Soil-tunnel interaction under the effect associated with the longitudinal direction

Longitudinal structural analysis of shield tunnels is studied by considering the tunnel as a Timoshenko beam based on elastic foundations under Vlasov's theory. This article presents the structural behavior of a Timoshenko-Vlasov beam jointly, using a single differential system that brings together all the equilibrium and deformation equations. Solving the presented formulation, shield tunnels can be covered under any type of action, ground pressure and support or boundary conditions. This new compacted notation facilitates the possibility of expressing the interaction between soil and structure by introducing the variability of longitudinal support conditions on the elastic springs. This differential system is resolved with the numeric procedure named Finite Transfer Method. To verify the effectiveness of the procedure followed, the structure of the subway tunnel in Shanghai has been modeled and the results obtained have been compared with those offered in the literature. The proposed model has been exemplified by introducing the variability of longitudinal elastic spring conditions representing actual soil behavior.