New artificial boundary condition for saturated soil foundations

A new artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic analysis. Since shear waves (S-waves) are the same in a saturated soil foundation and a single-phase medium foundation, a tangential visco-elastic boundary condition for a single-phase medium foundation can also be used for saturated soil foundations. Thus, the purpose of the artificial boundary proposed in this paper is primarily to absorb two types of P-waves in a saturated soil foundation. The main idea is that the stress of the P-waves in the saturated soil foundation is decomposed into two types. The first type of stress, σra, is absorbed by the first artificial boundary. The second type of stress, σrb, is balanced by the stress generated by the second artificial boundary. Ultimately, both types of P-waves (fast-P-waves and slow-P-waves) are absorbed by the artificial boundary model proposed in this paper. In particular, note that the fast-P-waves and slow-P-waves are absorbed at the position of the first boundary. Thus, the artificial boundary model proposed herein can simultaneously absorb P-fast waves, P-slow waves and shear waves. Finally, a numerical example is given to examine the proposed artificial boundary model, and the results show that it is very accurate.

[1]  Renato Vitaliani,et al.  Silent boundary conditions for wave propagation in saturated porous media , 1996 .

[2]  B. Jin,et al.  Horizontal vibrations of a disk on a poroelastic half-space , 2000 .

[3]  K. Fuchida,et al.  General absorbing boundary conditions for dynamic analysis of fluid-saturated porous media , 1998 .

[4]  Gu Yin,et al.  3D CONSISTENT VISCOUS-SPRING ARTIFICIAL BOUNDARY AND VISCOUS-SPRING BOUNDARY ELEMENT , 2007 .

[5]  Z. Liao,et al.  Numerical instabilities of a local transmitting boundary , 1992 .

[6]  Chongbin Zhao,et al.  Non-reflecting artificial boundaries for modelling scalar wave propagation problems in two-dimensional half space , 2002 .

[7]  Warwick D. Smith.  A nonreflecting plane boundary for wave propagation problems , 1974 .

[8]  Mihailo D. Trifunac,et al.  The reflection of plane waves in a poroelastic half-space saturated with inviscid fluid , 2005 .

[9]  Yu-Yong Jiao,et al.  Viscous boundary of DDA for modeling stress wave propagation in jointed rock , 2007 .

[10]  G. Roeck,et al.  An absorbing boundary condition for wave propagation in saturated poroelastic media — Part II: Finite element formulation , 1993 .

[11]  Guanglan Liao.  FEATURE SELECTION BASED ON SOM NETWORKS , 2005 .

[12]  Du Yi-xin,et al.  Consistent viscous-spring artificial boundaries and viscous-spring boundary elements , 2006 .

[13]  Zhenpeng Liao,et al.  A TRANSMITTING BOUNDARY FOR TRANSIENT WAVE ANALYSES , 1984 .

[14]  Jin Bo.  The vertical vibration of an elastic circular plate on a fluid-saturated porous half space , 1999 .

[15]  F. Hu.  Absorbing Boundary Conditions , 2004 .

[16]  B. Engquist,et al.  Absorbing boundary conditions for acoustic and elastic wave equations , 1977, Bulletin of the Seismological Society of America.

[17]  Jian Zhang,et al.  DIMENSIONAL ANALYSIS OF STRUCTURES WITH TRANSLATING AND ROCKING FOUNDATIONS , 2009 .

[18]  Mark Randolph,et al.  Axisymmetric Time‐Domain Transmitting Boundaries , 1994 .

[19]  J. Sochacki.  Absorbing boundary conditions for the elastic wave equations , 1988 .

[20]  Zhang Chuhan,et al.  Influence of Seismic Input Mechanisms and Radiation Damping on Arch Dam Response , 2009 .

[21]  Semyon Tsynkov,et al.  High-Order Two-Way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering , 2000 .

[22]  Semyon Tsynkov,et al.  Artificial boundary conditions for the numerical simulation of unsteady acoustic waves , 2003 .

[23]  Robert L. Higdon,et al.  Absorbing boundary conditions for acoustic and elastic waves in stratified media , 1992 .

[24]  Björn Engquist,et al.  Absorbing boundary conditions for wave-equation migration , 1980 .

[25]  J. Lysmer,et al.  Finite Dynamic Model for Infinite Media , 1969 .

[26]  Shao Xiu-min,et al.  Finite Element Methods for the Equations of Waves in Fluid‐Saturated Porous Media , 2000 .

[27]  Chongmin Song,et al.  The scaled boundary finite-element method—alias consistent infinitesimal finite-element cell method—for elastodynamics , 1997 .

[28]  Geert Degrande,et al.  An absorbing boundary condition for wave propagation in saturated poroelastic media — Part I: Formulation and efficiency evaluation , 1993 .

[29]  Benjamin Loret,et al.  A viscous boundary for transient analyses of saturated porous media , 2004 .