Analytical stress and displacement due to twin tunneling in an elastic semi‐infinite ground subjected to surcharge loads

The construction of twin tunnels at shallow depth has become increasingly common in urban areas. In general, twin tunnels are usually near each other, in which the interaction between tunnels is too significant to be ignored on their stability. The equivalent arbitrarily distributed loads imposed on ground surface were considered in this study, and a new analytical approach was provided to efficiently predict the elastic stresses and displacements around the twin tunnels. The interaction between 2 tunnels of different radii with various arrangements was taken into account in the analysis. We used the Schwartz alternating method in this study to reduce the twin‐tunnel problem to a series of problems where only 1 tunnel was contained in half‐plane. The convergent and highly accurate analytical solutions were achieved by superposing the solutions of the reduced single‐tunnel problems. The analytical solutions were then verified by the good agreement between analytical and numerical results. Furthermore, by the comparison on initial plastic zone and surface settlement between analytical solution and numerical/measured results of elastoplastic cases, it was proven that the analytical solution can accurately predict the initial plastic zone and its propagation direction and can qualitatively provide the reliable ground settlements. A parametric study was finally performed to investigate the influence of locations of surcharge load and the tunnel arrangement on the ground stresses and displacements. The new solution proposed in this study provides an insight into the interaction of shallow twin tunnels under surcharge loads, and it can be used as an alternative approach for the preliminary design of future shallow tunnels excavated in rock or medium/stiff clay.