Analytic Solutions of the Forces and Displacements for Multicentre Circular Arc Tunnels

A complex variable method for solving the forces and displacements for multicentre circular arc (MCA) tunnels by using analytical solutions is presented. The governing equations for the stresses and displacements are expressed in terms of series expression. Combined with the boundary conditions at lining inner region, lining-surrounding rock-mass interface, and infinity area, the undetermined coefficients of the analytic functions are obtained by solving a linear equation set. Forces solutions for linings are also presented according to the tangential stress at the two boundaries. Conformal mapping function for the MCA tunnel is given from the optimization method. Calculation results show that solutions with high accuracy can be obtained when the number of terms of power series is greater than 30. The effects of the degrees from the tunnel crown to the invert, coefficient of the lateral earth pressure, and distance from the rock-mass to the interface on regulations of the lining forces and rock-mass stresses are also thoroughly investigated