Diffraction of plane P waves by a canyon of arbitrary shape in poroelastic half-space (II): Numerical results and discussion

Abstract

This paper investigates in detail the nature of diffraction of plane P waves around a canyon in poroelastic half-space, and studies the effects of incident frequency, drainage condition, porosity, etc, on the diffraction of waves. It is shown that the surface displacement amplitudes of the drained case are close to those of the undrained case, however, the surface displacement amplitudes of the dry case are very different from those of the saturated (either drained or undrained) cases. There are large phase shift between the dry case and the saturated cases, as well as slightly longer resultant wavelengths for the undrained case than those for the drained case and longer resultant wavelengths for the drained case than those for the dry case. For small porosity the surface displacement amplitudes for the saturated cases are almost identical to those for the dry case; while for large porosity, the effect of drainage condition becomes significant, and the surface displacement amplitudes for the undrained case are larger than those for the drained case. As the incident frequency increases, the effect of porosity becomes significant, and more significant for the undrained case than that for the drained case. As the porosity increases, the pore pressures increase significantly but their oscillations become smoother. As the incident frequency increases, the pore pressures become more complicated.

Indirect boundary element method for modelling 2‐D poroelastic wave diffraction by cavities and cracks in half space

“…For half plane problems, the use of half plane Green's functions in the boundary integral equations is highly beneficial, because the free surface conditions are automatically satisfied, and the half plane boundary does not need to be discretized, saving the computational effort. The half plane poroelastic Green's functions derived in Liang and Liu 57 have been utilized to solve various half plane problems with objects such as canyon, valley, cavity, and tunnel 58–61 …”

Dynamic Response of Underground Circular Lining Tunnels Subjected to Incident P Waves

“…Davis et al [11] studied the transversal response of underground cylindrical cavities to incident SV waves and derived analytical solutions to evaluate the dynamic response of a flexible buried pipe during the Northridge earthquake. Just recently, Liang et al [12][13][14], Ji et al [15], and You and Liang [16] investigated the dynamic stress concentration of a cylindrical lined cavity in an elastic half space for incident plane P and SV waves and derived the series solution to study the amplification of ground surface motion due to underground group cavities for incident plane P waves. Kouretzis et al [17] employed the 3-D shell theory in order to derive analytical expressions for the distribution along the cross section of axial, hoop, and shear strains for long cylindrical underground structures (buried pipelines and tunnels) subjected to seismic shear wave excitation.…”

“…The stress and displacement functions of the tunnel lining for incident plane P waves can be solved from (9). Generally, under the action of steady state P waves, the dynamic stress distribution of tunnel lining can be studied through solving the coefficient of dynamic stress concentration of the inner surface of tunnel lining on the toroidal direction [13,14].…”

The method of fundamental solution for 3‐D wave scattering in a fluid‐saturated poroelastic infinite domain

“…Liang and Liu developed the poroelastodynamic MFS on the basis of the SWP fundamental solutions. The SWP‐MFS has been applied by Liang and Liu and Liu et al to solve problems of 2‐D scattering of seismic waves by a cavity or an alluvial valley in a poroelastic half‐plane. Xu et al solved the diffraction of Rayleigh wave by twin cavities in half‐plane.…”