Ground Response Curve for the Crown, Wall and Floor of Shallow Tunnels under Non-Isotropic Stress Field: Application range of analytical Solutions

Ground response curve is a component of convergence-confinement method in rock support interaction analysis which is used for determining the displacement around tunnels excavated by New Austrian Tunneling Method. Analytical solution of the ground response curve is based on the assumption of isotropic in-situ stress field and is applicable for deep tunnels. Today, urban tunnels mainly excavated in shallow levels and often under anisotropic in-situ stress field. In this paper, for 2D models with geometry and specific environmental characteristics, the response curves for different depths and different in-situ stress ratios, are determined in two ways: 1) By analytical solution and using anisotropic stress field equivalent to an isotropic stress field. 2) Numerical solution. The results of these analyzes were compared with together and range of application of analytical solution of the ground response curve is determined. Based on the results, tunnel wall displacement is mainly influenced by the ratio of the initial in-situ stresses in comparison of tunnel depth. The results showed that crown and floor numerical displacements deviate more from analytical solution than the wall displacement. The only displacement that can be accurately obtained from the analytical solution for the shallow tunnel is the displacement of the tunnel wall under isotropic stress. In the case of isotropic stress field, the results given by the analytical solution agree with the numerical ones at depths higher than 14 times radius of the tunnel. The difference between numerical and analytical solutions becomes higher while increasing the initial in-situ stress ratio, even for deep tunnels.