Multi-transmitting formula for finite element modeling of wave propagation in a saturated poroelastic medium

An absorbing boundary condition that is called the multi-transmitting formula (MTF) was originally proposed by Liao and Wong for wave propagation in an elastic medium. In this paper, the MTF was extended for modeling wave propagation in a saturated poroelastic medium using the finite element method. Reflection coefficients of the MTF that is applied to the boundaries of a finite element grid were analytically derived for the incidence of SV, P1 and P2 waves, respectively. The effects of the excitation frequency and the artificial wave velocity on the reflection coefficients of the MTF were theoretically investigated. The MTF was then implemented into a finite element code to examine its capacity to absorb the one-dimensional longitudinal/shear wave, the plain-strain waves, the moving-load generated waves and the three-dimensional waves in the saturated poroelastic medium. It is found that the reflection coefficients evaluated from the numerical simulation agree with the predicted values in the theoretical investigations.