One-dimensional Infiltration Research Articles

On the implementation of the surface conductance approach using a block-centred surface–subsurface hydrology model

• The surface conductance (SC) approach is explored for rainfall partitioning in a block-centred code. • A discrepancy arises between saturation of the uppermost node and the head reaching the land surface. • Previous research suggests the exchange interface be represented by the uppermost half-cell in MODHMS. • Our work suggests that the previous recommendation prevents accurate simulation of rainfall partitioning. • Adding a thin surface layer improves model accuracy with minimal increase in run time. In physically based catchment hydrology models, dynamic surface–subsurface interactions are often represented using the surface conductance (SC) coupling approach. Guidance on SC parameterisation within block-centred codes is limited, and common practice is to express the SC coefficient as the quotient of the vertical saturated hydraulic conductivity and the half-cell thickness of the uppermost layer. This study evaluates the implementation of the SC approach utilising a popular block-centred, surface–subsurface hydrology model (MODHMS) to simulate one-dimensional infiltration experiments under Hortonian conditions. Results show that defining the SC coefficient based on a half-cell thickness of the uppermost subsurface cell inhibits accurate prediction of infiltration rates ( q e ) and the time to initiate surface runoff ( t ro ) for the adopted rainfall–runoff scenario. Increasing the SC coefficient independently of the grid allows for accurate simulation of q e , but not t ro . The addition of a thin layer at the surface is shown to improve model accuracy substantially, such that q e and t ro approach those obtained using an equivalent mesh-centred model (i.e. where the surface and upper subsurface nodes are coincident). Whilst the addition of a single thin layer in block-centred codes allows improved prediction of surface–subsurface interaction, it does not provide a surrogate for fine discretisation throughout the subsurface that is necessary for accurate simulation of unsaturated zone flow. This study offers guidance on the implementation of the SC approach in a block-centred code and demonstrates the importance of systematic testing of parameters (that are otherwise calibrated) in physically based surface–subsurface hydrology models.

Response parameters for characterization of infiltration

Rainwater infiltration is of particular interest with respect to slope stability hazard management. The process of rainfall infiltration into unsaturated soil is complex due to the number of soil parameters involved and the random nature of moisture flux boundary conditions. In this paper, the effect of rainfall intensity on infiltration is investigated through the use of finite element seepage modeling for a 5 m high soil column subjected to various rainfall intensities. The numerical modeling study identified three response parameters that can be used to describe one-dimensional infiltration into an unsaturated soil. The response parameters are the depth of wetting front, the matric suction reduction depth, and the sectional infiltration rate. The practical application of the rainfall response parameters in slope stability analysis is illustrated.

Rainfall Infiltration Pattern in an Unsaturated Silty Sand

One-dimensional infiltration tests were conducted to investigate the effects of rainfall intensity and initial water content on the transient infiltration pattern of unsaturated silty sand. For a constant rainfall intensity greater than the saturated permeability but smaller than the maximum infiltration capacity of soil, the infiltration curve is divided into preponding and postponding stages. The time to ponding reduces with increasing rainfall intensity and initial water content. After ponding, the infiltration rate reduces with time and its reducing rate increases with rainfall intensity but does not vary significantly with initial water content. The infiltration pattern can be simulated qualitatively by solving Richard’s equation numerically with the use of the flux and head type boundary conditions at the soil surface in the preponding and postponding stages, respectively.

Green-Ampt One-Dimensional Infiltration from a Ponded Surface into a Heterogeneous Soil

Saturated hydraulic conductivity and wetting front pressure head (as soil properties) on an abrupt Green-Ampt front are assumed to increase and decrease with depth of a porous heterogeneous soil subject to a constant ponding or infiltration-evaporation depleted ponding on the surface. The corresponding Cauchy problem for a nonlinear ordinary differential equation describing the wetting front propagation in the soil profile is solved by computer algebra routines. Sensitivity of the cumulative infiltration to variation of hydraulic conductivity and capillarity is studied. A concave-convex infiltration graph is obtained for some values of parameters of the assumed exponential growth/decay of conductivity/capillarity. Texture of soil samples collected from a pedon is used for calculation of conductivity from a pedotransfer function. Synthesis of heterogeneity resulting in a specified front dynamics is discussed.

Physically Based Model for Simulating Flow in Furrow Irrigation. I: Model Development

Researchers developed several mathematical models for simulating furrow irrigation using the Saint-Venant equations. Most of these irrigation models use numerical techniques to solve these equations, which in general, require extensive programming and computational skills. Moreover, several of these models consider uniform soil and use empirical equations for modeling infiltration. In this article, a physically based furrow irrigation model was presented for simulating flow in irrigated furrows under both uniform and layered soils. The model consisted of an overland flow and an infiltration module that are modeled using analytical solution of the zero-inertia and the Green and Ampt [one-dimensional and two-dimensional infiltration equations) equations, respectively. Furthermore, the infiltration was also modeled using the Kostiakov-Lewis infiltration equation. The model considered all possible furrow shapes and included graphical user interface. The developed model was evaluated using the field data and the model performance was discussed in the second part of the article.

Infiltration analysis to evaluate the surficial stability of two-layered slopes considering rainfall characteristics

Shallow slope failures in residual soil during periods of prolonged infiltration are common throughout the world. Using a one-dimensional infiltration model and an infinite slope analysis, this study examines an approximate method of determining how infiltration influences the surficial stability of two-layered slopes. The method extends Moore's infiltration model, which is based on the Green–Ampt model, to cover more general situations, including those where water moves upward from a perched water table in decreasingly permeable soil. The method has also been used to evaluate the likelihood of a shallow slope failure being induced by a particular rainfall event. In making this evaluation, the method takes into accounts the rainfall intensity and duration of various return periods in a two-layered soil profile. A comparison of the results of the infiltration model with the results of numerical analyses shows that, with the use of properly estimated input parameters, the proposed model compares reasonably well with other model that rely on more rigorous finite element method.

CFD Analysis of One-Dimensional Infiltration in Vadose Zone

This study presents a CFD analysis constructed around PHYSICA, an open framework for multi-physics computational continuum mechanics modelling, to investigate the water movement in unsaturated porous media. The modelling environment is based on a cell-centred finite-volume discretisation technique. A number of test cases are performed in order to validate the correct implementation of Richard's equation for compressible and incompressible fluids. The pressure head form of the equation is used together with the constitutive relationships between pressure, volumetric water content and hydraulic conductivity described by Haverkamp and Van Genuchten models. The flow problems presented are associated with infiltration into initially dry soils with homogeneous or layered geologic settings. Comparison of results with the problems selected from literature shows a good agreement and validates the approach and the implementation.

Explicit Infiltration Function for Furrows

This study addresses infiltration from furrows or narrow channels. The basic approach is to develop the two-dimensional infiltration as a combination of the corresponding one-dimensional vertical and an edge effect. The idea is borrowed from previous applications for infiltration from disc and strip sources. The assumption is tested directly with numerical experiments using four representative soils and three furrow shapes (triangular, rectangular, and parabolic). The edge effect is the difference between the cumulative infiltration per unit of adjusted wetting perimeter and the corresponding one-dimensional infiltration. A general conclusion is that the edge effect is linearly related to time. In addition, it was observed that the two empirical parameters in the function used to relate the edge effect with time have narrow ranges and are related to soil hydraulic parameters, furrow shape, the boundary and initial conditions and additional geometric factors. The approach leads to a physically based infilt...

Quantification of infiltration processes in urban areas by accounting for spatial parameter variability

As a consequence of human living and activity, water infiltration to the urban subsurface occurs from a variety of different sources, like precipitation, irrigation, leaking pipes and sewers, septic tanks and rainwater infiltration ponds. This infiltration is strongly related with quality issues of the infiltrated water and further impact on groundwater quality. In order to set up an integrated urban water balance it becomes essential to estimate the infiltration processes, i.e. water flow and solute transport, from these different infiltration sources and to take into account the large spatial variability of sediment properties, the geometric settings of these sources and the groundwater table. For that purpose, the development of simple, physically-based quantification approaches is required in order to establish an efficiently working prediction and risk analysis tool within the framework of an integrated urban water management system. The scope of the presented work was to demonstrate the applicability of the developed approaches at urban scale. Since a detailed, three-dimensional, numerical quantification of the infiltration processes within the entire urban area is not possible, the individual sources were considered as independent within the EU AISUWRS project. Different models were developed for balancing infiltration from areal and point sources with respect to the related flow pattern. The analytical model UL_FLOW, based on one-dimensional, steady state analytical solutions, allows the estimation of conservative tracer residence times in layered sediments under varying infiltration rates. The numerical model WSTM, based on a three-dimensional random walk approach, calculates water and solute transport from pipe leaks. Additionally, the sources were classified in accordance to the spatial distribution of the parameters determining the infiltration processes. UL_FLOW was applied to data sets from the city of Rastatt within a case study of the AISUWRS project. Each neighbourhood of water balance computation by the Urban Volume and Quality Model (UVQ) was defined as an areal infiltration source with unique parameter values for sediment depth, profile and properties, as well as infiltration rate time series. Groundwater recharge and residence time series were computed for each neighbourhood. Relevant statistical parameters obtained by time series analyses from those time series could be mapped by GIS. Point infiltration, particularly from sewers, was classified due to the sediment parameters and the distance to the groundwater table at each source location in order to reduce computational efforts. WSTM computations provided time series of groundwater recharge and tracer breakthrough for some specific cases. The analytical model UL_FLOW provides fast and efficient computation of groundwater recharge and residence times accounting for storage effects within the unsaturated zone of urban areas. The reliability of this model has been shown by cross validation with HYDRUS1D. Because of the high computational effort, WSTM could provide only short-term simulations for some specific parameter sets for which residence time estimates could be derived. UL_FLOW provides an analytical modelling tool for balancing one-dimensional areal infiltration and estimating residence times under varying conditions including spatial parameter variability. These balances could be used for assessing the impact of those infiltration sources on groundwater quality. The tracer breakthrough from point infiltration sources computed by WSTM could also be used for such kinds of assessment. The larger spatial parameter variability associated with these sources could be handled by classification in GIS environments. Similar to the areal sources, a simple balance approach for point sources based on analytical solutions needs to be developed for estimating residence times in order to avoid large computational efforts. Such a model would complete the balancing of all kinds of infiltration sources in urban areas efficiently. Since the approaches are based on the balance of the physical processes, they have a large predictive capability and could be included into an integrated urban water balance and management system. The mapping of the statistical values of the residence times provides a tool to compare parts of the urban areas and to visualize differences between urban water management scenarios.

Aggregation of vertical flow in the vadose zone with auto- and cross-correlated hydraulic properties

Summary Quantifying water flow across larger areas of the vadose zone has applications in water resources management and climate modeling. The nonlinearity of unsaturated flow and the variability of vadose zone parameters make it difficult, if not impossible, to accurately simulate near-surface water content and flux with large-scale models. Monte Carlo simulations of one-dimensional infiltration and evaporation were conducted with the Richards equation to simulate moisture content and flux in a heterogeneous field according to the streamtube concept. A set of 126 retention curves and saturated hydraulic conductivities from the UNSODA database was used to generate random fields of hydraulic parameters with pre-defined auto- and cross-correlation. Two stochastic parameters were used: the retention shape factor, ln mn , and either the retention scale parameter θ s or ln h G or the saturated hydraulic conductivity, ln K s . Infiltration is mostly governed by ln K s . The evaporative flux is strongly determined by the “structural” parameter ln h G and also by the “textural” parameter ln mn . The water content in the upper part of the soil depends mostly on ln mn and somewhat on θ s . Cross-correlations all resulted in clusters with consistently low or high water contents and moisture fluxes. Aggregation to obtain results at larger scales was done by a posteriori averaging of local results. This procedure is a convenient benchmark for large-scale modeling approaches. In an example of a priori aggregation, effective retention parameters were optimized to synthetic retention curves for the larger pixel scale and subsequently used in the Richards equation. The amount of infiltrated water was overestimated by up to 40%, large parts of the upper profile were erroneously predicted to be saturated. Although effective hydraulic properties have been used successfully in evaporation studies, considerable errors, which increased with pixel size, also occurred for evaporation. The stream tube modeling offers a convenient and accurate, albeit mundane, approach to elucidate the role of hydraulic properties and to obtain large-scale hydrological data.

Modified Kostiakov Infiltration Function: Accounting for Initial and Boundary Conditions

The effect of specific initial and boundary conditions is generally not considered when applying the Kostiakov infiltration functions. A methodology is developed to account for changes in water levels and initial soil moisture. First, Richards’ equation is solved numerically to generate a database of one-dimensional infiltration values, with varying initial (water content or pressure head) and boundary (ponding depth) conditions for three contrasting soils. These are then used to calibrate corresponding coefficients for modified Kostiakov models and, by considering linear regressions, to obtain simple correction factors. Results show that the correction factors are not universally valid, and only the correction to the Kostiakov k parameter shows statistically consistent applicability. However, examples demonstrate potentially significant improvement in the accuracy of irrigation models by correcting the Kostiakov equation to account for initial and boundary conditions.

Unified macroscopic model for unsaturated water flow in soils of bimodal porosity

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.

Non-passive transport of volatile organic compounds in the unsaturated zone

A detailed model was formulated to describe the non-passive transport of water-soluble chemicals in the unsaturated zone and used to illustrate one-dimensional infiltration and redistribution of alcohol–water mixtures. The model includes the dependence of density, viscosity, surface tension, molecular diffusion coefficient in the liquid-phase, and gas–liquid partition coefficient on the aqueous mixture composition. It also takes into account the decrease in the gas–liquid partition coefficient at high capillary pressures, in accordance with Kelvin’s equation for multi-component mixtures. Simulation of butanol–water mixtures infiltration in sand was in agreement with the experimental data and simulations reported in the literature. Simulation of methanol infiltration and redistribution in two different soils showed that methanol concentration significantly affects volumetric liquid content and concentration profiles, as well as the normalized volatilization and evaporation fluxes. Dispersion in the liquid-phase was the predominant mechanism in the transport of methanol when dispersivity at saturation was set to 7.8 cm. Liquid flow was mainly due to capillary pressure gradients induced by changes in volumetric liquid content. However, for dispersivity at saturation set to 0.2 cm, changes in surface tension due to variation in composition induced important liquid flow and convection in the liquid-phase was the most active transport mechanism. When the Kelvin effect was ignored within the soil, the gas-phase diffusion was significantly lower, leading to lower evaporation flux of water and higher volumetric liquid contents near the soil surface.

Soil Temperature Change over Time during Infiltration

Heat of wetting (HOW) effects release energy during infiltration of water into soil and temperature changes result. We call these changes infiltration transient temperature (ITT). Experiments determined ITT frequently during one‐dimensional infiltration events. We measured ITT in columns of silty clay and loam soils, at several initial water contents, during constant‐rate infiltration. There was a directly increasing, but nonlinear, relationship of ITT to clay content and a decreasing, nonlinear relation to initial water content, ranging from 1°C maximum in loam at 0.04 g g−1 initial water content to 11°C maximum in silty clay at 0.00 g g−1 We compared the resulting experimental temperature profiles to those generated from a one‐dimensional soil water and heat transport model using the relevant initial and boundary conditions. The model‐predicted ITT profiles exhibited the major features of the experimentally measured profiles. Disabling the HOW effect part of the model resulted in a much smaller predicted temperature peak and a subsequent temperature decrease below ambient behind the wetting front. Since experiments and a numerical model have shown ITT to be appreciable, it is important to understand more completely the role of HOW in coupled soil water and heat transport.

Modeling Two-Dimensional Infiltration from Irrigation Furrows

Numerical simulation of the two-dimensional (2D) infiltration process during furrow irrigation requires considerable computational effort, which can be reduced by analytical modeling. This paper deals with the further development of the semianalytical infiltration model FURINF (furrow infiltration). Considering the varying impact of gravity and furrow geometry, the new approach models the impact of furrow geometry on infiltration progress using a transient geometric shape factor as a function of infiltration time and furrow geometry. FURINF portrays 2D infiltration from the wetted furrow perimeter by a series of one-dimensional (1D) infiltration computations that are performed in this paper on the basis of an analytical as well as a numerical solution of the 1D Richards equation. Comparing the FURINF results provided by the analytical and numerical 1D infiltration model confirmed the adequacy and reliability of the robust and simple analytical approach, which only requires soil parameters provided by rather simple measurements. The results and performances of the analytical FURINF model (FURINF-A) are compared within the frame of a sensitivity and error analysis with the outcome of the numerical subsurface flow model HYDRUS-2D considering three different soils.

Numerical Simulations of One-Dimensional Infiltration into Layered Soils with the Richards Equation Using Different Estimates of the Interlayer Conductivity

Transient water flow processes in unsaturated soils are usually modeled using the Richards equation. This paper compares several numerical approximations to this equation for vertical infiltration in layered soil profiles. Three formulations of the governing flow equation (i.e., the h-based, θ-based, and mixed forms) are compared for the critical test problem of infiltration into a layered soil profile with initially relatively low soil water contents. An efficient, yet relatively simple weighting algorithm is employed that improves the estimation of the interlayer hydraulic conductivity in an h-based finite-difference formulation. Results highlight improvements in the mass conservative properties of this model, which is termed the H-IL model A comparison is then performed between the finite-difference H-IL model and a finite-element model for infiltration toward a water table. The H-IL model was found to be computationally very efficient for this test problem. For both illustrative flow examples, the different numerical models were evaluated in terms of their ability to reproduce an exact solution developed by Srivastava and Yeh (1991) in their work on one-dimensional, transient infiltration toward the water table in homogeneous and layered soils.

One-dimensional steady infiltration with water extraction

Exact solutions of the one-dimensional steady infiltration with water extraction are obtained for a particular but realistic form of the soil–water conductivity. The results are compared with numerical solutions for slightly different forms of the soil–water conductivity function, showing the sensitivity of the shape of the profiles on the exact representation of the soil–water conductivity. The exact solutions are an extension of Warrick's (1974) solution for the case where the soil can become saturated.

Numerical Simulations of One-Dimensional Infiltration into Layered Soils with the Richards Equation Using Different Estimates of the Interlayer Conductivity

Transient water flow processes in unsaturated soils are usually modeled using the Richards equation. This paper compares several numerical approximations to this equation for vertical infiltration in layered soil profiles. Three formulations of the governing flow equation (i.e., the h-based, θ-based, and mixed forms) are compared for the critical test problem of infiltration into a layered soil profile with initially relatively low soil water contents. An efficient, yet relatively simple weighting algorithm is employed that improves the estimation of the interlayer hydraulic conductivity in an h-based finite-difference formulation. Results highlight improvements in the mass conservative properties of this model, which is termed the H-IL model A comparison is then performed between the finite-difference H-IL model and a finite-element model for infiltration toward a water table. The H-IL model was found to be computationally very efficient for this test problem. For both illustrative flow examples, the different numerical models were evaluated in terms of their ability to reproduce an exact solution developed by Srivastava and Yeh (1991) in their work on one-dimensional, transient infiltration toward the water table in homogeneous and layered soils.

Infiltration through Deformable Porous Media

The equations driving the flow of an incompressible fluid through a porous deformable medium are derived in the framework of the mixture theory. This mechanical system is described as a binary saturated mixture of incompressible components. The mathematical problem is characterized by the presence of two moving boundaries, the material boundaries of the solid and the fluid, respectively. The boundary and interface conditions to be supplied to ensure the well-posedness of the initial boundary value problem are inspired by typical processes in the manufacturing of composite materials. They are discussed in their connections with the nature of the partial stress tensors. Then the equations are conveniently recast in a material frame of reference fixed on the solid skeleton. By a proper choice of the characteristic magnitudes of the problem at hand, the equations are rewritten in non-dimensional form and the conditions which enable neglecting the inertial terms are discussed. The second part of the paper is devoted to the study of one-dimensional infiltration by the inertia-neglected model. It is shown that when the flow is driven through an elastic matrix by a constant rate liquid inflow at the border some exact results can be obtained.

Experimental evidence and theoretical analysis of anomalous diffusionduring water infiltration in porous building materials

The infiltration of liquid and the propagation of the moisturefront in non-saturated porous media are generally described by a diffusionequation that predicts a scaling law of the type x/(t)1/2 in onedimension. This model, generally referred to as the theory of unsaturatedflow, was systematically applied to account for water movements in porousbuilding materials. In this paper, two sets of nuclear magnetic resonance(NMR) one-dimensional water absorption profiles, respectively measured ina fired-clay brick and a limestone specimen, are re-examined according tothis model. The reinterpretation of the NMR absorption data providesevidence that the infiltration front does not propagate as t1/2neither in brick nor in limestone, i.e. the absorption process does notconform to the predictions of the unsaturated flow theory in thesematerials. A new theoretical model for infiltration, based on theassumption of a non-Fickian diffusion mechanism, is thus introduced. Thewater transfer in partially saturated materials is assumed to follow thegeneral nonlinear diffusion equation (∂θ/∂t)-(∂/∂x)[D(θ)(∂θ/∂x)n] = 0, withn real. For one-dimensional infiltration, the water content θ canbe expressed in terms of the single variable ϕ* = xt-α, withα = 1/(n + 1) and the cumulative water infiltration I is given at anytime by I = ∫θ0θ1x dθ = tα∫θ0θ1ϕ* dθ = S*tα. The NMR absorption data are shown to be compatible witha non-Fickian diffusion process scaling as t0.58 in brick and ast0.61 in the limestone specimen. The application of the new anomalousdiffusion model to brick indicates that the previous t1/2 relationmay underestimate the volume of absorbed water by about 30% after only100 hours. This result has particular relevance for evaluating thedurability of building structures.