Richards Equation

To better understand root-soil water interactions, a mature white fir (Abies concolor) and the surrounding root zone were continuously monitored (sap flow, canopy stem water potential, soil moisture, and temperature), to characterize tree hydrodynamics. We present a hydrodynamic flow model, simulating unsaturated flow in the soil and tree with stress functions controlling spatially distributed root water uptake and canopy transpiration. Using the van Genuchten functions, we parameterize the effective retention and unsaturated hydraulic conductivity functions of the tree sapwood and soil, soil and canopy stress functions, and radial root zone distribution. To parameterize the in-situ tree water relationships, we combine a numerical model with observational data in an optimization framework, minimizing residuals between simulated and measured observational data of soil and tree canopy. Using the MCMC method, the HYDRUS model is run in an iterative process that adjusts parameters until residuals are minimized. Using these optimized parameters, the HYDRUS model simulates diurnal tree water potential and sap flow as a function of tree height, in addition to spatially distributed changes in soil water storage and soil water potential.

The unsaturated hydraulic conductivity K(θ) and Soil Water Characteristic Curve (SWCC) for saline soil or soil directly contacted with saline water are not permitted using several apparatus to determining. Approach: A simplified method to determine K(θ) and SWCC by using simple apparatus is presented. Using the proposed numerical model with the van Genuchten equations and inverse calculation for K (θ) and SWCC to produce the best fit of this model calculation to the experimental cumulative capillary flow in dry soil columns. These are found by an optimization procedure which adjusts the parameters of K(θ) and SWCC. In addition, the resulting SWCC from the model was used to evaluate the K(θ) for the Gardner equation. Results: Values of saturated hydraulic conductivity K sat for the van Genuchten equations were lower than those based on the Gardner equation. The K sat values of dense soil were nearly overall lower than loose soil. Conclusion: Good agreement (R 2 value) was obtained in the SWCC and K sat values from the experiment and those calculated from the van Genuchten and Gardner equations this suggests that the simplified method provides a useful means of determining unsaturated flow parameters.

In this paper we describe the numerical code for a three-dimensional groundwater flow model. The model is developed for the case of variably saturated porous media, applicable to both the unsaturated (soil) zone and the saturated (groundwater) zone. The governing equation is nonlinear, and is linearized using either Picard or Newton iteration. The large sparse systems of linear equations generated by the finite element discretization are solved using efficient preconditioned conjugate gradient-like methods. Tetrahedral elements and linear basis functions are used for the discretization in space, and a weighted finite difference formula is used for the discretization in time. The code handles: temporally and spatially variable boundary conditions, including seepage faces and evaporation/precipitation inputs; heterogeneous material properties and hydraulic characteristics, including saturated conductivities, porosities, and storage coefficients; and various expressions to describe the moisture content-pressure head and relative conductivity-pressure head relationships. The model solves for nodal pressure heads, and uses these values to compute the water saturations and velocities over the flow domain. The water saturation and velocity values can be used as input to the LEA3D and NONLEA3D transport codes, which are described in a companion paper.

Flows in unsaturated medium are frequent in the field of civil engineering and more particularly in geotechnics. The study undertaken here tries to solve the unsaturated transient flow equation in porous media using the finite element method. Numerical solution of a finite element discretization is used along with an implicit integration scheme of the time stepping. A functional one that makes it possible to find the distribution of the hydraulic load has been proposed and a calculation program has been developed. The results obtained by this program called TFAP (Transient Flow Analysis Program) are compared to other previous work in the subject. The authors show the importance of this study through two real examples. Liakopoulos conducted several experiments on the water drainage through a vertical column filled with Del Monte sand. One of these experiments was chosen to perform a simulation by the model. The results of the calculation are compared with the experimental data as well.

The quaternary aquifer of Abidjan city, is often subjected to pollution because groundwater occurs at shallow depths (<6 m). However, this water is increasingly sought by one part of the population. Unfortunately the properties of this aquifer are not well known to define a management plan. This work aims to study quaternary aquifer through the hydrodynamic properties determination (porosity, saturated and unsaturated hydraulic conductivity and water retention curve) by prediction methods (Kozeny Carman, Kovac's modified and Brooks and Corey).The methods for predicting hydrodynamic properties tested gave good results. These methods have the advantage of using the physical properties of soil easy to measure. This is an original approach to the study of the hydrodynamic properties of the very extensive aquifers like the quaternary aquifer of Abidjan. These parameters are difficult to measure in situ.This work also highlighted risk areas for human settlements and infrastructure construction. Indeed, it is created permanent moisture above the water table in the fine sands. This moisture is the result of capillary rise which is important in fine soil particles.

The purpose of this article is to present the developed methodology, a brief algorithm of mechanical-and-mathematical modeling to investigate the causes and mechanism of soil disruption from the hillsides and the results of its use for restoring the pre-landslide stress state using the example of one of the tragic landslides. The numerical finite element algorithm of studying the stress–strain state (SSS) of soil deposits of slopes of the inclined-layered structure is briefly described, with specific features of the use of isoparametric elements of the quadrangular shape with four nodes of arbitrary shape. For detailed studying the SSS, the cover soils of the steep slope of the inclined-layered structure, in height from the arch to the foot, are conventionally divided into three zones, each of which has layered structures. Studies of the geometry of its area and the angle of inclination of the slope showed that the two-layer structure of its original structure made a curved path rep...

We consider the Si flux resulting from sand grain dissolution on beaches under the pressure of the intensive and continuous shaking by the waves, a potential source of oceanic DSi that is not currently considered. Today, DSi source and sink fluxes are balanced within large uncertainties, at ca. 10.4 ± 4.2 and 14.6 ± 7.8 × 10 12 mol yr -1 , respectively, underlining that some processes are not well constrained and possibly overlooked so far. To quantitatively explore this idea, we first realized an experimental dissolution of quartz grains in a stirred vessel designed to simulate the sediment orbital motion induced by the waves. These experiments lead to the calculation of a solidliquid mass-transfer coefficient directly linked to the rotation speed of the shaker. This coefficient being itself related to the energy communicated to the liquid, we could apply the Nienow relationship to calculate a mass-transfer coefficient for beach sand exposed to 1 m height waves. Extrapolation of this value to the whole sandy beaches led us to conclude that this mechanism could be significant, shortening the calculated residence time of oceanic DSi by up to a factor 2.

Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated fl...

Accurate numerical simulation of infiltration in the vadose zone remains a challenge, especially when very sharp fronts are modeled. In this work, we used the mixed hybrid finite element (MHFE) method, which allows a simultaneous approximation of both pressure head and velocity and can handle general irregular grids with highly heterogeneous permeability. For many problems dealing with unsaturated water flow, however, the MHFE solutions exhibit significant unphysical oscillations. To avoid this phenomenon, we developed an efficient mass‐lumping scheme with the MHFE method for solving the mixed form of the Richards equation. In this work, the standard and lumped MHFE formulations were compared and the ability of the lumped formulation to reduce unphysical oscillations was determined for one‐ and two‐dimensional infiltration problems. Theoretical analysis based on the M‐matrix property, which guarantees the discrete maximum principle, and practical test cases performed in this study u...

Cette these porte sur la modelisation de l’ecoulement et du transport en milieu poreux ;nous effectuons des simulations numeriques et demontrons des resultats de convergence d’algorithmes.Au Chapitre 1, nous appliquons des methodes de volumes finis pour la simulation d’ecoulements a densite variable en milieu poreux ; il vient a resoudre une equation de convection diffusion parabolique pour la concentration couplee a une equation elliptique en pression.Nous nous appuyons sur la methode des volumes finis standard pour le calcul des solutions de deux problemes specifiques : une interface en rotation entre eau salee et eau douce et le probleme de Henry. Nous appliquons ensuite la methode de volumes finis generalises SUSHI pour la simulation des memes problemes ainsi que celle d’un probleme de bassin sale en dimension trois d’espace. Nous nous appuyons sur des maillages adaptatifs, bases sur des elements de volume carres ou cubiques.Au Chapitre 2, nous nous appuyons de nouveau sur la me...

In this study, we investigate the triggering of shallow landslides through the analysis of physical experiments performed in an artificial hillslope. The physical model consists of a reinforced concrete box containing a soil prism with maximum height of 3.5 m, length of 6 m, and width of 2 m. In order to analyse and examine the factors leading to the failure and the triggering modes, the hillslope is equipped with sensors to monitor the pore water pressure and moisture content response to rainfall in a 60 cm thick sand layer overlying a sandy clay soil. Two experiments were performed with different degrees of the sand initial compaction, to investigate the role of porosity on the hydrologic response and the subsequent failure. The experimental results showed that, with initially loose sand, the failure occurred suddenly, without premonitory signs, the soil behaving like a viscous fluid. The collected data showed a rapid increase of the water pressure contextual to the failure of the...

This paper describes a coupled, distributed, hydrological‐geotechnical model, GEOtop‐FS, which simulates the probability of occurrence of shallow landslides and debris flows. We use a hydrological distributed model, GEOtop, which, models latent and sensible heat fluxes and surface runoff, and computes soil moisture in 3‐D by solving Richards&#39;equation numerically, together with an infinite‐slope geotechnical model, GEOtop‐FS. The combined model allows both the hydraulic and geotechnical properties of soil to be considered and realistically modelled. In particular, the model has been conceived to make direct use of field surveys, geotechnical characteristics and soil moisture measurements. In the model the depth of available sediments is also used to characterize the hydraulic properties of the area examined.To account for the uncertainty related to the natural variability in the factors influencing the stability of natural slopes, the safety factor is computed with a probabilisti...

The nature of pollutant connectivity between unsealed forest roads and adjacent nearby streams is examined numerically in terms of spatial and temporal patterns of runoff generation, erosion, and sediment transport. In this paper we consider the relative effects of rainfall intensity and duration, surface roughness, infiltration rate, macropore flow and sediment detachment and transport. The objective of the numerical simulation of this hillslope system is to identify the dominant processes and parameters that affect the degree of pollutant connectivity between roads and streams. The St. Venant equations are applied to extract a two-dimensional diffusion wave model with variable conductivity and diffusivity to represent the behaviour of flow dynamics mathematically. The resulting nonlinear partial differential equation was solved with appropriate initial and boundary conditions using the MacCormack finite difference numerical technique. Sediment detachment due to rainfall and flow dynamics is linked to the equations for mass conservation and continuity to represent erosion and was solved numerically using the finite difference method. The current numeric representation involves numerous parameters, many of which are unavailable for practical field application. Therefore, present work deals with the selection and/or development of methods to determine the relative significance of each process or parameter, so as to ultimately reduce the parameter space of this complex hillslope problem, improving our ability to scale-up the impacts of forest roads on catchment water quality in future works.

Predicting simultaneous movement of liquid water, water vapor, and heat in the shallow subsurface has many practical interests. The demand for multidimensional multiscale models for this region is important given: (a) the critical role that these processes play in the global water and energy balances, (b) that more data from air‐borne and space‐borne sensors are becoming available for parameterizations of modeling efforts. On the other hand, numerical models that consider spatial variations of the soil properties, termed here as multiscale, are prohibitively expensive. Thus, there is a need for upscaled models that take into consideration these features, and be computationally affordable. In this paper, a multidimensional multiscale model coupling the water flow and heat transfer and its respective upscaled version are proposed. The formulation is novel as it describes the multidimensional and multiscale tensorial versions of the hydraulic conductivity and the vapor diffusivity, tak...

A practical methodology is proposed to estimate the three-dimensional variability of soil moisture based on a stochastic transfer function model, which is an approximation of the Richard's equation. Satellite, radar and in situ observations are the major sources of information to develop a model that represents the dynamic water content in the soil. The soil-moisture observations were collected from 17 stations located in Puerto Rico (PR), and a sequential quadratic programming algorithm was used to estimate the parameters of the transfer function (TF) at each station. Soil texture information, terrain elevation, vegetation index, surface temperature, and accumulated rainfall for every grid cell were input into a self-organized artificial neural network to identify similarities on terrain spatial variability and to determine the TF that best resembles the properties of a particular grid point. Soil moisture observed at 20 cm depth, soil texture, and cumulative rainfall were also used to train a feedforward artificial neural network to estimate soil moisture at 5, 10, 50, and 100 cm depth. A validation procedure was implemented to measure the horizontal and vertical estimation accuracy of soil moisture. Validation results from spatial and temporal variation of volumetric water content (vwc) showed that the proposed algorithm estimated soil moisture with a root mean squared error (RMSE) of 2.31% vwc, and the vertical profile shows a RMSE of 2.50% vwc. The algorithm estimates soil moisture in an hourly basis at 1 km spatial resolution, and up to 1 m depth, and was successfully applied under PR climate conditions.

The heterogeneity of field scale soils poses a challenge to predictive large scale flow and transport modeling. The theory of effective macroscale parameters holds good and is applicable in dealing with such problems. But the validity of the analytic stochastic solutions obtained for randomly heterogeneous soils is debatable, as the test cases under which they are validated are of limited scope due to linearization and perturbation approximations. In this study, samples of heterogeneous soils are generated using sets of spatially correlated random field parameters that are either geometrically isotropic, or else, geometrically anisotropic with either horizontal or vertical stratification (perfect or imperfect). Several combinations of ratios of correlation length and capillary dispersion lengths are considered. Numerical simulations of unsaturated flow are performed on each randomly heterogeneous soil sample. The principal components K ii (Ψ) of the macroscale effective unsaturated conductivity are then obtained as a function of the mean suction Ψ of the sample. They are compared to stochastic spectral perturbation theory, and to a probabilistic semi-empirical Power Average Model (PAM). They are also compared with arithmetic, geometric and harmonic mean conductivity-suction curves. The numerically upscaled principal conductivity curves match quite well the PAM, better than the classical means (Arithmetic, Geometric, Harmonic), and also somewhat better than the curves obtained from stochastic spectral perturbation theory. It is observed that the upscaled principal components K ii ( ), obtained numerically and with the PAM along directions "i " orthogonal/parallel to perfect stratification coincide with the harmonic/arithmetic mean curves at low suctions (i.e., near saturation), but deviate from it and come closer to the geometric mean at higher suctions. The PAM appears suitable for generation of approximate upscaled conductivity curves, e.g., for obtaining the mesh-scale or block-scale conductivity curves in large scale simulation codes. Transient solute transport simulations are then performed on the detailed random velocity fields obtained from the steady state simulations of unsaturated flow in the randomly heterogeneous soil samples. Snapshots of solute concentration C(x,z,t) are taken at different times. The temporal evolution of spatial moments of concentration is analyzed in order to characterize the macroscale advection and dispersion of the unsaturated concentration plume, and in particular, its macro-dispersion coefficient (D) and dispersivity length scale (A). For the synthetic soil samples considered in this study, the macro-dispersive spreading of the solute is stronger for flow parallel to vertical stratification, compared to flow perpendicular to horizontal stratification, and also, compared to flow in statistically isotropic non-stratified soil.

analysis of water and heat balances in Tokyo metropolis is conducted by applying a distributed model. The subgrid heterogeneity of land covers is considered by using a nesting method . Evapotranspiration is computed by the Penman-Monteith equation and sensible heat flux by the aerodynamic method . Surface temperature is solved by the Force-Restore method. Infiltration excess during heavy rains is simulated by a generalized Green-Ampt model which considers soil stratification and rain unsteadiness. Saturation excess during the left periods is obtained by balance analysis in unsaturated soil layers. Two dimensional groundwater flow is simulated to consider the interactions between grid cells and the impact of groundwater table on surface runoff generation and heat flux partition . The simulated water and heat balances are dually verified both in the whole study area and in a catchment inside it . It is shown that both urbanization and weather variation have big impacts on water and heat balances in Tokyo metropolis.

One of the most familiar equations for examining the properties of infiltration in unsaturated regions of soil like a porous media is known as Richards' equation. The main aim of this paper is to illustrate the behaviour of the water transport problem in an unsaturated soil. The Variational Iteration Method and the Modified Variational Iteration Method have been used to determine an approximate analytical solution for Richards Equation at different cases. A comparison of the solution has been made with the exact solution, Finite Difference Method, and Elzaki Adomain Decomposition Method (EADM) solutions. For the numerical and graphical representation, MAPLE and MATLAB software are used.

A method for determining soil hydraulic parameters based on periodic point source solutions of the linearized Richards equation is proposed. Closedform solutions were derived for buried and surface point sources with a sinusoidally varying flux. These solutions describe the dependence of the matric flux potential (MFP) amplitude and phase shift on the distance from the point sources, frequency of source flux alternations, and soil hydraulic parameters. The Fourier series representation of square waves was used to extend the point source solutions for sinusoidally varying flux to square-wave cyclic inputs of water with a 50% duty cycle-a preferable operating mode for field experiments. Close to the sources, the amplitudes and shape of MFP waves from a step input were more pronounced than those from a sinusoidal input, but the difference diminished as distance increased. The proposed method involves recording the pressure head variations with a continuously reading tensiometer installed below a pressure-compensating emitter controlled by an irrigation computer. Among 16 cyclic step-input irrigation tests, one series involved pressure-head measurements at a single depth and varied water-pulse durations; the second involved pressure-head measurements at various depths with a fixed water-pulse duration. The soil saturated hydraulic conductivity, the coefficient a of Gardner's conductivity model, and the coefficient k of the linearized unsteady-flow equation were estimated by matching the periodic solution for cyclic step inputs to the measured pressure-head data with a two-step inversion procedure: an amplitude-shift (AS) estimation procedure followed by the Levenberg-Marquardt (LM) optimization algorithm. The AS procedure was effective, and the LM optimization yielded only minor improvements. Our main findings are: (i) the periodic solution for step inputs yields reasonably good predictions of pressure-head variations measured at various depths below an emitter for different periods of water application; and (ii) the proposed point-source method seems to yield consistent and reliable estimates of the three soil hydraulic parameters.

Foram realizados vários ensaios laboratoriais para avaliar o desempenho de um modelo numérico em simular o processo unidimensional da evaporação da água do solo. Este modelo foi desenvolvido a partir da linearização da equação de Richards no espaço e do uso da técnica iterativa de Newton-Raphson, para resolver essa equação não-linear no tempo, e leva em conta o fluxo de vapor dentro do perfil de solo e a taxa de evaporação na sua superfície. Os resultados mostraram que o modelo foi capaz de simular satisfatoriamente o processo, tanto em meios porosos homogêneos quanto estratificados

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore‐size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten&#39;s parameters α and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infilt...

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Peat soils respond to drying/wetting cycles due to evapotranspiration and precipitation with reversible deformations induced by variations of water content in both the unsaturated and saturated zone. This process results in short-term vertical displacements of the soil surface that superimpose to the irreversible long-term subsidence typically occurring in drained cropped peatlands because of bio-oxidation of the organic matter. Yearly sinking rates due to the irreversible process can be comparable with short-term deformation rates (swelling/shrinkage) and the latter must be assessed to achieve a thorough understanding of the whole phenomenon. A mathematical model describing swelling/shrinkage dynamics in peat soils under unsaturated conditions has been derived from simple physical considerations, and validated by comparison with laboratory shrinkage data. The two-parameter model expresses the void ratio of the soil as a function of the moisture ratio. This approach is implemented i...

Este trabajo usa la técnica de caracterización de materiales conocida en la bibliografía como "Small Punch Test" (SPT), considerada no destructiva y de bajo costo, debido a que, para su aplicación, se utiliza pequeñas muestras de material, si comparamos con otros tamaños de muestras usadas en otros ensayos, tanto la técnica como el modelo computacional son presentados juntos debido a su interrelación. Los resultados de la simulación son altamente correlacionados con los publicados. Luego de la puesta a punto y calibración del modelo, se presentan resultados optimizados de la caracterización del acero API 5L-X70 usado em gaseoductos, objetivo principal de este trabajo.

Este trabajo usa la técnica de caracterización de materiales conocida en la bibliografía como "Small Punch Test" (SPT), considerada no destructiva y de bajo costo, debido a que, para su aplicación, se utiliza pequeñas muestras de material, si comparamos con otros tamaños de muestras usadas en otros ensayos, tanto la técnica como el modelo computacional son presentados juntos debido a su interrelación. Los resultados de la simulación son altamente correlacionados con los publicados. Luego de la puesta a punto y calibración del modelo, se presentan resultados optimizados de la caracterización del acero API 5L-X70 usado em gaseoductos, objetivo principal de este trabajo.

This study focuses on the quantification of non-isothermal soil moisture transport and evaporation fluxes in vegetated area. A one-dimensional numerical model is developed by integrating a multi-phase flow model with a twolayer energy-balance model. The non-isothermal multi-phase flow model solves four governing equations for coupled air, vapour, moisture, and heat transport in soil porous medium. The two-layer energy balance model estimates evaporation fluxes from transpiration, interception, and soil surface. The model was implemented to an oak forest area in Missouri, USA. For model calibration and validation, measurements of energy fluxes, soil moisture, and soil temperature were used. The proposed model is compared with a simple model that couples the Penman-Monteith equation with the Richards’ equation. The results indicate that the simple model underestimate the total evaporation rate. On the contrary, the proposed model includes a more detailed description of energy transfer...

Resumo. O transporte de poluentes nos rios é fonte de estudo para vários autores, sendo que o problema considerado aqui tratou de um estudo de caso realizado no Rio Macaé. O objetivo do estudo foi determinar os valores dos parâmetros de dispersão que melhor ajustam o modelo ao conjunto de dados experimentais. A metodologia baseou-se na resolução por problemas inversos, em que o problema direto utilizou solução analítica e o inverso o método heurístico Simulated Annealing, também conhecido como "Recozimento simulado". Foi possível ajustar o modelo e testar o método em um espaço de busca contínuo com uma função objetivo baseada no erro de predição no problema inverso. Os resultados foram satisfatórios e permitiram um melhor ajuste do modelo quando compardo àquele obtido por Telles (2009).

Resumo. Neste artigo é resolvido um problema de difusão de calor bidimensional em uma geometria quadrangular com duas superfícies adiabáticas e duas apresentando fluxo de calor por convecção, de modo a apresentar transferência de calor linear no domínio de estudo, a partir dos métodos numéricos Volumes Finitos e Soluções Fundamentais, sendo o segundo utilizando pontos-fonte dentro do domínio, se assemelhando ao Método dos Nós de Contorno. Os dois métodos foram eficazes na determinação do perfil de temperatura no domínio. O Método das Soluções Fundamentais apresentou melhores resultados em relação à precisão e a velocidade em todos os casos estudados.

Enchentes sao fenomenos extremos e por isso a modelagem por distribuicoes de valores extremos e uma forma razoavel de abordar tais dados para suas analises de comportamento. O presente trabalho tem como finalidade ajustar dados de enchentes no Rio Negro, na cidade de Manaus - AM, durante o periodo de 2000 a 2015, com as distribuicoes de valores extremos Weibull, Gumbel e Fr´echet, estimando os parâmetros utilizando computacao bayesiana aproximada (ABC). Especificamente, e aplicado um metodo melhorado do algoritmo ABC original, chamado ABC-SMC, no qual e usado para a estimacao de parâmetros das distribuicoes propostas. Alem disso, o ABC-SMC tambem foi utilizado para selecao de modelos.

Soil water diffusivity (D) is an important hydraulic property that is fundamental to characterize unsaturated watertransport. Its determination is complex, time-consuming and requires expensive instruments. The objectives of this workwere: to propose a simple and low-cost laboratory methodology to determine D function; and to analyze the influence of soilmanagement systems on D and Sorptivity (S). The studied soil was classified as a vertic Paleudol. The first 10 cm of the soilunder three different management systems (T1: Natural grassland, T2: direct drilling, and T3: Polyphitic Pasture) was sampled.The samples were sieved and packed into horizontal columns. The columns were analyzed under horizontal infiltration and Dwas determined by variations of water content as a function of time for fixed positions, obtained from low-cost soil moisturecapacitance sensors. The results showed that the proposed methodology is valid in the studied soils. Soil management systemsignificantly affect...

In this study we develop a first‐order, nonstationary stochastic model for steady state, unsaturated flow in randomly heterogeneous media. The model is applicable to the entire domain of a bounded vadose zone, unlike most of the existing stochastic models. Because of its nonstationarity, we solve it by the numerical technique of finite differences, which renders the flexibility in handling different boundary conditions, input covariance structures, and soil constitutive relationships. We illustrate the model results in one and two dimensions for soils described by the Brooks‐Corey constitutive model. It is found that the flow quantities such as suction head, effective water content, unsaturated hydraulic conductivity, and velocity are nonstationary near the water table and approach stationarity as the vertical distance from the water table increases. The stationary limits and the critical vertical distance at which stationarity is attained depend on soil types and recharge rates. Th...

) is a mathematical model developed to foresee the triggering of rainfall-induced shallow landslides (soil slips) and the unstable condition of slopes affected by these phenomena. This physically-based model gives the factor of safety in function of the principal variables influencing the trigger of soil slips: rainfall, geometry, soil state, mechanical and hydraulic characteristics of soil. The specific characteristics of SLIP allowed to use the same means to model the phenomenon from the scale of the representative elementary volume (i.e. flume laboratory tests) to the medium and large scale (regional and national level). This paper (Part I), that is companion of another one published in this Conference (Part II), contains a brief description of the model and focuses on the approach followed in the application of the SLIP model at laboratory scale.

This paper presents the analytical solution to Richards' equation of hydrology for unsaturated soils. In order to facilitate the design and analysis of a real-time automatic irrigation system, an accurate model must be developed for the system. Richard's equation of water hydrology may be used to model part of the irrigation system. The major problem with the application of Richard's equation is in the linearization of the non-linear partial differential equation (PDE). In this paper, an empirical relationship stated by Gardner [1] was used to linearize the nonlinear PDE. The solution for the PDE was obtained using separation of variables technique.

We combine electromagnetic inversion of ground penetrating radar (GPR) signals with hydrodynamic inverse modeling to identify the effective soil hydraulic properties of a sand in laboratory conditions. Ground penetrating radar provides soil moisture time series that are subsequently used as input in the hydrodynamic inverse procedure. The technique relies on an ultrawide band (UWB) stepped frequency continuous wave (SFCW) radar combined with an off‐ground monostatic transverse electromagnetic (TEM) horn antenna. Ground penetrating radar signal forward modeling is based on the exact solution of the three‐dimensional Maxwell equations for describing free wave propagation and on linear systems in series and parallel for describing wave propagation in the antenna. Water flow in the sand is described by the one‐dimensional Richards equation using the Mualem–van Genuchten parameterization. Both model inversions are formulated by the classical least‐squares problem and are performed iterat...

Introductory Remarks by the Chairman "I believe the day must come when the biologist will-without being a mathematician-not hesitate to use mathematical analysis when he requires it." This statement was made by Karl Pearson in the January 17, 1901, issue of "Nature." The day has come, indeed, not oniy for the biologist but also for his brother the soil scientist, as the author proves in his excellent contribution to this symposium. It may be appropriate to supplement Pearson's words by the following remarks which Dr. Johnson made in the fourteenth "Rambler, 11 May 5, 1750: "The mathematicians are well acquainted with the difference between pure science, which has to do only with ideas, and the application of its .Laws to the use of lif~, i!! '.Vhich they are constrained to submit to the imperfections of matter and the influence of accident. 11

Subsurface drainage systems are used to control the depth of the water table and to reduce or prevent soil salinity. Water flow in these systems is described by the Boussinesq Equation, and the Advection-Dispersion Equation coupled with the Boussinesq Equation is used to study the solute transport. The objective of this study was to propose a finite difference solution of the Advection-Dispersion Equation using a lineal radiation condition in the drains. The equations’ parameters were estimated from a methodology based on the granulometric curve and inverse problems. The algorithm needs the water flow values, which were calculated with the Boussinesq Equation, where a fractal radiation condition and variable drainable porosity were applied. To evaluate the solution descriptive capacity, a laboratory drainage experiment was used. In the experiment, the pH, temperature, and electric conductivity of drainage water were measured to find the salt’s concentration. The salts concentration ...

At the interface between two dissimilar soils there are typically discontinuities in the water‐content and the gradients of both the flux and the soil matric potential (SMP). As the equation of motion for water depends on the gradient of flux, care must be taken to insure that the solution at such an interface obeys the relevant physical conditions. When a SMP‐based nodal average scheme is applied to a heterogeneous interface, a fundamental assumption (smoothness in the SMP profile) is violated, which typically leads to poor water balance and/or slow convergence with respect to grid size. We solve the water‐content based form of Richards&#39; Equation using continuity in flux and soil matric potential as boundary conditions. Our scheme builds in excellent water balance and typically converges as fast as water‐content based schemes for homogeneous soils. We show results for infiltration into a dry, stratified soil.

Water flow in partially saturated heterogeneous porous formations is modelled by regarding the hydraulic parameters as stationary random space functions (RSFs). As a consequence, the flow variables are also RSFs, and we aim to develop a procedure to derive the effective hydraulic conductivity (EHC). The methodology relies on a perturbation approach which regards the variances of the hydraulic parameters as small quantities. By using the GardnerÕs [Gardner WR. Some steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table. Soil Sci 1958;85:228-32] two-parameters (K s , a) model for the local unsaturated conductivity, we obtain the EHC for any dimensionality d of the flow domain, and arbitrary correlation functions of the input RSFs. Unlike previous studies [e.g. Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 1. Statistically isotropic media. Water Resour Res 1985;21;447-56, Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 2. Statistically anisotropic media with variable a. Water Resour Res 1985:21:457-64], the EHC is represented here as product between the local scale conductivity valid for a domain of mean parameters, and a correction function j * which depends on the medium heterogeneity structure and the mean pressure head. Generally, the correction function j * is expressed by d-fold quadrature. These quadratures are further reduced after adopting specific (i.e. exponential and Gaussian) structure for the (cross) correlation functions involved in the computation of j * . We have also focused on some particular formation structures which are relevant for the applications, and permit simplification of the computational aspect, as well. We investigate effects of the heterogeneity formation properties as well as the mean head on the structure of j * . Overall, results suggest that, given the formation statistics, the impact of the heterogeneity upon j * is enhanced as the medium becomes drier. This is particularly so when the variability of the fluctuation of Y = lnK s is small compared with that of f = lna. Conversely, when the heterogeneity of Y is prevalent upon that of f, j * is influenced solely by the anisotropic structure of the formation unless the horizontal correlation scales are much greater than the vertical ones.

The sustainable exploitation of groundwater resources is a multifaceted and complex problem, which is controlled, among many other factors and processes, by water flow in porous soils and sediments. Modeling water flow in unsaturated, non-deformable porous media is commonly based on a partial differential equation, which translates the mass conservation principle into mathematical terms. Such an equation assumes that the variation of the volumetric water content (θ) in the medium is balanced by the net flux of water flow, i.e., the divergence of specific discharge, if source/sink terms are negligible. Specific discharge is in turn related to the matric potential (h), through the non-linear Darcy–Buckingham law. The resulting equation can be rewritten in different ways, in order to express it as a partial differential equation where a single physical quantity is considered to be a dependent variable. Namely, the most common instances are the Fokker–Planck Equation (for θ), and the Ri...

Subsurface flow and storage dynamics at hillslope scale are difficult to ascertain, often in part due to a lack of sufficient high-resolution measurements and an incomplete understanding of boundary conditions, soil properties, and other environmental aspects. A continuous and extreme rainfall experiment on an artificial hillslope at Biosphere 2's Landscape Evolution Observatory (LEO) resulted in saturation excess overland flow and gully erosion in the convergent hillslope area. An array of 496 soil moisture sensors revealed a two-step saturation process. First, the downward movement of the wetting front brought soils to a relatively constant but still unsaturated moisture content. Second, soils were brought to saturated conditions from below in response to rising water tables. Convergent areas responded faster than upslope areas, due to contributions from lateral subsurface flow driven by the topography of the bottom boundary, which is comparable to impermeable bedrock in natural environments. This led to the formation of a groundwater ridge in the convergent area, triggering saturation excess runoff generation. This unique experiment demonstrates, at very high spatial and temporal resolution, the role of convergence on subsurface storage and flow dynamics. The results bring into question the representation of saturation excess overland flow in conceptual rainfall-runoff models and land-surface models, since flow is gravity-driven in many of these models and upper layers cannot become saturated from below. The results also provide a baseline to study the role of the coevolution of ecological and hydrological processes in determining landscape water dynamics during future experiments in LEO.

Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. We first study this problem which results into a variational inequality. We propose a discretization by an implicit Euler's scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem. Résumé: L'équation de Richards modélise l'écoulement d'eau dans un milieu poreux partiellement saturé souterrain. Lorsqu'il pleut, des conditions aux limites de type Signorini doiventêtre imposées sur la surface. Nousétudions tout d'abord ce problème qui se traduit par une inéquation variationnelle. Nousécrivons une discrétisation par schéma d'Euler implicite en temps etéléments finis en espace. La convergence de cette discrétisation permet de vérifier que le problème est bien posé.

Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. We first study this problem which results into a variational inequality. We propose a discretization by an implicit Euler's scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem. Résumé: L'équation de Richards modélise l'écoulement d'eau dans un milieu poreux partiellement saturé souterrain. Lorsqu'il pleut, des conditions aux limites de type Signorini doiventêtre imposées sur la surface. Nousétudions tout d'abord ce problème qui se traduit par une inéquation variationnelle. Nousécrivons une discrétisation par schéma d'Euler implicite en temps etéléments finis en espace. La convergence de cette discrétisation permet de vérifier que le problème est bien posé.

Heterogeneity in unsaturated soils and sediments is well known to exist at different scales, from microscopic scale to macroscopic scale. Characterization of different types of heterogeneity in deep vadose zones is challenging because of the usual lack of information at such sites. In this paper, we considered a site with detailed geological, chemical, and hydraulic properties measurements throughout an approximately 16‐m deep vadose zone consisting of unconsolidated, alluvial deposits typical for the alluvial fans of the eastern San Joaquin Valley, California. At the agricultural site, data were also available for a 7‐yr long field fertilization experiment that we used to independently estimate the amount of nitrate stored within the vadose zone at the end of the experiment. Simple mass balance calculations were performed and compared to six conceptually different two‐dimensional and three‐dimensional vadose zone numerical models that were implemented to represent varying degrees o...

In this paper, a modeling study is presented to simulate the fluid infiltration in fibrous media. The Richards' equation of two-phase flow in porous media is used here to model the fluid absorption in unsaturated/partially saturated fibrous thin sheets. The required consecutive equations, relative permeability, and capillary pressure as functions of medium's saturation are obtained via fiber-level modeling and a long-column experiment, respectively. Our relative permeability calculations are based on solving the Stokes flow equations in partially saturated three-dimensional domains obtained by imaging the sheets' microstructures. The Richards' equation, together with the above consecutive correlations, is solved for fibrous media inclined with different angles. Simulation results are obtained for three different cases of upward, horizontal, and downward infiltrations. We also compared our numerical results with those of our long-column experiment and observed a good agreement. Moreover, we establish empirical coefficients for the semianalytical correlations previously proposed in the literature for the case of horizontal and downward infiltrations in thin fibrous sheets.

In this paper, a modeling study is presented to simulate the fluid infiltration in fibrous media. The Richards’ equation of two-phase flow in porous media is used here to model the fluid absorption in unsaturated/partially saturated fibrous thin sheets. The required consecutive equations, relative permeability, and capillary pressure as functions of medium’s saturation are obtained via fiber-level modeling and a long-column experiment, respectively. Our relative permeability calculations are based on solving the Stokes flow equations in partially saturated three-dimensional domains obtained by imaging the sheets’ microstructures. The Richards’ equation, together with the above consecutive correlations, is solved for fibrous media inclined with different angles. Simulation results are obtained for three different cases of upward, horizontal, and downward infiltrations. We also compared our numerical results with those of our long-column experiment and observed a good agreement. Moreo...

RESUMEN Be presenta un modelo numerico para la simulacion de infiltracion y flujo subteml.neo unidimensional en medios porosos de saturacion variable. El algoritmo consiste en una discretizacion de la ecuacion de Richards que combina una linealizacion temporal usando un esquema de Picard con una aproximacion espacial utilizando un metodo mixto h.ibrido de elementos finitos. El algoritmo es computacionalmente eficiente y conservativo. Be incluyen ademas algunas caracteristicas relevantes del problema algebraico asociado y un ejemplo numerico de infiltracion en una zona de llanura.

This work consists in the presentation of a computational model to study normal and pathological behavior of red blood cells in slow transient processes that can not be accompanied by pure particle methods (the required time steps are very small). The basic model, inspired by the best models currently available, considers the cytoskeleton as a discrete non-linear elastic structure. The novelty of the proposed work, which will extend the simulation times and the robustness of the code, is to couple this skeleton with continuum models instead of the more common discrete models (molecular dynamics, particle methods) of the lipid membrane. The interaction of the solid cytoskeleton with the membrane, which is a two-dimensional fluid, will be done through adhesion forces adapting efficient solid-solid adhesion algorithms. The continuous treatment of the fluid parts is well justified by scale arguments and leads to much more stable and precise numerical problems when, as is the case, the s...