Abstract
An analytical solution for the seismic-induced thrust and moment of the circular tunnel in half-space under obliquely incident P waves is developed in this study, which is the superposition of the solution for deep tunnels under incident and reflected P waves and the reflected SV waves. To consider tangential contact stiffness at the ground-tunnel interface, a spring-type stiffness coefficient is introduced into the force-displacement relationship. Moreover, the tunnel lining is treated as the thick-wall cylinder, providing more precise forecasts than beam or shell models used in previous analytical solution, especially for tunnels with thick lining. The reliability of the proposed analytical solution is assessed by comparing with the dynamic numerical results. Based on the proposed analytical solution, parametrical studies are conducted to investigate the effect of some critical factors on the tunnel’s seismic response, including the incident angles, the tangential contact stiffness at the ground-tunnel interface, and the relative stiffness between the ground and the tunnel. The results demonstrate that the proposed analytical solution performs well and can be adopted to predict the internal forces of circular tunnels under obliquely incident P waves in seismic design.
Highlights
As the essential part of infrastructures, tunnel structures play an important role in public transportation facilities, sanitation frameworks, irrigation utilities, and so on
In the last several decades, plenty of seismic analysis and design methods have been developed for tunnels and other underground structures, which can be divided into analytical solution, quasi-static analysis method, and dynamic time history analysis method
An analytical solution for the seismic-induced internal forces of the circular tunnel in half-space, which is subjected to obliquely incident P waves, is developed. e new analytical solution is different from other previous analytical solution in three respects
Summary
As the essential part of infrastructures, tunnel structures play an important role in public transportation facilities, sanitation frameworks, irrigation utilities, and so on. Seismic damage cases in recent years indicate that tunnel structures are vulnerable to earthquake loading [1,2,3,4]. In the last several decades, plenty of seismic analysis and design methods have been developed for tunnels and other underground structures, which can be divided into analytical solution, quasi-static analysis method, and dynamic time history analysis method. Compared with the quasistatic analysis method and dynamic time history analysis method, the analytical solution can quickly and estimate the force and displacement of the tunnel under seismic loadings, which can identify the most relevant variables of the problem. Wang [5] proposed the analytical solution for thrust, moment, and deformation of the circular tunnel under vertically propagating shear waves. Penzien and Wu [6] put forward a simple formula for calculating the deformation and corresponding stress of bored tunnels resulting from earthquake loading. en, Penzien [7] supplemented the previously published by Penzien and Wu [6] and proposed a
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