An elastic stress–displacement solution for a lined tunnel at great depth

By using the complex potential theory proposed by Muskhelishvili, an elastic plane strain solution for stresses and displacements around a lined tunnel under in situ stresses is presented. The tunnel is assumed to be driven in a homogeneous and isotropic geomaterial, and the tunnel construction sequence is properly taken into consideration. Numerical analyses indicate that, in order to simultaneously meet the needs of structural strength and rigidity, the relative rigidity and thickness of liner should be in an appropriate range. Either too high or low values for these parameters are unfavorable for the structural stability. The variations of stresses in the geomaterial intensively rely on the relative rigidity and thickness of liner when the ratio between the distance of the point under investigation to the tunnel axis and the outer radius of the liner is in the range from 1 to 2. In addition, the present solutions contain previously known results as the special cases.