Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems

Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research.     

Consolidation around a heat source buried deep in a porous thermoelastic medium with anisotropic flow properties

A solution is derived for the heat flow and consolidation which occur when a heat source is buried deep in a porous thermoelastic soil having anisotropic flow properties. This solution is used to examine the pore pressure generation and dissipation near both point and cylindrical heat sources. An increase in temperature will tend to generate an increase in excess pore pressure. However, the pore water will tend to flow from regions of high excess pore pressure to regions of low excess pore pressure, and so consolidation will occur, and temperature-generated excess pore pressures will tend to dissipate. Many natural soils exhibit horizontal layering and so have a higher horizontal than vertical permeability. It is shown that in soils the excess pore pressure generated by a heat source is significantly less than that in an isotropic soil having an equal vertical permeability.     

A semi-analytical method for the wave-induced seabed response

A general semi-analytical method is presented for the analysis of seabed response under wave action during a storm. The seabed is idealized as a poro-elastic medium filled with a single compressible fluid with anisotropic flow. The coupled process of fluid flow and deformation of soil skeleton is formulated in the framework of Biot's theory. The analysis for the response of homogeneous seabed of finite thickness under a plane progressive wave is developed first, followed by an extension for the case of a layered seabed. A generalization for three-dimensional response of seabed is also developed for a general wave field which provides the analyses for seabed response under short-crested or standing waves in the vicinity of a structure. Some numerical examples illustrating the proposed analyses are also presented.     

The consolidation of a deep clay stratum subject to an impermeable axisymmetric surface loading

Previous analytic solutions to the problem of the consolidation of a deep clay stratum subjected to a surface loading, have been obtained for the assumed condition of a completely permeable upper surface. This may not be so in many applications, where the foundation causing the loading may be impermeable, and therefore only that part of the clay surface outside the loading is free to drain.In this paper a method is presented which may be used to obtain the time-settlement behaviour of a circular loading applied over an impermeable region of the surface of the clay. The solution technique involves representing the continuous values of fluid flow along the surface boundary as uniform blocks of flow. The solution is found in Laplace transform space and a numerical inversion technique is then used to obtain the time dependent solution.Two types of surface loading are examined; a completely uniform loading and a loading distribution which is approximately that of a rigid footing. For the uniform loading case, comparisons are made with previous solutions (permeable surface) and it is shown that the assumption of an impermeable loaded region leads to significant changes in the time-settlement behaviour of the loading.     

Pollutant migration from deeply buried repositories

Semi-analytic solutions are developed for the migration of pollutants from cylindrical and spherical repositories buried deep in a homogeneous and isotropic soil in the presence of a uniform and unidirectional advection. The techniques adopted involves taking the Laplace transform of the governing equations, finding an analytic solution in transform space and then numerically inverting the transform to obtain the concentrations of the contaminants at selected positions and times. Numerical results are presented, and practical implications discussed.     

Finite layer analysis of viscoelastic layered materials

A method is presented for obtaining the creep settlement of strip or circular loadings applied to horizontally layered soil profiles. The solution method involves applying a fourier (strip loading) or Hankel (circular loading) transform to the governing equations, which reduces the two of three dimensional problem to one involving a single spatial demension. This leads to great savings in computer storage and data preparation time, and since an exact solution may be found for each layer of material, the method has advantages over conventional finite layer techniques where field quantities must be approximated at a number of positions within each layer. The type of formulation presented hearein makies it possible to work in terms of the creep functions of the soil rather than the relaxation functions. This has distinct advantages, as it is often easier to measure the creep behaviour of a soil in the laboratory. Numerical techniques are used to invert the laplace and Hankel transforms and this means that any type of creep function (which is invertible) may be used to describe the material properties of the soil.     

The behaviour of an impermeable flexible raft on a deep layer of consolidating soil

Analytic solutions to the problem of the time-settlement behaviour of raft foundations have been limited in the past to flexible or rigid loadings, and have treated the foundation as being completely permeable. In this paper, solutions are presented for smooth circular rafts of any flexibility causing consolidation of a deep homogeneous clay layer, where the raft may be considered permeable or impermeable. Results for the time-dependent behaviour of contact stresses, pore pressures, raft displacements and moment in the raft are presented.