A Lattice Boltzmann model for studying transient effects during imbibition–drainage cycles in unsaturated soils

Abstract

This paper presents a numerical model based on the Lattice Boltzmann Method (LBM), developed for studying dynamic responses of an unsaturated porous medium to periodic imbibition and drainage induced by a cyclic water table movement. The model includes gravity which helps defining an hydraulic head. The model predicted an incremental increase of the overall water content in the medium over each cycle prior to a quasi-steady oscillatory state, a hydraulic ratcheting effect that has been previously observed in laboratory experiments. An empirical model was proposed to combine the transient and harmonic variations of the volumetric water content. The parameters of this empirical model were examined against physical quantities including the frequency of the driving water table oscillations and the porosity of the porous medium. The findings presented here may help to improve the formulation of constitutive models that are able to describe hydraulic processes of unsaturated soils.