Limitations of the Ground Reaction Curve Concept for Shallow Tunnels Under Anisotropic In-situ Stress Conditions

Abstract: The deep mining industry and civil engineering need to perform rock stability analyses during excavation projects. These analyses are closely related with displacements in tunnel contours. The ground reaction curve is a powerful tool to characterize these displacements that is widely used in the New Austrian Tunneling Method. However, the analytical solutions that exist are only applicable under isotropic stress conditions for deep tunnels. This study aims to investigate when it is possible using the analytical methods to determine the ground reaction curves with enough accuracy in the case of shallow tunnels under anisotropic in-situ stress conditions. The method begins with a literature study. After that, with the help of a 2D model, a comparison between the analytical and the numerical solutions for ground reaction curves at different depths and at different initial in-situ stress ratios was carried out. The results show that both crown and floor displacements deviate more from the analytical solution than the wall displacement. The crown and floor can even move upwards under high initial in-situ stress ratios for shallow tunnels. Because of that, the analytical solution of the ground reaction curve at shallow depths under anisotropic stress conditions should not be used. In the case of isotropic stress field conditions for the analysis in this study, the results given by the analytical solution agree with the numerical ones at depths higher than 14 times the radius of the tunnel. On the other hand, the difference between numerical and analytical solutions becomes higher while increasing the initial in-situ stress ratio, even for very deep tunnels. Furthermore, an empirical equation to obtain the displacements of the ground surface, tunnel wall and tunnel crown has been obtained after a multiple linear regression analysis.