Dynamic response of shallow dual unlined circular tunnels subjected to incident P, SV, or Rayleigh waves in an elastic half-plane

Abstract

This paper investigates the dynamic response of shallow dual circular unlined tunnels in an elastic half-plane during earthquakes. The scattered wave fields are constructed using the complex variable method and image method. General expressions for the displacement and stress components of the soil are derived through the conformal mapping technique. The half-plane surface and the tunnels in the physical domain are mapped onto ring regions in the image plane using two conformal mapping functions. Additional boundary conditions along the half-surface are imposed to solve the multiple-connected problem of the dual tunnel system. The boundary value problem yields a series of algebraic equations according to the traction-free boundary conditions. The unknown coefficients in the infinite series of algebraic equations are numerically solved by truncating the series numbers. A parametric study is conducted to investigate the dynamic response of the dual tunnels to incident SV waves. Numerical results reveal that the embedment ratio, the tunnel separations, the incident SV wave angle, and the wave frequency significantly affect the dynamic response of the dual tunnel system. The shielding effects of the tunnels against the incident SV waves are pronounced. The tunnel-to-tunnel interactions are evident.