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The effect of compaction and shear deformation of saturated soil on hydraulic conductivity / W.R. Whalley; G.P.
Matthews; S. Ferraris. - In: SOIL & TILLAGE RESEARCH. - ISSN 0167-1987. - 125(2012), pp. 23-29.
Original Citation:
The effect of compaction and shear deformation of saturated soil on hydraulic conductivity
Published version:
DOI:DOI: 10.1016/j.still.2012.05.020
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The
effect
of
compaction
and
shear
deformation
of
saturated
soil
on
hydraulic
conductivity
W.R.
Whalley
a,*
,
G.P.
Matthews
b,
S.
Ferraris
c aRothamstedResearch,Harpenden,HertfordshireAL52JQ,UKb
EnvironmentalandFluidModellingGroup,UniversityofPlymouth,Plymouth,DevonPL48AA,UK
c
InteruniversityDepartmentofRegionalandUrbanStudiesandPlanning,Universita` degliStudidiTorinoePolitecnicodiTorino,vialeMattioli39,Torino10125,Italy
1. Introduction
When soil is damaged in the field, because of traffic by agricultural machinery, it is often referred to as ‘‘compacted’’. However,inpracticeinthetopsoil,so-calledcompactionevents areusuallyacombinationofdensificationandsheardeformation.
Greenetal.(2003)havereviewedtheeffectsofvarioustypesofsoil deformation on hydraulic conductivity. Their conclusion, in agreement with many other studies (Matthews et al., 2010; Reynoldsetal.,2008;WangandHuang,1984),isthatsaturated hydraulic conductivityis very sensitive tochanges in porosity. Manyoftheeffectsofsoiltypeandcompactioncanbetakeninto accountwiththeuseofaneffectiveporosity.Carman(1939)was oneofthefirsttoproposethisapproachtoallowthesaturated hydraulicconductivityksatinclaysandsandstobedescribedbya
singleequation.TheKozeny–Carman(KC)equationiswidelyused to explore the effects of changes in porosity on hydraulic conductivity.Itiswrittenas:
ksat¼
t
1 S2r
2 wgnr
2 s e3 1þe (1)whereSisthespecificsurfacearea,
t
isatortuosityfactor,gisthe accelerationduetogravity,r
wandr
sarethedensityofwaterandsoilrespectively,
n
isthedynamicviscosityofwaterandeisthe voidratio(note:e=f
/(1f
),wheref
isporosity)(seeChapuis and Aubertin, 2003). However, Chapuis and Aubertin (2003)observed that the KC equation is rarely used because of the difficultyofmeasuringtheparameters,especiallyS.Anadditional complicationisthat
t
isaconstantthattakesaccountofdifferences intortuositybetweendifferentsoils,andifksatistobepredictedt
needs to be known. However, Carman (1939) expected that
t
wouldonlyhaveanarrowrangeofvalues.
Therelationshipbetweensoilporosityandhydraulic conduc-tivityisoftendescribedbyanempiricalpowerlaw(Ahujaetal., 1989;Aminrunetal.,2004;Greenetal.,2003):
ksat¼B
f
ne (2)whereBandnarefitted,and
f
eistheeffectiveporositywhichisdefinedasthedifferencebetweenthewatercontentatsaturation
u
sandatamorenegativematricpotential.ThereisageneralviewthatEq.(2)isaKozeny–Carmenderivedrelationship,althoughthe resemblanceisnotverystrongasfarastheformoftheequationis concerned.Infactthefunctionalrelationshipisdifferenttotheone describedbyCarman(1939).Typicallynisassumedhaveavalue between4and5,andBmayvarywithsoiltype(Ahujaetal.,1989). The approach recognises that the hydraulic conductivity of saturated soil depends mainly on the larger voids (i.e. those affecting the saturated end of the water retention curve). The choiceofthelowervalueofmatricpotential,usedtoestimate
f
e,isARTICLE INFO Keywords: Consolidation Criticalstate Claysoil Empiricalmodels ABSTRACT
Thispaperdescribeshowinaclaysoil,consolidationandthensheardeformationataconstantporosity
affectthehydraulicconductivityofthesaturatedsoil.WeusedaBishopandWesleytriaxialcellto
consolidatethesoilalongthenormalconsolidationlineandthentoshear-deformthesoilataconstant
porositytothepointwherethecriticalstateconditionhadbeenreached.Therelationshipbetween
hydraulicconductivity(ksat)andsoilporosityforsoilconsolidatedonthenormalconsolidationlinewas
similarto previouslypublisheddata. However,sheardeformation ofsoilwhenheldataconstant
porositygreatlyreducedksatespeciallyathighporosity,whereksatwasreducedto5%ofitsoriginalvalue.
Indensesoiltheeffectsofsheardeformationonksatweresmaller.Weusedpreviouslypublishedwater
releasedataforthevariouslycompactedandsheardeformedsoiltoestimatewaterreleasecurvesforthe
soilinourexperiment. Weshowedthatanempiricalmodel topredictksatgaveagoodfit toour
experimentaldatacollectedinthelaboratory.Wetestedtheempiricalmodelonawidersetoffielddata
obtainedfromtheHYPRESdatabase.
ß2012ElsevierB.V.Allrightsreserved.
*Correspondingauthor.
E-mailaddress:richard.whalley@rothamsted.ac.uk(W.R.Whalley).
ContentslistsavailableatSciVerseScienceDirect
Soil
&
Tillage
Research
j o urn a l hom e pa g e :ww w . e l se v i e r. c om / l oca t e / st i l l
0167-1987/$–seefrontmatterß2012ElsevierB.V.Allrightsreserved.
arbitrary. Ahuja et al. (1989) recommend 33kPa whereas
Aminrun et al. (2004) suggest that a more negative value of 66kPamayworkbetterforsoilwithhigherclaycontent.Han etal.(2008)estimated
f
efromthepointofinflexionofthewaterretention curve, which was determined from a fit of the Van Genuchten function (van Genuchten, 1980). With this general approach, it does seem possible to obtain an approximately commonrelationshipbetweenksatand
f
efordifferentsoilsaswellasdescribetheeffectsofsoildamagebycompactiononksat(Green et al., 2003). However, individual soil types have systematic variationsfromtheaveragecurvefittedtoanumberofsoils(see Fig.4ainAhujaetal.,1989).AssoulineandOr(2008)outlinehow, inadditiontoporosity,theairentrypotentialcanbeusedinan improvedapproachtotakeaccountoftheeffectsofcompactionon hydraulicconductivity.
Matthews et al. (2010) have proposed a simple model for saturated hydraulic conductivity using the water retention characteristic.They considered theinterconnectionof cylinders ofdifferentsizesacrossasectionofaporousmaterial.Inaspecial caseitwasassumedthattheseinterconnectionswererandom.A distributionF(r)ofcylindricalporeradiirwasderivedfromthe waterretentioncurve(
u
,c
)as:FðrÞ¼d
u
dr¼ dc
dr du
dc
(3)where
c
isthematricpotential.Assumingthattheflowofwater througha cylinderwas proportionaltoits cross-sectional area, then, ksat/½ Z 1 0 rFðrÞdr 2 (4)Commonly this expressionis incorporatedinto a model for relative permeability or unsaturated hydraulic conductivity, appearingasadenominatorinsuchamodel(Mualem,1976).
A constantofproportionality isrequiredtoachieve absolute valuesofksatfromEq.(4)whichmaybewrittenas:
ksat/ Z 1 0 1
c
du
" #2 (5)Matthewsetal.(2010)usedthevanGenuchtenfunctionforthe waterretentioncharacteristic(vanGenuchten,1980)toevaluate thisintegralandusedthestandardconstraintm=11/nforthe twoshapeparametersofthewaterretentioncharacteristic.
Withthechangeofvariable
Q
¼u
u
ru
su
r(6)
where
u
sandu
raretherespectivesaturatedandresidualwatercontents,Eq.(5)became:
ksat/ð
u
su
rÞ2 Z 1 0 1c
dQ
" #2 (7)whichwasrewrittenas:
ksat/
a
2ðu
su
rÞ2 Z 1 0Q
1=m 1Q
1=m !1m dQ
2 4 3 5 2 (8)where
a
wasthethirdfittingparameterfortheVanGenuchten function.TheintegralinEq.(8)equatesto1anditcanbewrittenas: ksat/
a
2ðu
su
rÞ2 (9)Aconstantofproportionalityneededtoachieve absolutevalues maybeinsertedinEq.(9)togive:
ksat¼
r
w g 8v
2g
r
wg 2a
2 ðu
su
rÞ2 (10)where
n
istheviscosityofwaterandg
isthesurfacetension of water.Hereweassumenorequirementforacorrectionfactorto accountfortortuosity.Eq.(10)simplifiesto:ksat¼
g
22
vr
wga
2ðu
s
u
rÞ2 (11)Matthews et al. (2010) explored the effects of isotropic compression on thehydraulic conductivity of soil. They found thatbothEq.(11)andaporenetworkmodelgavegoodpredictions of the effects of consolidation on the change in hydraulic conductivity, although the absolute predicted values were in someerror.
Soildeformationscanbemorecomplexthanmerelyanincrease insoildensityandmayincludetheeffectsofsheardeformation. The critical state description of soil behaviour allows the relationships between compression,shear deformation and soil porositytobedefined.Duringcriticalstatedeformationthesoilis completelydestructured(MitchellandSoga,2005)totheextent thatthereisnoevidenceofanyaggregationandtheentirepore spacecanbeassumedtobetextural.Atthecriticalstate,theshear stressanddensityremainconstantwhileshearstrainincreases. Dependingontheinitialstateofthesoil,itsporositywilleither increaseordecreaseasitissheardeformedtoapproachthecritical state.KirbyandBlunden(1991)consideredtheeffectofboth of thesetransitionstothecriticalstateonsoilhydraulicproperties. Innewlycultivatedsoilsitislikelythatporositywilldecrease during shear. We were interested to discover if relationships betweensoilporosityanditshydraulicconductivityforsaturated soilweredifferentfornormallyconsolidatedsoilcomparedwith soil which had beenshear deformed. Althoughtheeffects of a changeinporosityonhydraulicconductivityarewidelyreported, there are very little published data on the effect of shear deformationon soil hydraulicconductivity(Kirbyand Blunden, 1991).
2. Materialsandmethods
2.1. Soilsampleandpreparation
WeusedRowdensoil(Gregoryetal.,2010a,b;Matthewsetal., 2010)whichisaclaysoilfromNorthWyke,Devon,UK.Basicsoil
Table1
Basicsoilproperties.
Location NorthWyke,Devon
Field Rowden
Gridreference GBNationalGrid SX652994
Longitude 03,54,50W
Soiltype Latitude 50,46,43N
SSEWgroup Stagnogleysoil
SSEWseries Hallsworth
FAO GleyicLuvisol
Landuse Permanentgrass
Sand2000–63mm gg1 drysoil 0.147 Silt63–2mm gg1 drysoil 0.396 Clay<2mm gg1 drysoil 0.457
Texture SSEW Clay
Particledensity gcm3 2.466
Organicmatter gg1drysoil 0.076
W.R.Whalleyetal./Soil&TillageResearch125(2012)23–29 24
propertiesweremeasuredbystandardmethods(Table1).Theair driedsoilwascrumbledtopassa4mmsieveandlefttoair-dryina singlebulked sample.Beforeusethesoil wasequilibratedtoa watercontentof0.55gg1byaddingwaterandstoringinafridge.
Thesoilwaspackedintoamould38mmindiameterand78mm long in thin layers, approximately 1cm deep. Each layer was compressed uniaxiallywitha pneumaticpress at a pressureof 10kPa.
2.2. Measuringksatinconsolidationandsheardeformedsoil
Weuseda Bishopand Wesleytriaxialcell(Ngand Menzies, 2007)todeformthesoilandmeasurehydraulicconductivity(see
Fig. 1). Once in the triaxial cell, the soils were saturated by increasingthepressureofthewaterconfiningthesoilsampleand thepressureofthesoilwaterto600and590kParespectivelyover aperiodof24h. Thesoilswerethenconsolidatedtoarangeof effectivestressesbetween10(initialcondition)andapproximately 500kPa. Isotropic compression was achieved by adjusting the relativevaluesoftheporepressureandcellpressuretoincrease the effective stress on the saturated soil sample. The normal consolidationlinewasdeterminedfromanumberofindependent consolidation tests. Following consolidation of samples, shear
deformationwasappliedbyraisingthepedestal(seeFig.1).During sheardeformation,thevolumeofthesamplewaskeptconstantby fixingthevolumeofthepore-pressurepressurevolumecontroller andthechangeintheporepressurewasmonitored(seeFig.1). During shear deformation,thesoilsample shape changedfrom cylindrical(attheendofnormalconsolidation)tobarrel-shaped (attheendofsheardeformation).
Thetriaxial cellweusedhad anadditional pressurevolume controllerconnectedtothebaseofthesample,sowewereableto measurethefluxofwaterthroughasampleatanygivenhydraulic gradient. We applieda hydraulic gradient of20kPa acrossthe sample as described by Matthews et al. (2010). The hydraulic conductivityofthecylindricalsampleswasreadilycalculated.
To convert the flux of water measured through the barrel-shapedshear-deformedsamplesintoahydraulicconductivitywe assumed that the soil had thediameter ofa cylinderwiththe volumeofthebarrelandwiththesameheight.Todeterminethe magnitude of any error arising from the assumption of an equivalentvolume cylinder,theDarcy equation wasintegrated inanaxialsymmetricaldomainbyafinitevolumecode(Manzini andFerraris,2004)fortwogeometries;abarrelshapedsampleand acylinderofthesameheightwithanequivalentvolumediameter. Foragivenvalueofksat(1.14cm/s)andhydraulicgradient(20kPa)
Fig.1.BishopandWesleycellusedtoconsolidateandshearthesoilandthentomeasurethesaturatedhydraulicconductivityofsoil.Ahydraulicgradientcanbeappliedby adjustingthepressureofthewateratthetopofthesampleP1relativetothepressureofthewateratthebaseofthesampleP2.
the modelled fluxes from these two geometries were similar (30.4cm3/h for the barrel compared to 34.1cm3/h for the equivalentdiametercylinder).
2.3. Useofpublisheddata
Empirical models to predict ksat usually require the water
retentioncharacteristictobeknowntosomeextent.Toestimate thewaterretentioncharacteristiccurvesofthedeformedsoilsin thispaperweusedthedatapublishedbyGregoryetal.(2010a). Theyreportedwaterrelease characteristicdataforRowdensoil whichwascompresseduniaxiallyandalsosoilsheardeformed,by remoulding,whichwasfittedtothefollowing:
u
¼u
su
r ð1þðf
bc
ÞnvÞ1ð1=nvÞ 2 4 3 5 þu
r (12)where
f
isthesoilporosityandbisaparameterthatdependson soildamage.Parametersu
s,u
r,a
(herea
=f
b)andnvarethoseofthevanGenuchten function.The valueof bincreaseswithsoil damage.We assumedthat remouldingofsoil byGregoryet al. (2010a,b)hadthesameeffectsassoildeformationatthecritical stateandhencethatthevaluesofbforremouldedsoilappliedto soilatthecriticalstate.
Totestempiricalmodelsforksatmorewidelyweusedhydraulic
conductivitydataforsaturatedfromtheHYPRESdatabasealong withestimatesof theVan Genuchten parameters for thesame soils.Themostcomprehensive(‘L’)datasetoftheHYPRESdatabase (Wo¨stenetal.,1999)wasused.Theextracteddatawererestricted totopsoils(notallwerecultivated)andsubsoils,todepthsof2.3m. Buried,organicorambiguoushorizonswereomitted.
3. Resultsanddiscussion
3.1. Soildeformation
The normal consolidation curve is shown in Fig.2A. This is consistentwithdatapublishedforthesamesoilbyMatthewsetal. (2010). Thecritical stateline is alsoshown inFig.2Aand it is consistentwithpreviouslypublisheddataforclaysoils(O’Sullivan andRobertson,1996)inthatitsslopeisslightlysteeperthanthatof thenormal consolidation line. In Fig. 2B thedeviator stress is plottedagainstthemeanstress.Thedeviatorstressvarieslinearly withthemeanstress.Inallcasessheardeformationresultedin visiblebarrellingofaninitiallycylindricalsoilsample(seeMitchell andSoga,2005).
3.2. Deformationandhydraulicconductivity
Thehydraulicconductivityofsoilisplottedagainstporosityin
Fig.3.Fornormallyconsolidatedsoilthedataaretypicalofwidely reportedcorrelations betweenconsolidation andhydraulic con-ductivity(e.g.Matthewset al.,2010). When thesoilwasshear deformed to the critical state, ksat was smaller for any given
porositycomparedtoitsinitialvaluewhenthesoilwasnormally consolidated(seeFig.3).Wefitted
log10ksat¼R
f
þQ (13)to the data in Fig. 3 where
f
is porosity. The values of theparameters, R and Q are given in Table 2, together with the standarderrors(SE).Thefittedcurvesexplained90percentofthe variance(P<0.002)inksatforthenormallyconsolidatedsoiland
85percentofthevariance(P<0.005)inksatforsoilatthecritical
state.
Inthisclaysoilataporosityof62percent,sheardeformation reduced ksat to 5 percent of its original value. In the most
compactedsoiltheeffectofsheardeformationonksatwassmaller.
IfthefittedlinesinFig.3areextrapolatedtolowerporosities,they meetat56percent.Therefore,ifsoilataporosityofaround56%, wassheardeformed,theeffectonksatislikelytobeverysmall.
Fig.2.(A)Porosityasafunctionofthelogarithmofmeaneffectivestressforsoil which iseither normallyconsolidated(open symbols)orinthe criticalstate condition(closedsymbols).(B)Deviatorstressplottedagainstthemeanstressfor soilwhichhasbeensheardeformedtotheextentthatitisinthecriticalstate condition.
Table2
FittedvaluesofRandQinEq.(13)andtheirstandarderrors.
Soilcondition Parameter PercentageofvarianceaccountedforandPvalue
R SE Q SE
Normallyconsolidated 0.4836 0.0683 29.35 4.20 90.8,P<0.002
Criticalstate 0.3024 0.0547 19.22 3.36 85.5,P<0.005
W.R.Whalleyetal./Soil&TillageResearch125(2012)23–29 26
3.3. Empiricalpredictionsofksatbasedonthewaterrelease
characteristic:laboratorydata
Mostempiricalmethodsusedtopredicthydraulicconductivity, includingEqs.(2)and(9),requiresomeinformationfromthewater release characteristic. We used published data for variously damagedRowdensoil(Gregoryetal.,2010a)whicharelistedin
Table3toestimatewaterreleasecharacteristicswithEq.(12)(see
Fig.4).Theseestimatedwaterreleasecharacteristicswereusedto estimate
f
e anda
(u
su
r) of the loose soil, dense soil, sheardeformedloosesoilandsheardeformeddensesoil(seeTable3). The effective porosities were determined from the difference betweenthesaturatedwatercontentsandthewatercontentsata matricpotentialof33kPa(seeTable3).
Thevaluesofksatcorrespondingtothoseporositiesofsoilsfor
whichwater releasedatawereavailableweredeterminedwith Eq.(13)andRandQvaluesgiveninTable2.Thefittedvaluesofthe exponentandconstantinEqs.(2)and(9)aregiveninTable4(see
Fig.5). ThevalueoftheexponentinEq.(2)was4.04,similarto thosepreviouslyreported(Ahujaetal.,1989;Greenetal.,2003), althoughMavkoandNur(1997)observedthatthenexponentin Eq.(2)isanadhocsolutiontotheproblemofempiricallyreducing ksatwithporosityandthatnvariesfrom3to8dependingonsoil.
ThefittedexponentinEq.(9)was1.651anditwasnotstatistically significantly differentto the expected value of 2 (Table 4 and
Fig.5B).
3.4. Empiricalpredictionsofksatbasedonthewaterrelease
characteristic:fielddata
WeexploredthepossibilityforthemoregeneraluseofEq.(9)
usingdatafromawiderrangeofsoilsfromtheHYPRESdatabase. InFig.6thefittedksatdataareplottedagainstthemeasuredvalues
withtherelationship:
log10ksat¼2log10ð
a
ðu
su
rÞÞþ4:119: (14)We kept theexponentatits theoreticalvalueof2 and only adjustedthelinearconstantduringthefittingprocess.
Thelaboratorydatacollectedinthisstudyandfielddatafrom HYPRESdidnotseemtobeingoodagreement.Fig.6showsthat Eq. (14) overestimated the saturated hydraulic conductivities measuredinthisworkbyupto2½ordersofmagnitude,although theerrorswerewithinthescatteroftheHYPRESdata.However, Eq.(14)correctlypredictedthetrendinthemeasureddata.The differences could be attributed to the fact that oursoils were
Fig.4.Estimatedwaterreleasecurvesfornormallyconsolidatedlooseandcompact soilaswellassheardeformedlooseandcompactsoil.Thesecurveswereestimated usingparametersofEq.(12)inTable3forvariouslycompactedandsheardeformed RowdensoilpublishedbyGregoryetal(2010).
Table4
ValuesoftheparametersfittedtoEqs.(2)and(9)usingthedatainFig.5.
Equation UnitsofKs Unitsofspecified
parameter
Fittingparameter Valueoffitting parameter
Percentageofvariance accountedforandPvalue
ksat¼Bfne mmday1 B 348,096 89.5%,P=0.036
n 4.04
ksat¼CavðusurÞv mmday1 a(kPa1) C 243 97.5%,P=0.023
v 1.651a
a
Thisexponentiswrittenas2inEq.(9).Herethefittedvalueisgiven. Table3
ParametersderivedfromtheestimatedwaterreleasecharacteristicsshowninFig.4alongwiththeksatdatacalculatedfromtheappropriateporosity,i.e.usthesaturated
watercontentwithEq.(12).
Soilcondition Effectiveporosity usur b us nv a
i.e.fb
a(usur) ksat(mmday1calculatedwithEq. (12)forappropriateporosityus)
Loose 0.135 0.451 1.25 0.650 1.187 1.713 0.7727 121.388
Looseandsheardeformed 0.030 0.205 6.72 0.650 1.187 0.0554 0.0114 0.0624
Compact 0.045 0.303 4.04 0.582 1.187 0.1123 0.0339 2.7289
Compactandsheardeformed 0.014 0.138 6.71 0.582 1.187 0.0264 0.0036 0.0239
Fig.3.Thelogarithmofhydraulicconductivityfornormallyconsolidatedsoil(open symbols)andforsoilinthecriticalstate(closedsymbols)plottedagainstporosity. ThedataarefittedtoEq.(13)andthefittedparametersaregiveninTable2.
repackedwhereasthesoilsusedtogeneratetheHYPRESdatabase wereundisturbed,orthatweusedestimatedandnotmeasured waterreleasedata(Fig.4).NeverthelessitisclearthatEq.(14), withonly onearbitraryfittingparameterandotherparameters obtainable from the water retention characteristic, provides a
usefulfittotheHYPRESdataandtheexperimentaldataobtained fromrepackedsoil.
3.5. Theimplicationsofourfindings
Ourdataimpliesthatsoilmacrostructureinloosesoilisvery sensitivetodamagebysheardeformation.Inthefield,isotropic consolidationislikelytobearareoccurrence.Uniaxial compres-sion is often used in the laboratory to replicate the effects of compaction (Gregory et al.,2006), but this is a combination of consolidationandsheardeformationandwillprobablyresultina ksatforanygivenporositythatisbetweenthelimitsofthosevalues
for‘‘normalconsolidation’’andthe‘‘criticalstate’’showninFig.3. Thetwoempiricalmodelsforksatappearedtobeeffectiveat
describingtheeffectsofcomplexdeformationsonksat.However,
the requirement for prior knowledge of the water release characteristic makestheseempirical approachesdifficulttouse inpractice.Nevertheless,wehaveshownthatthereisscopetouse relativelysimpleempiricalapproachestodescribetheeffectofsoil deformationonthewaterreleasecharacteristicwhichcanthenbe usedtoexplainhowksatvarieswithsoildeformation.Theeffective
porosity approach (Eq. (2)) required the water content at saturation and one other more negative matric potential. The useofEq.(9)wasfurthercomplicatedbecausethevalueof
a
also neededtobeknownorestimated.Whenwaterreleasedatawere available, a relatively simple model for ksat (Eqs. (9) and (14))appearedtobeusefuloverawiderangeofsoilswhichhadbeen variouslydamaged.
4. Conclusions
Sheardeformationofloosesoilataconstantporositycanresult inalarge reductioninthesaturatedhydraulicconductivityksat.
Reductionsinksatfollowingcompactionand/orsheardeformation
arepredictableiftheeffectofsoildeformationonthewaterrelease characteristiciseitherknownorcanbeestimated.Wehavetested anempiricalequationtoestimateksatusingtheHYPRESdatabase,
andestablisheditsutilityforpredictingksatinthefield.
Acknowledgements
ThisworkwasfundedbyagrantfromtheUKEngineeringand PhysicalSciencesResearchCouncil(EPSRC)(EP/H040064/1)and ItalianGovernmentgrantPRIN2007‘‘Experimentalmeasurement of the soil-vegetation-atmosphere interaction processes and numerical modellingof their response toclimate change’’. The facilities at Rothamsted Research were funded by the UK BiotechnologyandBiologicalSciencesResearchCouncil(BBSRC). We are indebted to Allan Lilly of the James Hutton Institute, AberdeenwhoextractedhydraulicdataofsoilfromtheHYPRES databaseon27thJuly2011.
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