Abstract:In order to get the stress solutions and displacement solutions in rock around a tunnel excavation by taking into account of the internal pressure, an analytical solution is presented for excavation stress and displacement of tunnel with arbitrar shape and size by analytic continuation method in anelastic half plane. As a special case, two closed solutions are given respectively for stress and displacement field around a lined circular and horseshoe shaped tunnel at great depth considering the influences of lining forces of tunnels. Because the depth is larger than the size of the tunnel, the effect of gravity gradient can be ignored, and gravity loads can be simplified as uniform normal loads along far field boundary. Comparison between the results of numerical analysis by two dimensional finite element method and those from the closed solutions indicates that the closed solution is reliable and applicable for assessment of the stress and displacement field around the tunnel in the arbitrary shape and size at great depth.
