On the indentation of a poroelastic layer

SUMMARY The paper examines the axisymmetric contact problem related to the indentation of a fluid saturated poroelastic layer by a smooth rigid punch. The layer rests in bonded contact with a rigid impermeable base and the surface of the layer is considered to be either permeable or impermeable. The paper develops the integral equations governing the problem for the generalized case where the pore fluid exhibits compressibility. The numerical results presented in the paper illustrate the influence of the relative layer thickness, drainage conditions and the compressibility of the pore fluid on the degree of consolidation settlement of the indenting punch.

[1]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[2]  Kenny S. Crump,et al.  Numerical Inversion of Laplace Transforms Using a Fourier Series Approximation , 1976, J. ACM.

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

[4]  R L Schiffman,et al.  CONSOLIDATION DUE TO TANGENTIAL LOADS , 1965 .

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

[6]  J C Small THE TIME- SETTLEMENT BEHAVIOUR OF RAFTS OF FINITE FLEXIBILITY , 1985 .

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

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

[9]  R. Taylor,et al.  The Numerical Treatment of Integral Equations , 1978 .

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

[11]  A. Cheng,et al.  Transient boundary element formulation for linear poroelasticity , 1987 .

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

[13]  Gwidon Szefer,et al.  Axisymmetric problem of the punch for the consolidating semi-space with mixed boundary permeability conditions , 1978 .

[14]  K. Atkinson,et al.  A survey of numerical methods for the solution of Fredholm integral equations of the second kind , 1977 .

[15]  R. E. Gibson,et al.  PLANE STRAIN AND AXIALLY SYMMETRIC PROBLEMS OF THE CONSOLIDATION OF A SEMI-INFINITE CLAY STRATUM , 1960 .

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

[17]  Bending settlement of a slab resting on a consolidating foundation , 1942 .

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

[19]  G. Szefer,et al.  Axisymmetric punch problem under condition of consolidation , 1975 .

[20]  R. E. Gibson,et al.  DISPLACEMENT FUNCTIONS AND LINEAR TRANSFORMS APPLIED TO DIFFUSION THROUGH POROUS ELASTIC MEDIA , 1960 .

[21]  J. R. Booker,et al.  THE TIME-SETTLEMENT BEHAVIOUR OF A RIGID DIE RESTING ON A DEEP CLAY LAYER , 1975 .

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

[23]  The time-deflection behaviour of a circular raft of finite flexibility on a deep clay layer , 1984 .

[24]  A. Talbot The Accurate Numerical Inversion of Laplace Transforms , 1979 .