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Validation of an analytical method for determining soil hydraulic properties of stonysoils using experimental data

DongHao Ma a,b,c,⁎, MingAn Shao b, JiaBao Zhang a, QuanJiu Wang b

a State Experimental Station of Agro-Ecosystem in Fengqiu, State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science, Chinese Academy of Sciences,Nanjing 210008, Chinab State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Chinese Academy of Sciences, Yangling 712100, Shaanxi, Chinac Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China

a b s t r a c ta r t i c l e i n f o

Article history:Received 28 August 2009Received in revised form 20 July 2010Accepted 1 August 2010

Keywords:Stony soilsRock fragment contentSoil water characteristic curveHydraulic conductivity

Soil unsaturated hydraulic properties are an important input for simulations of water and solute movementin the vadose zone. However, in the case of soils containing rock fragments, direct measurement ofunsaturated hydraulic properties remains difficult. Recently, an analytical method was proposed (Ma et al.,2009) for determining soil hydraulic properties from horizontal water absorption experiments. Here, we testif this method could be used in the determination of the hydraulic properties of stony soils with a set ofexperiments. The results show that the method can predict accurately and quickly the hydraulic parametersof stony soils using the cumulative infiltration volume and the rate of wetting front advancement duringwater absorption into a horizontal soil column. The influence of rock fragment content on some soilhydraulic properties including air entry suction, saturated hydraulic conductivity and the shape coefficientsof hydraulic functions was further evaluated. Both air entry suction and shape coefficient show a large rangeof variation with rock fragment content. Globally, the saturated hydraulic conductivities of stony soilsdecreased with increasing rock fragment content. However, when the volumetric rock fragment content isabout 0.08 cm3 cm−3, the stony soil displayed a greater saturated hydraulic conductivity compared to thefine earth at 95% confidence level. The relationship between saturated hydraulic conductivity and rockfragment content is not accurately estimated by different equations relating saturated hydraulic conductivityof stony soils to that of non-stony soils. These findings imply that other factors than the reduction of crosssectional area for water flow influence the hydraulic properties of stony soils.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Understanding water and solute movement in soils and groundwater has important implications for the determinations of hydrologicprocesses and management of field water and nutrient conditions.Accurate prediction of water flow and solute transport dependslargely on reliable and accurate measurement of soil hydraulicproperties (Wang et al., 2002). Many studies have been focused onthe hydraulic properties of homogeneous soils and studies on thehydraulic properties of heterogeneous soils do not reach accuratepredictions of water flow and solute transport, especially in soilswith rock fragments. Soils containing rock fragments (N2 mm) are

common inmany areas due to soil development processes and humanactions (Poesen and Lavee, 1994). Rock fragments can reduce porevolume available for water flow and increase the tortuosity of soilwater flow (Mehuys et al., 1975; Childs and Flint, 1990). On the otherhand, rock fragmentsmay also create new voids at the rock fragment–fine earth interfaces (Fies et al., 2002; Tokunaga et al., 2003) and somerock fragment types (e.g. catogene, shale, ironstone and limestone)can hold water (Coile, 1953; Hanson and Blevins, 1979; Brouwer andAnderson, 2000; Cousin et al., 2003), and may provide pathways forwater flow. Therefore, the existence of rock fragments in stony soilscan lead to hydraulic properties that are highly different from those ofnon-stony soils (Mehuys et al., 1975; Sharma et al., 1993; Fies et al.,2002).

Knowledge on the hydraulic properties of stony soils is ratherlimited. This is due, mainly, to the fact that no simple methods areavailable for determining the unsaturated hydraulic properties of soilscontaining rock fragments. The presence of rock fragments isproblematic for the measurement of water content, water potentialor water flow (Reinhart, 1961; Koshi, 1966; Fleming et al., 1993)

Geoderma 159 (2010) 262–269

⁎ Corresponding author. State Experimental Station of Agro-Ecosystem in Fengqiu,State Key Laboratory of Soil and Sustainable Agriculture, Institute of Soil Science,Chinese Academy of Sciences, Nanjing 210008, China. Tel.: +86 25 8688 1262; fax: +8625 8688 1000.

E-mail addresses: dhma@issas.ac.cn (D. Ma), mashao@ms.iswc.ac.cn (M. Shao),jbzhang@issas.ac.cn (J. Zhang), wquanjiu@163.com (Q. Wang).

0016-7061/$ – see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.geoderma.2010.08.001

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because of practical issues in inserting probes in soils (such as TDRprobes, tensiometers) or installing lysimeters (Cousin et al., 2003) insuch soils without altering the soil structure, especially when thecontent of rock fragments is great. In order to guarantee represen-tative samples, the volume of soil sampled must be relatively large(Buchter et al., 1984; Flint and Childs, 1984) which involvesconsiderable labour and extended times required for equilibriumwhen using pressure plate apparatus. Thus, although traditionalmethods (Bruce and Klute, 1956; Green et al., 1986; Klute andDirksen, 1986) have proved reliable for determining the hydraulicproperties of homogeneous soils, they may lead to difficulties forstony soils. For these reasons, many previous studies focused on thedetermination of saturated hydraulic conductivities of stony soils(Bouwer and Rice, 1984; Ravina and Magier, 1984; Brakensiek et al.,1986) and the relationships between the saturated hydraulicconductivity of stony soils and their homogenous counterpart(Bouwer and Rice, 1984; Brakensiek et al., 1986). Hydraulic propertiesof the fine earth are often assumed to be the same as those of soilswithout rock fragments. Nevertheless, it has been found (Mehuys etal., 1975; Fies et al., 2002; Ma and Shao, 2008) that the presence ofrock fragments in soils can result in a pore structure of the fine earththat differs from that of soils without rock fragments. Until now,explicit unsaturated hydraulic conductivities of stony soils seeminglyremained elusive for simulations of the infiltration into stony soils bydeterministic models (Cousin et al., 2003).

Methods for determining unsaturated hydraulic properties instony soils from horizontal absorption experiments may be apromising approach, by avoiding direct measurements of watercontent or potential. Shao and Horton (1998) and Wang et al.(2002) used horizontal absorption experiments for estimatingparameters of the van Genuchten (1980) and Brooks-Corey (1964)hydraulic functions respectively. Although the applicable soil typesare limited, their methods are simple, requiring only data forcumulative infiltration, infiltration rate and wetting front advanceversus time during horizontal absorption. In that case, measurementsof the required data show the same difficulty for stony as well as fornon-stony soils. Recently, Ma et al. (2009) further improved themethod of Wang et al. (2002) for application to a wider range of soiltextures.More experimental tests are however required, especially forsoils containing rock fragments.

The first objective of this paper was to test whether the methoddeveloped by Ma et al. (2009) could be used to measure the hydraulicproperties of soils containing rock fragments. The second objectivewas to evaluate the influence of rock fragments on the soil hydraulicproperties.

2. Theory

2.1. Model of water movement in stony soils

Ma et al. (2009) proposed and compared several models includingthe non-equilibrium dual-porosity model (NDPM), the equilibriumdual-porosity model (EDPM) and the equilibrium single-porositymodel (ESPM) to simulate water movement in stony soils. Theirresults indicated that the dual-porosity model could accuratelysimulate many phenomena especially non-equilibrium flows duringwater movement in stony soils. However, it is difficult to measure thehydraulic properties of fine earth and rock fragments separately toallow for the influence of rock fragments on soil pore structure. Analternative method is to consider the mixed fine earth and rockfragments as a homogeneous effective medium. Water movementtheory for homogeneous soils (the ESPM model) can then be used tosimulate water flow in stony soils. Although the exact waterdistribution cannot be described, in that case, for non-equilibriumflows, the single-porosity model could give good estimations of thecumulative infiltration and wetting front advance in soils with rock

fragments. For one-dimensional horizontal absorption, the ESPM canbe written as (Richards equation)

∂θ∂t =

∂∂x K hð Þ ∂h∂x

� �ð1Þ

θ 0; xð Þ = θi ð2Þ

θ t;0ð Þ = θs ð3Þ

θ t;∞ð Þ = θi ð4Þ

where θ is the volumetric soil water content (cm3 cm−3), θi is theinitial water content (cm3 cm−3), θs is the saturated water content(cm3 cm−3), h is the soil water potential (cm), K is the soil hydraulicconductivity (cm min−1), x is the horizontal distance from the inlet(cm), and t is time (min).

Soil water retention curves and unsaturated hydraulic conductiv-ities can be described using the equations proposed by Brooks andCorey (1964)

S =θ−θrθs−θr

= αhð Þ−n h≤1=α

S = 1 h N 1=αð5Þ

K Sð Þ = Ks αhð Þ−m = KsSl+1+2=n ð6Þ

where θr is the residual water content (cm3 cm−3), S is the effectivewater saturation, α is an empirical parameter (cm−l) whose inverse isoften referred to as the air entry value or bubbling pressure, n is theshape coefficient,Ks is the saturated hydraulic conductivity (cmmin−1),l is the soil pore tortuosity factor, andm=n (l+1)+2. The factor l canbe any value, but 2 is applied tomost soils (Brooks and Corey, 1964) andis also adopted here. For notational convenience, let hd=−1/α for theremainder of this article which is positive and still denote the air entrysuction (cm).

2.2. Method for estimating soil hydraulic properties

Combining the power function flux–concentration relationship(Kutilek, 1980) with the Boltzmann transformation method (Philip,1960), Ma et al. (2009) deduced a simple approximate analyticalsolution to the problem of horizontal absorption (Eqs. (1) to (4)) andproposed a method for estimating hydraulic parameters of theBrooks-Corey model from horizontal absorption experiments and isdesignated as unimproved method (UM) in this paper. In the UM,Brooks-Corey model parameters can be obtained from the followingformulas

n =a

1− l + 1−βð Þa ð7Þ

hd =sd

2Ksb 1− l + 1−βð Þa½ � ð8Þ

where β is the shape coefficient of water flux distribution on soilprofile and is assumed to be constant with no relation to soil texture.Ma et al. (2009) recommended the β value of 1.145 when the UMwasused. However, the β value was found to be close to 1 according to themeasured water flux distributions for several soil types (White et al.,1979; Boulier et al., 1984). Thus, UM with β=1 and β=1.145 weretested here using experimental data to acquire an appropriate value ofβ. a and b are parameters concerning soil water content distributionwhich can be calculated by the two formulas as follows

a =θs−θr

A + θi−θr−1 ð9Þ

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b = 1−S1ai ð10Þ

b can be approximated to 1 because the initial water content (θi) orinitial water saturation (Si) required for this method is very low. A, sand d are the average increase of profile water content (cm), thesorptivity (cm min−0.5) and the characteristic length of the wettingzone (cm), respectively, which can be obtained by fitting observeddata series with the following equations

I = A · xf ð11Þ

xf = d · t1=2 ð12Þ

I = s · t1=2 ð13Þ

where I is the cumulative infiltration (cm) and xf is the wetting frontadvance(cm). Obviously, if β is known in advance, all the hydraulicparameters of the Brooks-Corey model can be easily estimated fromEqs. (7)–(13).

To further improve the estimation of soil hydraulic parameters,based on the experimental results from 19 typical soils, Ma et al.(2009) developed an improved method (IM) using the experimentalrelationship between the real hydraulic parameters and thoseestimated by UM with β=0.

n =a 0

1− l + 1ð Þa0 ð14Þ

hd =sda 0

2Ksb″a″ 1− l + 1ð Þa 0½ � ð15Þ

where

a′ = 0:77a−0:01 ð16Þ

a″ = a−0:028 ð17Þ

b″ = 1−S1a″i ð18Þ

The parameters a, A, s and d are same to those of UM. Similarly, b″can also be approximated to 1 when a soil is initially very dry. But inthe improved method, β becomes a function of the parameter n andthe average water saturation of the wetting zone rather than aconstant with no relation to soil texture.

β = l + 1 + 1 = nð Þ− 1a″

ð19Þ

3. Materials and methods

One-dimensional water absorption experiments were performedusing horizontal soil columns to test the analytical model andinvestigate how rock fragments affect soil hydraulic properties.Experiments were conducted using a horizontal cylindrical column,50 cm long with an inner diameter of 11 cm. Soils containing rockfragments were sampled from the surface 0–20 cm soil layer at theLiudaogou Basin experimental station located in the Shenmu Districtof the Loess Plateau, Shaanxi Province in China (38°46′–38°51′ N,110°21′–110°23′ E). The rock fragments were calcium concretionsfrom sediments containing calcium salts. Samples were air-dried androck fragments (N2 mm)were separated from the fine earth (b2 mm)by sieving. The rock fragments were sieved again to obtain rocks of10–20 mm equivalent diameter. The rocks were approximatelyspherical in shape. The particle density, bulk density and saturatedwater content of the rock fragments were 2.66 g cm−3, 1.94 g cm−3

and 0.27 cm3 cm−3, respectively. The fine earth was a Sand (86.3%

sand, 13.4% silt, and 0.2% clay, 0.1% organic matter) according to theparticle size classification of USDA. The particle density of the fineearth was 2.59 g cm−3. The saturated water content of the fine earthwas 0.42 cm3 cm−3 at a bulk density of 1.5 g cm−3. The initial watercontents of the rock fragments and thefineearthwere0.0084 cm3 cm−3

and 0.0173 cm3 cm−3, respectively. Rock fragments and fine earthwerepacked uniformly into Plexiglas columns with five different gravimetricrock fragment contents Rm of 0, 10%, 20%, 30% and 40% whichcorresponded to volumetric contents Rv of 0, 0.08, 0.17, 0.25 and 0.35.The weight of fine earth was calculated to reach a bulk density of1.5 g cm−3. In order to fill rock fragments and fine earth into thecolumns as uniformly as possible, they were weighed separately foreach layer of 10 cmandmixed in one container before beingpacked intocolumns. Horizontal absorption experiments were performed at zerowater head maintained by Marriott tubes at the water inlet. Thecumulative infiltration volume and wetting front advance versus timewere measured during the experiments. At the completion ofinfiltration experiments, the soil columns were saturated and arrangedvertically to determine the saturated hydraulic conductivity using aconstant water head of about 10 cm. The soil columns were weighedbefore and after experiments to determine the total porosity. Eachtreatment was replicated three times, but for the relative standarderrors of cumulative infiltration orwetting front advancewere less than4% for Rmb40%, the treatment for Rm=40% was replicated only twice.

The analytical method of Ma et al. (2009) was used to estimate thehydraulic parameters of soils with different rock fragment contents.HYDRUS-1D software (Šimůnek et al., 2005) was used to calculate thecumulative infiltration and wetting front advance versus time forcomparisonwith the observed values. To evaluate the influence of dataseries length on the stability of the estimated parameters, theexperimental data from Rm=0 with final times of 50, 100, 150 and173 min were used to further test the analytical method of Ma et al.(2009). Finally, the average values of the estimated hydraulicparameters of the stony soils for each treatmentwere used to evaluatethe influence of rock fragments on the soil hydraulic properties.

4. Results and discussion

4.1. Test of the methods for stony soils

The UM with β=1, the UM with β=1.145 and the IM were allevaluated (Ma et al., 2009). Using the observed data for cumulativeinfiltration and wetting front advance versus time, the Brooks-Coreyhydraulic model parameters for all replications were estimated fromθi, θs, θr, Ks, A, s and d with Eqs. (7)–(13) or Eqs. (14)–(18). Averagevalues of the estimated hydraulic parameters (hd and n) are shown inTable 1 as well as the measured saturated hydraulic conductivities(Ks). Parameters estimated by the three methods are not verydifferent from each other but have obvious differences in theirrelative magnitudes. The UM with β=1 predicted slightly greater nvalues for all treatments than did the UM with β=1.145 whichfurther predicted greater n values than did the IM. The air entrysuction (hd) values calculated by the UM with β=1 are greater thanthose predicted by the two other methods. Obviously, a lesser β valuein the UM will result in greater hd and n values. This will result in asteeper soil water characteristic curve with greater air entry suctionwhen β is treated as constant.

As discussed earlier, β values are related to soil texture and initialsoil water saturation (Eqs. (9), (17) and (19)). Since the initial soilwater contents used in the testings are close to residual watercontents, β values mainly change with soil texture (with rockfragment content). Using Eq. (19), β values were calculated and arealso shown in Table 1. The results in Table 1 indicate that most of the βvalues are less than 1 that is conjectured to be the upper theoreticallimit (Philip, 1973) and that β values change with soil texture. Thus,

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Eq. (19) may be more reasonable for describing the relationshipbetween β and soil texture than using a constant β.

To test the validation of the predicted soil hydraulic properties, theHYDRUS-1D software was used, with estimated parameters, tocalculate cumulative infiltration and wetting front advance forcomparison with observed values. The calculated and observedcumulative infiltration and wetting front advance are plotted inFigs. 1 and 2, respectively, and compared with 1:1 lines for the threemethods. Root mean square errors (RMSE) were also calculated(Table 2) for the three differentmethods between the observed valuesfor cumulative infiltration and wetting front advance and calculatedvalues. The plotted data all agree well with the 1:1 lines (Figs. 1 and 2)except that the RMSE increases from the IM to the UMwith β=1 andthe UM with β=1.145.

As shown in Figs. 1 and 2, the IM slightly improves the estimations ofsoil hydraulic parameters compared with the UM. The UM withβ=1.145 seems to be a poorer predictor of soil hydraulic propertiesas when β=1. Although five different contents of rock fragments weremixed with fine earth, only one type of fine earth was used. Thecalculated values of β from Eq. (19) are very close to 1 for soilscontaining no rock fragments and are mostly in the range from 0.8 to 1for soils with rock fragments (Table 1). The fact that β are close to 1 forall treatments, results in little differences of the calculated cumulativeinfiltration or wetting front advance by the IM from the UMwith β=1.However, for soils under natural conditions with a wider range oftextures, the β valuemay be far from1. In such cases, the UMwould notbe valid for estimating soil hydraulic parameters. Moreover, using auniformβ value for typical soils covering large rangeof texturesmaynotbe applicable for a particular soil. Therefore, it can be concluded that theIM should have wider applicability than the other two methods and isexpected to be an accurate and time savingmethod for determining thehydraulic properties of soils containing rock fragments.

Sufficient data series acquisition time is necessary for obtainingconfident hydraulic parameter values. Fig. 3 shows the observed andcalculated cumulative infiltration and wetting front advance curvesobtained from HYDRUS-1D while Table 3 presents soil hydraulicparameters for Rv=0 estimated by the IM using data with differenttime length. The root mean square errors (RMSE) between theobserved and calculated cumulative infiltration and wetting frontadvance are also shown in Table 3. A shorter time length of data leadsto a greater hd or n value but not a greater RMSE (Table 3). Thecalculated results were significantly overestimated when data fortimes less than 50 min were used (Fig. 3) while the calculatedcumulative infiltration andwetting front advance together are in goodaccordance with the observed values when the data time length isgreater than 100 min. Thus, the IM is reliable as long as experimentaldata with sufficient length of time is available.

4.2. Influence of rock fragments on the soil water characteristic curve

Air entry suction (hd) and shape coefficient (n) are the two mostimportant parameters of the Brooks-Corey hydraulic model. Fig. 4aand b show themean and standard errors of air entry suction (hd) and

shape coefficient (n), predicted by the IM, as a function of thevolumetric rock fragment content. The air entry suctions of stony soilsexhibit no single increasing or decreasing relationship but show twosignificant turning points with increasing rock fragment content.Values of hd fall to a local minimum when the rock fragment contentby volume increases from 0 to about 0.08 and then rise gradually to amaximum at a rock fragment content by volume of about 0.25. Thevalues of hd then decrease again with rock fragment content. Incontrast, the shape coefficient n increases to a maximum when therock fragment content is about 0.25 and then decreases.

Both air entry suction and shape coefficient depend on soil particlesize distribution and pore structure (total porosity and pore sizedistribution). If rock fragments were non-porous and did not changethe pore structure of the fine earth fraction, hd and n would beconstant and only a linear offset for the soil water characteristic curvewould occur irrespective of rock fragment content of the soil. Fig. 4aand b show that this is obviously not the case. The results indicate thatboth hd and n vary with increased rock fragment content. Somestudies (Mehuys et al., 1975; Brakensiek and Rawls, 1994) havereported that the main effects of rock fragments on the fine earthwater characteristic curve occurred in the low and high suctionregions. Air entry suction is associated with the high suction regionwhile the shape coefficient of the soil water characteristic curve canbe influenced by the whole region of suction. Several reasons mayexplain the variations of hd and n with rock fragment content shownin Fig. 4. First, rock fragments (N2 mm) will add new particle sizegrades and the ratio of them to finer solid particles (b2 mm) willincrease with rock fragment content. Second, rock fragments maycreate some new voids especially big pores (Ravina andMagier, 1984)at the rock fragment–fine earth interfaces (Fies et al., 2002; Tokunagaet al., 2003). Third, rock fragments may influence the ability of soils toresist local compaction (Ravina and Magier, 1984), hence resulting inmore heterogeneity of bulk density and pore distribution within soils.As a result, a greater total porosity of stony soil was found in theexperimentswhenRv=0.08 cm3 cm−3 compared toRv=0.0 cm3 cm−3

(Fig. 4c). Finally, some rock fragments contain considerable numbersof pores (Hanson and Blevins, 1979; Jones and Graham, 1993;Brouwer and Anderson, 2000; Cousin et al., 2003) rather than beingnon-porous rocks (Unger, 1971; Mehuys et al., 1975; Peck andWatson, 1979; Khaleel and Relyea, 1997). In these experiments, theaverage porosity of rock fragments can reach up to 0.27 cm3 cm−3,which represents 64% of fine earth porosity (0.42 cm3 cm−3). Thepores within rock fragments are mainly small sized and then in thelow water potential range, their porosity may make them the maincontributor to water storage instead of fine earth pores within thissuction range (Sharma et al., 1993; Tokunaga et al., 2003). Withincreasing rock fragments, the soil–rock fragment mixture mayundergo an intrinsic change from a soil containing rock fragments toa mixture with fine earth embedded into pore spaces among rockfragments (Ma and Shao, 2008). The influence of rock fragments onsoil hydraulic properties is therefore of great complexity and thebehavior of the soil water characteristic curve could not be attributedto only one of the factors discussed above.

Table 1Measured saturated conductivity and predicted Brooks-Corey hydraulic model parameters obtained by the horizontal absorptionmethod for soils containing different rock fragmentcontents.

Rv (cm3 cm−3) Ks (cm min−1) IM UM

β=1 β=1.145

β hd (cm) n hd (cm) n hd (cm) n

0.00 0.0463±0.0013 1.00±0.03 80.1±3.2 0.380±0.038 88.5±3.1 0.474±0.041 82.8±2.6 0.443±0.0360.08 0.0520±0.0001 0.96±0.04 68.2±2.7 0.437±0.057 74.4±2.1 0.534±0.059 69.1±1.5 0.495±0.0510.17 0.0419±0.0004 0.87±0.02 84.5±3.2 0.608±0.053 88.5±2.2 0.704±0.049 80.3±1.5 0.639±0.0410.25 0.0372±0.0017 0.87±0.04 88.5±11.2 0.640±0.123 91.5±8.8 0.728±0.111 82.6±6.8 0.656±0.0890.35 0.0424±0.0032 0.94±0.04 61.6±4.4 0.475±0.071 66.9±3.7 0.556±0.074 61.9±2.7 0.513±0.063

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Fig. 1. Observed cumulative infiltration versus calculated cumulative infiltration fromHYDRUS-1D with the estimated parameters by the (a) IM, (b) UM with β=1, and(c) UM with β=1.145.

Fig. 2. Observed wetting front advance versus calculated wetting front advance fromHYDRUS-1D with the estimated parameters by the (a) IM, (b) UM with β=1, and(c) UM with β=1.145.

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4.3. Influence of rock fragments on soil hydraulic conductivity

Unsaturated soil hydraulic conductivity usually can be expressedas a product of saturated hydraulic conductivity and a dimensionlessfunction of water saturation with values between 0 and 1. Due to thedifficulty of determining the unsaturated hydraulic conductivities ofsoils containing rock fragments, the dimensionless function or relativehydraulic conductivity is usually assumed to be that of fine earth. Tosimplify the calculation of unsaturated hydraulic conductivities ofstony soils, attempts have beenmade to relate the saturated hydraulicconductivity of the soil containing rock fragments to that of fine earth

(Peck and Watson, 1979; Bouwer and Rice, 1984; Ravina and Magier,1984). Four main methods have been proposed.

Using heat transfer theory as a basis, Peck and Watson (1979)derived a formula for a homogeneous medium containing non-porousspherical inclusions to calculate the hydraulic conductivity of a stonysoil from the hydraulic conductivity of the fine earth and thevolumetric rock fragment content

Ks;T =2 1−Rvð Þ2 + Rvð ÞKs;fe ð20Þ

where Ks,T and Ks,fe are the hydraulic conductivities (cm min−1), andthe subscripts s, T and fe denote saturated soil, total soil (i.e. stonysoil) and fine earth, respectively.

For easier application, Eq. (20) was simplified to a function of therock fragment content by weight according to experiential relations(Brakensiek et al., 1986)

Ks;T = 1−Rmð ÞKs;fe ð21Þ

Bouwer and Rice (1984) proposed the following equation thattakes porosity of rock fragments into consideration

Ks;T =θs;Tθs;fe

Ks;fe ð22Þ

where θs,T and θs,fe are the porosities or saturated water contents(cm3 cm−3) and the subscripts mean the same to the above.

Assuming that rock fragments were non-porous and did not exertan influence on the pore structure of the fine earth, Ravina andMagier(1984) considered that the relative hydraulic conductivity of a stonysoil to fine earth could be approximated to the volumetric percentageof bulk fine earth.

Ks;T = 1−Rvð ÞKs;fe ð23Þ

Fig. 5 shows the observed saturated hydraulic conductivities ofstony soils (Ks,T) as a function of rock fragment content (Rv), as well aspredicted values by Eqs. (20), (21), (22) and (23) for comparisonbetween models. Fig. 5 indicates that the observed saturatedhydraulic conductivities exhibit no consistent increase or decreasewith increased rock fragment content. At 95% confidence level,statistical analysis by Mathcad software (Mathsoft, 2001) shows anoverall decrease of the saturated hydraulic conductivity of the stonysoils with increasing stone content, but a greater saturated hydraulicconductivity compared to the fine earth is observed when the rockfragment content is about 0.08. With further increases in rockfragment content, the saturated hydraulic conductivity declines andthen increases again. Zhu and Shao (2006), using different kinds offine soil and stones from those used in this study, also observed thisphenomena for soils containing 0.08 volumetric rock fragments inrain runoff experiments. In Fig. 4c, the soils with Rv=0.08 cm3 cm−3

show the maximum porosity. Clearly, factors enhancing water flow instony soils, such as the generation of new voids and the change of thefine earth pore structure exert a greater influence on soil hydraulic

Table 2Root mean square error (RMSE) between the observed values for cumulativeinfiltration and wetting front advance, and calculated values from HYDRUS-1D for alltreatments using three different methods.

Method Cumulative infiltration (cm) Wetting front (cm)

IM 0.17 0.51UM (β=1) 0.31 0.65UM (β=1.145) 0.40 1.15

Fig. 3. Observed and calculated (a) cumulative infiltration curves and (b) wetting frontadvance curves from HYDRUS-1D with the estimated parameters by the IM using datawith different series length.

Table 3Estimated soil hydraulic parameters for Rv=0 by the IM using data for different serieslength, and the root mean square error (RMSE) between the observed and calculatedvalues of cumulative infiltration and wetting front advance from HYDRUS-1D.

Time(min)

hd(cm)

n RMSE (cm)

Cumulative infiltration Wetting front

50 90.1 0.373 0.22 1.01100 81.9 0.323 0.16 0.33150 79.9 0.320 0.18 0.46173 79.1 0.319 0.19 0.48

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conductivity than factors reducing flow, such as the reduction of crosssectional area for water flow and the possible increase of tortuosityinduced by rock fragments. The alternating dominance of theseopposite factors can be responsible for the fluctuation of themeasuredsaturated hydraulic conductivities with the rock fragment content.

As shown in Fig. 5, values estimated from Eq. (22) are the greatestand the closest to the observed saturated hydraulic conductivities,while Eqs. (20), (21) and (23) give lower estimated values thanobserved. Brakensiek and Rawls (1994) also found that Eq. (22) gavethe best estimations of saturated hydraulic conductivities of stonysoils. In both Eqs. (22) and (23), the cross sectional area available forwater flow is assumed to be directly proportional to the saturatedhydraulic conductivity. However, the rock fragments examined byRavina and Magier (1984) have very low porosity of 0.04 cm3 cm−3

contrasted to 0.27 cm3 cm−3 in this paper and thus the rock porositymay explain the discrepancy between the estimations of Eqs. (23) and(22). Eq. (20) was derived for non-porous spherical inclusions (Peckand Watson, 1979) but a perfect contact at the rock fragment–fineearth interface was assumed and the reorganization of the fine earthpore structure was not considered. The change of fine earth porestructure and the non-perfect contact between rock fragments andfine earth are responsible for the discrepancy between Eqs. (20)and (23).

As well as saturated hydraulic conductivity, air entry suction (hd)and the exponent m are main parameters determining the unsatu-rated hydraulic conductivity curve (Eq. (6)). Mehuys et al. (1975)reported that the influence of rock fragments on unsaturatedhydraulic conductivity was most important in the low and highsuction regions. Given that a linear relationship exists between theparameters m and n, rock fragment content should have the sameeffect on both of them.

This paper considered only disturbed soils. The field situationwould be more complex than discussed here. Apart from their directinfluence on soil porosity and pore structure, rock fragments may alsoaffect soil structure development processes. For example, rockfragments can serve as a skeleton to resist compaction and providemany opportunities for soil burrowing animals, which may promotesoil aggregate development (Ma and Shao, 2008). Rock fragmentscould force the plant roots to make morphological adaptations(Zwieniecki and Newton, 1995) which may also be an importantcontributor to soil aggregation. Therefore, further field experimentsare required to determine the influence of rock fragments on soil

Fig. 4. Influence of rock fragment content (Rv) on (a) the air entry suction (hd), (b) theshape coefficient (n) of the soil water characteristic curve predicted by the IM, and(c) the measured total porosities of stony soils. Error bars are standard errors.

Fig. 5. Influence of rock fragment content (Rv) on the saturated hydraulic conductivity(Ks,T), and comparisons among models relating the saturated hydraulic conductivity(Ks,T) of a stony soil to that of fine earth (Ks,fe). Error bars are standard errors ofmeasured values.

268 D. Ma et al. / Geoderma 159 (2010) 262–269

Author's personal copy

hydraulic properties and to depict more clearly the processes affectingwater movement in soils containing rock fragments.

5. Conclusions

Few simple and valid methods are available to measure theunsaturated hydraulic properties of soils containing rock fragments.Consequently, it is almost impossible to accurately simulate water orsolute transport in these kinds of soils using deterministic modelswhich require explicit hydraulic functions. In this study, thehorizontal absorption method proposed by Ma et al. (2009) wastested for determining the hydraulic properties of soils containingrock fragments. Using the estimated parameters, the effects of rockfragments on soil hydraulic properties were also evaluated. Theresults demonstrate that the Improved Method (IM) can give goodestimations of the hydraulic parameters of stony soils as shown withthe cumulative infiltration andwetting front advance calculated usingthe HYDRUS-1D software. Calculated cumulative infiltration andwetting front advance agreed favorably with observed values forsoils with rock fragment contents ranging from 0 to 0.35 cm3 cm−3.For the soil used, an Unimproved Method (UM) with β=1 orβ=1.145 predicted the Brooks-Corey model parameters close tothose calculated using the IM. All of the important hydraulicparameters of stony soils such as air entry suction, saturated hydraulicconductivity and curve shape coefficients vary with rock fragmentcontent. The soil containing about 0.08 rock fragments displayedgreater saturated hydraulic conductivity than the non-stony soil. Theobserved relationship between saturated hydraulic conductivity androck fragment content was not well fitted by any of the four methodsassessed. These findings suggest that rock fragments should not betreated as non-porousmedia in all situations. The hydraulic propertiesof the fine earth could not be approximated to those of soils withoutrock fragments especially when the fine earth contains great amountsof clay favorable to soil aggregation. Reduction of porosity withincreased rock fragment content is one of the most important factorsaffecting the hydraulic properties of stony soils but other factors mayalso take effects. For example, existence of rock fragments in field soilsmay affect the actions of soil animals and microorganisms and thegrowth of plant roots, all of them affecting the development of soilpore structure. Although further experimental tests are required onthe applicability of the horizontal absorption method to stony soilsover a wider range of textures, it provides a good tool for studyingunsaturated hydraulic properties and thus water and solute move-ments in soils containing rock fragments.

Acknowledgments

Thisworkwas supported by the National Nature Science Foundationof China (No. 50909090), National Basic Research Program of China(No. 2005CB121103), the Knowledge Innovation Program of theChinese Academy of Sciences (No. kzcx2-yw-406) and the State KeyLaboratory Foundation of Soil Erosion and Dryland Farming on theLoess Plateau (No. 10501-238). We thank two anonymous reviewersand Claude Doussan in INRA for their valuable suggestions and effortsmade in improving the quality of the manuscript.

References

Boulier, J.F., Touma, J., Vauclin, M., 1984. Flux-concentration relation-based solution ofconstant-flux infiltration equation: I. Infiltration into nonuniform initial moistureprofiles. Soil Science Society of America Journal 48, 245–251.

Bouwer, H., Rice, R.C., 1984. Hydraulic properties of stony vadose zones. Ground Water22, 696–705.

Brakensiek, D.L., Rawls, W.J., 1994. Soil containing rock fragments: effects oninfiltration. Catena 23, 99–110.

Brakensiek, D.L., Rawls, W.J., Stephenson, G.R., 1986. Determining the saturatedhydraulic conductivity of a soil containing rock fragments. Soil Science Society ofAmerica Journal 50, 834–835.

Brooks, R.H., Corey, A.T., 1964. Hydraulic properties of porous media. HydrologicalPaper 3. Colorado State University, Fort Collins, Colorado, pp. 22–27.

Brouwer, J., Anderson, H., 2000. Water holding capacity of ironstone gravel in a typicplinthoxeralf in southeast Australia. Soil Science Society of America Journal 64,1603–1608.

Bruce, R.R., Klute, A., 1956. The measurement of soil moisture diffusivity. Soil ScienceSociety of America Journal 20, 458–462.

Buchter, B., Leuenberger, J., Wierenga, P.J., Richard, F., 1984. Preparation of large coresamples from stony soils. Soil Science Society of America Journal 48, 1460–1462.

Childs, S.W., Flint, A.L., 1990. Physical properties of forest soils containing rockfragments. In: Gessel, S.P., Weetman, G.F., Powers, R.F. (Eds.), SustainedProductivity of Forest Soil. University of British Colombia, Vancouver.

Coile, T.S., 1953. Moisture content of small stone in soil. Soil Science 75, 203–207.Cousin, I., Nicoullaud, B., Coutadeur, C., 2003. Influence of rock fragments on the water

retention and water percolation in a calcareous soil. Catena 53, 97–114.Fies, J.C., Louvigny, N.D., Chanzy, A., 2002. The role of stones in soil water retention.

European Journal of Soil Science 53, 95–104.Fleming, R.L., Black, T.A., Eldridge, N.R., 1993. Water content, bulk density, and coarse

fragment content measurement in forest soils. Soil Science Society of AmericaJournal 57, 261–270.

Flint, A.L., Childs, S., 1984. Development and calibration of an irregular hole bulk densitysampler. Soil Science Society of America Journal 48, 374–378.

Green, R.E., Ahuja, L.R., Chong, S.K., 1986. Hydraulic conductivity, diffusivity, andsorptivity of unsaturated soils: field methods, In: Klute, A. (Ed.), Methods of soilanalysis, 2nd ed. : Part 1. Agronomy Monographs, vol. 9. American Society ofAgronomy and Soil Science Society of America, Madision, WI, pp. 771–798.

Hanson, C.T., Blevins, R.L., 1979. Soil water in coarse fragments. Soil Science Society ofAmerica Journal 43, 819–820.

Jones, D.P., Graham, R.C., 1993. Water-holding characteristics of weathered graniticrock in chaparral and forest ecosystems. Soil Science Society of America Journal 57,256–261.

Khaleel, R., Relyea, J., 1997. Correcting laboratory-measured moisture retention data forgravels. Water Resources Research 33, 1875–1878.

Klute, A., Dirksen, C., 1986. Hydraulic conductivity and diffusivity: laboratory methods,In: Klute, A. (Ed.), Methods of soil analysis, 2nd ed. : Part 1. AgronomyMonographs,vol. 9. American Society of Agronomy and Soil Science Society of America,Madision, WI, pp. 687–734.

Koshi, P.T., 1966. Soil-moisture measurement by the neutron method in rocky wildlandsoils. Soil Science Society of America Journal 30, 282–284.

Kutilek, M., 1980. Constant-rainfall infiltration. Journal of Hydrology 45, 289–303.Ma, D.H., Shao, M.A., 2008. Simulating infiltration into stony soils with a dual-porosity

model. European Journal of Soil Science 59, 950–959.Ma, D.H., Wang, Q.J., Shao, M.A., 2009. Analytical method for estimating soil hydraulic

parameters from horizontal absorption. Soil Science Society of America Journal 73,727–736.

MathSoft, 2001. Mathcad & Reference manual. MathSoft Inc, Cambridge, MA.Mehuys, G.R., Stolzy, L.H., Letey, J., Weeks, L.V., 1975. Effect of stones on the hydraulic

conductivity of relatively dry desert soils. Soil Science Society of America Journal39, 37–42.

Peck, A.J., Watson, J.D., 1979. Hydraulic conductivity and flow in non-uniform soil.Workshop on Soil Physics and Field Heterogeneity. CSIRO Division of Environ-mental Mechanics, Canberra, Australia.

Philip, J.R., 1960. General method of exact solutions of the concentration-dependentdiffusion equation. Australian Journal of Physics 13, 1–12.

Philip, J.R., 1973. On solving the unsaturated flow equation: I. The flux–concentrationrelation. Soil Science 117, 1–13.

Poesen, J., Lavee, H., 1994. Rock fragments in top soils: significance and processes.Catena 23, 1–28.

Ravina, I., Magier, J., 1984. Hydraulic conductivity and water retention of clay soilscontaining coarse fragments. Soil Science Society of America Journal 48, 736–740.

Reinhart, K.G., 1961. The problem of stones in soil-moisture measurement. Soil ScienceSociety of America Journal 25, 268–270.

Shao, M.A., Horton, R., 1998. Integral method for estimating soil hydraulic properties.Soil Science Society of America Journal 62, 585–592.

Sharma, P.P., Carter, F.S., Halvorson, G.A., 1993. Water retention by soils containing coal.Soil Science Society of America Journal 57, 311–316.

Šimůnek, J., van Genuchten, M.T., Šejna, M., 2005. The HYDRUS-1D Software Package forSimulating the Movement of Water, Heat, and Multiple Solutes in VariablySaturated Media. Version 3.0, HYDRUS Software Series 1. Department ofEnvironmental Sciences, University of California, Riverside, California, USA.

Tokunaga, T.K., Olson, K.R.,Wan, J., 2003.Moisture characteristics of Hanford gravels: bulk,grain-surface, and intragranular components. Vadose Zone Journal 2, 322–329.

Unger, P.W., 1971. Soil profile gravel layers: I. Effect on water storage, distribution, andevaporation. Soil Science Society of America Journal 35, 631–634.

Van Genuchten, M.Th., 1980. A closed form equation for predicting the hydraulicconductivity of unsaturated soils. Soil Science Society of America Journal 44, 892–898.

Wang, Q.J., Horton, R., Shao, M.A., 2002. Horizontal infiltration method for determiningBrooks–Corey model parameters. Soil Science Society of America Journal 66,1733–1739.

White, I., Smiles, D.E., Perroux, K.M., 1979. Absorption of water by soil: the constant fluxboundary condition. Soil Science Society of America Journal 43, 659–664.

Zhu, Y.J., Shao, M.A., 2006. Processes of rainfall infiltration and sediment yield in soils.Transactions of the CSAE 22 (2), 64–67 (In Chinese).

Zwieniecki, M.A., Newton, M., 1995. Roots growing in rock fissures — theirmorphological adaptation. Plant and Soil 172, 181–187.

269D. Ma et al. / Geoderma 159 (2010) 262–269