An Analytical Solution for 2D Dynamic Structure-Soil-Structure Interaction for Twin Flexible Tunnels Embedded in a Homogeneous Half-Space

Liguo Jin,Xujin Liu,Zhenghua Zhou,Hongyang Sun

doi:10.3390/app112110343

Abstract

The interaction between subway tunnels is investigated by using a 2D analytic model of a twin tunnels system embedded in a homogenous half-space. The closed-form analytical solution for tunnel displacement response is derived through the wave function expansion method and the mirror method, and the correctness of the solution is verified through residuals convergence and comparison with the published results. The analysis focuses on the effects of tunnel relative stiffness on tunnel–soil–tunnel interaction. Tunnel relative stiffness has a great influence on tunnel displacement response. For small tunnel relative stiffness, tunnel displacement amplitude can be enlarged by 3.3 times that of single rigid tunnel model. The response of the tunnel–soil–tunnel interaction system depends not only on the distances between tunnels but also on the frequency of the incident wave and the incident angle. The strength of the interaction between the tunnels is highly related to the tunnel spacing distance. The smaller the distance between tunnels, the stronger the interaction between them. When the distance between tunnels reaches s/a = 20, the interaction between tunnels can be ignored. It is worth pointing out that the seismic design of underground tunnels should consider the interaction between tunnels when the tunnel distance is small.

Highlights

An underground tunnel is a shallow-buried structure located under the surface of an infinite half-space
The analytical method mainly refers to the wave function expansion method, which mainly studies regular shape models embedded in a uniform half-space
An analytical two-dimensional (2D) dynamic tunnel-soil-tunnel interaction model was presented for the linear out-of-plane response of the seismic interaction between twin tunnels in the urban area

Summary

Introduction

An underground tunnel is a shallow-buried structure located under the surface of an infinite half-space. The analytical method mainly refers to the wave function expansion method, which mainly studies regular shape models embedded in a uniform half-space. The analytical method is only suitable for relatively simple and regular models, it has an advantage over the numerical method in revealing the essence of the problem. Pao and Mow [1] pioneered the application of the wave function expansion method of electromagnetic waves to the problem of seismic wave scattering and presented the outof-plane dynamic analytical solution of a single buried tunnel in the whole space. Scholars further solved the analytical solutions of the dynamic response of a single tunnel embedded in an isotropic half-space, respectively excited by plane SH-wave, P-wave, and SV-wave [2,3,4,5,6]

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Conclusion