Scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space, modeled using the indirect boundary element method

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

“…It can be seen from these figures that the porosity has more significant effect on the horizontal surface displacement amplitudes than on the vertical ones, which is similar to their free-field response (Lin et al, 2005); the porosity also has significant effect on the phase shift of the surface displacement amplitudes, and as the porosity increases the wavelengths of the surface displacement amplitudes increase. From these figures, it can also be seen that for small porosity (e.g., n = 0.1) the surface displacement amplitudes of the saturated cases (either drained or undrained) are almost identical to those of the dry case in Figure 1, and drainage condition has little influence on the surface displacement amplitudes; 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, which is identical to that for incident SV waves (Liang et al, 2006) and may be explained by that, for the undrained case, the pore pressure is larger since there is no energy overflow. It can also be seen that as the incident frequency increases, the effect of porosity gradually becomes significant, and more significant for the undrained case than that for the drained case.…”

“…From the figure large phase shift can also be easily observed between the dry case and the saturated cases, as well as the slightly longer resultant wavelengths for the undrained case than those for the drained case and the longer resultant wavelengths for the drained case than those for the dry case. The difference may be due to the wave interference around the canyon, which is identical to that for incident SV waves (Liang et al, 2006). For nearly grazing incident waves, a standing wave pattern can be observed at x/a < −1 for both the dry case and the saturated cases.…”

“…As the porosity increases, the pore pressures increase significantly but their oscillations become smoother, which implies that more energy is taken by the pore fluid and less by the soft solid frame for larger porosity, and larger porosity (with more pore fluid) results in smoother oscillation then. When the porosity approaches to its critical state (n=0.36), the modulus of the solid frame becomes very soft, and most of the energy is undertaken by the first P waves (Lin et al, 2005), therefore pore pressures increase significantly, which is very different from that for incident SV waves (Liang et al, 2006). For incident SV waves most of the energy is carried by SV waves and the second P waves (Lin et al, 2005), but SV waves do not produce pore pressures.…”

3D dynamic response of a multi-layered transversely isotropic half-space subjected to a moving point load along a horizontal straight line with constant speed

“…The wavenumber integrals are evaluated by the piecewise Gauss quadrature (see e.g., Liang et al, 2006) due to the oscillatory nature of the integrands, which schemes such as Simpson and trapezoidal quadrature with equal intervals are inefficient to conduct the integrals accurately. To ensure the accuracy of piecewise Gauss quadrature, the integrals with respect to wave number k x must be truncated at sufficiently large values k max , and the sampling spacing Δk x must be sufficiently small.…”

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

“…The numerical methods including the finite element method and the boundary element method were also introduced to examine the response of tunnels under dynamic excitations. By using the indirect boundary element method in the frequency domain, Liang et al studied the scattering of SV waves by a canyon in a fluid-saturated, poroelastic layered half-space 10 . Jiang and Yin presented the stress redistribution in the surrounding soil and the earth pressure acting on the shield tunnel, and the principal stresses was discussed in detail 11 .…”