The 3-D boundary integral equation is derived in terms of the reciprocal work theorem and used along with the 2.5-D Green's function developed in Part I [Lu, J.F., Jeng, D.S., Williams, S., submitted for publication. A 2.5-D dynamic model for a saturated porous medium: Part I. Green's function. Int. J. Solids Struct.] to develop the 2.5-D boundary integral equation for a saturated porous medium. The 2.5-D boundary integral equations for the wave scattering problem and the moving load problem are established. The Cauchy type singularity of the 2.5-D boundary integral equation is eliminated through introduction of an auxiliary problem and the treatment of the weakly singular kernel is also addressed. Discretisation of the 2.5-D boundary integral equation is achieved using boundary iso-parametric elements. The discrete wavenumber domain solution is obtained via the 2.5-D boundary element method, and the space domain solution is recovered using the inverse Fourier transform. To validate the new methodology, numerical results of this paper are compared with those obtained using an analytical approach; also, some numerical results and corresponding analysis are presented.
Lu, J-F., Jeng, D-S., & Williams, S. (2008). A 2.5-D dynamic model for a saturated porous medium. Part II: Boundary element method. International Journal of Solids and Structures, 45(2), 359-377. https://doi.org/10.1016/j.ijsolstr.2007.07.026