Extended precise integration method for consolidation of transversely isotropic poroelastic layered media

A new numerical method for calculating the consolidation behavior of the stratified, transversely isotropic and poroelastic material is presented by combining the extended precise integration algorithm with the integral transformation techniques. Starting with the governing partial differential equations of a saturated medium with transversely isotropic skeleton and compressible fluid constituents, an ordinary differential matrix equation is deduced with the aid of a Laplace-Hankel transform. An extended precise integration method for internal loading situations is proposed to solve the ordinary differential matrix equation in the transformed domain, and the actual solution is recovered by a numerical inverse transformation. Numerical examples are also provided to prove the feasibility of this method.

[1]  I. Vardoulakis,et al.  Numerical Laplace‐Fourier transform inversion technique for layered‐soil consolidation problems: I. Fundamental solutions and validation , 1986 .

[2]  Z. Ai,et al.  Analytical layer-element solution to axisymmetric consolidation of multilayered soils , 2011 .

[3]  J. Abate,et al.  Multi‐precision Laplace transform inversion , 2004 .

[4]  W. Zhong,et al.  A precise numerical method for Rayleigh waves in a stratified half space , 2006 .

[5]  W. Zhong.  Duality system in applied mechanics and optimal control , 2004 .

[6]  S. Chi,et al.  Boundary element analysis of Biot consolidation in layered elastic soils , 1994 .

[7]  Wanxie Zhong,et al.  The precise computation for wave propagation in stratified materials , 2004 .

[8]  R. Rajapakse,et al.  Exact stiffness method for quasi-statics of a multi-layered poroelastic medium , 1995 .

[9]  I. N. Sneddon.  The use of integral transforms , 1972 .

[10]  F. Gaspar,et al.  A finite difference analysis of Biot's consolidation model , 2003 .

[11]  John T. Christian,et al.  PLANE STRAIN CONSOLIDATION BY FINITE ELEMENTS , 1970 .

[12]  Zhong Wan-xie,et al.  A precise method for solving wave propagation problems in layered anisotropic media , 2004 .

[13]  Pieter A. Vermeer,et al.  An accuracy condition for consolidation by finite elements , 1981 .

[14]  Zhi Yong Ai,et al.  3-D consolidation of multilayered porous medium with anisotropic permeability and compressible pore fluid , 2013 .

[15]  Jie Han,et al.  Transfer matrix solutions to axisymmetric and non-axisymmetric consolidation of multilayered soils , 2010 .

[16]  Z. Yue,et al.  Extended Sneddon and Muki solutions for multilayered elastic materials , 2002 .

[17]  J. C. Small,et al.  Finite layer analysis of consolidation. I , 1982 .

[18]  J. C. Small,et al.  A method of computing the consolidation behaviour of layered soils using direct numerical inversion of Laplace transforms , 1987 .

[19]  I. Vardoulakis,et al.  Numerical Laplace-Fourier transform inversion technique for layered soil consolidation problems. II: Gibson soil layer , 1987 .

[20]  Z. Ai,et al.  Non-axisymmetric Biot consolidation analysis of multi-layered saturated poroelastic materials with anisotropic permeability , 2013 .

[21]  E. Wilson,et al.  FINITE-ELEMENT ANALYSIS OF SEEPAGE IN ELASTIC MEDIA , 1969 .

[22]  Jianguo Wang,et al.  State space solution of non-axisymmetric Biot consolidation problem for multilayered porous media , 2003 .

[23]  Boundary element method in Biot's linear consolidation , 1982 .

[24]  M. Biot.  General solutions of the equations of elasticity and consolidation for a porous material , 1956 .

[25]  Z. Ai,et al.  Analytical layer‐element method for non‐axisymmetric consolidation of multilayered soils , 2012 .

[26]  Xiaoli Ding,et al.  Consolidation analysis of a cross‐anisotropic homogeneous elastic soil using a finite layer numerical method , 2004 .

[27]  G. J. Chen,et al.  Consolidation of multilayered half space with anisotropic permeability and compressible constituents , 2004 .

[28]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[29]  Transfer matrix solutions to plane-strain and three-dimensional Biot’s consolidation of multi-layered soils , 2009 .

[30]  E. Pan.  Green's functions in layered poroelastic half-spaces , 1999 .

[31]  Jianguo Wang,et al.  The state vector solution of axisymmetric Biot's consolidation problems for multilayered poroelastic media , 2001 .