Elastic Analysis for Subaqueous Tunnel Surrounding Rock via the Complex Variable Method

Generally speaking, the subaqueous tunnels can be regarded as the shallow-buried ones. Consequently, the classical problem of an elastic half plane with a round cavity, loaded arbitrarily along the surface boundary, can be used to obtain the stress and displacement fields of the surrounding rock for this type of tunnels. The solution uses the complex variable method, with a conformal mapping onto a circular ring in the image plane. Because of the convergence of the complex potentials throughout the annular region, the coefficients in the Laurent series expansion form for complex functions can be determined by a system of liner recurrent equations, obtained from both the horizontal and the cavity boundary conditions. The stresses and deformations of the surrounding rock can then be calculated via some relevant equations. The whole calculation program should be coded by Fortran language. As an example, the case of a specific underwater tunnel is considered in some detail eventually.