Fractal Characteristics of the Horizontal Movement of Water in Soils

Abstract

Observed deviations from traditional concepts of soil-water movement are considered in terms of fractals. A connection is made between this movement and a Brownian motion, a random and self-affine type of fractal, to account for the soil-water diffusivity function having auxiliary time dependence for unsaturated soils. The position of a given water content is directly proportional to tn, where t is time, and exponent n for distinctly unsaturated soil is less than the traditional 0.50. As water saturation is approached, n approaches 0.50. Macroscopic fractional Brownian motion is associated with n < 0.50, but shifts to regular Brownian motion for n = 0.50.

Modeling water movement in horizontal columns using fractal theory

“…In both (Equations 1 and 2) the time exponent (n) was fixed at 0.5 (Clothier & Scotter, 2002). However in fractal characterization of water movement processes in the soil, the time empirical coefficient was estimated statistically, along with other hydraulic properties (Guerrini & Swartzendruber, 1994;Pachepsky & Timlin, 1998).…”

“…The diffusive process in a porous medium can be interpreted as a self-affine fractal. If this assumption holds, there is experimental evidence that the empirical coefficient n can be associated with fractal parameters such as the Hurst exponent (Guerrini & Swartzendruber, 1994). The objective of this study was to evaluate the correspondence between n and fractal parameters: fractal dimension (D) and the Hurst exponent (H).…”

Water transport in soils as in fractal media

“…They found a solution of the equation of water transport in unsaturated soil with time-dependent diffusivity. Later these authors suggested that a fractal Brownian motion can be a model for the soil water movement (Guerrini and Swartzendruber, 1994). Pachepsky et al (1995) conjectured that the fractal structure of soil pore space might cause an anomalous diffusion in soils.…”

Análise das características fractais do movimento vertical da água no solo, em condições de campo

“…Na área de fluxo da água no solo -um processo de difusão -alguns trabalhos de referência nessa área têm sido desenvolvidos para movimento horizontal em colunas de solo (Guerrini & Swartzendruber,1992, 1994e 1998Santos, 1997;Santos & Guerrini, 1998) e movimento vertical ( Guerrini et al, 1997), associando o processo de infiltração ao movimento browniano fracionário (fBm), que, como já foi citado, é um movimento reconhecidamente fractal.…”

“…Foi testado também outro modelo, proposto pelos mesmos autores, que é a equação de Weibull, um modelo estatístico: Hurst, baseando-se nos trabalhos de Feder (1988), Guerrini � Swartzendruber (1994, Santos (1997); Santos & Guerrini (1998). 25 6,5478!…”