Analytic Study on Interaction among Shallow Multiple Circular Tunnels under Slope Terrain

The requirements for transportation often make it unavoidable to excavate shallow multiple tunnels under slope terrain in mountainous areas. An analytical approximate solution of stresses and displacements around multiple shallow circular tunnels under slope terrain that takes the interactions among tunnels into consideration is proposed in this study. Using superposition principle, the original problem is decomposed into a slope plane without tunnels (solid slope) and several infinite planes containing only one tunnel loaded by virtual traction on the tunnel boundary. The solid slope is further divided into several half planes subjected to virtual tractions on the upper surfaces, Combined with complex variable method and Flamant’s solution, the virtual tractions acted on the half plane surfaces and tunnels boundaries are obtained through iterations, and thus the stresses and displacement around the tunnels are obtained. The analytical approximate solution is verified by the convergent iteration and the close agreement with the corresponding numerical and theoretical solutions. In addition, the effects of surcharge loads position, tunnels layout, tunnels radius and slope inclination on the ground responses are investigated through parametric analyses. The proposed analytical model is helpful for providing an alternative approach for the preliminary designs of shallow tunnels under slope terrain.