Fundamental Concept of Designing Tunnel Supports in Consideration of Elasto-plastic and Strain Softening Behavior of Rock

Abstract

The rapid increase in tunnelling projects requires better design methods which can deal with the post-peak behavior of soft rock subjected to heavy loads. The analytical solution for strain softening behavior of rock around a circular opening is derived from the strain energy theorem employing Coulomb's yield criterion. Using a simplified stress-strain relation, it is possible to obtain uniquely the magnitudes of stress, strain and displacement in elastic, softening and flow states by using only 10 input data : radius of a circular opening, hydro-static initial stress field, equivalent inner pressure to reaction of supports, elastic modulus, Poisson's ratio, negative gradient of deformation coefficient, and peak and residual strengths (uniaxial compressive strengths and angles of internal friction). Case studies conclude that a small increase of inner pressure has a large influence on the width of the plastic zone in rock which has induced softening. They also show that there is a big difference between a strain softening model and a conventional bi-linear elasto-plastic model, for the case of rock having a low competence factor. Herein, the authors discussed a procedure to design a support system, including rockbolts and shotcrete, by replacing the supports by an inner pressure acting on the surface of the tunnel wall.