New analytical method for predicting stresses around rectangular tunnels under arbitrary stress boundary conditions

Rectangular tunnels are often encountered in geotechnical engineering. To clarify the mechanical mechanism of the stresses around tunnels, this study presents new analytical approximant solutions for evaluating stresses around tunnels under arbitrary stress boundary conditions. The solutions consist of two parts: one is the solution for a half-plane before excavation, and the other is the solution for a half-plane with tunnels. The second part can be further decomposed into solutions of a half-plane without tunnels subjected to virtual tractions along the ground surface and solutions of an infinite plane with tunnels loaded by virtual tractions along tunnel boundaries. An efficient iterative procedure is proposed for determining the two sets of unknown virtual tractions, which are transformed into equivalent concentrated forces to simplify the computational process. The solutions agree very well with the results obtained by the finite element method. A parametric study is finally performed to investigate the influences of the tunnel buried depth, the tunnel shape, and surcharge loads on the stresses along the ground and around tunnels. The new proposed solutions potentially provide a potential alternative approach for preliminary designs of future rectangular tunnels.