ABSTRACT:

Sedimentary rock with layered structure accounts for 2/3 of global land area, and lots of metamorphic rock also has significant features of layered structure, so there are many stability problems about layered rock mass in geotechnical engineering. Layered rock mass is generally considered to be transversely isotropic solid. Based on the complex variable expression of stress function, the complex variable expression of displacement components of transversely isotropy is deduced; the displacement analytical solution of a deep tunnel with arbitrary cross section in transversely isotropic rock mass is derived by conformal mapping method. Although the cross section of the tunnel is assumed to be parallel to the isotropic plane, the displacement analytical solution indicates that radial displacement of surrounding rock is related not only to elastic modulus and poisson ratio on the isotropic plane but also to that in the direction normal to the isotropic plane.

1 INTRODUCTION

The displacement about a deep tunnel is of interest to the geotechnical engineers. In order to study the stability and support of the tunnel, it is essential to find the displacement analytical solution. Poulos (1974), Pender (1980), Carter (1982) andVerruijt (1997) gave the displacement analytical solution of a circular tunnel respectively under different boundary conditions. Exadaktylos (2002) gave the displacement analytical solution of a semi-circular tunnel, Muskhelishvili (1953) and Cai (2008) gave the displacement analytical solution of an elliptic tunnel respectively under different boundary conditions. Lu (1998) obtained the displacement analytical solution of a tunnel with arbitrary cross section. There have never been literatures on the displacement analytical solution of a tunnel with arbitrary cross section in anisotropic rock mass. Based on the above research, in this paper, the author tries to seek the displacement analytical solution of a deep tunnel with arbitrary cross section in transversely isotropic rock mass.

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