Analytic solution of a shallow buried tunnel excavated in orthotropic rock mass

Rock masses naturally exhibit significant anisotropy, however, majority of the analytic solution of a half-plane with a hole are based on the isotropic assumption, which would result in the larger difference from the real scenario. Hence, the purpose of present study is to derive the general form of the stress functions in an anisotropic medium because it can be easily used to solve the problem of the unbalanced forces by tunnel excavation. Since the affine transformation is used, the computing model may become asymmetrical and conventional mapping functions are difficult to be obtained. Without loss of generality, decoupling conformal mapping functions are introduced. By adopting Discrete Fourier Transform, all coefficients of the stress function can be determined. Compared with the numerical results, the analytical solution of stress around the unlined tunnel is higher precision. In the present study, the effects of the depth, the tectonic stress and the anisotropic parameters are discussed on the stress field and the displacement field. When compared to the isotropic case, it is unfavorable for the safety and stability of tunnel if the problem is solved under the isotropic condition.