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

Abstract

SUMMARYA time-domain viscous-spring transmitting boundary is presented for transient dynamic analysis of saturated poroelastic media with linear elastic and isotropic properties. The u-U formulation of Biot equation in cylindrical coordinate is adopted in the derivation. By this general viscous-spring boundary, the effective stress and pore fluid pressure on the truncated boundary of the computational area are replaced by a set of continuously distributed spring and dashpot elements, of which the parameters are defined assuming an infinite permeability and considering the two dilatational waves. Numerical examples demonstrate good absorption of both the two cylindrical dilatational waves by the proposed 'drained' boundary. For general twodimensional wave propagation problems, acceptable accuracy can still be achieved by setting the proposed boundary relatively far away from the scatter. Numerical comparison shows that the results obtained by using this boundary are more accurate for all permeability values than those by the traditional viscousspring or viscous boundaries established for u-U formulation.

Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain

“…For the two-dimensional viscoelastic boundary under multiple excitation sources, (26) could be rewritten as follows by (11) and (14):…”

“…Liu [12] and Du [13] proposed a viscoelastic boundary for the three-dimensional conditions using the theory of elastic wave motions. Li and Song [14] proposed a general viscous-spring transmitting boundary for dynamic analysis of saturated poroelastic media based on u-U formulation of Biot equation in cylindrical coordinate. However, these viscelastic boundary conditions are derived in the media where only one excitation source exists.…”

A local absorbing boundary condition for 3D seepage and heat transfer in unbounded domains

“…Deeks and Randolph 15 proposed a viscous‐spring boundary for radial wave travelling in an axisymmetric plane. Li and Song 16 constructed a viscous‐spring transmitting boundary for the three‐dimensional analysis of the longitudinal seismic response of a tunnel with an asynchronous wave input. As for the problems of fluid seepage or heat conduction in a one‐dimensional domain, Carslaw and Jaeger 17 derived the corresponding integral global ABCs.…”

Silent Boundary Scheme and Analysis of Existing Methods of providing Silent Boundary

“…It was found that proposed boundary is more efficient and capable of solving dynamic problems in saturated porous media. 5 Liu and Jerry (2003) proposed a gradually damped artificial boundary applied by an exponentially increasing function, to simulate a non-reflecting boundary condition. 6 Lysmer and Kuhlemeyer (1969) proposed a general method through which an infinite system is approximated by a finite system with a special viscous boundary condition by absorbing the striking waves towards the boundary.…”