Consolidation of multilayered half space with anisotropic permeability and compressible constituents

Abstract This paper presents analytical solutions of consolidation for poroelastic and multilayered half space, and anisotropy of the permeability and the compressibility of the pore fluid are considered. State vector method together with Laplace–Hankel transform techniques are used to solve the basic governing equations, and obtain the transfer matrix in a clearly arranged way. Forward and backward transfer matrix techniques are utilized in the analytical formulation of solutions for the multilayered half space. A numerical inversion scheme of Crump's method is adopted to obtain time-domain solution. Numerical results are presented for a single homogeneous soil layer and a multilayered half space, and they illustrate the influences of the anisotropy of permeability and the compressibility of the pore fluid on the consolidation of the soils.

[1]  Ching S. Chang,et al.  Consolidation analysis for partly saturated clay by using an elastic–plastic effective stress–strain model , 1983 .

[2]  S Pietruszczak,et al.  CONSTITUTIVE RELATIONS FOR PARTIALLY SATURATED SOILS CONTAINING GAS INCLUSIONS. DISCUSSION AND CLOSURE , 1997 .

[3]  D. G. Fredlund,et al.  Density and compressibility characteristics of air–water mixtures , 1976 .

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

[5]  Guangqi Chen,et al.  Analysis of pumping in multilayered and poroelastic half space , 2003 .

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

[7]  J. R. Booker,et al.  The consolidation of a finite layer subject to surface loading , 1974 .

[8]  Ir. E. Schuurman.  The Compressibility of an Air/Water Mixture and a Theoretical Relation Between the Air and Water Pressures , 1966 .

[9]  H. L. Koning.  Some observations on the modulus of compressibility of water , 1963 .

[10]  O. Madsen,et al.  Wave-induced pore pressures and effective stresses in a porous bed , 1978 .

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

[12]  S. Okusa,et al.  Wave-induced stresses in unsaturated submarine sediments , 1985 .

[13]  R. E. Gibson,et al.  PLANE STRAIN AND AXIALLY SYMMETRIC CONSOLIDATION OF A CLAY LAYER ON A SMOOTH IMPERVIOUS BASE , 1970 .

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

[15]  Hans Sellmeijer,et al.  On the response of a poro-elastic bed to water waves , 1978, Journal of Fluid Mechanics.

[16]  Charles A. Wentz,et al.  Hazardous Waste Management , 1989 .

[17]  Dong-Sheng Jeng,et al.  Response in Seabed of Finite Depth with Variable Permeability , 1997 .

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

[19]  J. Booker,et al.  Withdrawal of a compressible pore fluid from a point sink in an isotropic elastic half space with anisotropic permeability , 1987 .

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

[21]  K. T. Law,et al.  Excess pore pressure in a poroelastic seabed saturated with a compressible fluid , 1994 .

[22]  A. Cheng,et al.  Boundary integral equation method for linear porous‐elasticity with applications to soil consolidation , 1984 .

[23]  Jun Yang,et al.  Analytical study of saturation effects on seismic vertical amplification of a soil layer , 2001 .

[24]  A. Skempton.  THE PORE-PRESSURE COEFFICIENTS A AND B , 1954 .