Numerical appraisal of rock mass anisotropy effect on elastic deformations of a circular tunnel

Abstract

The paper describes effects of anisotropic mechanical properties of rock masses on elastic behaviour of a circular tunnel under both hydrostatic and non-hydrostatic in situ stress states. This study is based on field data obtained from two actual case studies. In both cases, the rock masses have transversely isotropic structures. Hence, a 2D finite element modelling based on the equivalent continuum approach is used for the analysis. The tunnel deformation behaviour has been investigated for both isotropic and transversely isotropic conditions. To evaluate the degree of anisotropy of rock mass, an “anisotropy index” and a “normalized displacement ratio” have been defined. The effect of orientation of the isotropic planes is further investigated. The results show that in a hydrostatic stress state, the maximum displacement always occurs in a direction perpendicular to the isotropic planes. In this case, three empirical equations have been developed to compute the normalized displacement ratio, the deviation, and the direction of displacement vector at any arbitrary point on the tunnel periphery. The results further show that if the anisotropy index increases, the displacement difference (the difference between the maximum and the minimum displacements) on the tunnel walls increases too. For the non-hydrostatic stress state, simultaneous effects of stress ratio, anisotropy index, and orientation of isotropic planes on normalized displacements have been investigated. In this case, the location of maximum displacement inclines towards the direction of major principal stress. This effect is more noticeable when the isotropic planes are oriented at an angle of 90° relative to the direction of the major principal stress. The paper also provides an empirical equation to determine the location of maximum displacement on the tunnel walls. Finally, the practical application of the results is further illustrated by an actual case study.