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

Authors :
Carlos Fuentes
Carlos Chávez
Fernando Brambila
Source :
Mathematics, Vol 8, Iss 12, p 2201 (2020)
Publication Year :
2020
Publisher :
MDPI AG, 2020.

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.

Details

Language :
English
ISSN :
22277390
Volume :
8
Issue :
12
Database :
Directory of Open Access Journals
Journal :
Mathematics
Publication Type :
Academic Journal
Accession number :
edsdoj.8100f5762e744bbaa4385a01e1fa31c7
Document Type :
article
Full Text :
https://doi.org/10.3390/math8122201