Download - Prediction of Infiltration of Water into Aggregated Clay Soil Samples1

Prediction of Infiltration of Water into Aggregated Clay Soil Samples1

F. A. GUMBS AND B. P. WARKENTIN2

ABSTRACTThe physical properties—stability, water retention, diffusivity

and conductivity—relevant to the study of infiltration intoaggregated media were measured for four aggregate sizes:2.38-2.00 mm; 1.168-0.840 mm; 0.417-0.295 mm; 0.105-0.053mm referred to in the study as sizes 1, 2, 3, and 4. There were< 15, 5, and 4% aggregate breakdown of sizes 1, 2, and 3during infiltration. These media were considered stable to infil-tration. The large volume changes (swelling and shrinking)which result from wetting and drying aggregates of sizes 4 andthe nature of the hysteresis curves suggest that aggregate rear-rangement rather than breakdown may be dominant. Therelease of water in two distinct steps and the several thousand-fold decrease in conductivity at the moisture content of thesetwo steps, particularly for sizes 1 and 2 suggest that these mediacan be described as well-aggregated, i.e. having a discontinuityof pore sizes.

The hysteresis in moisture retention, equilibrium moistureretention curves, and the changes in moisture retention withtime were measured for confined and unconfined samples of theaggregates. Wetting and drying diffusivities and conductivitiesof confined and unconfined samples were also measured andused in the prediction of horizontal and vertical infiltrationunder zero and small negative pressures into columns of eachof the four aggregate sizes using the diffusion equation. Diffu-sivities and conductivities were larger on wetting than on dry-ing and generally larger in unconfined than in confined samples.

Horizontal and vertical infiltration were reasonably well pre-dicted when water infiltrated under negative pressure and thediffusivities and conductivities used were calculated from infil-tration profiles developed under the same water tension. Pre-dictions of infiltration under zero pressure were generally notas successful.

For these media, the values of water tension, diffusivity andconductivity at any water content depend on the rate of wetting.The values to be used in the prediction of infiltration musttherefore be measured for times of wetting which correspondto the duration of infiltration.

The classical diffusion equation can be used to predict infil-tration into aggregated clay soils if the correct diffusivities andconductivities are used.

Additional Index Words: water retention, aggregate stability,diffusivity, conductivity, hysteresis.

THE PREDICTION of infiltration in laboratory soil columnsis considered an essential step in the successful predic-

tion of infiltration into field soils. Several workers have suc-cessfully predicted the rate of infiltration and the infiltrationprofile in columns of nonsoil media (Youngs, 1957) andin columns of soil (Davidson et al., 1963; Gupta and Staple,1964; Rawlins and Gardner, 1963; Nielsen et al., 1962;Miller and Klute, 1967; Staple and Gupta, 1966) with theuse of the diffusion equation. The infiltration of water intostable well-aggregated soils, where a large difference existsbetween the inter- and intra-aggregate pores, has not re-ceived as much attention. Philip (1968) proposed a theoryfor infiltration into well-aggregated soils, and concludedthat the size of the soil aggregates must be large and thepermeability of the aggregates must be low for this theoryto be required. There is therefore a need to test the applica-bility of the diffusion equation to well-aggregated soils. Thiswill have practical applications to infiltration into crackingand plowed aggregated soils.

The accuracy with which infiltration is predicted dependsboth on the models used and on the accuracy with whichthe required parameters are measured. Gupta and Staple(1964) showed that the calculated depth of infiltration issignificantly influenced by small changes in the conductivityand diffusivity values from the maximum soil-water contentregion.

256 SOIL SCI. SOC. AMER. PROC., VOL. 39, 1975

The amount of water retained in a soil at a given suctiondepends on a number of factors, e.g., method and rate ofwetting or drying through its effects on entrapped air, his-tory of wetting and drying, duration of wetting or drying,applied external load, and sample size. Confinement of aswelling sample is equivalent to an overburden pressure.On the other hand, if the sample is allowed to swell, bulkdensity and pore size distribution will change and waterretention cannot be related to the initial conditions of themedium. A water retention curve is, therefore, character-istic only for a set of defined conditions.

A number of methods (Childs and Collis-George, 1950;Marshall, 1958; Millington and Quirk, 1959) is availablefor computing hydraulic conductivity from water retention.The study of Kunze et al. (1968) has shown that each ofthe methods has its limitations and that best agreement be-tween computed and measured values was obtained byusing a modified Millington and Quirk equation. They alsofound that best results were obtained when the number ofpore classes is kept between 5 and 10. Nielsen et al. (1960)found that Marshall's method gave computed values thatwere higher than measured values.

If the porous medium is unstable, the wetting or dryinghydraulic conductivity, diffusivity, and water retention willbe a function of water content and time; time embodieschanges in structure in the medium. Many of the methodsavailable, and which have been used for measuring, dependon the system coming to equilibrium. Infiltration into well-aggregated soils is a rapid process and if the structure ofthe medium changes slowly with time then the method ofmeasurement of the parameters used to predict infiltrationmay be very important.

In this study the stability of the medium, and hysteresisin water retention, hydraulic conductivity, and diffusivityare examined. The definition of the medium in terms ofmacropores (interaggregate pores) and micropores (intra-aggregate pores) is examined. The diffusion equation is usedto predict the rate of infiltration and the moisture profilesfor water infiltrating under zero and negative pressure. Theerror made in predicting infiltration using the parametersmeasured under different conditions is studied.

MATERIALS AND METHODS

SoilThe soil used was the Ormstown silty clay loam belonging to

Grey Gleysolic Group and classified as an Orthic Humic Gley-sol. The soil was air-dried, crushed lightly with a wooden ham-mer and sieved with a 2.38-mm sieve. Aggregates larger thanthis size were then more severely crushed in an electricallydriven rotary crusher. The following aggregates were thenobtained by dry sieving: 2.38-2.00 mm; 1.168-0.840 mm;0.417-0.295 mm; 0.105-0.053 mm. These are referred to assizes 1, 2, 3, and 4.

Water Retention MeasurementsWater retention measurements at low suctions (0-120 cm

water suction) were carried out with a Haines-type apparatus(Haines, 1930). The water retained at higher suctions (up to15 bars) during drying was determined on pressure plate appa-ratus. No measurements were made at these suctions for thewetting process.

/) Wetting and Drying Equilibrium Curves—The water con-tent at a given suction was determined with a separate sample,3.2 cm diameter and 1 cm high. Duplicate samples showed verysmall differences for sizes 1, 2 and 3 (about = 0.05% watercontent); for size 4, if duplicates differed by more than 0.35%water content a third sample was used. The mean of the twosamples that did not differ by more than 0.35% was taken. Thismethod of measurement meant that the samples were rapidlywetted or dried to a given water content. The water contents areplotted on a weight basis, which will be the same on a volumebasis for sizes 1, 2, and 3 when they are confined since the bulkdensity is 1.0 g/cm3. The bulk densities of unconfined samplesvary with water content and the curves are not functions of theinitial bulk densities.

A sample was confined in its 1-cm high ring on the porousplate of the Haines apparatus by loading the top of the ring witha weight. The load on the sample during wetting would bemainly reaction of the load to the swelling pressure of the sam-ple. When samples of aggregate sizes 1, 2 and 3 were confinedduring saturation then no shrinkage was observed on subse-quent drying to 100 to 120 cm of water suction.

2) Wetting and Drying Time Curves—A confined sample(4.5 cm diameter and 1 cm height) was used for one completewetting and drying cycle on the Haines-type apparatus. Thesample was maintained at each suction for the specified timeand a new sample used at each of the succeeding times.

3) Scanning Hysteresis Curves—These were determined ona sample (4.5 cm diameter, 1 cm in height) of each of the ag-gregate sizes. The samples were wetted rapidly to zero suction,so that the first curve of the hysteresis loop was drying. Theprocess was reversed at 100 cm of water suction, except for size4 which was reversed at 120 cm of water suction. Equilibriumwas considered to be achieved if no uptake or release tookplace over a period of several hours.

DiffusivitiesDiffusivities were calculated from measured water content/

distance profiles developed in horizontal columns according tothe method of Bruce and Klute (1956). For water infiltratingat zero suction the porous plate separating the soil column fromthe water source was an aluminium disc perforated with holesabout 1 mm in diam. At higher suctions a sintered glass platewith air entry value about 10 to 15 cm of water higher thanthe suction of the infiltrating water was used to minimize plateimpedance.

Unsaturated Hydraulic ConductivityFour methods were used to measure or to estimate the un-

saturated hydraulic conductivity (USC).1) Unsaturated hydraulic conductivity was calculated from

diffusivity and the slope of the water retention curve on wetting,where K = Ddf!/d<l/. This could be done only for confinedsamples.

2) Unsaturated hydraulic conductivity was calculated fromthe water retention curve using the Marshall equation (Mar-shall, 1958). Wetting and drying conductivities were calculatedfor confined and unconfined samples. Different numbers of poreclasses were used; the largest was the number of pore classesequal to the number of 1% water content intervals between0% and saturation. A computer was used to calculate the con-ductivities. The conductivities calculated at each water contentfrom the water retention curve of wetting confined sampleswere higher than the conductivities calculated from measureddiffusivities. A matching factor was calculated for each aggre-gate size to make the conductivity calculated by the formermethod coincide at saturation with that from the latter method.The matching factors gave a good match of the two curves overa range of water contents. The matching factors were used toadjust wetting and drying conductivities of unconfined samples,and the drying conductivities of confined samples, from con-ductivities calculated from the relevant water retention curves.

GUMBS & WARKENTIN: PREDICTION OF INFILTRATION OF WATER INTO AGGREGATED CLAY SOIL 257

3) Unsaturated hydraulic conductivity was determined bythe method used by Nielsen and Biggar (1961). In this methoda constant rate of water flow was established in a horizontalsoil column 20 cm long with its ends at different water poten-tials.

4) Unsaturated hydraulic conductivity values were also ob-tained from the slow drying of vertical soil columns to a steadystate of capillary rise (method of Moore, 1939). These weremuch lower than values from the method of Bruce and Klute,particularly in the high moisture content range and were alsoless than conductivities calculated by the method of Marshall.The columns never came to a true steady state but the processwas stopped after 5 days when the changes in the rate of flowwere negligible. The difference between these results and thosefrom the above-named wetting methods is probably due to boththe hysteresis effect and the changes that take place in a wetmedium with time, e.g., swelling, aggregate breakdown and/orrearrangement, and microbial action. This latter can have sig-nificant effects in reducing the hydraulic conductivity as wasshown by Gupta and Swartzendruber (1964).

Saturated Hydraulic ConductivitySaturated hydraulic conductivity (SC) calculated from dif-

fusivity may be inaccurate at both the wet and dry ends. Thereare at least two sources of inaccuracies: in the measurement ofthe diffusivity itself and the slope of the water retention curve.The simple percolation test on confined samples was thereforeused to obtain another estimate of the SC. The time was takenas zero when water was issuing freely from the bottom of thesample.

Infiltration

Infiltration was studied with these aggregates packed in col-umns made up of Lucite rings 1 cm in height and 3.2 cm insidediameter. Aggregates of sizes 1, 2, and 3 always packed to abulk density of 1.0 g/cm3 and size 4, to 1.2 g/cm3, if the col-umns were tapped during filling. Attempts to obtain higher bulkdensities by loading resulted in fracture of the aggregates, par-ticularly in sizes 1 and 2.

The columns were confined at both ends. The water entryend had a fixed perforated aluminium disc or a fixed porousstone during the study of horizontal infiltration under zero suc-tion and negative pressures, respectively. The air entry value ofthe porous stone was always a few centimeters of water suctionabove the suction of the infiltrating water, to limit the effectof water impedance by the stone.

Vertical infiltration was measured in confined soil columnswith a 1-cm positive head or with water entering under nega-tive pressure. The top of the soil was confined by sealing a per-forated aluminium disc between the two lucite rings at the topof the column. The column of rings was loaded to hold themfirmly together. The constant head was achieved by a Mariotte-bottle apparatus. At zero time a measured amount of water waspoured onto the top of the soil column to establish the 1-cmhead of water and, simultaneously, flow from the Mariotteapparatus was initiated. Zero time for horizontal infiltrationwas also taken at the initiation of flow.

The distance to the wetting front (X) and cumulative amountof water that had entered the soil were measured at given timeintervals. At the end of infiltration the column, in a horizontalposition, was quickly cut up and the water content of each1-cm soil section determined by drying at HOC.

The rate of advance of the wetting front, the cumulative infil-tration (when the rate was not too fast to be measured), andthe final moisture profile were measured for water enteringhorizontal soil columns packed with each of the four aggregatesizes under 0, -4 or -5 cm, -10 cm, and -20 cm of water pressure,and vertical columns under 1 cm, -5 cm, -10 cm, and -20 cm ofwater pressure. Duplicate runs were normally made. The classi-cal diffusion equation was used to predict infiltration, as a testof its applicability to aggregated media.

RESULTSThe stability of the medium must be established before

any conclusions can be made on the applicability of a theoryof infiltration in aggregated media. Beds of aggregates weredefined as stable if the aggregate size or pore size distribu-tion remained the same after infiltration as before.

The aggregates did not slake visibly on wetting beds ofaggregates. The aggregates remained discrete after an infil-tration measurement. Pore size distribution calculated fromwater retention curves measured after percolation of waterfor 5 or 10 min through a 2-cm thick confined sample wasnot different from pore size distribution of confined samplesthat were allowed to wet from a shallow water table for thesame time intervals.

Dry sieving of samples which had been used for an infil-tration run under suction and then dried showed that therewas no measurable breakdown of aggregates. However,after infiltration under zero or small positive pressures,there may be some breakdown. Ninety-five (95), ninety-three (93), and eighty-two (82)% of aggregates of sizes3, 2 and 1, respectively, retained their original size. Theremaining percentages of aggregates were either smaller orlarger than the original aggregate size. Some of the meas-ured breakdown may not be due to wetting during infiltra-tion but to breaking up during handling and dry sieving ofaggregates that were weakened by saturation.

Unconfined samples show large volume changes on satu-ration and on subsequent drying. The water retention curvesdetermined with unconfined samples (Fig. la-Id) are there-fore not at a constant bulk density, and show the largeerrors that can occur. The differences between water re-tained in confined and unconfined samples are larger forthe smaller aggregates and at the lower suctions (Fig. la-Id). There is virtually no difference in the amount ofwater retained by confined and unconfined samples of sizes1, 2, and 3 beyond 40 to 80 cm of water suction. This isin-accord with the large volume changes at low suction andnegligible changes at higher suction. It is difficult to deter-mine accurately the moisture characteristic curve for size4 because of the relatively large volume increases whichtake place on wetting unconfined samples, and the largeshrinkage even for confined samples. Generally and for size3 in particular, the difference between wetting and dryingbecomes smaller as suction is increased. This may justifythe use of drying values at the dry end of the water retentioncurve in infiltration studies.

The differences between confined and unconfined sam-ples are greater when drying than when wetting. The hys-teresis of water retention in confined and unconfined sam-ples at suctions up to 120 cm of water increases withdecreasing size of the aggregates from size 1 to 3, which isprobably associated with greater swelling of the smalleraggregates. Size 4 shows a relatively small hysteresis butlarge differences of water retention between confined andunconfined samples. The calculation of conductivities fromwater retention curves gave values for unconfined samplesthat were as much as 10 to 30 times larger than those ofconfined samples at high water content.


0.560.682

W= moisture content by weighto drying confined•o- drying unconfined• wetting confined• wetting unconfined• wetting confined; larger sample

§0*Q"

.la3

w0.58

0.54

0.50

0.46

0.42

0.38

0.34

0.30

10 20 30 40 50 60 70 80 90 100 110cm of water suction

from infiltration profiles developed under

0 suction-

5 cm water suction

-to 0.742

W = moisture content by weighto drying confined

•o- drying unconfined• wetting confined••• wetting unconfined• wetting confined; larger sample

*--^ •*-••—.—̂ ""̂-̂---•—-TIT''̂ -.,.—.

0.1 0.2 0.3 e 0.4 • 0.5 0.6

0.74

0.70

0.66

0.62

0.58

0.54

0.50

10 20 30 40 50 60 70 80 90 100 110' 120cm of water suction

o drying confined•o- drying unconfined• wetting confined••• wetting unconfinedW= moisture content by weight

d

1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 0 0cm of water suction

Fig. 1 (a) , (b), (c), (d)—Wetting and drying equilibrium water retention curves of beds of aggregates of sizes 1, 2, 3, and 4,respectively. ;

Wetting- and Drying-Time Curves

The water contents for varying periods of wetting at agiven suction are presented in Fig. 2 and 3. The water con-tent at a given suction of a clay soil depends on the timefor which the sample has been wet because the water con-tent at a given suction increases as the sample swells or theclay particles reorientate. Since infiltration of water into

o drying for 2 mins+ wetting for 2 mins•o- drying for 5 mins•» wetting for 5 mins

• drying for lOmins• wetting for lOmins

aggregated media is rapid the time for which the aggregatesare wet is short. The suctions at equilibrium water contentsare unlikely to be the suctions at the water contents meas-ured in the profile. Thus equilibrium values may give poorerpredictions of infiltration in aggregated media. The watercontents are plotted as a percentage of the water contentat zero suction when the samples were first saturated, be-

o drying for 2 mins• wetting for 2 mins-o- drying for 5 mins<>• drying for 60 mins

90\- Vv \\\ * wetting for 60 mins

80

70

60

s« so20 30 80 90 100

10 ZO 30 8040 50 60 70cm of water suction

Fig. 2—Water retention-time hysteresis curve of beds of size 2aggregates.

40 50 60 70cm of water suction

Fig. 3—Water retention-time hysteresis curve of beds of size 3aggregates. Moisture content is calculated as a percentage ofthe value at zero suction when the samples were first satu-rated.


cause all samples of any of the aggregate sizes did not wetto the same water content at zero suction. The differenceswere, however, smaller than the differences in soil watercontent at 2, 5, and 60 min.

Plate impedance and low soil conductivity may cause themedium not to be at the suction imposed on the porousplate for the entire time interval. Similar porous plates were,however, used for both the water retention-time studies andthe infiltration studies. The water retention results cantherefore be used to predict infiltration under the experi-mental conditions described previously.

DiffusivityThe size 3 aggregates have the highest diffusivities at

low suction, while size 4 has the highest at intermediatesuctions (Fig. 4). Size 1 and 2 have the higher diffusivitiesat low suction but these values fall off rapidly with increas-ing suction. The relationship can have significance in affect-ing the shape of the moisture profile and the rate at whichit develops, since the abruptness of the moisture profile isa consequence of the sharp decrease in diffusivity a'nd con-ductivity with water content (Philip 1957). Generally, atany given water content, the larger the aggregate size thegreater the diffusivity (Fig. 5a-5d). The high diffusivityof size 4 at the wet end may not be a true value since themethod is not reliable at this water content.

Diffusivities measured from infiltration profiles devel-oped over different lengths of time should give an evalua-tion of D (6, i). One way of obtaining these infiltration-time profiles is to allow water to infiltrate the soil columnunder varying suctions. In this way a given water content

. Io"

10

01

10-'

. ID*

ID'3

ID'4

from infiltration profiles developedunder

.4 cm watersuction

K)cm water suction

0.1 0.3 0.4 0.5 0.6e

10


0 suction -

I Ocm water suction

0.2 0.3 e 0.4 0.5 0.6

10

01

ilCT'

ICT3

Iff4

4.0 3.0 20 1.0 0.0

Fig. 4—Diffusivity (D)-pF relationships for aggregates ofsizes 1, 2, 3, and 4. Moisture content is calculated as a per-centage of the value at zero suction when the samples werefirst saturated.

is attained over a different length of time. Since the diffu-sion equation may not describe the infiltration process whenthe suction at X = 0 is significantly above zero (Nielsenet al. 1962), low suctions of 0, 4, 5, and 10 cm of waterwere used. The results for the various size aggregates arepresented in Fig. 5a-5d. Diffusivity at a given water contentdecreases with time of wetting. The decrease is large at allwater contents for the larger aggregates (sizes 1 and 2) butis large only at high water content for size 3.

Unsaturated Hydraulic Conductivity (USC)Wetting conductivities calculated from diffusivities and

the wetting water retention curve of confined samples

o-2Q"

Iff3

IO-4


0 suction-

5cm water suction

0.1 0.2 0.3 0.4 0.5 0.6

10

01

I I f f '

Iff3

icf

from infiltration profiles developed under0 suction -

5cm watersuction

icm watersuction

0.1 0.2 0.3 0.4 0.5

Fig. 5 (a) , (b) , (c), (d)—Diffusivity (D)-water content relationships for aggregates of sizes 1, 2, 3, and 4, respectively; calculatedfrom infiltration profiles developed under different suctions.


10"

°io-9

io-6

iff7

iff8

o size I; (c.f.d)• size I; (c.f.m.)a size 2; (c.f.d.)• size 2; (c.f.m.)n size 3; (c.f.d.)• size 3; (c.f.m.)

•0- size 4; (c.f.d.)•o size Ij (s.s.f.)•* size 2; (s.s.f.)•f size 4; (s.s.f.)a size 2; (T)x size 4; (T)

0.16 0.22 0.28 0.349

0.40 0.46 0.52 0.58

Fig. 6—Wetting hydraulic conductivity-water content relation-ships of confined columns of aggregates of sizes 1, 2, 3, and 4.c.f.d. is calculated from diffusivity; c.f.m. is calculated fromMarshall equation; s.s.f, is slow drying of vertical columns tosteady-state flow; T is measurement by the tensiometer tech-nique.

(c.f.d.) compared to USC calculated from wetting retentioncurves of confined samples by the method of Marshall(c.f.m.) are shown in Fig. 6. Conductivities calculated bythe method of Marshall were larger than conductivities cal-culated from diffusivities for sizes 1, 2 and 3. These threelargest aggregate sizes also have wetting conductivities ofconfined samples (c.f.m.) that are larger than drying con-ductivities of confined samples (c.f.m.). In considering theconductivities of unconf ined samples it must be rememberedthat these samples are not at a constant bulk density and,therefore, the percentage saturation at a given water contentis different from the confined sample.

A very different relationship among the aggregatesevolves when wetting conductivities of confined samples areplotted against suction instead of moisture content (Fig.7 vs. 6). There is now no difference between sizes 1 and 2.Size 3 has conductivities at low suctions which are higherthan all other aggregates and size 4 has conductivities at

Table 1—The changes in saturated hydraulic conductivity(SC) with time for the four aggregate sizes

Timemtn

148

102030406080

140

SCSize 1 Size 2—— • cm/sec

0.880.460.300.270.200.150.130.11

———0.520.370.280.250.200.180.170.16

Size 3x IO-1

1.8

1.61.4

1.10.90.750.45

Timehours

0146

1020406080

120

SCSize 4x 10-'cm/sec

4.13.62.61.51.51.240.860.780.660.50

I

io"

Iff2

io-s

olO"4

§I<JS

icr7

id"8

Fig. 7—Wetting hydraulic conductivity-pF relationships ofconfined columns of aggregates of sizes 1, 2, 3, and 4.

intermediate suctions which are higher than all other aggre-gate sizes. Infiltration under suction is therefore expectedto reflect these differences.

Saturated Hydraulic Conductivity (SC)Hydraulic conductivity calculated from diffusivity is inac-

curate at both the wet and dry ends. There are two sourcesof inaccuracies: in the measurement of the diffusivity itselfand the slope of the water retention curve. The simple per-colation test on confined samples was therefore used toobtain another estimate of the SC. The changes of SC withtime for the four aggregate sizes are shown in Table 1. Thetime was taken as zero when water was issuing freely fromthe bottom of the sample. The decrease in SC with time israpid for sizes 1 and 2 but is much slower and more gradualfor sizes 3 and 4. These decreases can be explained by againpostulating changes that take place in a wet medium withtime; changes which serve to reduce the size of the conduct-ing channels. Saturated conductivity values correspondingto the time of infiltration in the infiltration studies were usedin predicting infiltration.

Prediction of Infiltration Under SuctionReasonably good agreement between measured and pre-

dicted slopes of X vs. t^ for horizontal and vertical infil-tration under the various suctions into the four aggregatesizes were obtained. The only exception to good predictionswas for vertical infiltration into size 3 where curves whichconcave up were measured while straight lines were pre-dicted. The close agreement between slopes for horizontaland vertical infiltration and the linear relationship of X vs./** for vertical infiltration in size 2 suggest that the depth ofvertical infiltration was not enough for gravity to have asignificant effect on the rate of infiltration. Gravity seem-ingly had a greater effect during vertical infiltration intosizes 1 and 3.

Measured moisture profiles 9(Z) of all aggregate sizesshow a transition zone for infiltration under suction. This


e0.60

0.50

0.40

O.30

O.ZO

0.10

0 suction

c ^ 4 cm suction, 529mins

V— predictiono measurementc measurement

9 12 isDistance, x cm

24

Fig. 8—Measured and predicted moisture profiles for horizon-tal infiltration under 0, 4-cm, and 10-cm water suction in size1 aggregates.

— prediction4-4 measurement4-4 measurement

624 secs

24 273 6 9 12 15 18 IDistance, x cm

Fig. 9—Measured and predicted moisture profiles for horizontalinfiltration under 0- and 5-cm water suction in size 2 aggre-gates.

30

is particularly marked for infiltration in aggregates of sizes3 (figure not shown). Diffusion analysis did not predict amarked transition zone but when water content of the tran-sition zone was included in the analysis (according to themethod of Gupta and Staple, 1964) a more accurate X vs.i* was predicted. In this technique, the water content atX — 0, / = 0 at the start of infiltration was assumed to be0.460 (extrapolated transmission zone water content). Thiswas then assumed to increase instantaneously to 0.560, theexperimentally measured water content at X = 0. The highdiffusivity for this water content was then used to computethe mean diffusivity of the next depth interval. In this waythe high diffusivity at 8 = 0.560 is made to contribute to thewet front advance.

In predicting the moisture profiles, 6(2), under suction,the water content at X — 0 was chosen, as a first approxi-mation, by extrapolating the measured transmission zonewater content to X = 0. The diffusion equation did notpredict the transition zone (Fig. 8, 9, and 10) for horizontalinfiltration into size 1 and horizontal and vertical infiltrationinto size 2 aggregates. It was, therefore, not possible topredict the moisture profile exactly. The slope of the trans-mission zone and the shape of the wet front were never-theless predicted.

Corrections to D and KSome of the problems associated with the measurement

of diffusivity and conductivity in these media have beenmentioned above. Inaccuracies in the prediction of infiltra-tion at 0 suction in these media could therefore be due toinaccuracies in the measurement of these two parameters.The generally good predictions of infiltration indicate thatthe diffusion equation can predict infiltration in these media

Table 2—Changes in the measured diffusivities (D's) andconductivities (K"s) for the correct prediction of infiltration

under zero suction

and that getting the correct values of D and K may be morefruitful than application of different models for infiltration.

Diffusivities were multiplied by a factor to give a goodprediction of horizontal infiltration and these diffusivities,together with corrected conductivities were then used topredict vertical infiltration (Table 2). These corrected val-ues may not be true estimates for all water contents sinceD and K at different water contents may be in error to dif-ferent degrees. Since D and K at high water content domi-nate infiltration, it may still give a reasonable estimate oferror in D and K at high water content.

The effect of multiplying D of size 4 aggregates by dif-ferent factors on the rate of advance of the wet front inhorizontal columns (as determined by the slope of X vs.t^) is shown in Table 3. The relationship is exponential sothat if the soil is slowly permeable a larger degree of errorin the measurement of diffusivity can be tolerated. Whendifferent values of D and K are used to predict verticalinfiltration, it is found that if D's and K's are large, X vs.f% will be a curve and the moisture profile will have a smallwater content gradient at the wetting front.

e0.60

0.50

0.40

0.30

0.20

0.10

0 cm suction 48 sees

,66secs_\

»72 sees *'•».5cm suction

A — 700 mins— predictioni measurement

280 mins 5454 .mins 1-694 mins

24 27 30

1.0 1.8 1.0 0.5 0.7

3 6 9 12 15 18 2Distance, x cm

Fig. 10—Measured and predicted moisture profiles for verticalinfiltration under 0- and 5-cm water suction in size 2aggregates.


Table 3—Predicted rates of advance of the wet front in hori-zontal columns of size 4 aggregates with changes in

diffusivities (D's)Measured

D's x 0.7 0.3 0.15 0.05

cm/mini 0.78 0. 69 0. 58 0.40

Experimentally measured X vs. t* for vertical infiltrationinto size 3 aggregates under 10 cm water suction is a curveand the measured moisture profile shows a nearly constantwater content for most of its length. This contrasts with thepredicted linear X vs. i* and steep gradient of water contentin the profile (Fig. 11 and 12). The K's measured andused in the prediction may have been underestimated andmay just have fallen below the K's needed to give a curvefor X vs. (^ and the low gradient in the moisture contentprofile. The measured and predicted (with and without thetransition zone in the solution) X vs. t^ for horizontal infil-tration are straight lines (Fig. 11) and the moisture profileshave large water content gradients.

Hysteresis and the Prediction of InfiltrationUnder Zero Suction

Diffusivities and conductivities for these soil aggregateshave been shown to be higher on wetting than on drying.Both values were used to predict vertical and horizontalinfiltration under zero suction in the four aggregate sizes.The predicted X vs. t^ relationships were linear except forvertical infiltration in size 4 where X vs. t was linear. Thepredicted rates calculated with wetting values were largerthan those with drying values by a factor of about 1.2 forhorizontal infiltration into sizes 1 and 3 and about 2.5 forhorizontal infiltration into sizes 2 and 4 and vertical infiltra-tion into size 3 (Table 4). This latter can be disregardedbecause the predicted moisture profiles were not like thosemeasured. The small differences for sizes 1 and 3 probablyreflect the small hysteresis in suction for the aggregates ofsize 1 and the small changes in D with suction (at low suc-tion) for size 3. The large differences for size 4 may be aconsequence of the instability of the medium so that thestructure is altered markedly on wetting and drying. Thereason for the large difference for size 2 is not known. The

32

28

24

.205

'.16

I l2

i8

4

P(KXIO)

XO.I)0.01)

I 2 3 4 5 6Time, minsi

Fig. 11—Predicted rates of vertical infiltration under 0 suc-tion into aggregates of size 4 when measured conductivitiesare multiplied by various factors.

Table 4—Predicted slopes of the X vs. f^ relation using wettingand dry soil properties. X is distance to the wetting front

measured at time, t

Size 3Wetting Drying Wetting Prying Wetting Drying Wetting Drytp)

\ cm/ mini*9. 2 6.6 2.7 3.0 2.55 1.83 ___0.71

* X is the slope of x vs ti.

prediction of a faster wetting front advance when wettingvalues are used are in agreement with the finding of Whislerand Klute (1965).

DISCUSSION

The accurate determination of conductivity and diffusiv-ity is still a problem. Techniques which involve the use oftensiometers have been found by the authors to be unsatis-factory for aggregates equal to or greater than 1 mm diame-ter. The most efficient method of measuring wettingconductivity in the larger aggregates was via diffusivity de-termined by Bruce and Klute method. The values found inthis way for K at saturation were usually much larger, bya factor of from 2 to 20, than equilibrium values measuredin a percolation test.

The percolation test K values decreased with time. Con-ductivities calculated with the Marshall equation and thewater retention-time curves, when the number of poreclasses was six, agreed with saturated K values from a per-colation test for the same time periods. When 60 poreclasses were used in the Marshall equation, the calculatedK values were too large, particularly at the wet end. Thisfinding is in agreement with that of Kunze et al. (1968). Inour study the inaccuracies in the estimation of K are greaterfor coarse aggregates where small changes in suction areaccompanied by large changes in moisture content. Thisinaccuracy in the measurement of K is of great concern be-cause the vertical downward infiltration rate in coarsemedia is very sensitive to changes in K at the wet end andhorizontal infiltration is sensitive to D at the wet end.

Horizontal and vertical infiltration under zero suctioninto aggregates of size 1 and 2 were very rapid and althoughthe times for the infiltrating water to reach a certain depth

e0.60

0.50

0.40

030

0.20

0.10

D's and K's as measured 17 0 mins

-{D's and KS) x 0.729.6 mins

-D's and K's as measured16.0 mins

190 mins

— predictione measurement

24 27Distance, x cm

Fig. 12—Measured and predicted moisture profiles for verticalinfiltration under 0 suction in size 4 aggregates.


in the column were reasonably well predicted there wereno sharp wet fronts during horizontal and vertical infiltra-tion in size 1 and during vertical infiltration into size 2.The water channelled down the largest inter-aggregate poresfastest so that at certain levels in the column behind the"wetting front" some aggregates may be wet and some dryat a given instant. While the predictions for rate of wetfront advance were apparently good, the shape of the mois-ture profiles were not predicted. The predicted profiles de-scended with the wetting end water content whereas themeasured moisture profile showed an approximate stepwisedecrease in water content.

The rate of advance of the wet front and the cumulativeinfiltration for the two largest aggregate sizes are much lessunder 5- and 10-cm water suction than under zero or 1-cmwater positive pressure. Under these suctions the waterseemingly moves only in the intra-aggregate pores since thewater content in the profile is less than the saturated intra-aggregate water content as determined from the water reten-tion curve and by calculation from the bulk density of thecolumn and of the aggregate themselves (measured bulkdensities of the aggregates are 1.575 and 1.628 g/cm3).Since there are no large discontinuities in pore sizes amongthe intra-aggregate pores it is not surprising that the classi-cal diffusion equation correctly predicts infiltration whendiffusivities and conductivities calculated from profilesdeveloped under the same suction are used.

X vs. i^ is a curve for vertical infiltration if infiltrationproceeds for a long enough time. From these studies itseems that if D's and K's are large, X vs. t^ is a curve forshorter distance of infiltration than if D's and ^'s are small.Where X vs. t^ is a curve the moisture profile shows a smallgradient in water content at the wetting front.

The inaccurate predictions of vertical infiltration in size3 and of horizontal and vertical infiltration in size 4 underzero suction are believed to be due to errors in the estima-tion of the diffusivities and conductivities in these media.Small errors in these parameters at high water content canseriously influence the accuracy of the predictions. Theerrors in measurement could be due to imprecision in themethods themselves and also to changes which take placein the medium with time. To minimize errors due to thelatter, diffusivities should be measured by the method ofBruce and Klute. Conductivities should then be calculatedfrom diffusivities and the slope of the water retention-timecurve, the time used being the time of infiltration. Althoughbetter predictions are obtained where diffusivities are calcu-lated from profiles developed under identical conditionsof infiltration, it is only the errors in diffusivities at highwater content measured by the different techniques thataffect the accuracy. Since accurate measurements of dif-fusivity are difficult to obtain in the maximum soil-watercontent range with the Bruce and Klute procedure, "satu-rated" hydraulic conductivity should be measured by thepercolation test method. The time of percolation shouldcorrespond with the time of infiltration. Diffusivity can thenbe calculated from this conductivity and the slope of therelevant water retention/time curve.

Methods of measuring wetting and drying diffusivitiesand conductivities which require the media to be wet for

different times will result in the parameters being affectedby the phenomenon of structural change in the media inaddition to hysteresis. The methods of measurement are,therefore, important in the study of hysteresis in theseparameters and the prediction of infiltration. Differencesin wetting and drying diffusivities and conductivities werefound and these differences significantly affected theaccuracy of predicting infiltration.

ACKNOWLEDGMENTSThe authors wish to acknowledge the assistance received from

Dr. W. J. Staple and Dr. G. C. Topp of Canada Department ofAgriculture, Ottawa, with both the infiltration predictions andwith some of the experimental measurements.

anns

Download - Prediction of Infiltration of Water into Aggregated Clay Soil Samples1

Top Related