A theoretical method to calculate ground stresses, strains and displacements around a circular tunnel under initially hydrostatic in situ stress field is newly presented. In the analysis, peak and residual strength criteria for rocks are proposed, and new boundary conditions between the peak and the residual strength regions are introduced in order to satisfy experimental results on failure strains and failure stresses. The influence of a non-linearity of stress-strain relationships, brittle-stress reduction, internal pressure and post-peak dilatancy on movements of the tunnel is analytically investigated.
Stresses and displacements in a rock surrounding a tunnel are fundamentally important in planning the tunnel and support systems, and which depend on stress-strain relationships, ground failure criteria, initial stresses of the ground and executive conditions. There are many literatures for calculation of ground response, most of which give closed form solutions to problems with hydrostatic initial stresses and circular geometry but some use numerical approaches such as a finite element method (FEM), a boundary element method (BEM) and a coupling method of FEM and REM, to solve problems involving more complex two or three dimensional tunnel geometry and stress fields[l-5]. Generally, stress-strain relationships for a rock show non-linearity, and mechanical parameters involved in the stress-strain relationships are affected by confining pressure. Also, under a high initial stress state, the strength of the rock surrounding the tunnel decreases from its peak strength to residual one and volumetric change in residual strength region gives big influence on tunnel displacements and support system. Experimental results show that the rock failure criterion can be expressed by stresses but there is a unique relation on failure strains. Yoshinaka and Yamabe[6] showed that the failure of rocks occurs nearly at the same strain regardless confining pressure. The failure condition of a rock surrounding a tunnel should satisfy the both experimental results on failure stresses and failure strains. If a linear stress-strain relationship in the peak strength region is used in the tunnel analysis, the residual strength region is determined only by using stress conditions at the boundary between the peak and the residual regions. In other words, the failure strains at this boundary is automatically determined from the stress conditions, and which do not coincide with experimental failure strains. Namely in this linear analysis, there is no way to satisfy the both conditions on failure stresses and failure strains. In order to make tunnel movements clear by taking into account the realistically mechanical behavior mentioned above and to contribute to practical tunnel engineering, this paper presents solutions to a simple axisymmetric tunnel problem. The influence of the non-linear stress-strain relationships, non-linear criteria, brittle stress reduction, internal pressure on tunnel movements is investigated.
The hyperbolic stress-strain equation was proposed by Kondner[7] to model the stress-strain curves of soils subjected to axial deformation. In this analysis, a generalized hyperbolic stress-strain relationship in octahedral space is employed until the stress reaches to the peak strength.
