvent these computational difficulties, several researchers have proposed various methods of linearizing the H-B failure criterion by obtaining equivalent M-C parameters. Most of the existing methods consider the plastic potential function to be linear. Recently, a novel method [2,3] was proposed to obtain the equivalent M-C dilation parameter for a non-linear plastic potential function corresponding to the H-B failure criterion. The underground opening was, however, considered to be circular and the in situ stress to be hydrostatic. However, in most of the practical situations, the underground opening is non-circular and the stress field is non-hydrostatic.

In this paper, the linearization method has been extended for the analysis of stresses and displacements around underground openings in the rock mass subject to non-hydrostatic in situ stresses. This is accomplished by using an analytical solution [3] for the axisymmetric plane strain analysis of underground openings. The equivalent hydrostatic in situ stress is assumed to be equal to the mean of the principal in situ stresses.

The proposed method is validated by conducting elastoplastic and elastic-brittle-plastic plane strain finite element analysis of circular and non-circular openings in dilatant and non-dilatant rock masses subject to hydrostatic and non-hydrostatic in situ stresses. The commercially available software Phase2 is used for the analysis. Several example problems are analysed and the proposed novel method is found to be very effective and efficient.

1

S.K. Sharan, "Analytical solutions for stresses and displacements around a circular opening in a generalized Hoek-Brown rock", International Journal of Rock Mechanics and Mining Sciences, 45, 78-85, 2008. doi:10.1016/j.ijrmms.2007.03.002

2

R. Naznin, "Equivalent Mohr-Coulomb dilation parameter for Hoek-Brown rock", M.A.Sc. thesis, Laurentian University, 2007.

3

S.K. Sharan, R. Naznin, "Equivalent angle of dilation for the analysis of underground openings in rock mass obeying Hoek-Brown plasticity", in "Proceedings of the Twenty-third Canadian Congress of Applied Mechanics", Vancouver, 140-143, 2011.

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