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

Carlos Fuentes, Carlos Chávez and Fernando Brambila
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Carlos Fuentes: Mexican Institute of Water Technology, Paseo Cuauhnáhuac Núm. 8532, Jiutepec 62550, Mexico
Carlos Chávez: Water Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Queretaro, Cerro de las Campanas SN, Col. Las Campanas, Queretaro 76010, Mexico
Fernando Brambila: Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Mexico City 04510, Mexico

Mathematics, 2020, vol. 8, issue 12, 1-14

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.

Keywords: areal porosity; volumetric porosity; fractal area-volume relationship; tortuosity factor; joint probability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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