A viscous boundary for transient analyses of saturated porous media

Abstract

SUMMARYAn absorbing boundary for saturated porous media is developed that can be used for transient analyses in the time domain. The elastic constitutive equations for the saturated porous media follow Bowen's formulation. The method consists of applying viscous tractions along the artiÿcial boundary. The absorbing boundary behaviour is assumed linear and isotropic. Hadamard's conditions provide the speeds of the dilatational and shear waves that propagate in saturated porous media. Since these expressions are frequency independent, the intensities of the viscous tractions are evaluated in the time domain, and the two dilatational waves are accounted for. The viscous tractions are deÿned from the drained characteristics, assuming an inÿnite permeability, at variance with the traditional 'undrained' method based on undrained characteristics and a null permeability. Solid media and materials with low permeability are also retrieved as subcases.The results show that, at no additional cost, this 'drained' method is more accurate for all permeabilities than the 'undrained' method, which disregards the existence of the second dilatational wave.

A local artificial‐boundary condition for simulating transient wave radiation in fluid‐saturated porous media of infinite domains

“…The linear elastic wave propagation theory based on the dynamic governing equations of the fluid‐saturated porous medium has been developed , ( ) . The theory stated that three kinds of body waves exist in the fluid‐saturated porous medium, that is, P1 wave, P2 wave and S wave, which were verified by laboratory experiments .…”

A general viscous‐spring transmitting boundary for dynamic analysis of saturated poroelastic media

“…The second example corresponds to the general two‐dimensional semi‐infinite wave radiation problem, and the accuracy of the proposed transmitting boundary is examined. Comparisons are also made between the proposed boundary and the viscous‐spring transmitting boundaries developed in and as well as the viscous boundaries developed in and . In all cases, a homogeneous, isotropic soil model without material damping is chosen with the following: Shear modulus G = 79.6 MPa; Poisson's ratio υ = 0.4; porosity n = 0.4; ρ s = 2650 kg/m 3 , ρ f = 1000 kg/m 3 , ρ a = 0 kg/m 3 ; the bulk moduli of the solid and the fluid are K s = 36 GPa and K f = 1.848 GPa, respectively.…”

“…The first‐order boundary is derived for cases of both vanishingly small and infinitely large viscous coupling. Assuming an infinite permeability, Zerfa and Loret developed a viscous boundary in the time domain. The effects of the second dilatational wave are taken into account, and numerical results show that it works correctly for all permeabilities.…”

“…This may lead to some loss of accuracy, especially for high‐frequency, high‐permeability, and short‐duration problems, in which the effect of P2 wave is considerable. The viscous boundary proposed by Zerfa and Loret has taken into account both the two dilatational waves, but a viscous boundary may have stability problems when dealing with low‐frequency dynamic loads, which may greatly limit its application scope.…”

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

“…His method is expected to be quite expensive for two-and three-dimensional systems. Zerfa and Loret [24] have established a viscous boundary for transient analysis of saturated porous media with u-w formulation. The transmitting boundary used in this paper is an extension of Kim et al's [25] work, which was a three-dimensional transmitting boundary for the dynamics of solids to the transmitting boundary for saturated porous media.…”