عنوان مقاله [English]
A powerful method for analysis of stress and deformation around underground structures is the analytical method. Among the analytical models the one that utilizes complex potential functions for the solution have the advantages of applicability and accuracy. Most of the governing solutions are applied to the circular shape tunnels or simple cross-section tunnels with one- or two-dimensional in-situ normal stresses conditions. For the elliptical shape tunnels, there are three methods of solution based on the complex potential analysis. They are Stevenson method, Mushkelishvilli method, and Series method for approximation of the complex potential functions. In the above models, the solutions are not unique in details, but all satisfy the boundary conditions on the tunnel surface and far field stress situation. The interested readers to these analytical methods' solutions to tunnels with different shapes can refer to the papers and books governing Timoshenko and Goodier, Savin, and Muskhelishvilli. In the above models, the Stevenson one is a powerful and robust model for analysis of stress and deformation on and around the elliptical tunnels. Therefore, in this research, the complex potential and conformal mapping functions of Stevenson model are applied to obtaining the stress around those openings. The analysis is a two-dimensional plane stress or plane strain conditions. Therefore, the solution can be used for stress concentration around long tunnels. The parameters of the governing complex potential functions are obtained by satisfying the boundary conditions and the problem hypothesis. Then by applying the sequence differentiations of the potential and conformal complex functions to the formulation the normal and shear stresses around the tunnel are calculated. The stress field, which is considered around tunnel, is uniaxial and biaxial compressive stresses. The results from three solved problems show the similarity between the calculated stresses on the tunnel surface with the Muskhelishvilli model. The solution can also be used for the situation of in-situ shear stress boundary condition around tunnel. It is suggested that the formulation be developed for the deformations on the surface and around the elliptic tunnels.