Computer construction of fractal soil structures: Simulation of their hydraulic and shrinkage properties

Abstract

To study relationships between soil hydraulic properties and soil structural properties, a computer micro model of soil is constructed. We present first a general method of building a two-dimensional porous structure, including both pores and particles, with different levels of aggregation resulting from a fragmentation process. A fractal structure is obtained when self similarity is imposed over the successive scales of fragmentation. Emphasis is put upon the modeling of the retention curve. A classical capillary model and methods taken from percolation theory enable us to simulate qualitatively the primary and secondary loops of this hysteretic curve. In the fractal case, theoretical analytical expressions proposed for adjusting retention data are tested. The unsaturated hydraulic conductivity is also calculated on the same simulated soil by analogy with an electrical network. The soil structures are deformable and simulation proves to be a useful tool to investigate the behavior of swelling soils. IntroductionKnowledge of the specific hydraulic behavior of a given soil is needed to model water transport in the unsaturated zone. The basic hydraulic properties, mainly the retention and conductivity curves, are usually determined by controlled flow experiments either in the laboratory or in the field. It is an old dream among soil scientists to directly relate these hydraulic properties to structural properties which could be obtained more easily on dry soil samples. Numerous attempts have been made to find either statistical relations or deterministic links between structural data and hydraulic properties. This paper is concerned with a deterministic approach.Research has been done [e.g.,Arya and Paris, 1981; Haverkampf and Parlange, 1986; Tyler and Wheatcraft, 1989, 1992] to link hydraulic properties to the particle size distribution in a soil, which structural information is easily and widely obtained through mechanical sieving. The texture models whose definition of the soil is based on matrix properties such as particle diameter or particle shape (e.g., the spheres models) view the solid phase as a set of discrete particles and the void phase as a continuum. The complex geometry of the remaining voids makes the analysis of flow too difficult unless one works at the Navier-Stokes scale, dealing with only a few particles as in lattice gas simulations [di Pietro et al., 1994]. At the pore scale, the pore space must be divided into a set of simple geometric parts, such as cylinders or parallepipeds, so that integrated forms of the fluid movement equations can be used. A common approach is therefore to invent a pore space model with a simple geometry that can be associated with the particle distribution. For example, Arya and Paris [1981] associated a tube with each particle size class and treated the pore space as a bundle of capillary tubes. However, to obtain good agree-Paper number 95WR02214. 0043-1397/95/95WR-02214 $05.00 ment between calculated and observed retention data, they needed to add an empirical fi...

Fractal analysis of the heat treatment response for multiphase Al alloys

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Water retention of prefractal porous media generated with the homogeneous and heterogeneous algorithms

“…There has been considerable debate about the validity of the approaches presented in these papers because they generally neglect pore connectivity [Bird et al, 1996;Rieu and Perrier, 1998]. One way that this limitation can be surmounted is to compute retention in simulated realizations of known fractal porous media using a method that explicitly accounts for pore connectivity [Perrier et al, 1995;Bird and Dexter, 1997;Stepanek et al, 1999]. As these and other types of simulations in fractal porous media become more widespread, it is valuable to examine the methods used to generate the media and their properties.…”

Unsaturated hydraulic conductivity from nuclear magnetic resonance measurements

“…P c (S w ) and k rw (S w ) are hysteretic functions describing the dependence of capillary pressure and water relative permeability, respectively, on water saturation. From a theoretical perspective and with particular emphasis on drainage-type displacements, much effort has been directed toward explaining the form of P c (S w ) and k rw (S w ) functions in terms of soil structure and pore-scale fluid distribution [e.g., Tyler and Wheatcraft, 1990;Rieu and Sposito, 1991;Perrier et al, 1995;Kosugi, 1996;Or and Tuller, 1999;Hunt and Gee, 2002;Chan and Govindaraju, 2003], offering physically meaningful alternatives to commonly used empirical expressions [e.g., Brooks and Corey, 1964;Mualem, 1976;van Genuchten, 1980].…”