Analytical solutions of the tunnels under the fault creeping by elastic foundation beam model with considering tangential interaction

The fault zone plays a vital role in the internal force responses of the tunnel. An analytical solution of the tunnel under the fault zone creeping is developed by taking account of normal and tangential interaction between the ground and tunnel. First, the elastic foundation beam model is used. Wherein, the normal interaction is considered by applying the displacements of the free field on the distal end of normal foundation springs. And the tangential interaction is transformed into bending moment applied on the beam. The analytical solution of the tunnel's response is gotten based on the model. Secondly, the numerical solutions from finite element model of 3D are provided to verify the validity of the proposed analytical solutions. Finally, the effect of the fault zone width, the elastic modulus of the fault and the concrete's grade of the lining are investigated. The results show that with the width of the fault zone increasing, the internal force decrease. The concrete's grade of the lining has opposite effects on the internal force of the tunnel. And with the growth of the elasticity modulus of the fault zone, the shear force and bending moment increase and decrease, respectively.

Automated summary

A study developed an analytical solution for the response of tunnels under fault zone creeping, taking into account the normal and tangential interaction between the tunnel and the ground. The solution was based on an elastic foundation beam model, where the normal interaction was considered by applying displacements of the free field on the distal end of normal foundation springs, and the tangential interaction was transformed into bending moment applied on the beam. Numerical solutions from a 3D finite element model were used to verify the validity of the proposed analytical solutions. The effects of fault zone width, elastic modulus of the fault, and concrete's grade of the lining on the tunnel's internal force were also investigated.