Relating Hydraulic Conductivity Curve to Soil-Water Retention Curve Using a Fractal Model

Abstract

In the study of water transference in soil according to Darcy law, the knowledge of hydrodynamic characteristics, formed by the water retention curve θ(ψ), and the hydraulic conductivity curve K(ψ) are of great importance. The first one relates the water volumetric content (θ) with the water-soil pressure (ψ); the second one, the hydraulic conductivity (K) with the water-soil pressure. The objective of this work is to establish relationships between both curves using concepts of probability theory and fractal geometry in order to reduce the number of unknown functions. The introduction of four definitions used at the literature of the pore effective radius that is involve in the general model has permitted to establish four new specials models to predict the relative hydraulic conductivity. Some additional considerations related to the definitions of flow effective area and the tortuosity factor have allow us to deduce four classical models that are extensively used in different studies. In particular, we have given some interpretations of its empirical parameters in the fractal geometry context. The resulting functions for hydrodynamic characteristics can be utilized in many studies of water movement in the soil.

Evaluation of Soil-Water Characteristic Curves for Different Textural Soils Using Fractal Analysis

“…The water retention capacities for the 12 soil textures were consistent with soil's fractal characteristics. It could draw a conclusion that the fractal dimension is sensitive to soil texture and hydraulic properties [77]. The shape and parameter changes of SWCCs with different textures could be determined by the value of fractal dimension.…”

Estimating the Soil-Water Retention Curve of Arsenic-Contaminated Soil by Fitting Fuentes’ Model and Their Comparison with the Filter Paper Method

“…where Ts is the superficial tension, and R corresponds to the radius of the pore. The model by Fuentes [36] helps establish a relationship between the particle size distribution and porosimetry curve, where the physical volume of the soil is characterized by spheres of equivalent diameter, as indicated in Equation (3):…”

“…To reduce the number of unknown functions in the aerated soil zone, Fuentes [36] introduced the fractal relation to the common parameters. This was performed by hypothesizing the flow resistance, which is a function of capillary pore size.…”

“…Hence, there is uncertainty about whether such models can be directly used to evaluate the SWRC of the contaminated soils. Thus, the objective of the present study was to elucidate if Fuentes' model [36] can be used to estimate the SWRC of arsenic-contaminated soil, by comparing it with the reported filter paper method data [29] at the wetting path.…”

Preface to “Mathematical Methods, Modelling and Applications”

“…Papers [4][5][6] are linked to step (ii). All the remaining papers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] are related to step (iii) covering a wide spectrum of methods, deterministic and random, algebraic and differentials, in different fields Hydrodynamic, Physics, Health Sciences.…”