Bulk Density, Saturation Water Content and Rate of Wetting of Soil Aggregates1

F. A. GUMBS AND B. P. WARKENTIN2

ABSTRACTBulk density, degree of saturation, volume increase on wetting, and not as useful. Clods and aggregates of the soil and of pumice samples

rate of wetting were measured for aggregates and clods of Ormstown did not fully saturate; entrapped air accounted for 25 to 27% of thesilty clay loam (Humaquept) of sizes from 5 cm to 0.036 cm diameter. total pore volume.

Bulk density increased with a decrease in diameter. For 2.2-mm to Aggregates of 1 and 2.2 mm diameter and clods of 1.0 and 5.0 cm di-0.36-mm diameter aggregates this increase was due to a surface area ameter took about 1, 1.7, 45, and 1,000 seconds, respectively, to satu-effect, i.e., loss in porosity as a result of subdividing larger aggregates. rate. This rapid wetting would minimize differences in potential be-Both surface area effects and increased porosity from root channels tween inter-and intra-aggregate water during infiltration,and fissures were required to explain the increase for clods between 5and 1 cm diameter. Additional Index Words: clay soils, swelling, infiltration.

An evaporation and a sorption technique are described and used toestimate the water content of aggregates at saturation, i.e., the intra- ————————————————————aggregate water content. The evaporation technique gave reliable __results at specific rates of evaporation, but the sorption technique was 'T'WO CLASSES of pores can be distinguished in an ag-_____ JL gregated soil, the larger inter-aggregate pores and the

'Contribution from the Dep. of Soil Science, Macdonald College of much smaller intra-aggregate pores. Inter-aggregate poresMcGill University, Ste. Anne de Bellevue, Quebec. Part of the work sub- imnr>rfant in Hra inaop anH apratirm uyhi lp in framitted as a Ph.D. thesis by the senior author. This study was supported by are important in drainage and aeration, while mtra-a Grant-in-Aid of Research from the National Research Council, Canada. aggregate pores are important for retention of plant-avail-

^GrTdtm^Rese'a^^ of Soil Science The abk WatCI" and plant nutrients' PhiliP>s theory for the pre-senior^uthor is no^ iecwreTi/Soil Science,' UnTversityof th^West in*? diction of infiltration into aggregated media depends on thedies, Trinidad. . relative diffusivities and conductivities of water in inter-

GUMBS AND WARKENTIN: PROPERTIES OF SOIL AGGREGATES 29

and intra-aggregate pores (Philip, 1968). The rate of wet-ting of the aggregates is another parameter which must beknown. A slow rate of wetting creates a local disequilibriumin the profile, with water in the intra-aggregate pores underlower potential than the water in inter-aggregate pores. Athird parameter which must be accurately measured is themaximum water content of the aggregate. This is deter-mined by intra-aggregate pore volume, which may increaseon wetting, and by the degree of saturation with water.Some air is normally present in the intra-aggregate voids.

The bulk density of aggregates must be known to obtainvalues for maximum water content at saturation. Several au-thors (Chepil, 1950; Mclntyre and Stirk, 1954; Currie,1966; Voorhees, Allmaras, and Larson, 1966) have pro-posed methods for measuring the bulk density of smallaggregates. There are different views in the literature aboutwhether bulk density of small aggregates increases withdecreasing aggregate size (Wittmuss and Mazurak, 1958),or whether differences are due to surface area effects (Cur-rie, 1966) or to inaccuracies in the techniques used in themeasurements.

This study reports measurements of bulk density of ag-gregates of different sizes, and evaluates the contribution ofsurface area to the measured bulk density. An evaporationtechnique is proposed and used for the estimation of themaximum water content at saturation of intra-aggregatepores in small aggregates. The rate of wetting of aggregatesimmersed in water is measured, and is also predicted withan equation from the theory of heat conduction. Thesemeasurements, which are difficult to make on small ag-gregates, are required for a description of infiltration ofwater into aggregated soils.

MATERIALS AND METHODS

Soil Characteristics and Aggregate Preparation:The Ormstown silty clay loam used in this study was classified

as a Humic Gleysol (Baril and Mailloux, 1950), and would comein the order Inceptisol, suborder Humaquept. This soil has highlystable aggregates. The clay fraction is dominantly clay mica andchlorite, with minor amounts of quartz, feldspar, amphibole, andmontmorillonite.

Soil samples taken from the 0-30 cm depth were air dried,crushed lightly with a wooden hammer and sieved through a 2.38-mm opening sieve. Aggregates > 2.38 mm diameter were thencrushed in an electrically driven rotary crusher. The following sizeranges of aggregates were obtained by dry sieving: 2.38-2.00 mm;1.17-0.84 mm; 0.42-0.30 mm; referred to subsequently as sizes1, 2, and 3, respectively, with mean aggregate diameters of 2.2,1.0, and 0.36 mm, respectively.

Clods of various sizes were hand picked or cut to size, for usewhere larger units were required.

Particle size distribution was determined by the pipette methodas described by Day (1965), with organic matter destroyed duringthe pretreatment procedure by digesting with hydrogen peroxide.Organic matter content was determined on separate subsamples bydichromate oxidation.

Bulk Density of The AggregatesTwo techniques were used to determine the bulk density of all

three sizes of aggregates. A third technique was used to determinebulk density of the larger clods. All three techniques were basedon Archimedes principle.

The first technique, denoted by Tx in this study, was the tech-

nique of Mclntyre and Stirk (1954). A sample of about 10 cm3 ofaggregates of known weight was saturated with kerosene oil, andthen drained under low suction (10 cm for sizes 1 and 2, 30 cm forsize 3) to remove oil from the inter-aggregate pores and outer sur-faces of the aggregates. The volume was measured as the increasein volume of kerosene oil in a narrow cylinder on the addition ofthe sample of aggregates.

The second technique, to be referred to as Ty, was a modifica-tion of Tx, which involved weighing. A known weight of ag-gregates was placed in a wire basket of about 5 cm3 capacity,which was immersed in kerosene oil in a dessicator. Saturationwas assured by de-airing under vacuum. The volume of the satu-rated aggregates was then determined from the loss in weight ondisplacement in kerosene.

In the third technique, Tz, clods of known dry weight werecoated with paraffin wax, and the volume of the clod determinedfrom the loss in weight by displacement in water (Blake, 1965).

The intra-aggregate porosity («) was calculated from the bulkdensity (Dt) and a measured value of 2.67 g/cm3 for particle den-sity (Dp), using the equation n = (Dp - Db)/Dp.

Intra-aggregate Water ContentThe large difference in size between inter-aggregate pores (mac-

ropores) and intra-aggregate pores (micropores) was utilized intwo techniques to evaluate the intra-aggregate water content onsaturation. It was assumed that the rate of evaporation from, orsorption into, the macropores is greater than for the micropores. Aplot of water evaporated or adsorbed against time should show twodistinct regions (i) free water evaporation or infiltration into mac-ropores, and (ii) micropore water evaporation or infiltration.

In the evaporation technique, aggregates in a single layer, or in-dividual clods, were immersed to half of their diameters in wateron indented aluminum holders. After about 1 hour, the free waterwas siphoned off and the holders were rotated at a constant speedof about 6 rpm on a 20 cm diameter turntable. A hairdrier was usedas a source of warm air. Different rates of evaporation wereachieved by regulating the distance between the air vent of thehairdrier and the aggregates and/or the temperature of the air fromthe hairdrier. Evaporative demand was calculated by multiplyingthe grams of free water evaporated per square centimeter of watersurface per minute by 540 cal/g (the latent heat of vaporization ofwater at 100C). Free water was contained on indented aluminumholders, and the surface area of water was estimated from theweight and depth of water on the holder using a density of water of1 g cm"3. The holders plus water or aggregates were weighed atintervals to calculate water lost by evaporation as a function oftime. A low rate of evaporation allowed the aggregates to conductwater rapidly enough to the surface so that the system was understeady-state water flow conditions during most of the evaporationprocess, resulting in a delayed break in the weight loss curve.When the evaporative energy supply was too high, surface layersof water on the aggregates evaporated too quickly to allow distinc-tion from evaporation of free water. Again the break would comeat too low a water content. Therefore, there was a maximum in thewater content identified by the break in the curve as the evapora-tive energy increased. The maximum, which should coincide withthe change in evaporation of inter- to intra-aggregate pores wouldoccur when the conductivity of water to the surface of the ag-gregates was marginally less than the evaporative demand.

The other method used to measure intra-aggregate water contentwas by sorption of water into the aggregates. The sorption ap-paratus consisted of a filter funnel with porous stone. The bottomwas attached to a horizontal pipette, whose position could bevaried a few centimeters above or below the level of the porousstone. A single layer of 2.2 mm diameter aggregates, isolated sothat they were not touching, was placed on the porous stone. Thena stopcock was opened to allow water to move up through theporous stone to wet the aggregates. Five pressure heads (+2, 0,— 2, —50, and —100 mm) were used in this study and measure-ments were made on three samples at each pressure head. The vol-

30 SOIL SCI. SOC. AMER. J., VOL. 40, 1976

ume of water entering the aggregates was read from the pipette as afunction of time.

Volume of Saturated Clods

Clods were saturated for about 2 hours with water that enteredby capillary rise from shallow water tables held in dishes. Theclods had about one-third of their height submerged. Clod volumewas then determined by displacement in water after coating withparaffin wax (technique Tz). Molten paraffin wax was applied to awet clod with a small paint brush. The area of the clod in contactwith the dish was coated after carefully rotating the clod to exposethe uncoated portion. The weight of dry soil and the water contentof the clod were found by cutting the wet clod plus wax and dryingfor 48 hours at 40 to 45C. This length of time was found to be ade-quate for drying to a constant equilibrium value. At this tempera-ture there was negligible loss in weight of the wax, as measured ona separate sample of wax. The weight of soil was then corrected tothe oven dry basis.

Rate of Saturation of Immersed Samples

Spherical clods of 2, 5, and 10 cm diameter were cut andshaped from larger clods. At zero time a sample was immersed inwater which just covered its top surface. After a given time thesample was removed, wrapped momentarily in absorbent paper orallowed to drain to remove excess surface water, weighed, andoven dried. The percent saturation was then calculated using twoassumptions, swelling or no swelling during wetting. The formerassumption probably gives a better estimate of the percent satura-tion, because it is known that most of the swelling of unconfinedsoil clods takes place rapidly (Gumbs and Warkentin, 1972).

Predicting the Rate of Saturation of AggregatesThe entry of water into spherical aggregates can be described by

the equation

rj/3 .A 2 /3 O 3 flOP j_ O (7 ^ OC7

Ht= I*2 +7a7' 0 , t>Q [1]

where 6 = volumetric water content, t = time, r = distance fromthe surface of the sphere to the wetting front, D = water dif-fusivity, and a = radius of the spherical aggregate. With the fol-lowing initial and boundary conditions:

0, = 0 when t = Q,0^r

Of= 60, whenr = a, / > 0.

Equation [1] has the solution

+ (J exp [-*»•"•"•

[2]

[3]

Table 1 — Distribution of particle sizes and organic matter withinaggregates of different sizes

Soil separate

ClaySilt (intermediate)Silt (USDA)Very fine sandFine sandMedium sandCoarse sandVery coarse sandOrganic matter

Diameterlimits

IJmbelow 2

2-202-50

50-100100-250250-500500-1,000

1,000-2,000

Size 12. 38-2.00 mm

24.227.962.3

5.23.61.52.01.14.9

Aggregate

Size 21.1 7-0.84 mm

24.726.963.0

5.13.21.52.5

4.9

Size 30.42-0.30 mm

24.427.062.44.33.75.2

5.2

where 0, and 6f are initial and final water contents, 6, is the watercontent at any point r in the sphere at any time t, and 60 is the watercontent at saturation.

Equation [1] is analogous to heat conduction, and the solutionfor the initial and boundary conditions of Eq. 2 and 3 is in Carslawand Jaeger (1963).

RESULTS AND DISCUSSION

Particle Size Distribution

There was no significant difference in particle size amongthe aggregates (Table 1). Sizes 1 and 2 had the same com-position, and size 3 differed only, as expected, in the sandrange near the size limit of these smaller aggregates.

It was, therefore, assumed that the aggregates were simi-lar structurally, and could be expected to have similar waterretention and conducting properties.

Bulk Density of The Aggregates

The pumice samples which were porous, but with a rigidframework, were used to test whether the three techniquesgave the same value for bulk density. The mean bulk densi-ties obtained by techniques Ty and Tz were not significantlydifferent, but Tx gave a value about 7.5% higher than themean value by technique Tz (Table 2). One of the limita-tions in Tx is the uncertainty in determining the suction thatremoves kerosene oil only from the inter-aggregate poresand outer surfaces of the aggregates. Thus, there may begreater reliability in the results from Ty and Tz than fromTx.

Both techniques Tx and Ty showed an increase in bulkdensity of aggregates with decreasing size (Table 2). Therelationship between aggregate density and aggregate diam-eter for sizes 1, 2, and 3 was curvilinear (Fig. 1). The meanbulk densities from Tx and Ty were used to plot Fig. 1 sincethe greater reliability of Ty over Tx was not proven.Wittmuss and Mazurak (1958) obtained a similar rela-tionship between aggregate density, measured by themethod of Chepil (1950), and aggregate diameter of a siltyclay loam soil (Fig. 1). The bulk densities measured in ourstudy were, however, higher than those of Wittmuss andMazurak.

Currie (1966), in discussing the effect of aggregate sizeon porosity, showed that surface area of aggregates couldhave a substantial effect on their bulk density. He set up amodel of spherical aggregates, considered the amount ofpore space which was lost on subdividing the aggregates,

Table 2—Measured bulk densities of air-dry aggregates and clods bydifferent techniques

Mean diameteof aggregate

Material or clod

Aggregate size 1Aggregate size 4Aggregate size 3ClodfClodClodPumice

mm2.21.00.36

50104

• 2

r Mean bulk density by method

Tx*

1.570 ±0.0041.652 ±0.0161.787 ±0.058

0.788 ±0.026

Ty*

1.582 ±0.0151.603 ±0.0101.792 ±0.016

0.740 ±0.0215

Tz

1.5461.5581.5690.733 ±0.018

* Each value represents the mean of three measurements, given as the mean andstandard deviation.

f Clods selected were visually free of holes or fractures.

GUMBS AND WARKENTIN: PROPERTIES OF SOIL AGGREGATES 31

o Prediction from Curries Eq'n.• Experimental,for [},= 2.67g.cm~3

1.5 2.1 2.21.6 1.7 1.8 1.9 2.0Bulk density, g.cm'3

Fig. 1—Measured and predicted bulk densities of small aggregates.

and derived an expression for the effective porosity. Usingthis expression, the predicted changes in bulk density for auniform material crushed to different sizes are shown inFig. 1 and 2. Figure 1 shows the measured and predictedchanges in bulk density of the 2.2 to 0.36 mm diameteraggregates used in this study. The changes in bulk densityseem to be explained entirely by surface area effects. Figure2 shows the measured values of bulk density for large clodsand the changes predicted due to surface area effects. Thesemeasured changes in bulk density of the clods were not ex-plainable as surface area effects only, but were likely areflection of both surface area and the heterogeneity of thematerial, e.g., holes or fissures.

Saturated Water Content of the AggregatesBased on a bulk density of 1.58 g/cm3 and a particle den-

sity of 2.67 g/cm3, the total porosity of 2.2 mm diameteraggregates was 0.408. This was, therefore, the maximumvolumetric water content of the aggregates if they did notswell. On a weight basis the water content at saturationwould be 0.260 g/g. Entrapment of air would reduce thevolume of pores containing water, and swelling of theaggregates would give greater porosity and higher watercontent. In order to estimate the percent water saturation ofthe aggregates (or the volume of air entrapped) from mea-surements of water content on a weight basis, it was neces-sary to know the volume increase that took place when theaggregates were saturated from the air-dry condition.

Volume increases were measured on three sizes of clods,

5.0

3.0

i 1.0

1.55 1.56 1.57Bulk density, gem"-3

Fig. 2—Measured and predicted bulk densities of clods (predictionmade using Currie's equation).

chosen at one extreme as the smallest which could conve-niently be handled and at the other, as not large enough toallow the presence of visible holes or fissures. Initial dryvolume was calculated from weight and bulk density mea-sured by method Tz. Volume of saturated clods was alsomeasured by coating with paraffin as described. Final watercontent of the samples, calculated volume increases, andcalculated total pore volume per cm3 and per g are given inTable 3. Saturation water content of the clods calculatedfrom these results was 0.42 cm3/cm3 out of a total pore vol-ume of 0.55 cm3/cm3, and therefore, about 24% of the porevolume was air filled. There were no replicates within clodsizes. However, percent volume increases were the samefor all clods, and differences in water content among clodswere small. It seems, therefore, that the swelling behaviorof this material did not depend upon clod size in this range.In this study, it was assumed that the smaller aggregates(2.2 to 0.36 mm diameter) would swell in a manner similarto the clods.

The same methods could not be used for the aggregatesbecause the volumes of wet aggregates could not be mea-sured on small diameter aggregates. The evaporation tech-nique described under "Methods" was, therefore, used toestimate saturated water content of the 2.2 mm diameteraggregates. The water content at the break in the curve ofwater loss versus time varied with the evaporative energysupplied (Fig. 3). At low evaporation rates, water conduc-tance to the aggregate surface was apparently rapid enoughto maintain steady water loss. At high evaporation rates, theprecision of the method was not good enough to show anydifference in the rate of water loss between inter-aggregateand intra-aggregate pores. Therefore, in both cases thebreak in the curve occurred after intra-aggregate water wasalready being evaporated, and the measured water contentwas too low. A maximum water content of 0.335 g/g was

Table 3—Final water contents, volume increases, bulk densities, and calculated saturation water contents for clods of different sizes

Air dry volume Volume of wet Percent volumeof clod clod increase

4.0611.9625.20

6.3318.6439.25

Mean

55.955.955.9

55.9

Bulk densityof wet clod*

g/cm3

1.2171.2071.190

1.205

Pore volume atsaturation

cm3/cm3

0.5440.5480.554

0.549

Final watercontent of clod

0.3500.3490.358

0.352

Water content calculatedat 100% saturation

0.4470.4540.466

0.456

* Weight of dry clod/volume of wet clod.

32 SOIL SCI. SOC. AMER. J., VOL. 40, 1976

0.8

0.7

0.6

0.5

0.4

0.3

5 0.2

0.1

WATER CONTENT AT BREAK1 0.240 ± 0.007 g/g2 0.335 i 0.002 g/g3 0.196 ±0.010 g/g4 0.135 ±0.014 g/g5 0.160 ±0.007 g/g6 0.120 ± 0.012 g/g

14 22 30 38 46 54 62

TIME, mins.70 78 94 102

Fig. 3—Water content change during evaporative drying of 2.2 mmdiameter aggregates, showing breaks (numbered 1 to 6) in curveswhere infra-aggregate water loss begins. The intra-aggregate watercontents at these breaks are given in the inset. The evaporativedemands are: A = 1.61, B = 3.13, C = 4.90, D = 8.29, E = 12.02,and F = 15.63 cal cnr2, min"1.

measured for an evaporat ive demand of 3.13 calcm~2min~1. This is the best estimate from this method forthe water content of intra-aggregate pores. This water con-tent was nearly equal to the value of 0.35 g/g measured forclods (Table 3). An evaporative demand of 3.13 cal cm~2

minute"1, therefore, appeared to be the critical value for the2.2 mm diameter aggregates.

Measurements by the evaporation technique on pumicewhere swelling was not involved, and on larger soil clodswhere the smaller surface area to volume should reduceinaccuracies in the method, are shown in Table 4. Therewas a remarkably constant value of about 25% of the poresremaining air-filled, or 13% of the total soil volume. Thecritical evaporation energies for pumice and the clods were3.59 and 3.13 cal cm~2 minute"1. These values were againclose to the values for the smaller aggregates.

The water contents of intra-aggregate pores for isolated2.2 mm diameter aggregates measured by the water absorp-

Table 4—Intra-aggregate water contents and percent air-filled porespace for different aggregates and clods using evaporation, sorption,

and capillary rise techniques

Material

Aggregates 2.2 mmdiam.

Pumice 4 mm diam.Pumice 10 mm diam.Clod 1.0 cm diam.Clod 2.0 cm diam.Aggregates 2.2 mm

diam.

Clod 1.0cm diam.

1.4 cm diam.

1.8 cm diam.

Air-filledCritical pores as %

evaporative Intra-aggregate of totalMethod energy water content pore space*

cal cm~ m

Evapora ion 3.13Evapora ion 3.59Evapora ion 3.59Evapora ion 3.13Evapora ion 3.13

Sorption 2 mm head0 mm head

-2 mm head-50 mm head

—100 mm headSaturation by

capillary riseSaturation by

capillary riseSaturation by

capillary rise

n l slS

0,335 ±0.0020.610 ±0.0170.620.330.34

0.44 ±0.0420.42 ±0.0330.41 ±0.0300.31 ±0.0200.27 ±0.010

0.35

0.35

0.36

2625252726

23

23

23

tion technique for different pressures of wetting are pre-sented in Table 4. Values given are for 50 minutes of wet-ting. At 2, 0, -2, and -3 mm pressure, the surface of theaggregates glistened from the presence of a film of water.The aggregates, therefore, contained more than intra-aggregate water. This excess water drained at a suction be-tween 3 and 50 mm of water; the aggregates had a dull ap-pearance at the latter suction. The saturated water content ofintra-aggregate pores after 50 minutes wetting was, there-fore, between 0.31 and 0.41 g/g, which confirmed that thevalue of 0.34 g/g estimated by the evaporation techniquemust be approximately correct.

The sorption technique could not estimate intra-aggregatewater content when beds of aggregates were used becausethe rate of capillary movement into inter-aggregate poreswas not distinctly faster than the rate of entry into intra-aggregate pores. Several rates of entry of water into thebeds of aggregates were measured. The slowest rates wereinterpreted as water entry between the particles of the ag-gregates by absorption causing swelling.

Rate of Saturation of Aggregates Immersed in WaterThe time required for clods of known diameter to saturate

when immersed in water was measured, and an equationfrom the theory of heat conduction was used to predict therate of saturation for different sizes of aggregates. Thedegree of saturation measured on the 2 cm diameter clodswas the same for 45 and 100 seconds of immersion (Table5), showing no increase in the degree of saturation for im-mersion times beyond 45 seconds. The maximum watercontent of 0.299 g/g was lower than 0.34 g/g measured inTable 4. This was probably due to the short time of immer-sion (100 seconds) which was not long enough for completeswelling.

The rate of saturation of aggregates was predicted fromEq. 4 using the following assumptions (i) the surface of theaggregate saturated instantaneously; and (ii) D was indepen-dent of water content and equal to 5 x 10"3 cm2/second, thevalue measured at intra-aggregate pore saturation (Gumbs,1971).3 This latter assumption may not introduce seriouserrors because the diffusivities at high water contents areexpected to dominate the rate of flow, particularly over theshort infiltration distances for the small aggregates.

Figure 4 shows the calculated percent saturation at dif-ferent fractional distances from the surface of a 2-cm diame-ter clod. Since Eq. 4 could be used to calculate the watercontent at the center of the clod, water content was calcu-

3F. A. Gumbs. 1971. Infiltration of water into aggregated soils. Ph.D.Thesis. McGill University.

Table 5—Measured and predicted rates of saturation of 2-cmdiameter clods immersed in water

seconds

15304560

100

Percent saturation if swelling assumed*

Measuredf

41 ±0.2262 ±0.4465 ±0.8866 ±0.4465 ±0.66

Calculated

71.289.595.099.6

f Calculated on basis of the amount of swelling measured in Table 3. t Duplicate samples used.

GUMBS AND WARKENTIN: PROPERTIES OF SOIL AGGREGATES 33

r ^ i — i ^_^ , __^ SOsecs tween inter- and intra-aggregate pores during infiltration^ ~~°~-~-—-a.——___o was not likely to be serious.

90 N^N^^x^^^osecs Gumbs (1971)3 has shown that the rate of wetting of\ NN^ ^^ ^~~~~~^~--(K___^ aggregates of Ormstown silty clay was markedly reduced if

\ N. Ti aosecs ~~~~~~~o wetting took place under suction; at suctions of 4 or 5 cm ofTO- \ ^v ^\^^ water, infiltration in media of 2.2- and 1-mm diameter

NW \^ ^ ' --^^^^ aggregates took place almost entirely via intra-aggregate1 \ X20secs ^~^~° pores. The theory of infiltration using the diffusion equation2 so - \ N. for porous media with continuously varying pore size dis-5? \ N. tribution was applicable to infiltration under suction in these

40 \ ^x_ media (Gumbs and Warkentin, 1975). Differences in the30. \ ^^^<> diffusivity of water in, or the rate of saturation of, inter-and

\ - intra-aggregate pores would, therefore, indicate how20 \ serious local disequilibrium would be during infiltration0 \ under zero or positive water pressures.

Ql 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Fractional distance from surface.

Fig. 4—Calculated wetting profiles of a 2-cm diameter clod immersedin water.

lated as a fraction of the saturation water content (= 60) atvarious radial distances from the surface. The percentagesaturation of the entire aggregate at any of the times givencould be calculated from the water contents of a number ofimaginary concentric spheres of the original aggregate. Thewater content of the outer spheres would contribute more tothe mean water content of the aggregates than the innerspheres because of their greater volumes. The theory as-sumed no effects of air entrapment so that the maximumpercent saturation is 100. Calculations showed that 95.0 to99.6% saturation was achieved in 40 to 60 seconds (Table5). The measured values in Table 5 reveal that the max-imum saturation for the 2 cm diameter clod was attainedafter 60 seconds, and that a significant increase in percent-age saturation may not have occurred after 45 seconds. Thetheory, therefore, estimated the correct time for saturation.For 5.0 cm clods 95 to 98% saturation was predicted in 900to 1,200 seconds.

The theory predicted that 2.2 mm and 1 mm diameteraggregates should saturate in 2 and 1 seconds, respectively.With these rates of saturation, disequilibrium of water be-