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[1] When the unsaturated flow equation is solved with the finite difference method, the water flux between two adjacent nodes of the grid is approximated with a discrete form of Darcy's law. It requires the average value of the hydraulic conductivity in the considered grid block. Since the hydraulic conductivity in unsaturated soil is a highly nonlinear function of the water potential, the nodal conductivities can vary by multiple orders of magnitude, which makes the choice of the appropriate averaging procedure a nontrivial task. In this paper we present a new method to calculate the internodal conductivity for an arbitrary type of the conductivity function and arbitrary large grid size. It is based on the analysis of approximate profiles of the water potential head for steady flow between nodes. Numerical experiments show that the method is reasonably accurate for a wide range of soil types, for both steady and unsteady flow simulations.

The HYDRUS-based flow package for MODFLOW (the HPM or the HYDRUS package) is an existing unsaturated zone flow package for MODFLOW. In MODFLOW with the HPM, the groundwater modeling domain is discretized into regular grids that can be combined into multiple zones based on similarities in soil hydrology, topographical characteristics, and the depth to the groundwater. Each of these zones is assigned one unsaturated soil profile (the HPM profile). In this model, after every MODFLOW time step, the flux at the bottom of the HPM profile is given as an input recharge flux to MODFLOW. MODFLOW simulates groundwater flow, and the water table depth at the end of the MODFLOW time step is assigned as the bottom boundary condition in the HPM profile. The current coupling algorithm assumes that the groundwater table in the HPM profile remains constant throughout the entire MODFLOW time step. This results in unrealistic sudden inflow and/or outflow fluxes at the bottom of the HPM profile after every time step. The objective of this study was to develop a methodology to eliminate the error in the determination of the recharge flux at the bottom of the HPM profile. This was achieved by updating or modifying the pressure head profile in the HPM profile after every MODFLOW time step. The effectiveness and the applicability of the new coupling algorithm were evaluated using different case studies. The new coupling algorithm is effective in eliminating unrealistic sudden variations in the bottom flux in the HPM profiles.Abbreviations: 1D, one-dimensional; 3D, three-dimensional; HPM, HYDRUS Package for MODFLOW.In the past few decades, the coupling of one-dimensional (1D) unsaturated zone models with three-dimensional (3D) groundwater flow models to simulate various processes in and interactions between unsaturated and saturated soil zones has received a lot of attention. This is mainly because of the computational complexity and requirements of fully 3D variably saturated flow models when modeling larger domains with unsaturated soil zones (e.g., SHE model [Abbott et al., 1986], MODFLOW-SURFACT [HydroGeoLogic, 1996], FEFLOW [Diersch and Kolditz, 1998], TOUGH2 [Pruess et al., 1999] MODFLOW (Harbaugh et al., 2000) is a widely accepted 3D groundwater flow model. There have been many attempts to incorporate unsaturated zone flow models into MODFLOW (e.g., Havard et al., 1995;Facchi et al., 2004;Niswonger et al., 2006;Twarakavi et al., 2008;Lin et al., 2010;Zhu et al., 2011;Xu et al., 2012). The basic principle behind linking independent models for unsaturated and saturated soil zones is the exchange of information regarding the recharge flux from the unsaturated zone to the saturated zone and the elevation of the water table at appropriate time steps.The HYDRUS-based flow package for MODFLOW (further referred to as the HPM or the HYDRUS package) was developed by Seo et al. (2007) and Twarakavi et al. (2008) to simultaneously evaluate transient water flow in unsaturated and saturated zones. In this package, the subroutines from the comput...

[1] This paper presents experimental verification of the mathematical model of unsaturated flow in double-porosity soils developed by the asymptotic homogenization method. A series of one-dimensional infiltration experiments was carried out in a column filled with a double-porosity medium composed of a mixture of sand and sintered clayey spheres arranged in a periodic manner. The unsaturated hydraulic properties of each porous material were obtained from independent infiltration experiments by inverse analysis and some additional tests. They were used to calculate the effective parameters of the double-porosity medium, i.e., the effective hydraulic conductivity and the effective capillary capacity. The numerical solution of the macroscopic boundary value problem, consisting of a highly nonlinear integrodifferential equation, was obtained using the Fortran code DPOR_1D presented by Lewandowska et al. [2004]. The calculated time evolutions of both water infiltrating into and flowing out from the double-porosity medium were compared with the experimental results. A very reasonable qualitative and quantitative agreement between simulations and observations is obtained, showing the capacity of the model to capture the main features of the process.

International audienceIn this paper the development and experimental validation of a numerical model of two-dimensional unsaturated flow in a double-porosity medium is presented. The model is based on the coupled formulation for flow in macro- and micropores obtained by homogenization. It was applied to simulate the axisymmetrical tension disk infiltration experiments that were carried out in a double-porosity medium. The physical model was a three-dimensional periodic structure, composed of porous spheres made of sintered clay and embedded in Hostun fine sand HN38. The hydraulic parameters of both porous materials were determined by inverse analysis of independent infiltration experiments performed on sand and sintered clay. The effective parameters of the double-porosity medium were calculated from the solution of the local boundary value problem, obtained from the homogenization procedure. The cumulative infiltration curve and the global dimensions of the humidified zone obtained from the numerical solution are in good agreement with the observations. Moreover, numerical simulations showed the existence of a narrow zone of local nonequilibrium that moves with the infiltration front. Upstream of this zone, the infiltration bulb is in the local equilibrium conditions

Natural soils very often contain micro-and macropores, having different hydraulic properties. At the macroscopic scale, the unsaturated flow in such soils can be described with various models, depending on the hydraulic diffusivity ratio of the components and the connectivity of the most conductive component. Three macroscopic models recently derived by the homogenization method are discussed. The limit passages between the models are studied. A unified model suitable for the entire range of the hydraulic diffusivity ratio is proposed. A numerical example shows the application of the model to macroscopically one-dimensional infiltration in a porous medium containing inclusions. A parametric study for varying conductivity (diffusivity) ratio is performed.Key words double-porosity media; homogenization; soil heterogeneity; subsurface flow, unsaturated zone; up-scaling Modèle macroscopique unifié d'écoulement insaturé dans les sols à porosité bimodaleRésumé Les sols naturels contiennent très souvent des micro-et des macropores dont les propriétés hydrauliques sont très différentes. A l'échelle macroscopique, l'écoulement insaturé dans ce type de sols peut être décrit par différents modèles selon le rapport de diffusivité hydraulique des composantes et selon la connectivité de la composante la plus conductrice. Nous discutons trois modèles macroscopiques récemment développés grâce à la méthode de l'homogénéisation. Les passages à la limite entre les modèles sont étudiés. Un modèle unifié est proposé, qui couvre toute la gamme du rapport de diffusivité hydraulique. Un exemple numérique montre l'application du modèle à l'infiltration macroscopiquement unidimensionnelle dans un milieu poreux comportant des inclusions. Une étude paramétrique selon le rapport de conductivité (diffusivité) est conduite.

Estimation of contaminant travel time through the vadose zone is needed for assessing groundwater vulnerability to pollution, planning monitoring and remediation activities or predicting the effect of land use change or climate change on groundwater quality. The travel time can be obtained from numerical simulations of transient flow and transport in the unsaturated soil profile, which typically require a large amount of data and considerable computational effort. Alternatively, one can use simpler analytical methods based on the assumptions of steady water flow and purely advective transport. In this study, we compared travel times obtained with transient and steady-state approaches for several scenarios. Transient simulations were carried out using the HYDRUS-1D computer program for two types of homogeneous soil profiles (sand and clay loam), two types of land cover (bare soil and grass) and two values of dispersion constant. It was shown that the presence of root zone and the dispersion constant significantly affect the results. We also computed the travel times using six simplified methods proposed in the literature. None of these methods was in good agreement with transient simulations for all scenarios and the discrepancies were particularly large for the case of clay loam with grass cover.