Analytical solution for longitudinal seismic response of long tunnels subjected to Rayleigh waves

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 44; no. 10; pp. 1371 - 1385
• Main Authors: Yang, Yusheng, Yu, Haitao, Yuan, Yong, Zhao, Mi
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.07.2020
• Subjects: Acceleration; analytical solution; Axial forces; Bending moments; Computer simulation; Convolution; Deformation; Dynamic loads; Exact solutions; Finite element method; Forces (mechanics); integral transform; Integral transforms; long tunnel; Mathematical analysis; Mechanical properties; Parametric analysis; Rayleigh waves; Seismic activity; Seismic response; Shear forces; Soil; Soil dynamics; Soil investigations; Soil structure; Stiffness; Tunnels; Vertical motion; Viscoelasticity; Wave frequency; Waves
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.3066

Summary The longitudinal seismic response of a long tunnel subjected to Rayleigh waves is investigated in this paper. The tunnel is assumed to be infinitely long, has a uniform cross section, and rests on a viscoelastic foundation. The free‐field deformation under Rayleigh waves traveling parallel to the tunnel axis is decomposed into two directions, namely, the axial motion and the vertical motion, and transformed into dynamic loads imposed on the tunnel. Based on the Fourier and Laplace integral transform techniques, the governing equations of tunnels are simplified into algebraic equations, and the analytical solutions are obtained with the convolution theorem. The final solutions of the tunnel responses in terms of deflection, velocity, acceleration, axial force, bending moment, and shear force are investigated. The proposed solution is verified by comparison of its results and those from the finite element program ABAQUS. Further parametric analysis is carried out to investigate the influence of soil‐structure relative stiffness ratio and wave frequency on dynamic longitudinal responses of the tunnel.