Scattering of plane P, SV or Rayleigh waves by a shallow lined tunnel in an elastic half space

Dynamic interaction of twin vertically overlapping lined tunnels in an elastic half space subjected to incident plane waves

“…The analytical method such as wave function expansion method (WFEM) has been widely used to solve the scattering of seismic waves by a lined tunnel (Lee and Trifunac 1979;Liang and Ji 2006;Liu et al 2013;Yi et al 2014). Due to the fact that the analytical methods are usually restricted to simple calculation models, for complex geometrical and material characteristics, it is necessary to develop numerical methods, such as the finite element method (FEM), finite difference method (FDM), the boundary element method (BEM), etc.…”

“…Yu and Dravinski (2009) investigated the scattering of plane P, SV, and Rayleigh waves by a cavity embedded in an isotropic half space by BEM. Liu et al (2010) further discussed the diffraction of P, SV waves by a tunnel in an elastic half space using a special BEM. Panji et al (2013) studied the displacement response of an unlined truncated circular cavity in a homogenous isotropic medium under SH waves by BEM.…”

Seismic ground amplification by unlined tunnels subjected to vertically propagating SV and P waves using BEM

“…Later, Liang et al [17,18] represented an analytical solution on scattering of in-plane P waves around a cavity and implemented several numerical examples in poroelastic medium. Moreover, Liu et al [19,20] presented an analytical solution for scattering of plane harmonic P, SV, SH and Rayleigh Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/soildyn waves by a shallow lined circular tunnel in an elastic half-space. This solution was developed based on the plane complex variable theory and the image technique.…”

Dynamic interaction of two circular lined tunnels with imperfect interfaces under cylindrical P-waves

“…It has been of high interest for determining the stress distribution in the liner and rock medium under static overburden and dynamic loadings. The analytical methods including the wave function expansion [5][6][7][8] and the series expansion techniques 9 have been widely used to simulate the displacement potentials around the circular tunnels embedded in the rock medium. By using wave function expansion method, the seismic dynamic response of piecewise liners embedded in the porous medium was investigated 5 .…”