A simple hysteretic constitutive model for unsaturated flow

TL;DR

This paper introduces a simple hysteretic constitutive model for unsaturated flow that captures hysteresis phenomena and relates permeability to porosity using fractal pore distributions, fitting experimental data effectively.

Contribution

The paper presents a novel hysteretic model for unsaturated flow with simple expressions for saturation, hydraulic conductivity, and permeability-porosity relationship based on fractal pore structures.

Findings

Model fits experimental data well

Predicts permeability and hydraulic conductivity accurately

Hysteresis captured effectively in the model

Abstract

In this paper we present a constitutive model to describe unsaturated flow that considers the hysteresis phenomena. This constitutive model provides simple mathematical expressions for both saturation and hydraulic conductivity curves, and a relationship between permeability and porosity. The model is based on the assumption that the porous media can be represented by a bundle of capillary tubes with throats or "ink-bottles" and a fractal pore size distribution. Under these hypotheses, hysteretic curves are obtained for saturation and relative hydraulic conductivity in terms of pressure head. However, a non-hysteretic relationship is obtained when relative hydraulic conductivity is expressed as a function of saturation. The proposed relationship between permeability and porosity is similar to the well-known Kozeny-Carman equation but depends on the fractal dimension. The performance of the constitutive model is tested against different sets of experimental data and previous models. In all of the cases the proposed expressions fit fairly well the experimental data and predicts values of permeability and hydraulic conductivity better than others models.