A method of computing the consolidation behaviour of layered soils using direct numerical inversion of Laplace transforms

Abstract

A method is presented for obtaining the consolidation behaviour of a layered soil subjected to strip, circular, or rectangular surface loadings, or subjected to fluid withdrawal due to pumping. The solution method involves applying a Fourier or Hankel transform to the field quantities along with a Laplace transformation. The effect of the Fourier or Hankel transform is to reduce a twoor three-dimensional problem or one involving axial symmetry, to one involving only a single spatial dimension. In cases where the soil is horizontally layered, this has great advantages over conventional methods, such as finite element or finite difference methods, since very little computer storage and data preparation time is required. Solution of the time-dependent problem is achieved by applying a Laplace transformation to the field variables, obtaining solutions in Laplace transform space, and then numerically inverting the transformed solutions to obtain the real time behaviour. This eliminates the need for 'marching type' schemes where a solution is found from one at a previous time. By direct inversion of the Laplace transform, a solution may be obtained directly at any given time.

Time-dependent analysis of 3D thermo-mechanical behavior of a layered half-space with anisotropic thermal diffusivity

“…The Gauss-Legendre quadrature of 32 points and 8 points is adopted for the first integrated interval and the other integral intervals of the function e i(xξ x j +yξ yk ) , and the precision and stability of the approach have been illustrated in references [23,24]. [14,15] To illustrate the accuracy of the presented solutions in this study, numerical results for the thermo-mechanical response of the isotropic material system containing a decaying point heat source and a non-decaying point heat source are presented to compare with the existing results of references [14,15], as shown in Figs.…”

“…Then, we employed the compound Gauss quadrature and compiled a FORTRAN program to realize the double Fourier inverse transform [23,24], i.e.,…”

The Composite Ground Finite Layer Method and its Application to Pile Foundation Analysis

“…In early research, the FLM was proposed by Cheung et al (1982) for the analysis of structural components as a semi-analytic numerical method. Booker and Small et al (1982a, 1982b, 1987 then developed the FLM to adapt to the layered ground and applied it to consolidation problem and shallow foundation analysis by Swaddiwudhipong et al(1992) and Senjuntichai et al(2006).…”

Consolidation analysis of a cross‐anisotropic homogeneous elastic soil using a finite layer numerical method

“…This disadvantage can be overcome by using the finite layer method for certain classes of problems [10][11][12][13][14][15][16]. The finite layer method of Booker and Small [15] is different from the method proposed by Cheung and Tham [14]. By applying integral transforms, Booker and Small [15] first obtained the consolidation solution in the transformed domain, and then numerically inverted the transformed solution, whereas the method of Cheung and Tham [14] treated the problem by a standard stiffness approach using shape functions.…”