The analysis of pollutant migration through soil with linear hereditary time-dependent sorption

This paper presents a non-equilibrium sorption dispersion–advection transport model for the analysis of pollutant migration through soil. The formulation involves a convolution integral of the product of the rate of change of concentration and a time-dependent sorption coefficient, suggesting an integral transformation of the governing equations. This facilitates the primary purpose of this paper, to incorporate a time-dependent solute sorption process into a computationally efficient and accurate semi-analytic Laplace transform method. An application of the non-equilibrium sorption model for backfiguring dispersion–advection equation parameters from experimental data is presented, and the implications of non-equilibrium sorption on the design of landfill liners is explored by means of an illustrative example.     

Boundary integral analysis of transient thermoelasticity

A simple and efficient method for the solution of uncoupled transient thermoelastic problems using boundary integral techniques is presented. The method employs a Laplace transformation to remove temporarily the time dependence of the governing equations. Numerical analysis is then carried out in the transform space, and results in the time-position space are found by numerical inversion of the Laplace transform. The method has the advantage that it avoids time-stepping and the costly evaluation of domain integrals. Boundary element and analytic solutions are compared, and the effect of cooling on the stresses around a deep underground opening is examined.     

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

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 two- or 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.     

Finite layer analysis of consolidation. I

A method for the analysis of the consolidation of a horizontally layered soil under plane conditions is developed. The method depends upon the transformation of the governing equations by a Fourier trasform. This transformation has the effect of reducing the partial differential equations of consolidation to ordinary differential equations. The ordinary differential equations are then solved using a finite layer or finite difference approach. Once the solution in the transformed plane has been found, the actual solution is synthesized by Fourier inversion. The method leads to a considerable reduction in the amount of core storage necessary for solution and enables the solution of quite significant problems to be obtained on a mini-computer.     

Elastic consolidation around a point sink embedded in a half-space with anisotropic permeability

The complete solution is presented for the transient effects of pumping fluid from a point sink embedded in a saturated, porous elastic half-space. It is assumed that the medium is homogeneous and isotropic with respect to its elastic properties and homogeneous but anisotropic with respect to the flow of pore fluid. The soil skeleton is modelled as a linear elastic material obeying Hooke's law, while the pore fluid is assumed to be incompressible with its flow governed by Darcy's law. The solution has been evaluated for a particular value of Poisson's ratio of the solid skeleton, i.e. 0.25, and the results have been presented graphically in the form of isochrones of excess pore pressure and surface profile for the half-space. The solutions presented may have application in practical problems such as dewatering operations in compressible soil and rock masses.     

The analysis of deformations caused by loading applied to the walls of a circular tunnel

An analytical solution to the problem of a load applied to a portion of the wall of a circular tunnel installed deep in a homogeneous isotropic material has been found. The solution is obtained by taking a Fourier transform, in the axial direction, of the field quantities and then representing these as a Fourier series in the polar angle. The integration which is necessary for the inversion of Fourier transforms has to be performed numerically using Gaussian quadrature. The solution has been used to analyse the problem of uniform normal loading applied over rectangular patches of the tunnel wall. An indication of how the solution can be applied to the tunnel jacking problem is given.     

The analysis of finite elasto-plastic consolidation

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto-plastic soil subject to finite deformations. The soil is assumed to be a two-phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto-plastic skeleton which obeys a Morh–Coulomb yield criterion and a non-associated flow law.     

A method of analysis for horizontally embedded anchors in an elastic soil

A general method is presented for the analysis of horizontally embedded anchors in an elastic soil. Provision is made in the analysis for the consideration of anchor shape, layer depth, anchor–soil interface condition, breakaway of the anchor from the underlying soil and interaction between groups of anchors. Application of the analytical technique is illustrated for strip and circular anchors, and these solutions are presented in the form of influence charts which may be used directly in hand calculations to predict the elastic load deflection behaviour, of anchor plates for a wide variety of material and geometric conditions.     

Predicting wetted width in any river at any discharge

Coefficients describing at‐a‐station power‐law relationships between discharge and width were calculated by applying multilevel models to field data collected during routine hydrological monitoring at 326 gauging stations across New Zealand. These hydraulic geometry coefficients were then estimated for each of these stations using standard stepwise multiple‐linear regression models. Analysis was carried out to quantify how the relationship between width and discharge changed in relation to several available explanatory variables. All coefficients describing the at‐a‐station hydraulic geometry were found to have statistically significant relationships with catchment area. Statistically significant relationships between each of the coefficients were also found with the addition of catchment climate as an explanatory variable. Further statistically significant relationships were found when station elevation and channel slope, as well as hydrological source of flow and landcover of the upstream catchment were added to the explanatory variables. The level of confidence that can be associated with estimates of width at ungauged sites, and sites with limited data availability, was then assessed by comparing model predictions with independent paired data on observed width and discharge from 197 sites. When compared against these independent data, model predictions of width were improved with the addition of predictor variables of the hydraulic geometry coefficients. The greatest improvements were made when climate was added to catchment area as predictor variables. Minor improvements were made when all available information was used to predict width at these independent sites. Although the analysis was purely empirical, results describing relationships between hydraulic geometry coefficients and catchment characteristics corresponded well with knowledge of the processes controlling at‐a‐station hydraulic geometry of river width. Copyright © 2010 John Wiley & Sons, Ltd.     

SURFACE DISPLACEMENTS OF A NON-HOMOGENEOUS ELASTIC HALF-SPACE SUBJECTED TO UNIFORM SURFACE TRACTIONS. PART I: LOADING ON ARBITRARILY SHAPED AREAS

A numerical technique is presented for the analysis of surface displacements of a non-homogeneous elastic half-space subjected to vertical and/or horizontal surface loads uniformly distributed over an arbitrarily shaped area. The non-homogeneity considered is a particular form of power variation of Young's modulus with depth. Since the exponent which determines the degree of non-homogeneity may vary from zero to unity, both the homogeneous half-space and the Gibson soil may be included as limiting cases in a single numerical scheme. In order to account for the arbitrary shape of the loading, the boundary of the loaded area is linearized piecemeal. This enables the modeling of any load pattern according to the desired degree of accuracy. Special attention is focused on the integration scheme, since the singularity associated with the Green's function becomes progressively more pronounced the greater the non-homogeneity parameter gets. The performance of the numerical procedure is studied using analytical solutions for rectangular shaped areas. Further comparisons with well-known solutions based on integral transform techniques for a uniformly distributed load acting on a circular area of the non-homogeneous soil mass show excellent agreement as well. © 1997 John Wiley & Sons, Ltd.