Complex variable solution for tunneling-induced ground deformation considering the gravity effect and a cavern in the strata

Abstract

Hidden caverns of the stratum are often encountered during the excavation of shallow tunnels in cities. These caverns will cause ground deformations and threaten the safety of tunnel and surrounding buildings. Nevertheless, there are few studies on this problem, and the theoretical research is lacking. In this study, an analytical method is established to solve the problem of a shallow tunnel with a nearby cavern. This method not only takes into account the non-uniform radial displacement on the tunnel boundary and the gravity effect of the excavated soil, but also considers the stress-free condition on the cavern boundary. Complex variable method is applied in the problem solving procedure and the Schwarz alternating method is applied to study the interaction between the tunnel and the cavern. And then, the precision of this solution is discussed from the aspects of numerical calculation. Furthermore, the accuracy of the analytical solution is verified by comparing the theoretical initial boundary with numerical results. Finally, the effects of the cavern on ground deformation are analyzed through the parametric studies. The proposed solution provides an insight into the effects of hidden caverns and can serve as a tool for evaluating the ground deformation during the preliminary design.