Funneled flow mechanisms in a sloping layered soil:

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WATER RESOURCES
RESEARCH,
VOL. 36, NO. 4, PAGES 841-849, APRIL 2000
Funneled flow mechanismsin a sloping layered soil:
Laboratory investigation
M. T. Walter,• J.-S. Kim,2 T. S. Steenhuis,
3 J.-Y. Parlange,3 A. Heilig,3
R. D. Braddock,4 J. S. Selker,5 and J. Boll6
Abstract. Artificial capillarybarriersare beingusedto divert water awayfrom sensitive
undergroundregions.Conversely,funneledflow over natural capillarybarriersmay
increasethe dangerof groundwatercontaminationby decreasingthe travel time and
contactarea. There havebeen relativelyfew experimentalstudiesof capillarybarrier flow
patterns.In this study,waterwasapplieduniformlyacrossthe top surfaceof a backlit
tilting chamber,1 cm thick, 110 cm high, and 180 cm long, in which a coarsesandlayer
wasimbeddedin a fine sand.Beddingslopeand water applicationrateswere varied
between 0ø and 12ø and 1 and $ cm h-,• respectively.
After attainingsteadystate,matric
potentialwasmeasuredalongthe texturalinterface,and photosof dye traceswere taken
in order to visualizestreamlines.The funneledflow was characterizedby three discrete
regions:an initial capillarydiversion,a breakthroughregion,and a toe diversion.The
breakthroughregionconsistedof a significantzone of partial breakthroughwhere the
vertical flux into the coarselayer was lessthan the water applicationrate. The lateral
distanceof the capillarydiversionwas explainedwell by previouslypublishedrelationships
when the water entryvalue at the texturalinterfacewasreplacedby lower, observed
matric potentialat whichbreakthroughoccurredat the mostupslopepoint. The lengthof
the capillarydiversionwasoverpredictedusingthe air entryvalue.Finally, the toe of the
coarselayer had significant,observedeffectson funneledflow patterns,which have
previouslyreceivedlittle, if any, attention.The resultsof this studyimply that the slopeof
the coarselayer and infiltrationrate will largelygovernthe effectiveness
of capillary
barriersand that capillarybarriersare lesseffectivethan previouslyassumed.
Glasset al., 1989]; and (3) lateral flow, in which the flow of
water and solutesis concentratedand moveslaterallyalongan
Preferentialflowhasbeenimplicatedin the increasedrate of inclined soil-layer interface. Theoretical understandingand
contaminanttransport,particularlypesticides,to groundwater subsequent
mathematicaldescriptions
of the pertinenthydrau[Steenhuis
andParlange,1991;Flury,1996].Preferentialflow is lic mechanismsare critical to anticipating and preventing
definedas the unevenmovementof water and solutesthrough groundwaterpollution. This study investigatespreferential
porousmedia, typicallysoil, characterizedby regionsof en- flow due to lateral flow.
hancedflux suchthat a smallfractionof the mediaparticipates
There are two primarymechanicalcategories
of lateralflow.
in most of the flow. There are a numberof preferentialflow The mostfamiliar categoryis typicallyreferredto as saturated
mechanisms:
(1) physicalconduitssuchas macropores,struc- interflow [Betsonet al., 1968], subsurfacestorm flow [Hursh,
tural cracks, and biopores that provide preferential paths 1936],or throughflow[Kirbyand Chorley,1967]andmayoccur
throughwhichwatermaybe rapidlytransmitted[Bouma,1981;
where an upper soil region is underlain by a hydraulically
Beven,1981;Bevenand Germann,1982]; (2) fingerphenomrestrictivelayer suchas bedrockor a fragipan [Hewlettand
ena, in either layered[Hill and Parlange,1972]or nonlayered
Hibbert, 1963; Whipkey,1965;Dunne and Black, 1970;Pilgram
soils[Tarnaiet al., 1987;Selkeret al., 1992], that arisesfrom
et al., 1978;Stagnittiet al., 1986]. Becauseof the low permewetting-frontinstability[Parlangeand Hill, 1976;Hillel, 1987;
abilityof the underlyinglayer,water movingverticallythrough
a soilprofileis partiallyimpededat the interfacecausingwater
•Department
of Environmental
Science,
Universityof Alaska,Ju- to accumulateabovethe restrictivelayer and to flow laterally
Beau.
The secondmajor category,first shown
2Department
of Agricultural
Engineering,
Chungbuk
NationalUni- acrossit (downslope).
by Gardner[1960], is commonlynow referred to as funneled
versity,Chongju,SouthKorea.
3Department
of Agricultural
andBiological
Engineering,
Cornell flow [Kung,1990].Funneledflowis an uniquecategoryof flow
University,Ithaca, New York.
phenomenareferringto the situationin whicha capillarybar4Environmental
Sciences,
GriffithUniversity,
Nathan,Queensland,
rier developsabovea coarselayerwhichunderliesa relatively
Australia.
et al., 1990].At
5Department
of Bioresource
Engineering,
OregonStateUniversity, fine soil[Miyazaki,1988;Kung,1990;Steenhuis
Corvallis.
low flows,whenthe matticpotentialat the texturalinterfaceis
6Department
of Biological
andAgricultural
Engineering,
University so low that water cannotenter into the coarse,underlyingsoil,
of Idaho, Moscow.
the capillarybarrier effectivelyrestrictsvertical water flux,
Copyright2000 by the AmericanGeophysicalUnion.
forcingthe water to movelaterallyalongthe beddinginterface.
Capillarybarriershavereceivedincreasedattentionas an apPaper number 1999WR900328.
0043-1397/00/1999 WR900328509.00
plication for isolatingburied wastesfrom hydrologicfluxes
1.
Introduction
841
842
WALTER
ET AL.: FUNNELED
FLOW
MECHANISMS
IN SLOPING
LAYERED
SOIL
.• Oscillating
Dripper
180
cm
Unsaturated,
?e
Drippers
at20
em
Intervals
Fine Soil
Fine Soil Layer
HI
Tensiometers
(spaced
at
19
cm
intervals)
•
CapillaryFringe
•
1cm
Figure 2. Schematicof the experimentalsetup(not to scale).
CoaU•sSea•j•lt•da'ye
Figure 1. Schematicof the funneledflow systemdividedvertically into three regionsand a graphical representationof
deflectionof streamlinesas they passthe boundariesbetween
regions.Here tk• is the slopeof the coarselayer.
[Morrisand Stormont,1997;Selker,1997].Zaslavskyand Sinai
[1981],Mualem[1984],andYehet al. [1985]studiedlateralflow
causedby severallayersof fine and coarsesoil.
We will focus in this study on the flow over and through
capillarybarriers.Three regionsare distinguished
(Figure 1):
an upper unsaturated,fine soil layer region;a lower unsaturated, coarsesoil region; and, between these two, a tensionsaturatedfine layer or capillaryfringe. The capillaryfringe is
wettest
near
the coarse-fine
interface
and is drier
near
the
upper edge of the fringe. Becauseof textural differencesbetween the layers,there can be a sharpboundarybetweensoil
moisturecontents;that is, thoughthe matric potentialis continuousacrossthe soil layer interface,differencesin pore size
distributionsbetweenthe layersresultin discretedifferencesin
moisture
content.
It is commonlyassumedthat the "water entry"suctionvalue
[Hillel and Gardner, 1970;Hillel and Baker, 1988] of the underlying coarse layer is a critical parameter for describing
and/or predictingflow throughtextural interfaces.The water
entryvalue, generallyconsidereda propertyof the underlying
soil,wasmeasuredby bothHillel and Gardner[1970]andHillel
and Baker [1988]for horizontallayeringas the potentialat the
interface
coarselayer. The vertical movementof water into the coarse
layer is referred to asbreakthrough.Ross[1990] calculatedfor
steadystate conditionsthe distanceto where there is no net
downslopelateral flow beyondthe point of breakthrough;Pan
et al. [1997]simulatedtransientflowthroughslopinglayersand
foundthat the flowof wateris directedpartiallyupslopeduring
heavyrains.Modeling studiesby Oldenbergand Pruess[1993]
and Webb[1997]suggested
a partialbreakthroughregionalong
the fine-coarseinterface in which, at steadystate, the vertical
flux is lessthan the water applicationrate. There is disagreement in thesemodelingstudiesabouthow the flow changesin
the partial breakthroughregion.
There have been few detailedlaboratorystudieswhere the
flow throughand alongthe interfacehavebeenmeasured.The
objectiveof thispaperis to givebetter informationon the flow
throughand alongthe capillarybarriersunder well-controlled
conditions.Specifically,this study(1) qualitativelycharacterizes the funnel flow regimesalong a fine over coarselayer
interfaceof finite lengthunderconstantrainfall intensity;(2)
describes,explains,and quantifiesthe effects of the rainfall
rate and slope on these regimes;and (3) definesmeasured
parametersfor quantifyingfunnel flow and breakthrough.
after the water started to flow across the interface.
It
will be referred to as the effectiveinterfacewater entry matric
potential.
At the texturalinterfaceboth the quantityof flow and matric
potentialincreasedownslope.Once the potential increasesto
a high enoughvalue,water will startmovingdownwardinto the
2.
Materials
and Methods
Figure 2 is a schematicof the experimentalsetup.Experimentswere performedin a glasschamber180 cm long,110 cm
high, and 1 cm thick, backlitwith high-intensityfluorescent
light to help visualizethe streamlinesand the distributionof
moisturecontent [Glasset al., 1989]. The chamberwas filled
with fine sandembeddedwith a 15 cm thick, 160 cm longlayer
of coarsesand.Relevantpropertiesof the fine and coarsesand
are shownin Table 1. Figure 3 showsthe characteristicmatric
potential versussoil moisturerelationshipsfor the two sands.
Spatiallyuniformrainfallwasappliedoverthe top of the chamber usinga single,chain-driven,oscillatingdropper.The slope
Table 1. PhysicalPropertiesof the SoilsUsed in the Study
Saturated
Weight of Particle Size Classes,*%
Type
Fine
Coarse
*Particle
0.59-0.85
<0.25
0.25- 0.425
0.425- 0.59
7.0
0.6
32.7
20.5
35.8
3.2
6.8
23.6
diameters
are in millimeters.
0.85-1.4
4.1
65.8
Bulk
Density,
Hydraulic
Conductivity,
g cm-3
cmd- •
1.56
5443.2
11318.4
1.60
WALTER
ET AL.: FUNNELED
FLOW
MECHANISMS
3.
-20
-15
-5
0
,
•.
-50
-45
,
Fine
Sa'nd
-
-40
-35
-30
'• },.•k,•
Drying
-25
-20
.....
-10
0
I
5
0
10
20
30
40
50
60
70
80
90
100
% Saturation
Figure 3.
843
Results
develop(Plate 1). In most of the experimentsa clear lateral
flow regionwithoutwater flowingthroughthe coarselayer
formednear the toe of the coarselayer;thiswill be referredto
as the toe diversionin the subsequent
discussion.
Table2 showsthe lengthsof the threeobserved
flowregimes
for all the experiments,
namely,the capillarydiversionlength
occurringupslope on the fine-coarseinterface, the breakthrough region length, and the toe diversionwhich occurs
downslope
on the fine-coarse
interface.The lengthof capillary
diversionwas measuredfrom the inflectionpoint of the dye
trace closestto the upslopeend of the chamberto the point
wherethe dyefirstpenetratesinto the coarselayer.Thislength
is approximatelythe sameas from the top of the layer to the
beginningof the breakthroughregiontakinginto accountthe
"rainshadow"at the uppermostend.The breakthrough
region
wasmeasuredas the total lengthalongthe interfacethrough
which breakthroughwas observed.Toe diversionwas measuredasthe distancebetweenthe downslopeendof the breakthroughregionand the toe of the coarselayer. Becausethe
locationof the inflectionpoint, near the fine-coarseinterface,
of the most uphill dye trace was shiftedfrom experimentto
experiment,the total lengthof the three zonesvaried.Espe-
..........
AirEntry
----ar
-5
SOIL
witha flowrateof 120mmd-•, a breakthrough
zonedidnot
o.W_ett!
ng ' " a _..
•
-15
LAYERED
Plate 1 showsphotographsof the dyed streamlinesfrom
representativeexperimentalruns. The coarselayer appears
whitein the photographs.
Plate 1 showsthe coarselayersloping downhillfrom right to left, exceptof coursefor the three
horizontalcases.For all the slopedexperimental
runsthe dye
traceswere obviouslydiverteddownslope(referredto as capillarydiversion)and,in mostcases,penetratedthe coarselayer
at somepoint (breakthrough).Only for the run slopedat 7.1ø
-10
-55
IN SLOPING
Characteristiccurvesfor the fine soil.
({b•)waschangedbetweenexperiments
by tiltingthe chamber
on a centeredfulcrum(Figure 2). The matricpotentialalong
the interfacewasmeasuredwith ninetensiometers
placedat 19
cm increments(Figure 2); one tensiometeris located3 cm
from beyondthe end of the toe of the coarselayer. Between
experimentalrunsthe chamberwasdraineduntil there wasno
waterflowingout of the bottomof the chamber.The drainage
period lastedfrom 24 to 72 hours.
Combinationsof four slopesand three rainfall rates providednineexperimentalruns(Table2). Eachexperimentalrun
was initiated with uniform rainfall until steadystateflow was
øand7.1øslopes,
achievedand the flow lines did not changeanymore.This ciallyforthe280mmd-• flowrateforthe11.7
typically
tookabout48hoursfor a 120mmd- • rainfallrate,24 the uphill dye trace was bent to the left and resultedin a
hoursfor rainfallrate of 280 mm d-•, and about12 hoursfor shorterlength.Also, althoughthe flow domain describedin
rainfall rate of 680 mm d -•.
thisstudyis steadystate,theboundaries
betweenbreakthrough
Once steadystatewasachieved,the tensiometerswere read, and no breakthroughzoneswere somewhatdifficultto deterand a sequenceof three colors(red, yellow,and green)were minewith highprecisionbecauseof diffusionof the dyetracers
simultaneously
drippedat a slowrate at the surfaceat 20 cm and the coarsenetworkof dyedstreamlines.
A streamlineanalysis
wasalsoperformedto better quantify
intervals;eachcolorwas appliedtwiceso a total of 120 cm of
the soil surfacereceiveddye (Figure 2). With the aid of the the degreeof breakthroughalongthe interface.The distances
backlightingand the dye tracesit was simpleto visualizethe between
theverticalstreamlines
in thefinesoilLI andbetween
dyed streamlinesand measurethe different zones.
the breakthroughstreamlines
in the coarselayerL c weremea-
Table 2. The ObservedCharacteristic
Lengthsand the Characteristic
Parametersof the Funnelandthe Breakthrough
Flows
Lengthsof the Flow Regimes,cm
Run
1
2
3
4
5
6
7
8
9
Slope,
Flow Rate,
deg
mmd- 1
11.7
11.7
7.1
7.1
7.1
3.5
0
0
0
280
680
120
280
680
120
120
280
680
Toe
Diversion
16
0
NB
18
9
23
55
25
15
NB indicatesno breakthrough;
NA indicatesnot applicable.
Breakthrough
Capillary
Region
Diversion
24
95
NB
59
105
70
89
120
130
90
43
NB
54
29
53
0
0
0
Observed
•i, cm
-9.9
-9.2
NB
-9.4
-9.6
no data
NA
NA
NA
844
WALTER
ET AL.'
FUNNELED
-rio w
Slope 120 mm day-
FLOW
MECHANISMS
IN SLOPING
280 mm day-
LAYERED
SOIL
680 mm day-
11.7ø
7.1 ø
3.5 ¸
0
Plate 1. Photographsof experimentalrunswith dye tracers.
sured,asshownin Figure4. Usingcontinuityand basicflow net
theory, the ratio of the average leakagepenetratinginto the
coarselayerp to the rainfall or infiltrationrate i canbe implied
by the ratio of lengthsbetweenverticalstreamlinesin the fine
and coarselayers:
lines in the fine layer, and L c is the distancebetweenstreamlinespenetratingthe coarselayer (Figure4). Whenp/i = 1.0,
the average leakage, or breakthroughflow, is equal to the
rainfall rate; this is referred to as complete breakthrough.
Figure 5 showsthe p/i ratio along the slope for the three
experimentsfor which enough streamline data could be obp/i = Lc/Ll•
(1)
tainedfor thisanalysis.Eachp/i ratio is plotted at the midpoint
wherep is the averageflux penetratingthe coarselayer be- betweenthe two breakthroughstreamlines.As can be seen in
tweenthedyedstreamlines,
Lf isthedistance
betweenstream- Figure5a, therewere insufficientdata to calculatep/i for some
WALTER
ET AL.:
FUNNELED
FLOW
MECHANISMS
IN SLOPING
Dye Traces
LAYERED
SOIL
845
Dye Tracesx
'. •
Fine Soil
..
..
.__C__o?_se_
'::.
. "
Figure 4. Schematicof dye tracersobservedin the experimentalchamberand lengthsL betweenvarious
streamlines.
runs;in one run, therewasno breakthroughflow, and in others throughregionsof the horizontalexperimentswas0.99,which
there was only one or part of one streamlinein the break- is very closeto 1.00,indicatingfull breakthroughin the entire
through. Accordingto these results,of the three analyzed breakthroughlayer.
slopedexperiments
onlythe 7.1ø, 680 mm d-• run reached The measuredmatric potential along the fine-coarseintercompletebreakthrough;the others apparentlyattained only face for the 11.7ø sloped,7.1ø sloped,and horizontal(0ø) expartial breakthrough;that is, the magnitudeto the break- perimentsas well as the breakthroughregionsin each run
throughflow waslessthan the water applicationrate. For the (patternedareas)are shownin Figure 6. The right-handsides
0øslopethe ratio of flow throughthe layerwas approximately of the graphsin Figure 6 correspondto the upslopeend of the
1 (Figure 5b). The averageintegralof p/i acrossthe break- chamberwhichmatchesthe photographsin Plate 1. The position of the coarselayer toe is indicatedby the vertical,dashed
lines in Figure 6. The patterned areas in Figure 6 showthe
extentof the breakthroughfor eachinfiltrationrate; the light-
est area corresponds
to the 680 mm d-• experiments,
the
intermediate
areacorresponds
withthe280mmd-•, andthe
mostdensepatterncorresponds
withthe 120mm d-•. In all
1.2
1
0.8
0.6,
0.4
0.2
0
0
20
40
60
80
100
120
140
160
DownslopeDistance Along Interface (cm)
. X,•
_i=680 ..•
0.8
0.t5.
0.4 o(Horizontal)
0.2.- Slope=0
(b)
cases,as expected,the highestcurve (least negativematric
potential)corresponds
to the highestflow rate, and the lowest
curve corresponds
to the lowestflow rate. Also, as expected,
matric potential increasesin the downslopedirection as divertedwater inducesmoistureaccumulation(Figure6).
In the experimentwith the 0ø slope,there are very small
differencesin the matric potential alongthe fine-coarseinterfacein the breakthroughzone (Figure6), indicatingthat there
is very little sidewaysflow, and thus full breakthroughis expected.This conclusion
is corroboratedby the streamlineanalysis presentedbefore, adding credenceto our experimental
and streamlineanalysismethods.
The matricpotentialsin the breakthroughzone at whichfull
breakthroughoccurs(i.e., breakthroughcapacityequals the
infiltrationcapacityof the overlyingsand)are nearlyconstant
foreachflowrate:½eequals--7.7cmfor680mmd-•; -8.7 cm
for 280 mm d-•; -9.5 cm for 120mm d-•. We refer to these
potentialsas "the effectiveinterfacewater entry values"be0
I
I
causethe flow conditionsat full breakthroughare similar to
0
20
40
60
SO
100
120
140
160
thoseoccurringin columnstudiesbyHillel and Gardner[1970].
DownslopeDistanceAlong Interface (cm)
The matricpotentialdata in the breakthroughregionfor the
Figure 5. Leakageto infiltration ratios,p/i, for six experi- slopedexperimentssuggestthe presenceof a partial break-
ments(i is in mmd-•). (a) Slopedcoarselayerexperiments.through. In the sloped experiments,breakthroughoccursat
(b) Horizontalcoarselayer.
matricpotentialslessthan ½e(Figure 6); for example,for the
846
WALTER
ET AL.: FUNNELED
FLOW
MECHANISMS
IN SLOPING
LAYERED
SOIL
Toe
ofCoarse
Layer
Distance
Along
Interface
(cm) _•Downhill
-20
20
40
60
80
100
120
140
160
-6.0
-10.0
-12.0
-14.0
-16.0
-18.0
Shaded Areas
Show Extent &
-20
0
20
40
60
80
100
120
140
160
Location of
Breakthrough
-6.0
Zones
-8.o
-lO.O
Ii•.•___680
mm
day
4
-12.o
-14.o
280
mm
day
4
-16.o
-18.0
?[•120
mm
day
4
-20
0
20
40
60
80
100
120
140
1 i0
-6.0
-lO.O
-12.0
-14.0
-16.0
-18.0
Figure 6. Steadystatematricpotentialsalongthe fine-coarse
interfaceandlocationof breakthrough
regions
for eight experimentalruns.
680mmd-•, horizontal
experiment,
½eis about-7.7 cm,yet breakthroughregion, which suggeststhat there is a partial
in the slopedexperiments
with the samewaterapplicationrate,
breakthroughoccursat a lowermatricpotential,approximately
-9.5 cm. This valuevaried slightlyfrom experimentto experiment (Table 2) but was generallyabout -9.5 cm (standard
deviationof 0.3 cm) and is shownby the horizontaldashed
lines in Figure 6. This value will be referred to as the initial
interfacewater entrymatricpotential½i, at whichthe narrowest pores at the interfaceform a continuousnetwork.Under
low flow conditions
the effective
and initial
interface
breakthroughregion on both sidesof the complete breakthroughregion.Thoughtherewerenot enoughmeasurements
to preciselydefinethe pressuredistributionnearthe toe of the
coarselayer, in most experimentsa linear interpolationbetweentensiometers
spanningthe downslope
edgeof the breakthroughlayer suggests
that ½i may be the point for which
breakthroughceases(Figure6).
water
entrymatricpotentialare equal,and the originaldefinitionof
Hillel and Gardner[1970]is valid for ½i.
Thoughthe matricpotentialdatafor the slopedexperiments
suggest
completebreakthrough
for severalof the runs(Figure
6), regionsof constantmatric potential are only observed
amongtwo or three tensiometers.A longer chamberwould
haveallowedbetterverificationif the matricpotentialcontours
are parallel within the completebreakthroughregions.The
observation
of breakthroughat matricpotentialslowerthan ½e
corroborates
the existence
of a partialbreakthrough
zoneidentifiedin the streamlineanalysis(Figure5). Figure6 showsthat
the matric potential dropsnear the downslopeedge of the
4.
Discussion
The experimentsshowthreefunneledflowregimes:capillary
diversion,breakthrough,and toe diversion.Figure 7 is a schematic,basedon the resultsof this study,whichsummarizesthe
theoreticalpartition of flow alongan inclinedcoarselayer of
finite lengthembeddedin a fine soil.Table 3 summarizesthe
importantcharacteristics
for each of thesefunneledflow regimes.Dependingupon the conditions,this three-regimedescriptioncan developfully or partially.Kung's[1990]original
"funnelflow" wasactuallythe casewherea breakthroughzone
doesnot develop.Each of the three flow regimeswill now be
discussed
separately,startingat the upslopeend.
WALTER
ET AL.:
FUNNELED
FLOW
MECHANISMS
IN SLOPING
LAYERED
SOIL
847
nfiltratingWater
Lateral
Capillary
Fringe-.x,
Lateral
--CoarseSoilLayer
D wnslopePartial'
reaKtnrougn ,
'
,
'
,
Ddkwns
[ø.,Pe'
Pa,rtial
....
•reaKtnrougn
-• ,
/
] •._
_ 1oe.
I
•
:•:
• :•.•
•
,-'•
,
'
,
Upslope
Partial
'
/$-'B•a•ough
Complete
Breakthrough
_iversionii
Breakthrough
i -Diversiøn
I
!
I
I
I
I
I
I
I
I
!
I
I
!
XoXa
Xe
I
Xi
0
Figure 7. Schematicof the funneledflow systemdividedlaterally into zonesof flow alongthe coarse-fine
interface.
Capillary Diversion
dry and that water would enter at the water entry value obThe results in Table 2 show that the length of capillary tained from the wetting branch of the water characteristic
diversionis inverselyproportionalto the rainfall rate and di- curveof the coarsesoil.In our experimentthe water enteredat
rectly proportionalto the inclinationof the coarselayer; that an initial interfacewater entry matric potential ½i - -9.5 cm
4.1.
is, a high infiltration rate resultsin a relativelyrapid accumulation of water alongthe fine-coarseinterfaceand thereforea
relatively steep increasein matric pressure [Warrick et al.,
1997]. A rapid increasein matric pressuretranslatesinto a
short distancealong the interfacebefore the matric potential
reachesthe initial water entry suction.Steenhuiset al. [1991]
extendedwork by Ross[1990]whichmathematicallydescribes
the maximumlength of the capillarydiversionLcd, basedon
the aboveprinciplesand an exponentialconductivityfunction:
(_+0.3cm),whichis obviously
differentthanthevaluederived
from the wetting curve of the coarsesoil. It is likely that these
laboratoryexperimentsrepresentfield conditionsmore realisticallythanthe "verydry" scenarioassumed
for (2). Evenwhen
the coarselayeris verydry,vapordiffusionwill eventually"wet
up" the coarse layer when the fine layer is wet as shown.
DiCarlo et al. [1999] found for a similar sharp boundaryin
fingeredflow that vaporwould move acrossthe boundarywetting up the dry soil. Thus the assumptionthat the coarsesoil
staysdry might not be reasonable.Using the initial interface
water entrymatricpotential½i - -9.5 cm, insteadof ½*w,
capillarylengthspredictedwith (2) fit the observedlengths
with
R2 = 0.98 anda standard
errorof 10%(Figure8). The
whereha is the effectiveair entryvaluefor the finesoil;½*wis
mcd• tan(qb•)a-•
+ -•-
(2)
the water entryvalue for the soilwater characteristicfunction pointslyingbelowthe 1:1line are verycloseto the line and can
of the coarselayer, and a is the coefficientin the conductivity be reasonablyexplainedby experimentalerror. The experifunctionof theformK = Kfsexp(-a½) for ½ < ½*•andK = mental run with a slopeof 7.1ø and water applicationrate of
meaning
Kfsfor ½ >- ½*w.As shownin Figure3, ha is between-9 and 120mm d-1 (Table2) did not havebreakthrough,
- 10cmand½*w
= - 5 cm.Thevaluefor a is0.58cm-1.Using that the capillarydiversionwasgreaterthan 140 cm.Equation
the capillarydiversion(125 cm), becausethe
thesevalues,(2) predictscapillarydiversionlengthswhichare (1) underpredicts
3 to 4 timesgreaterthan thoseobservedin theseexperiments. toe of the coarselayer began to affect the flow before breakIn the derivationof (2) it was assumedthat the soilwasvery throughcommenced.
Table 3. Characterizationof the Funnel Flow Zones Along the Inclined Fine-CoarseInterface
Location*
Flow Regime
0 < x < x,
X, • X < Xe
xe -< x < x,
x, -< x < Xo
Xo < x < L
capillarydiversion
breakthroughregion(partial, upslope)
breakthroughregion
breakthroughregion(partial, downslope)
toe diversion
*See Figure 7 for graphicaldetails.
Matric
Potential ½
0 <
0, •
0 =
0i •
0 <
0i
0 < ½e
½e
0 < ½e
0,
Downslope
Lateral Flow
Leakage
increasing
decreasing
no flow
increasing
increasing
no breakthrough
increasingdownslope
constant,completebreakthrough
decreasingdownslope
no breakthrough
848
WALTER
ET AL.: FUNNELED
FLOW
MECHANISMS
IN SLOPING
LAYERED
SOIL
slopeandverylowrainrate(120mm d-j) in whichthe toe
o
120
diversionwasenhanced(55 cm) and(2) steepslope(11.7ø)and
highrainfallrate(680mmd-j) in whichtherewasnoclearly
lOO
•
80
20
o data
0
20
40
60
80
100
120
Observed
definedtoe diversion.The relative similarityof toe diversion
length suggeststhat matric potential gradientsimmediately
below the toe may be more significantto the toe diversion
mechanismthan slopeor water applicationrate. In Figure 6
the drop in potentialnear the toe is relativelyconstant,corroboratingthe similarityin toe lengths.The relativelylongtoe
diversion
in the horizontal,120mm d-• run maybe better
describedby studyingthe temporal developmentof funneled
flow; this type of investigationwas outsidethe focusof this
study.
Figure 8. Observedcapillary diversionlengthsversuspredictedmaximumlengthsusingthe relationshipfrom Steenhuis 5.
et al. [1991].
Conclusions
This studydemonstratedfunneledflow and breakthrough
flow underlaboratoryconditions.The resultsagreedwell with
For the two soilsusedin this experiment,the air entryvalue the theory and providedsomenew insightsinto the mechaof the fine sandha is almostequalto the initial interfacewater nismsinvolved.Three zoneswere experimentallyobservedand
entrymatricpotential.The lastterm in (1) is theninsignificant theoreticallyidentified:capillarydiversion,breakthrough,and
comparedwith the first term, and (1) resemblesthe relation- toe diversion.
ship presentedby Ross[1990]. The equationof Ross[1990]
Of particularinterestis the experimentalobservationof an
thenalsofitsthedataverywell(R2 -- 0.97, standard
errorof initial interfacewater entry matric potential •i, whichdiffers
•%).
conceptuallyfrom other studies.This value appearsto influence location of the upslopeboundary of the breakthrough
4.2. Breakthrough
region as well as, thoughnot as confidently,the downslope
As mentionedin section1, once the pressureincreasesto boundary.This is particularlyimportant if previouslyderived
initial water entryvalue(•i), waterwill movedownwardinto relationships[e.g.,Ross,1990;Steenhuis
et al., 1991]are to be
the coarselayerinitiatingbreakthrough.As longasthe leakage usedto predictthe magnitudeof a capillarydiversion.Paraminto the coarselayer is lessthan the vertical flux from above, eterizingsuchrelationshipswith water entry valuesobtained
water will accumulatealongthe interface.Once the pressure from soil characteristiccurvesmay lead to grossoverpredicreachesthe effectivewater entryvalue •e, the flowthroughthe tionsin the lengthof capillarydiversion.Unlike the effective
coarselayer is equal to the infiltration rate, and there is no interfacewater entrysuction•e, the initial water entrysuction
"net" downslopelateral flow eventhoughthe streamlinescon- ½t
i appearsto be independentof the flow regime and is likely
tinue to be refractedin this region.
equalto the matricpotentialat whichthe smallestporesin the
The graphof the slopedexperimentsshownin Figure5 is two media form a continuouspath.
instructivewhen comparedto p/i ratiosfrom earlier research.
Inasmuchas the typestratadescribedin thisstudyoccursin
Ross [1990] did not addressthe valuesof p/i in the partial nature,understanding
the mechanisms
controllingflowaround
breakthroughzone alongthe interface.He derivedthe break- it will be invaluableto practicalapplicationsinvolvingpollutant
throughlengthfor p/i = 1. By neglectingthe partial break- transport, groundwater recharge, and perhaps subsurface
throughzone,he thusoverpredictedthe lengthof the capillary storm flow. It may also help in the designof waste disposal
diversion.Webb[1997]showednumericalsimulationresultsin facilities.
whichthe capillarydiversion(p/i = 0) transitioninto complete breakthroughwas smoothedinto an "S" curve. The
Acknowledgment.Thanksgo to Ole Wendrothand StephenWebb
curvesin Figure5 are distinctlydifferentthoughexactlywhy is
for their helpful review.
currentlyunclearand requiresfurther investigation.
4.3.
Toe Diversion
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