Journal of Contaminant Hydrology 104 (2009) 74–83

Contents lists available at ScienceDirect

Journal of Contaminant Hydrology

j ourna l homepage: www.e lsev ie r.com/ locate / jconhyd

Darcian preferential water flow and solute transport through bimodalporous systems: Experiments and modelling

Antonio Coppola a,⁎, Vincenzo Comegna a, Angelo Basile b,Nicola Lamaddalena c, Gerardo Severino d

a Dept. for Agro-Forestry Systems Management, Hydraulics Division, University of Basilicata, Potenza, Italyb Institute for Mediterranean Agriculture and Forestry Systems (ISAFOM), National Research Council (CNR), Ercolano, Italyc Mediterranean Agronomic Institute, IAMB, Bari, Italyd Dept. of Agricultural Engineering and Agronomy, University of Napoli Federico II, Portici, Italy

a r t i c l e i n f o

⁎ Corresponding author.E-mail address: antonio.coppola@unibas.it (A. Cop

0169-7722/$ – see front matter © 2008 Published bydoi:10.1016/j.jconhyd.2008.10.004

a b s t r a c t

Article history:Received 28 October 2007Received in revised form 3 October 2008Accepted 8 October 2008Available online 17 October 2008

Soils often exhibit a variety of small-scale heterogeneities such as inter-aggregate pores andvoids which partition flow into separate regions. In this paper a methodological approach isdiscussed for characterizing the hydrological behaviour of a heterogeneous clayey–sandy soil inthe presence of structural inter-aggregate pores. For the clay soil examined, it wasdemonstrated that, coupling the transfer function approach for analyzing BTCs and waterretention data obtained with different methods from laboratory studies captures the bimodalgeometry of the porous system along with the related existence of fast and slow flow paths. Tobe effectively and reliably applied this approach requires that the predominant effects of thesoil hydrological behaviour near saturation be supported by accurate experimental data of bothbreakthrough curves (BTCs) and hydraulic functions for high water content values. This wouldallow the separation of flow phases and hence accurate identification of the processes andrelated parameters.

© 2008 Published by Elsevier B.V.

Keywords:Soil structurePreferential flowBimodal approachesTwo-domain models

1. Introduction

Natural porous media often exhibit complicated pore-sizedistributions, with the pore system frequently partitionedinto intra-aggregate or textural pores and inter-aggregate orstructural pores (Fies, 1992; Tamari, 1994). In these soils pore-size distributions are often bimodal (Bruand and Prost, 1987;Smettem and Kirkby, 1990; Othmer et al., 1991; Durner, 1994;Zurmühl and Durner, 1998; Mohanty et al., 1997; Coppola,2000), with one maximum in the range of textural pores andanother in the range of structural pores. In bimodal soils, theintra-aggregate porous system is frequently separated bycutans on thewalls of the aggregates from the inter-aggregatepores (Othmer et al., 1991). The coatings on aggregate faces

pola).

Elsevier B.V.

reduce the water transfer into the intra-aggregate pores(Gerke and Köhne, 2002).

Soil structure critically affects soil hydraulic properties andhydrodispersive properties and is consequently the core ofmuch research on heterogeneity effects on water flow andsolute transport. Draining of the inter-aggregate poresfrequently results in a steep slope of the retention curvenear saturation (Thony et al., 1991) along with a considerabledrop in hydraulic conductivity, which any model assuming aunimodal pore-size distribution fails to adequately reproduce(Smettem and Kirkby,1990; Othmer et al., 1991; Durner, 1994;Mallants et al., 1997; Coppola, 2000).

Although inter-aggregate pores cannot be treated as realmacropores (fissures or cracks), the rate of flow in inter-aggregate pores is substantially higher than in the matrix,that is in the system of intra-aggregate pores, and a relativelyfaster-transporting flow region can develop. Even if in thesepores of intermediate size capillary forces may be prevailing,

75A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

theymay significantly contribute to channelling flow.Wildingand Hallmark (1984) made a detailed review of the impor-tance of the inter-aggregate pores for preferential flow.

The differences between preferential flow in real macro-pores and in inter-aggregate pores can be summarized asfollows (for a detailed review see Simunek et al., 2003; Gerke,2006; Jarvis, 2007):

1. Preferential flow in real macropores (or non-capillarypores): A two-domain approach to account for a fast and aslow transport region is generally applied (Germann andBeven, 1985; Coppola and Greco, 1997; Greco, 2002). Atleast in principle, Richards' equation is not applicable forthe fast domain, where fluxes are usually notably acceler-ated. The kinematic wave, or the Hagen–Poiseuille equa-tion, is preferably applied. The strength of all the availabletwo-domain models, which seek a deterministic descrip-tion of each of the mechanisms involved, is also theirweakness since each of these models has considerableparameter requirements, which limit the practical applic-ability of the models in many cases. Actually, the relevantanalyses require that the separate zones and at least someof their hydraulic properties be specified, when in practicethey frequently may not be available.

2. Preferential flow in inter-aggregate pores: Richards' equa-tion is applicable since the pores are in the category ofcapillary pores. The fluxes are accelerated compared tothose in the matrix, when infiltration and redistributionare considered, but less accelerated compared to the fluxesin item 1. If the preferential flow is due mainly to inter-aggregate pores, then their sizes along with involved fluxdensities may reasonably legitimate the assumption thatDarcy's equation is either exact or at least a very goodapproximation for also describing preferential flow (Kuti-lek and Nielsen,1994). In themodel proposed by Gerke andvan Genuchten (1993), Richards' equation for the fast flowdomain was conceptually linked to the inter-aggregatemacropores.

Based on the assumption in item 2, in the 1990s, somesimple approaches (composite porosity approaches) wereproposed which view aggregated soils as consisting of twopore systems, each with its own retention function (Othmeret al., 1991; Durner, 1992, 1994; Wilson et al., 1992; Ross andSmettem, 1993). The retention function of the whole porousmedium was described by linearly overlapping functions ofthe same form (e.g., Durner, 1992) or of different form (e.g.,Ross and Smettem, 1993). Based on a large water retentionand hydraulic conductivity data set, Coppola (2000) gaveexperimental evidence for the predictive capability of theRoss and Smettem relation for bimodal porous media.

The composite porosity approach is generally based on theassumption that an equivalent pore-size system can bededuced from the water retention curve. Even when abimodal porous system is detected by water retention, thequestion of the degree of interaction between the twosubsystems remains unresolved. This is no secondary issuebecause the interaction degree means different approachesfor hydraulic conductivity being adopted (Ross and Smettem,1993).

In this paper we will show that the problem can be solvedif specifically designed miscible experiments are coupled to

the classical water retention method to deduce the geometryof these porous systems (Comegna et al., 2001; Ma and Selim,1994). In soils with two non-interacting flow domains, theremay be two separate or distinct breakthrough curves (BTCs),one with shorter travel times (preferential flow paths), andthe other with longer travel times. In such a case, doublepeaks BTCs are expected. If the two subsystems are interact-ing, preferential flow generally results in asymmetry andtailing of a unimodal BTC.

In the next sections, after investigating this issue and therelated mathematical formulation, we shall provide a meth-odological approach for simultaneously quantifying the pore-size system of an aggregated soil, the interaction degreebetween pore subsystems and the related macropore-typepreferential flow and solute transport.

2. Conceptual model

In this study, one-dimensional water flow in rigidvariably-saturated porous medium is described usingRichards' equation:

AθAh

AhAt

=A

dzK hð Þ Ah

Az−1

� �� �ð1Þ

where Aθ/Ah is the differential moisture capacity, equal to theslope of the water retention function being θ and h the soilwater content and the pressure head, respectively. K(h) is thehydraulic conductivity function, z is the vertical spacecoordinate and t is the time.

One-dimensional transient flow of an inert solute in ahomogeneous and isotropic porous medium may bedescribed by the classical convection-dispersion differentialequation:

AθCAt

=A

AzθD

ACAz

� �−AvθCAz

ð2Þ

where C is the solute concentration, D the dispersioncoefficient, v=q/θ the average pore water velocity and q thedarcian velocity. Assuming diffusive transport to be negligi-ble, the dispersion coefficient is defined as: D=λv where λ isthe dispersivity.

The retention function introduced by Ross and Smettem(1993) for bimodal porous systems is as follows:

Se = β1 1 + αRSjhjð Þexp αRSjhjð Þ + β21

1 + αVGjhjð Þn� �m

Se =θ−θrθ0−θr

0 b βi b 1 and ∑βi = 1 i = 1;2

ð3Þ

where θ0 and θr are the water content at h=0 and for h→∞,respectively. In Eq. (3) a simple one-parameter (αRS) function(the first term on the right side) accounts for inter-aggregateporosity, and a van Genuchten (1980) function (the secondterm on the right side) accounts for water retention of thematrix and is generally used for describing unimodal porousmedia. αVG (cm−1), n andm are curve-fitting parameters. βi isthe weighting of the total pore space fraction to be attributed

76 A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

to the ith subcurve. Note the effective saturation, Se, is to beconsidered as a cumulative distribution function of pore sizewith a density function f(h) which may be expressed by:

f hð Þ = dSedh

ð4Þ

Mualem's expression is based on the capillary bundletheory (Mualem, 1986) and relates relative hydraulic con-

ductivity, Kr, to f(h) by the equation:

Kr hð Þ = K hð ÞK0

= Sτe g hð Þ=g 0ð Þ½ �2

g hð Þ = ∫∞−∞h−1f hð Þdhð5Þ

in which K0 is the hydraulic conductivity at h=0, and τ is aparameter accounting for the dependence of the tortuosityand the correlation factors on the water content.

For the bimodal case, Eq. (5) becomes:

Kr hð Þ = K hð ÞK0

= Sτe ∑2

i = 1βigi hð Þ= ∑

2

i = 1βigi 0ð Þ

� �2ð6Þ

with parameters as defined earlier and, according to thewaterretention of Eq. (3):

g1 hð Þ = αRSexp αRShð Þ

g2 hð Þ = αVGnB S1=me ; m + 1=n; 1−1=n� � ð7Þ

where B( ) is the incomplete beta function.Eq. (6) assumes that all pores in the material can interact

(Ross and Smettem, 1993). In this case, an instantaneousequilibrium (i.e. instantaneous exchange of water) betweenthe two pore systems is implicitly assumed.

Nevertheless, for some materials part of the pore spacemay bypass the rest. This is the case when for example thecutans on the walls of the aggregates reduces the watertransport between intra- and inter-aggregate spaces. Theconductivities of the two porous spaces are parallel and, forsuch independent distributions, the following equationsapply:

K hð Þ = ∑2

i = 1K0iKri hð Þ

Kri hð Þ = Sτe gi hð Þ=gi 0ð Þ½ �2:ð8Þ

An initial question to be answered is how we can establishwhether Eq. (6) or, alternatively, Eq. (8) applies.

As iswell known, thegeometryof theporous systemsaffectsthe soil porewater velocity distribution.Accordingly, thedegreeand shape of soil structure can have a large impact on solutetransport paths and solute breakthrough curves (BTCs) (Bouma,1991; Li and Ghodrati, 1994; Vervoort et al., 1999).

Several studies have dealt with the facilitated solutetransport in aggregated soils by adopting a mobile-immobileapproach, in which the porous medium is conceptuallydivided into a dynamic water region (the inter-aggregatepores) and a stagnant region (intra-aggregate pores) (vanGenuchten and Wierenga, 1976; Brusseau et al., 1989). Thesmaller soil pores serve as storage and larger pores areconduits for transport pathways, with diffusional mass

transfer taking place between the mobile and immobilewater zones. Once again, when “two-region” approaches areused, the problem remains how to define the boundary andinteractions between regions and how to measure thephysical parameters within each domain independently(Comegna et al., 2001; Kung et al., 2006).

What is more, mobile-immobile models are not able topredict double or even multiple peaked BTCs frequentlyobserved in laboratory soil columns (Ma and Selim, 1994) andin the field (Butters and Jury, 1989; Roth et al., 1991), whichare to be generally ascribed to soil aggregation with minordiffusional mass transfer (Rosqvist and Destouni, 2000). Thisis the behaviour expected when the conductivities of the twoporous spaces are in parallel, as is assumed in Eq. (8). For thiscase, solute advection through both fast and slow flow pathshas to be accounted for. A possible model with two advectiveregions in a stochastic framework could be based on abimodal probability density function, f (t,z) of solute traveltimes (Destouni et al., 1994; Rosqvist and Destouni, 2000;Garrido et al., 2001):

f z; tð Þ = u1f1 t; zð Þ +u2f2 t; zð Þ

fi t; zð Þ = 1σ it

ffiffiffiffiffiffi2π

p exp −ln tð Þ−μ i½ �2σ2

i

2( )

0 bui b 1 and ∑ui = 1 i = 1;2:

ð9Þ

In Eq. (9) μi and σσi (i=1, 2) are the mean and standarddeviation of the fast and slow peak of the travel time, t,distribution at depth z, while φi is a weighting parameterexpressing the flow fraction through fast and slow paths (i=1,2, respectively). As discussed by Destouni (1993), though thequantification of the diffusional mass transfer could also beadded to the model in Eq. (9), it has been shown to have onlyminor effects when φ2N0 and can be therefore neglected.

Garrido et al. (2001) and Rosqvist and Destouni (2000)assumed the weights φ1=θ1/θ0 and φ2=θ2/θ0 with θ1 and θ2being the pore space fraction attributed to the water contentof the fast and slow flow phases, respectively and θ0 the watercontent at h=0. For the case of negligible interactionsbetween adjacent domains of pores, the BTC of a shortchemical pulse is the summation of the BTCs of the individualdomains of pores and θ1 and θ2 can be assumed to be themaximum water contents (at h=0) for the two sub-curves ofEq. (3). The hydraulic conductivity and dispersivity have to beconsidered distinct for each individual porous domain andcan be deduced through Eqs. (8) and (9), respectively. In termsof parameters of Eq. (9), dispersivity was calculated as λ=0.5z[exp(σ2)−1].

On the other hand, when the soil is relatively dry, thematric potential will restrict water and solute movement tothe smaller matrix pores and the transport through thesepores is likely to cause a thorough solutemixing so that awell-defined chemical front forms with unique values of velocityand spreading. Under this scenario, a single peaked BTC isexpected and a lumped value of dispersivity can describe thesolute transport process. Aquestion to be answered is how thisunsaturated soil dispersivity is related to the dispersivities ofthe saturated two-peak BTC of the same soil.

Table 1Physical characteristics of the soils examined

Texture(USDA

Sand(%)

Silt(%)

Clay(%)

BulkDensity(g cm−3)

Structure Organicmatter(%)

θ0(−)

K0

(cm h−1)

Clayey–sandy

39.72 25.43 34.85 1.15 Moderate,angularblocky

2.9 0.55 3.17

77A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

To some extent, it can be said that the water retentioncurve contains the information for establishing whether ornot the soil is bimodal while the BTC can be used to establishwhether or not the two porous systems are in parallel suchthat Eq. (8) or alternatively Eq. (6) has to be applied forhydraulic conductivity.

When the hydrological response of a soil is used to inferthe characteristics of the pore system, a final question shouldbe posed. One should be aware that different retention curvescan be obtained according to the measurement method andthe interpretative model used. Typically, the water retentioncurve is measured in the laboratory under equilibrium (static)conditions during drainage. Nevertheless, some comparisonsof water retention data obtained using static and dynamicapproaches indicate that more water will be held at a givensuction in the dynamic case. Schultze et al. (1999) showedthat such dynamic effects have to be attributed to the non-negligible resistance of air flow. If there are dynamic effects,the water retention curve cannot be reliably used forunequivocally deducing the equivalent pore-size distributionas the latter would change depending on the measurementmethod used. Likewise, the same can be said when hystereticeffects exist such that different pore-size geometries may bededuced for the same porous medium.

Based on this premise, we examine the possibility ofquantifying the pore-size systems of an aggregated soil andthe related macropore-type preferential flow and solutetransport by looking at all the questions posed above. To doso, the paper is organized as follows: first, the question as towhether or not two pore sub-systems exist and are interact-ing is assessed by means of transport experiments carried outon the same soil sample at the maximumwater content θ0 (ath=0) and at two lower water contents. The first experimentwas especially devoted to ascertaining whether the two poresystems are in parallel, through the analysis of the peak/s ofthe corresponding BTC. It was emphasized above that this isespecially important for selecting the right approach (Eqs. (6)or (8)) for estimating hydraulic conductivity. The second andthird miscible experiment were specifically set up forverifying what type of relationship exists between thedispersivities of a bimodal BTC obtained when preferentialpathways are active and that of a unimodal BTC obtained onthe same porous medium by excluding the inter-aggregatepores from the transport volume. Second, different methods(static and dynamic) will be considered for obtaining the soilwater retention in order to quantify the possible differences inpore-size distribution estimation to be related to the differentmeasurement methods and interpretative models used.

3. Materials and methods

The data used in this paper were obtained on undisturbedcolumns, 150 mm in diameter and 150 mm in length, from aclayey–sandy soil in southern Italy. Representative samplesizes for the soil examined were chosen according tosuggestions given by Bouma (1985). For the sake of brevity,herein only the results from the column labelled as “column2”will be presented. The columnwas extracted from the topsoilof a grass covered hillslope close to the Sauro river, near thetown of Corleto Perticara (PZ). The main physical character-istics of the soil column examined, as determined in the

laboratory, are reported in Table 1. In the laboratory thecolumns were slowly wetted from the bottom in four waterlevel increments, until the top of the columnwas reached. Wethen determined the maximum water content, θ0, gravime-trically and the related hydraulic conductivity, K0 (at h=0),with a permeameter applying the constant-head method(Klute and Dirksen, 1986). θ0 is to be distinguished from thesaturated water content, θs, because of the air possiblyentrapped in the pores. BTCs and hydraulic properties weredeterminedwith different methods which were performed asfollows:

3.1. Miscible experiments

Before performing the hydraulic tests, miscible flowexperiments were carried out at three different watercontents (θ0=0.55, θ=0.50 and θ=0.46). The columns weresubjected to one-dimensional flow processes with a specifi-cally constructed experimental leaching configuration. Theleaching unit allows saturated and unsaturated flow experi-ments to be conducted (see Comegna et al., 2001 for furtherdetails). In order to conduct the miscible experiments, eachsoil column underwent a preliminary conditioning phase byfeeding, with different steady water flux densities dependingon the water content to be reached in the soil during theexperiment, the flow system with a 0.01-N CaSO4 solutionuntil the steady flow was reached. Contemporaneous mea-surements of θ, h and water flux, q, allowed us to determinethe onset of steady state. At steady state, the solution wasshifted with a step feeding by another solution containing1.86 g/l of KCl corresponding to 25 meq/l of Cl−. Duringleaching tests, the leachate was periodically collected. Thechloride concentration at the outlet boundary was deter-mined by titrating 10 ml of aliquot against standard AgNO3

using 5% K2CrO4 as an indicator (Richards, 1968).

3.2. Multi-step method

Multi-step outflow experiments (Eching and Hopmans,1993; van Dam et al., 1994) were carried out on soil cores byimposing no flux across the top of the column and a multi-step pressure head decrease at the lower boundary, startingfrom saturation and stepwise decreasing the pressure head toa value of h=−180 cm and going back again to saturation.Thus, a complete drainage and wetting cycle was carried out,while in both cases measuring cumulative outflow andpressure head at two different depths. The unknownhydraulic function parameters were determined by couplingexperiments to an inverse modelling technique, whileminimizing an objective function containing the observedand predicted quantities. Tensiometers were installed at three

Fig. 1. BTCs from the miscible experiments carried out under saturatedconditions. C/C0 are relative concentrations and C0 is the input concentration.Full circles refer to measured C/C0, dashed and solid lines refer to unimodaland bimodal simulation, respectively.

78 A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

different depths (4.0 cm, 8.0 cm and 12 cm from the samplebottom) in order to improve parameter estimation.

3.3. Wind's method

Like the multistep method, the evaporation method(Wind, 1968), with the modifications suggested by Tamari etal. (1993) and Romano and Santini (1999) for laboratoryhydraulic characterization allowed us to determine simulta-neously the water retention and hydraulic conductivityfunctions, subjecting the soil samples to an evaporationprocess. The method requires only certain quantities to berecorded during the transient obtained, starting fromassigned boundary conditions. The sample drying processwas conducted by starting from hydrostatic equilibriumconditions (h=0 cm at surface and h=15 cm at the bottom)setting a zero-flux at the bottom surface, monitoring at the

Fig. 2. BTCs from the miscible experiments carried out under differentunsaturated conditions (plot a and b). C/C0 are relative concentrations and C0

is the input concentration. Full circles refer to measured C/C0, dashed linerefers to unimodal simulation.

same time, at appropriately preset time intervals, the weightof the whole sample and the pressure heads at three differentdepths. The pressure heads were measured by using threetensiometers consisting of a porous ceramic cup 0.6 cm indiameter and 3 cm long, inserted into the soil at heights of4.0 cm, 8.0 cm and 12 cm from the sample bottom throughappropriately drilled holes in the cylinder wall and connectedto pressure transducers. Control of the equipment and dataacquisition were performed by using specifically developedsoftware. In relation to the texture of the different samples,each test lasted 4 or 5 days overall.

3.4. Suction table method

Before carrying out the test, the height of each columnwasreduced to 4.0 cm by removing the upper and lower part ofthe soil column. The removed part of the column was thenused to determine particle-size distribution. Moreover, thereduction in sample height also allowed equilibrium condi-tion to be achieved in reasonable times during the determi-nation of the water retention points. Each soil column wasslowly wetted from below in different steps to obtain the h=0conditions. The θ(h) data points were measured using aconventional suction table apparatus. Water retentions wereobtained at the following pressure heads: −2, −3, −5, −7, −9,−15, −20, −30, −50, −70, −100, −150, −200 cm (referred to themiddle of the column). We assumed that the average watercontents actually corresponded to the indicated pressurehead values.

4. Results

4.1. Miscible experiments

Some experimental BTCs for the soil examined arerepresented by Figs. 1 and 2. Graphs refer to the experimentsconducted on the column at the different water contents andflux densities summarized in Table 2. Symbols representexperimental values while lines are the curves fitted by usinga conventional nonlinear optimization algorithm whichminimizes the sum of the squares of the residuals betweenthe measured values and those calculated with the analyticalsolution given in Eq. (9). For three simulations (dashed lines)the weight φ1 was set to zero so that Eq. (9) represented asimple one advective-region model (Table 2). Fig. 1 refers tothe experiment carried out at the maximum water content(θ=0.55). The curves in the figure were obtained by assuminga two/one advective-region model. Assuming solute advec-tion through both fast and slow flow paths enabled descrip-tion of the double-peaked experimental curve observed in the

Table 2Water contents and flux densities adopted for miscible displacementexperiments

θ (−) q (cm h−1) Model λ1 (cm) λ2(cm) ϕ1

0.55 3.0 Bimodal 6.5 2.2 0.220.55 3.0 Unimodal 41.50.50 0.1 Unimodal 2.40.46 0.03 Unimodal 2.5

Fig. 3. Measured (symbols) and unimodal (solid lines) and bimodal (dashed lines) simulated cumulative inflow and outflow multistep experiments. Negative andpositive fluxes are for wetting and draining, respectively.

79A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

laboratory soil column (solid line). As amply discussed inSection 2, this is the behaviour expected when the con-ductivities of the two porous spaces are in parallel, as isassumed in Eq. (6). Limited interaction between two regionsdiffering in dispersivity and flow velocity may be the cause ofearly breakthrough and observed double peaks for the non-reactive solute used in the experiment. The very early traveltime of the first peak would indicate a small residence time ofsolute in the rapidly conducting fraction of the porous systemthat would limit the transfer by diffusion into the slowadvective region. The parameters obtained for this curvefitting and shown in Table 2 indicate a fast flow fraction (φ1)of about 22% of the total porosity estimated by the maximumwater content at h=0 and dispersivity values for the fast (λ1)and slow (λ2) regions of 6.5 cm and 2.2 cm, respectively.

As expected, the model assuming a unimodal flow systemprovided an unacceptable description of the experimentalBTC and resulted in a dispersivity value (41.5 cm) which

Fig. 4. Retention curves from parameters estimated from unimodal (cross and solidsquare and solid line for VGopt_wet) and bimodal (full symbols and solid lines) destatic desorption (full circles) and Wind's method (empty circles) are also shown.

makes no physical sense when compared to the columnlength.

Fig. 2a,b represent the experiments carried out at θ=0.500and θ=0.460, respectively. As expected, desaturation in thissoil with the presence of macropores produces a narrowing ofthe hydraulically effective pore-size distribution thus result-ing in breakthroughs approaching a symmetrical one-peakedshape with decreased water content. This can be related tothorough solute mixing such that a well-defined chemicalfront forms with unique values of velocity and spreading. Thedispersivity values for the two experiments conducted underunsaturated conditions are comparable to that of the slowpath fraction obtained at h=0. Dispersivity is known to be acharacteristic fundamentally tied to soil structure. It isgenerally estimated by carrying out miscible experimentsunder saturated conditions. The value obtained is generallyused for also predicting solute BTCs under unsaturatedconditions. This is largely justified for soils with weak

line for VGfix_wet, empty triangle and solid line for VGopt_drain and emptyscriptions of the multistep experiments. Experimental retention points from

Fig. 5. Hydraulic conductivity curves from parameters estimated from unimodal (cross and solid line for VGfix_wet, empty triangle and solid line for VGopt_drainand empty square and solid line for VGopt_wet) and bimodal (full symbols and solid lines) descriptions of the multistep experiments and experimental points (fullcircle for Ks and empty circles for K(h)).

80 A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

aggregation as, in such soils, dispersivity was frequentlyfound to be constant with water content (Comegna et al.,2001; Vanderborght and Vereecken, 2007). To the contrary,our experiments show that for the well-structured soilexamined, unsaturated BTCs can be predicted from thatobtained at h=0 if only the dispersivity value of the slow flowpath is considered.

Summarizing, two main findings were obtained from themiscible experiments:

1. Two porous systems exist which are in parallel, such thatEq. (8) has to be applied for hydraulic conductivity;

2. The BTCs for unsaturated conditions for these type ofbimodal soils can be predicted by only the solute transportparameters of the slow advective region of the whole flowsystem.

4.2. Inflow–outflow experiments

In Fig. 3 the wetting and drying branch of the multistepexperiments are illustrated for column 2. Symbols aremeasured inflows/outflows, solid and dashed lines areunimodal and bimodal simulated inflows/outflows, respec-tively. Corresponding retention and hydraulic conductivitycurves are shown in Figs. 4 and 5, respectively. Retentioncurves are compared to experimental retention data mea-sured on the same sample by using a classical staticdesorption method (suction table method) in the pressurehead range 0b|h|b200 cm, as well as Wind's method in thepressure head range 0b|h|b500 cm. Hydraulic conductivity

Table 3Optimized parameters for water retention and hydraulic conductivity functions fro

Experiment Model θ0 αRS (cm−1)

Draining Unimodal 0.65 optimized (parameter at bound)Draining Bimodal 0.55 fixed 0.571Wetting Unimodal 0.48 optimizedWetting Unimodal 0.55 fixedWetting Bimodal 0.55 fixed 0.336

Parameter at bound means that it was the maximum value allowed in the optimiza

curves are compared to the experimental conductivity dataobtained by Wind's method.

As described in Section 3.2, the unknown hydraulicfunctions were determined by coupling experiments to aninverse modelling technique, while minimizing an objectivefunction containing the observed and predicted quantities.Concerning the unimodal case, the van Genuchten θ(h) wasapplied either with the θ0 parameter optimized (VGopt), forgivingmore flexibility to the retention formulation, or fixed tothe measured value (VGfix). Parameter values resulting fromoptimization are reported in Table 3. Mualem's model forhydraulic conductivity was applied in its unimodal formula-tion and thus with a unique value of hydraulic conductivity ath=0, K0micr, as a matching point.

By contrast, for the bimodal case (RSbim) θ0 was set at thevalue measured in the laboratory. Of course, for this case, thehydraulic conductivity model represented in Eq. (8) was usedto be consistent with the results of parallel porous systemsobtained from miscible experiments. Accordingly, two differ-ent K0 parameters were considered, one for inter-aggregatepores, K0macr, and one for intra-aggregate pores, K0micr.

4.2.1. Water retention curvesThe experimental data in Fig. 4 show an abrupt change in

water content as h varies near saturation, which may bejustified if we assume the presence of a secondary system oflarge pores which may desaturate rapidly in response to asmall variation in h. Such behaviour was detected to a greateror lesser extent in the other columns examined. It is worthnoting that for the Wind method this behaviour can only be

m multistep experiments

αVG (cm−1) n β1 K0macr (cm h−1) K0micr (cm h−1)

0.072 1.09 1000 (parameter at bound0.037 1.12 0.12 9.84 1.130.268 1.18 1000 (parameter at bound0.050 1.50 1000 (parameter at bound0.029 1.12 0.15 4.38 0.64

tion procedure.

)

))

81A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

detected if one starts from a positive pressure head profile. Infact, if the test was conducted, as it is generally done, bystarting from the hydrostatic pressure head profile with h=0at the column bottom, the first inflection point at about 10 cmin Fig. 4 would not be visible and a very different retentioncurve would be extrapolated. The preferential flow dynamicduring the evaporation process is expected to be differentfrom that observed during a draining process. It could behypothesized that the evaporative water flux is first sup-ported by the larger pores at the sample surface. These poresimmediately start to become air-filled. The water from theinter-aggregate pores at greater depths is then transferredinto the matrix, moved upwards, and then evaporated fromthe matrix surface. This remains water-filled and represents atransmission zone between the deep inter-aggregate poresand the surface. In a second stage, for hb−15 cm, a dryingfront also forms in the soil matrix. This drying sequence maywell explain the double inflection of theWind retention curveshown in the figure.

As regards the VGopt curve, optimization produces eitheran unacceptable underestimate (wetting branch) or over-estimate (draining branch) of retention over the wholepressure head range. The quite acceptable fittings obtainedfor both the wetting and draining branch, especially fordraining, of the multistep experiments are misleading as theyare obtained with K0micr and/or θ0 parameters which arephysically unrealistic, as shown in Table 3.

The VGfix retention curve, which refers to the wettingmultistep experiment, shows a behaviour typical of a sandysoil, with a high n value and a consequent rapid water contentdecrease with pressure head. The singular behaviour of theretention curve, with two apparent inflection points, fails tobe described. As expected, the loss of flexibility with θ0 fixedat the measured value results in a worse description of thewetting branch multistep experiment, as shown in Fig. 3.

By contrast, experimental retention points are alwaysconsistent with the retention curves described by theparameters in Table 3 estimated from multistep experimentsand assuming a composite porosity approach (bimodal case).In the bimodal approach, the larger number of parametersappearing in RSbim, lending greater flexibility, allows detaileddescription of the behaviour of curve θ(h) near saturationshown in Fig. 4. The wetting branch of the multistepexperiments is described much more effectively and physi-cally reasonable K0s are obtained. Besides being consistentwith the experimental curves, the multistep estimated curvesare comparable and show an insignificant hysteresis. In otherwords, if aggregation is expressly considered satisfactorysimulation of the measured outflow is obtained and thebimodal multistep curves, with independent pore domains,allow pore-size distribution to be univocally identified.

4.2.2. Hydraulic conductivity curvesThe reliability of hydraulic conductivity estimates depends

primarily on the accurate prediction of the pore-size distribu-tion in the range of the large pores. As discussed by Durner(1994), the formulation itself of Mualem's conductivity modelor,more generally, of themodels basedon theHagen–Poiseuillelaw, and which integrate the reciprocal of h to obtain hydraulicconductivity, assume that the contribution of variations inwater content to the integral of conductivity is higher for

suction values close to zero. To bemore precise, the value of theintegrand at the numerator of Mualem's model depends onhow rapidly the effective saturation approaches zero as happroaches zero. Thismakes themodel particularly sensitive tothe slopeof the retention curve near saturation. This subject hasreceived considerable theoretical and experimental treatmentwhich shows that relatively small variations inwater content athigher h values may be amplified by the algorithm fordetermining hydraulic conductivity (van Genuchten andNielsen, 1985; Vogel and Cislerova, 1988).

From the graphs of Fig. 5, it is possible to verify to whatextent the shape of the retention curve toward saturation isdirectly reflected in that of the conductivity curve. Theconductivity curves k(h) are those estimated using Mualem'sconductivity expression combined alternatively with therelations VGopt, VGfix, and RSbim. The empty circles in thegraph denote the laboratory-measured unsaturated K valuesby using the Wind method and served to assess the goodnessof the predicted K(h) functions. In the graph the saturatedhydraulic conductivity as measured by the constant headmethod is also reported (full circle in the figure).

In general, the predictions based onVGopt_wet, VGopt_drainand VGfix_wet deviate severely from the measurements. In allthese cases, large overestimates are obtained and in no case dothe estimated curves describe the steep decrease in measuredhydraulic conductivity values near saturation generally expectedin soils with a secondary system of large pores which desaturaterapidly with the application of relatively low suction head.

This unrealistic behaviour is avoided when the bimodalfunction is used, the conductivity shape being shifted to aphysically more realistic region. The laboratory-measuredunsaturated conductivity values compare well when thebimodal approach RSbim is used (full symbols and solidlines). The predictions adequately reproduce the singularshape of the measured hydraulic conductivity of this bimodalsoil. This was only to be expected, given the accuratedescription of experimental retention values obtained byusing the RSbim.

5. Conclusions

Some physically based approaches were illustrated andused to quantify the relationships between the degree ofstructural development and physical parameters related topreferential flow. Based on our own experimental findings,questions such as the accuracy of models and their potentialuse were discussed. The discrepancy between observedprocesses and those predicted by models assuming homo-geneous unimodal porous media may result from thelimitation of accurately characterizing the effects of pore-scale heterogeneities in determining nonideality of transportin soils. To be effectively and reliably applied, all theapproaches require that the predominant effects of the soilhydrological behaviour near saturation be supported byaccurate and detailed preliminary experimental descriptionsof BTCs, retention curve and hydraulic conductivity for highwater content values, which would allow less uncertainidentification of the processes and related parametersinvolved. If in attempting to decipher soil hydrologicalbehaviour the effect of structure and related preferentialfloware not explicitly accounted for, only false interpretations

82 A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

of reality can be achieved and modelling becomes a purelyacademic practice.

For the clay soil examined, the measured transportresponse was heterogeneous with at least two identifiablevertical flow phases. First, it was demonstrated that, couplingthe transfer function approach for analyzing BTCs and waterretention data obtained with different methods from labora-tory studies, allows us to preliminarily capture the existenceof fast and slow flow paths. The combination of thesetechniques may be used to separate water flow transportphases in heterogeneous media, which is crucial for relatinglaboratory results to field behaviour.

In conclusion, we demonstrated that any measurementmethods may allow correct determination of pore-sizedistribution and geometry, provided that accurate measure-ments of the hydraulic functions near saturation are available.Nonetheless, even if such accurate measurements exist, usingthe wrong interpretative model can still have considerabledeleterious effects on the prediction of soil hydraulicbehaviour. However, the proposed method deserves furtherinvestigation in different pedological conditions.

References

Bouma, J., 1985. Soil variability and soil survey. In: Nielsen, D.R., Bouma,J. (Eds.), Soil spatial variability. PUDOC, Wageningen, Netherlands,pp. 130–145.

Bouma, J., 1991. Influence of soil macroporosity on environmental quality.Adv. Agron. 46, 1–37.

Bruand, A., Prost, R., 1987. Effect of water content on the fabric of a soilmaterial: an experimental approach. J. Soil Sci. 38, 461–472.

Brusseau, M.L., Jessup, R.E., Rao, P.S.C., 1989. Modeling the transport of solutesinfluenced by multi process nonequilibrium. Water Resour. Res. 25 (9),1971–1988.

Butters, G.L., Jury, W.A., 1989. Field scale transport of bromide in anunsaturated soil. 2. Dispersion modeling. Water Resour. Res. 25,1583–1589.

Comegna, V., Coppola, A., e Sommella, A., 2001. Effectiveness of equilibriumand physical non-equilibrium approaches for interpreting solutetransport through variously structured soils. J. Contam. Hydrol. 50,121–138.

Coppola, A., 2000. Unimodal and bimodal descriptions of hydraulic proper-ties for aggregated soils. Soil Sci. Soc. Am. J. 64, 1252–1262.

Coppola, A., Greco, R., 1997. Preferential flow through swelling and shrinkingclay soil columns. Proceedings of the International Conference on Watermanagement, salinity and pollution control towards sustainable irriga-tion in the Mediterranean region (Bari). Italy.

Destouni, G., 1993. Stochastic modeling of solute flux in the unsaturated zoneat the field scale. J. Hydrol. 143, 45–61.

Destouni, G., Sassner, M., Jensen, K.H., 1994. Chloride migration in hetero-geneous soil 2. Stochastic modeling. Water Resour. Res. 30, 747–758.

Durner, W., 1992. Predicting the unsaturated hydraulic conductivity usingmultiporosity water retention curves. In: van Genuchten, M.Th., Leij, F.J.,Lund, L.J. (Eds.), Indirect methods for estimating the hydraulic propertiesof unsaturated soils. Univ. of California, Riverside, CA, pp. 185–202.

Durner, W., 1994. Hydraulic conductivity estimation for soils with hetero-geneous pore structure. Water Resour. Res. 30, 211–223.

Eching, S.O., Hopmans, J.W., 1993. Optimization of hydraulic functions fromtransient outflow and soil water pressure data. Soil Sci. Soc. Am. J. 57,1167–1175.

Fies, J.C., 1992. Analysis of soil textural porosity relative to skeleton particlesize, using mercury porosimetry. Soil Sci. Soc. Am. J. 56, 1062–1067.

Garrido, F., Ghodrati, M., Campbell, C.G., Chendorain, M., 2001. Detailedcharacterization of solute transport in a heterogeneous field soil. J. Environ.Qual. 30, 573–583.

Gerke, H.H., 2006. Preferential flow descriptions for structured soils. J. PlantNutr. Soil Sci 169, 382–400.

Gerke, H.H., van Genuchten, M.Th., 1993. A dual porosity model forsimulating the preferential movement of water and solute in structuredporous media. Water Resour. Res. 29, 305–319.

Gerke, H.H., Köhne, J.M., 2002. Hydraulic properties of soil aggregate skins.Soil Sci. Soc. Am. J. 66, 26–36.

Germann, P., Beven, K., 1985. Kinematic wave approximation to infiltrationinto soils with sorbing macropores. Water Resour. Res. 21 (7), 990–996.

Greco, R., 2002. Preferential flow in macroporous swelling soil with internalcatchment: model development and applications. J. Hydrol. 3-4,150–168.

Jarvis, N.J., 2007. A review of non-equilibriumwater flow and solute transportin soil macropores: principles, controlling factors and consequences forwater quality. Eur. J. Soil Sci. 58 (3), 523–546.

Klute, A., Dirksen, C., 1986. Hydraulic conductivity and diffusivity: Laboratorymethods, Methods of soil analysis, Part 1, physical and mineralogicalmethods, 2nd ed. Agronomy, vol. 9 (2). American Society of Agronomy,Madison, Wisconsin, pp. 687–734.

Kung, K.J.S., Kladivko, E.J., Helling, C.S., Gish, T.J., Steenhuis, T.S., Jaynes, D.B.,2006. Quantifying the pore size spectrum of macropore-type preferentialpathways under transient flow. Vadose Zone J. 5 (3), 978–989.

Kutilek, M., and Nielsen, D.R., Soil Hydrology, Catena. Verlag, GeosciencePubl., pp.370, 1994.

Li, Y., Ghodrati, M., 1994. Preferential transport of nitrate through soilcolumns containing root channels. Soil Sci. Soc. Am. J. 58, 653–659.

Ma, L., Selim, H.M., 1994. Tortuosity, mean residence time, and deformation oftritium breakthroughs from soil columns. Soil Sci. Soc. Am. J. 58,1076–1085.

Mallants, D., Tseng, P.H., Toride, N., Timmerman, A., Feyen, J., 1997. Evaluationof multimodal hydraulic functions in characterizing a heterogeneousfield soil. J. Hydrol. 195, 172–199.

Mohanty, B.P., Bowman, R.S., Hendrickx, J.M.H., Van Genuchten, M.Th.,1997. New piecewise-continuous functions for modeling preferentialflow in an intermittent-flood irrigated field. Water Resour. Res. 33,2049–2063.

Mualem, Y., 1986. Hydraulic conductivity of unsaturated soils: prediction andformulas, In: Klute, A. (Ed.), Methods of soil analysis, Part 1, Physical andmineralogical methods, 2nd ed. Agronomy, vol. 9 (2). American Society ofAgronomy, Madison, Wisconsin, pp. 799–823.

Othmer, H.B., Diekkrüger, B., Kutilek, M., 1991. Bimodal porosity andunsaturated hydraulic conductivity. Soil Sci. 152, 139–150.

Richards, L.A., 1968. Diagnosis and Improvement of Saline and Alkali soils.USDA Hand b, 60. U.S. Government Printing Office, Washington, DC.

Romano, N., Santini, A., 1999. Determining soil hydraulic functions fromevaporation experiments by a parameter estimation approach: experi-mental verifications and numerical studies. Water Resour. Res. 35,3343–3359.

Rosqvist, H., Destouni, G., 2000. Solute transport through preferentialpathways in municipal solid waste. J. Contam. Hydrol. 46, 39–60.

Ross, P.J., Smettem, R.J., 1993. Describing soil hydraulic properties with sumsof simple functions. Soil Sci. Soc. Am. J. 57, 26–29.

Roth, K., Jury, W.A., Flühler, H., Attinger, W., 1991. Transport of chloridethrough an unsaturated field soil. Water Resour. Res. 27, 2533–2541.

Schultze, B., Ippisch, O., Huwe, B., Durner, W., 1999. Dynamic nonequilibriumin unsaturated water flow. In: van Genuchten, M.Th., Leij, F.J., Wu, L.(Eds.), Proc. Int. Workshop on Characterization and Measurement of theHydraulic Properties of Unsaturated Porous Media. University ofCalifornia, Riverside, CA., pp. 877–892.

Simunek, J., Jarvis, N.J., van Genuchten, M.Th., Gardenas, A., 2003. Reviewand comparison of models for describing non-equilibrium andpreferential flow and transport in the vadose zone. J. Hydrol. 272(1-4), 14–35.

Smettem, K.R.J., Kirkby, C., 1990. Measuring the hydraulic properties of astable aggregated soil. J. Hydrol. 117, 1–13.

Tamari, S., 1994. Relations between pore-space and hydraulic properties incompacted beds of silty–loam aggregates. Soil Technol. 7, 57–73.

Tamari, S., Bruckler, L., Halbertsma, J., Chadoeuf, J., 1993. A simple method fordetermining soil hydraulic properties in the laboratory. Soil Sci. Soc.Am. J. 57, 642–651.

Thony, J.L., Vachaud, G., Clothier, B.E., Angulo-Jaramillo, R., 1991. Fieldmeasurement of the hydraulic properties of soil. Soil Technol. 4, 111–123.

van Dam, J.C., Stricker, J.N.M., Droogers, P., 1994. Inverse method fordetermining soil hydraulic functions frommultistep outflow experiment.Soil Sci. Soc. Am. J. 58, 647–652.

van Genuchten, M.Th., 1980. A closed-form equation for predicting thehydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44,892–898.

van Genuchten, M.Th., Wierenga, P.J., 1976. Mass transfer studies in sorbingporous media. I. Analytical solution. Soil Sci. Soc. Amer. Proc. 40,473–480.

van Genuchten, M.Th., Nielsen, D.R., 1985. On describing and predicting thehydraulic properties of unsaturated soils. Ann. Geophis. 3, 615–628.

Vanderborght, J., Vereecken, H., 2007. Review of dispersivities for transportmodeling in soils. Vadose Zone J. 6, 29–52.

Vervoort, R.W., Radcliffe, D.E., West, L.T., 1999. Soil structure developmentand preferential solute flow. Water Resour. Res. 35, 913–928.

83A. Coppola et al. / Journal of Contaminant Hydrology 104 (2009) 74–83

Vogel, T., Cislerova, M., 1988. On the reliability of unsaturated hydraulicconductivity calculated from the moisture retention curve. Transp.Porous Media 3, 1–15.

Wilding, L.P., Hallmark, C.T., 1984. Development of structural and microfabricproperties in shrinking and swelling clays. In: Bouma, J., Raats, P.A.C.(Eds.), Proc. ISSS Symposium on Water and Solute Movement in HeavyClay Soils. Publ. 37. Int. Inst. For Land Reclamation and Improvement,Wageningen, The Netherlands, pp. 1–18.

Wilson, G., Jardine, P., Gwo, J., 1992. Modeling the hydraulic properties of amulti-region soil. Soil Sci. Soc. Am. J. 56, 1731–1737.

Wind, G.P., 1968. Capillary conductivity data estimated by a simple method.In: Rijtema, P.E., Wassink, H. (Eds.), Water in the unsaturated zone. Int.Assoc. Sci. Hydrol., U.N. Educ. Sci. Cult. Org., Paris, vol. 1, pp. 181–191.

Zurmühl, T., Durner, W., 1998. Determination of parameters for bimodalhydraulic functions by inverse modeling. Soil Sci. Soc. Am. J. 62, 874:880.