Hydraulic Properties and Non-equilibrium Water Flow in Soils

Accurate knowledge of hydraulic properties for unsaturated soils is critical in the estimation of soil water fluxes by simulation models that are based on the Richards equation. The purpose of this chapter is to review the characterization of unsaturated soil hydraulic properties for their applicability in models simulating unsaturated water transport. We start with a short review of the fundamentals that lead to the definition of the hydraulic functions in the framework of continuum hydromechanics. Next, we address problems of common parameterizations of hydraulic functions in the critical regions near and at saturation, towards dryness, and on hysteresis. We find that traditional approaches have deficiencies, but recent progress has been significant in particular with respect to including film and corner flow components in the hydraulic conductivity function. The chapter closes with a discussion of the phenomenon of dynamic non-equilibrium in soil water flow, which shows to our opinion toward the need for a paradigm change in the modeling of soil water transport.

[1]  Randel Haverkamp,et al.  Application of a simple soil-water hysteresis model , 1988 .

[2]  John R. Nimmo,et al.  Modeling of soil water retention from saturation to oven dryness , 1994 .

[3]  Nunzio Romano,et al.  Soil moisture at local scale: Measurements and simulations , 2014 .

[4]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[5]  R. A. Shcherbakov,et al.  SCALING OF SOIL WATER RETENTION USING A FRACTAL MODEL , 1995 .

[6]  Feike J. Leij,et al.  Characterization and measurement of the hydraulic properties of unsaturated porous media : proceedings of the International Workshop on Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media, Riverside, California, October 22-24, 1997 , 1999 .

[7]  Y. Mualem,et al.  General scaling rules of the hysteretic water retention function based on Mualem’s domain theory , 2009 .

[8]  William B. Haines,et al.  Studies in the physical properties of soil. V. The hysteresis effect in capillary properties, and the modes of moisture distribution associated therewith , 1930, The Journal of Agricultural Science.

[9]  Horst H. Gerke,et al.  Preferential flow descriptions for structured soils , 2006 .

[10]  M. Th. van Genuchten,et al.  Effect of the shape of the soil hydraulic functions near saturation on variably-saturated flow predictions , 2000 .

[11]  Van Genuchten,et al.  A closed-form equation for predicting the hydraulic conductivity of unsaturated soils , 1980 .

[12]  Ulrich Fischer,et al.  Dependence of hydraulic and pneumatic characteristics of soils on a dissolved organic compound , 1998 .

[13]  Delwyn G. Fredlund,et al.  A study of hysteresis models for soil-water characteristic curves , 2005 .

[14]  Marcel G. Schaap,et al.  Improved Prediction of Unsaturated Hydraulic Conductivity with the Mualem‐van Genuchten Model , 2000 .

[15]  Hannes Flühler,et al.  Lateral solute mixing processes — A key for understanding field-scale transport of water and solutes , 1996 .

[16]  Diganta Bhusan Das,et al.  Experimental investigation of hysteretic dynamic effect in capillary pressure–saturation relationship for two‐phase flow in porous media , 2013 .

[17]  Hans-Jörg Vogel,et al.  Virtual Soils: Moisture Measurements and Their Interpretation by Inverse Modeling , 2013 .

[18]  Dani Or,et al.  Hydraulic conductivity of variably saturated porous media: Film and corner flow in angular pore space , 2001 .

[19]  Scott W. Tyler,et al.  Application of Fractal Mathematics to Soil Water Retention Estimation , 1989 .

[20]  Tetsu K. Tokunaga,et al.  Hydraulic properties of adsorbed water films in unsaturated porous media , 2009 .

[21]  Marc Van Meirvenne,et al.  Comparison of Unimodal Analytical Expressions for the Soil-Water Retention Curve , 2005 .

[22]  Keith Smettem,et al.  Describing soil hydraulic properties with sums of simple functions , 1993 .

[23]  N. Jarvis.  A review of non‐equilibrium water flow and solute transport in soil macropores: principles, controlling factors and consequences for water quality , 2007 .

[24]  John R. Nimmo,et al.  Soil water retention and maximum capillary drive from saturation to oven dryness , 1999 .

[25]  Kai-Uwe Goss,et al.  Estimation of water transport based on in situ measurements of relative humidity and temperature in a dry Tanzanian soil , 2007 .

[26]  Shmulik P. Friedman,et al.  Dynamic contact angle explanation of flow rate-dependent saturation-pressure relationships during transient liquid flow in unsaturated porous media , 1999 .

[27]  W. R. Purcell,et al.  Capillary Pressures - Their Measurement Using Mercury and the Calculation of Permeability Therefrom , 1949 .

[28]  Robert J. Mitchell,et al.  The Significance of Hysteresis in Modeling Solute Transport in Unsaturated Porous Media , 1998 .

[29]  A. Klute,et al.  Comparison of Water Content‐Pressure Head Data Obtained by Equilibrium, Steady‐State, and Unsteady‐State Methods , 1967 .

[30]  Keith L. Bristow,et al.  Equation for extending water-retention curves to dryness , 1991 .

[31]  W. Durner.  Hydraulic conductivity estimation for soils with heterogeneous pore structure , 1994 .

[32]  M. V. Genuchten,et al.  Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone , 2003 .

[33]  P. J. Wierenga,et al.  Effect of hysteresis on the prediction of infiltration, redistribution and drainage of water in a layered soil☆ , 1975 .

[34]  Y. Mualem.  A New Model for Predicting the Hydraulic Conductivity , 1976 .

[35]  Allen G. Hunt,et al.  Comparing van Genuchten and Percolation Theoretical Formulations of the Hydraulic Properties of Unsaturated Media , 2004 .

[36]  Feike J. Leij,et al.  Closed‐Form Expressions for Water Retention and Conductivity Data , 1997 .

[37]  Mitsuhiro Inoue,et al.  A Transient Evaporation Method for Determining Soil Hydraulic Properties at Low Pressure , 2003, Vadose Zone Journal.

[38]  J. Grifoll,et al.  A soil‐water retention function that includes the hyper‐dry region through the BET adsorption isotherm , 2007 .

[39]  Rudolf Hilfer,et al.  Capillary pressure, hysteresis and residual saturation in porous media , 2006 .

[40]  J. Rubin,et al.  Numerical Method for Analyzing Hysteresis-Affected, Post-Infiltration Redistribution of Soil Moisture1 , 1967 .

[41]  Z. Fred Zhang,et al.  Soil Water Retention and Relative Permeability for Conditions from Oven‐Dry to Full Saturation , 2011 .

[42]  A. C. Bumb,et al.  Flow-Testing Coalbed Methane Production Wells in the Presence of Water and Gas , 1987 .

[43]  L. E. Scriven,et al.  Pendular rings between solids: meniscus properties and capillary force , 1975, Journal of Fluid Mechanics.

[44]  Kai-Uwe Goss,et al.  Prediction of the water sorption isotherm in air dry soils , 2012 .

[45]  Hugh McNamara,et al.  An estimate of energy dissipation due to soil‐moisture hysteresis , 2014 .

[46]  E C Childs,et al.  THE HYSTERESIS OF PORE WATER: THE NON-INDEPENDENCE OF DOMAINS , 1971 .

[47]  M. V. Genuchten,et al.  A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media , 1993 .

[48]  P. Viaene,et al.  A STATISTICAL ANALYSIS OF SIX HYSTERESIS MODELS FOR THE MOISTURE RETENTION CHARACTERISTIC , 1994 .

[49]  R. Zhang,et al.  NEW MODELS FOR UNSATURATED SOIL HYDRAULIC PROPERTIES , 1994 .

[50]  D. Fredlund,et al.  Equations for the soil-water characteristic curve , 1994 .

[51]  N. T. Burdine.  Relative Permeability Calculations From Pore Size Distribution Data , 1953 .

[52]  Shmuel Assouline,et al.  Conceptual and Parametric Representation of Soil Hydraulic Properties: A Review , 2013 .

[53]  J. C. van Dam,et al.  Comparison of six methods to determine unsaturated soil hydraulic conductivity. , 1994 .

[54]  Wolfgang Durner,et al.  Inverse modeling of dynamic nonequilibrium in water flow with an effective approach , 2012 .

[55]  G. E. Laliberte,et al.  A MATHEMATICAL FUNCTION FOR DESCRIBING CAPILLARY PRESSURE-DESATURATION DATA , 1969 .

[56]  E. C. Childs,et al.  The permeability of porous materials , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[57]  W. E. Larson,et al.  Modeling the pore structure of porous media , 1972 .

[58]  A. Klute,et al.  Methods of soil analysis , 2015, American Potato Journal.

[59]  L. A. Richards.  Capillary conduction of liquids through porous mediums , 1931 .

[60]  Gerardo Severino,et al.  Using Bimodal Lognormal Functions to Describe Soil Hydraulic Properties , 2011 .

[61]  Bridget R. Scanlon,et al.  Numerical Analysis of Coupled Water, Vapor, and Heat Transport in the Vadose Zone , 2005 .

[62]  Michel Bechtold,et al.  On the applicability of unimodal and bimodal van Genuchten–Mualem based models to peat and other organic soils under evaporation conditions , 2014 .

[63]  Shmuel Assouline,et al.  A model for soil relative hydraulic conductivity based on the water retention characteristic curve , 2001 .

[64]  A. Klute,et al.  Measurement and Numerical Simulation of Hysteretic Flow in a Heterogeneous Porous Medium1 , 1979 .

[65]  Bernd Diekkrüger,et al.  BIMODAL POROSITY AND UNSATURATED HYDRAULIC CONDUCTIVITY , 1991 .

[66]  W. Durner,et al.  Extended multistep outflow method for the accurate determination of soil hydraulic properties near water saturation , 2010 .

[67]  Hans-Jörg Vogel,et al.  Direct Measurement of Unsaturated Conductivity including Hydraulic Nonequilibrium and Hysteresis , 2011 .

[68]  J. Parlange,et al.  Capillary hysteresis and the relationship between drying and wetting curves , 1976 .

[69]  Wolfgang Durner,et al.  Vorhersage der hydraulischen Leitfähigkeit strukturierter Böden , 1991 .

[70]  Denis M. O'Carroll,et al.  Direct Quantification of Dynamic Effects in Capillary Pressure for Drainage–Wetting Cycles , 2010 .

[71]  Andre Peters,et al.  A simple model for describing hydraulic conductivity in unsaturated porous media accounting for film and capillary flow , 2008 .

[72]  Angelo Basile,et al.  Hysteresis in soil water characteristics as a key to interpreting comparisons of laboratory and field measured hydraulic properties , 2003 .

[73]  Andre Peters,et al.  Simple consistent models for water retention and hydraulic conductivity in the complete moisture range , 2013 .

[74]  R. Hilfer,et al.  Macroscopic capillarity and hysteresis for flow in porous media. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[75]  D. Or,et al.  Adsorption and capillary condensation in porous media: Liquid retention and interfacial configurations in angular pores , 1999 .

[76]  W. R. Gardner.  SOME STEADY‐STATE SOLUTIONS OF THE UNSATURATED MOISTURE FLOW EQUATION WITH APPLICATION TO EVAPORATION FROM A WATER TABLE , 1958 .

[77]  E. Youngs,et al.  Fundamentals of Soil Physics. , 1982 .

[78]  Hans-Jörg Vogel,et al.  Validity limits for the van Genuchten–Mualem model and implications for parameter estimation and numerical simulation , 2006 .

[79]  John H. Cushman,et al.  On unifying the concepts of scale, instrumentation, and stochastics in the development of multiphase transport theory , 1984 .

[80]  C. Dirksen,et al.  Hydraulic Conductivity and Diffusivity: Laboratory Methods , 2018, SSSA Book Series.

[81]  Jean-Marie Konrad,et al.  A new capillary and thin film flow model for predicting the hydraulic conductivity of unsaturated porous media , 2010 .

[82]  A. S. Rogowski.  ESTIMATION OF THE SOIL MOISTURE CHARACTERISTIC AND HYDRAULIC CONDUCTIVITY: COMPARISON OF MODELS , 1972 .

[83]  Marnik Vanclooster,et al.  On the use of unsaturated flow and transport models in nutrient and pesticide management , 2005 .

[84]  Wolfgang Durner,et al.  Dynamic Nonequilibrium of Water Flow in Porous Media: A Review , 2012 .

[85]  Wolfgang Durner,et al.  Free‐form estimation of the unsaturated soil hydraulic properties by inverse modeling using global optimization , 2007 .

[86]  Arthur W. Warrick,et al.  Surfactant effects on unsaturated flow in porous media with hysteresis: horizontal column experiments and numerical modeling , 2001 .

[87]  Ole Wendroth,et al.  Non‐equilibrium water flow characterized by means of upward infiltration experiments , 2001 .

[88]  Jinzhu Ma,et al.  A new theoretical model accounting for film flow in unsaturated porous media , 2013 .

[89]  COLIN C. HARRIS,et al.  Pendular Moisture in Packings of Equal Spheres , 1964, Nature.

[90]  Gerardo Severino,et al.  Darcian preferential water flow and solute transport through bimodal porous systems: experiments and modelling. , 2009, Journal of contaminant hydrology.

[91]  Y. Mualem,et al.  A MODIFIED DEPENDENT‐DOMAIN THEORY OF HYSTERESIS , 1984 .

[92]  David Russo,et al.  Determining soil hydraulic properties by parameter estimation: On the selection of a model for the hydraulic properties , 1988 .

[93]  Diganta Bhusan Das,et al.  Dynamic effects in capillary pressure–saturations relationships for two-phase flow in 3D porous media: Implications of micro-heterogeneities , 2007 .

[94]  T. E. Skinner,et al.  Hydraulic Conductivity Limited Equilibration: Effect on Water Retention Characteristics , 2005, Vadose Zone Journal.

[95]  K. Kosugi.  Lognormal Distribution Model for Unsaturated Soil Hydraulic Properties , 1996 .

[96]  R. Kachanoski,et al.  Unified Solution for Infiltration and Drainage with Hysteresis Theory and Field Test , 2000 .

[97]  D. R. Nielsen,et al.  Reply [to Comment on the treatment of residual water content in a consistent set of parametric mod , 1991 .

[98]  Allen G. Hunt,et al.  What's wrong with soil physics? , 2013 .

[99]  R. Shakesby,et al.  Soil water repellency: its causes, characteristics and hydro-geomorphological significance , 2000 .

[100]  M. Schaap,et al.  Soil hydraulic properties near saturation, an improved conductivity model , 2006 .

[101]  Uwe Schindler,et al.  Evaporation Method for Measuring Unsaturated Hydraulic Properties of Soils: Extending the Measurement Range , 2010 .

[102]  A. Klute,et al.  Hydraulic Properties of a Porous Medium: Measurement and Empirical Representation 1 , 1976 .

[103]  J. Simunek,et al.  Flow rate dependence of soil hydraulic characteristics , 2001 .

[104]  Erik H. D'Hollander,et al.  Estimation of the pore size distribution from the moisture characteristic , 1979 .

[105]  Ken'ichirou Kosugi,et al.  Three‐parameter lognormal distribution model for soil water retention , 1994 .

[106]  David Russo,et al.  Numerical analysis of solute transport during transient irrigation: 1. The effect of hysteresis and profile heterogeneity , 1989 .

[107]  Kazunobu Takahashi,et al.  Evaluation of the tortuosity parameter for forest soils to predict unsaturated hydraulic conductivity , 2001, Journal of Forest Research.

[108]  Y. Mualem,et al.  Hydraulic Conductivity of Unsaturated Soils: Prediction and Formulas , 2018, SSSA Book Series.

[109]  J. Hutson,et al.  A retentivity function for use in soil–water simulation models , 1987 .

[110]  L. E. Scriven,et al.  Hydraulic Conductivity of Porous Media at Low Water Content , 1990 .

[111]  M. J. Fayer,et al.  Modified Soil Water Retention Functions for All Matric Suctions , 1995 .

[112]  D. R. Nielsen,et al.  On describing and predicting the hydraulic properties of unsaturated soils , 1985 .

[113]  Hans-Jörg Vogel,et al.  Virtual Soils: Assessment of the Effects of Soil Structure on the Hydraulic Behavior of Cultivated Soils , 2011 .

[114]  James Alfred Ewing.  VII. On the production of transient electric currents in iron and steel conductors by twisting them when magnetised or by magnetising them when twisted , 1882, Proceedings of the Royal Society of London.

[115]  Stephen W. Webb,et al.  A simple extension of two‐phase characteristic curves to include the dry region , 2000 .

[116]  A. Bruand,et al.  A conceptual model of the soil water retention curve , 1998 .

[117]  Y. Mualem,et al.  A conceptual model of hysteresis , 1974 .

[118]  Rainer Helmig,et al.  Chemical osmosis in two‐phase flow and salinity‐dependent capillary pressures in rocks with microporosity , 2014 .

[119]  A. Klute,et al.  Physical and mineralogical methods , 1986 .

[120]  J. Parker,et al.  Comparing Simulated and Experimental Hysteretic Two‐Phase Transient Fluid Flow Phenomena , 1991 .

[121]  Uwe Schindler,et al.  The evaporation method: Extending the measurement range of soil hydraulic properties using the air-entry pressure of the ceramic cup , 2010 .

[122]  I. Fatt,et al.  Relative Permeability Studies , 1951 .

[123]  S. Assouline.  Correction to “A model for soil relative hydraulic conductivity based on the water retention characteristic curve” , 2004 .

[124]  Jack C. Parker,et al.  Development and evaluation of closed-form expressions for hysteretic soil hydraulic properties , 1987 .

[125]  Marcel G. Schaap,et al.  Description of the unsaturated soil hydraulic database UNSODA version 2.0 , 2001 .

[126]  Peter Lehmann,et al.  Effect of hysteresis on water flow in a sand column with a fluctuating capillary fringe , 1998 .

[127]  Paul D. Bates.  Encyclopaedia of Hydrological Sciences , 2005 .

[128]  P. H. Groenevelt,et al.  A new model for the soil‐water retention curve that solves the problem of residual water contents , 2004 .

[129]  Eckart Priesack,et al.  Closed‐Form Expression for the Multi‐Modal Unsaturated Conductivity Function , 2006 .

[130]  C. Thirriot,et al.  Influence of the hysteresis effect on transient flows in saturated‐unsaturated porous media , 1977 .

[131]  L. G. King,et al.  DESCRIPTION OF SOIL CHARACTERISTICS FOR PARTIALLY SATURATED FLOW , 1965 .

[132]  A. Poulovassilis,et al.  HYSTERESIS OF PORE WATER IN GRANULAR POROUS BODIES , 1970 .

[133]  P. M. Driessen,et al.  Land-use systems analysis , 1992 .

[134]  Jan M. H. Hendrickx,et al.  Water and solute movement in a coarse-textured water-repellent field soil , 1990 .

[135]  Petros A. Ioannou,et al.  2. Parametric Models , 2006 .

[136]  Dirk Mallants,et al.  Evaluation of multimodal hydraulic functions in characterizing a heterogeneous field soil , 1997 .

[137]  Ken'ichirou Kosugi,et al.  General model for unsaturated hydraulic conductivity for soils with lognormal pore-size distribution. , 1999 .

[138]  Wilfried Brutsaert,et al.  PROBABILITY LAWS FOR PORE-SIZE DISTRIBUTIONS , 1966 .

[139]  Olaf Ippisch,et al.  Dynamic nonequilibrium in unsaturated water flow , 1999 .

[140]  Gürkan Sin,et al.  Simple modification to describe the soil water retention curve between saturation and oven dryness , 2006 .

[141]  R. H. Brooks,et al.  Hydraulic properties of porous media , 1963 .

[142]  Michael A. Celia,et al.  Dynamic Effect in the Capillary Pressure–Saturation Relationship and its Impacts on Unsaturated Flow , 2002 .