Analytical solution of stress around square tunnels by complex potential function method

Any physical problem can be explained by the mathematical model. Most of those models are partial differential equations. The mechanic behaviors of rock mass around any underground structure can be defined by partial differential equations. By solving this equation, the stresses and deformations around the tunnel can be calculated .The stability of tunnel can be defined by using the calculated stress concentration around tunnel. In this paper the stress concentration around the square tunnel is obtained by the analytical solution and using complex potential equations. The square cross-section of tunnel transfer to circular one by the method of conformal mapping. Here the rock mass considered elastic and isotropic. The results show, with increasing the components of mapping series, the tunnel surface becomes smoother. Also for the above cases, the tangential stress around tunnel increases.