Hydraulic Conductivity Evaluation of the Soil Profile fromSoil Water Retention Relations1

R. R. BRUCE2

ABSTRACTEvaluation of the water content-suction relation applicable to

field soil horizons that differ widely in texture was considered.Except for coarse-textured, organic matter-deficient horizons, itis concluded that soil water retention of sieved samples is sig-nificantly modified and does not represent the natural soilvolume. Water content-suction data from measurements oncarefully procured core samples of each horizon of a TypicHapludult adequately represent their water retention character-istics. Using appropriate water content-suction data, the hy-draulic conductivity-water content relation calculated bypublished procedures was compared with hydraulic conductivitymeasured on similar samples by a transient outflow procedure.The calculated hydraulic conductivity-water content relationsfor coarse grained systems or systems having a relatively narrowrange of pore size and well-defined bubbling pressure was suf-ficiently accurate for many purposes. However, to obtain auseful evaluation of the unsaturated hydraulic conductivity offine-textured horizons with a very wide range of pore size anda poorly defined bubbling pressure, the Marshall or Millingtonand Quirk methods had to be matched at a water content in the0.1- to 0.3-bar range. Indiscriminate use of such methods ofcalculating hydraulic conductivity is inadvisable.

Additional Index Words: unsaturated conductivity, permea-bility.

IN RECENT YEARS, a rigorous theoretical base for describ-ing water movement in porous media has been devel-

oped. Flow of water in unsaturated porous media is par-ticularly complex and mathematical description is difficult.Consequently, relatively simple laboratory flow systemswere used in the experimental examination of theory. Ex-ploitation of numerical methods of analysis and modernrapid computational procedures now allow application oftheoretical principles of flow to more complex systems.Yet there has been only limited exploitation of the theorydescribing water movement in soils by the hydrologists andothers in treating field problems. The necessity of havinga satisfactory description of the hydraulic conductivity-water content or suction relation and the water content-suction relation for each homogenous soil volume in thesystem has been a major deterrent.

Brutsaert (1967) recognized the particular problem ofsatisfactorily evaluating the hydraulic conductivity-watercontent relationship. He reviewed the methods of calculateing hydraulic conductivity, inherent assumptions in the cal-culations, and results of experimental testing of the meth-ods. In all cases the techniques for calculating hydraulic

556 SOIL SCI. SOC. AMER. PROC., VOL. 36, 1972

SOIL

.20

.15WATER

CONTENTg/g .10

.05

Ap HORIZONo-SIEVED•-CORE

0.25 0.50 1.0SOIL WATER SUCTION, bar

2.0

Fig. 1—Soil water content, by weight, as a function of soil wa-ter suction determined from sieved and core samples of Aphorizon of Cecil loamy coarse sand.

conductivity presume: (i) that the pore system contribut-ing to flow over the desired range of water content is ade-quately modeled; and (ii) that the water content-suctionrelation provides the appropriate input data. Although onemight expect the accuracy of. the calculated quantities todepend upon the degree to which the model fits the realsystem, there seem to be 'conflicting reports in the literatureabout the accuracy of such estimates of hydraulic conduc-tivity (Jackson et.al., 1965; Nielsen et al., 1960; Kunzeet al., 1968; Shaykewich, 1970; Green and Corey, 1971).

In this paper evaluation of the water content-suctionrelations of field soils will be considered. Using the appro-priate water content-suction relation, the hydraulic con-ductivity-water content relations calculated by publishedprocedures are compared with hydraulic conductivity mea-sured by a transient outflow method.

MATERIALS AND METHODS

A site classified as a Cecil loamy sand, a Typic Hapludult,with characteristic horizon depths, textures, and bulk densitiesas shown in Table 1, was selected. From each of the designatedhorizons undisturbed soil volumes were obtained using shortsections of stainless steel tubing having a wall thickness between0.10 and 0.18 cm. The wall on one end of each tube section wasacutely bevelled on the outside, thus providing a sharp edge forinsertion into the soil. Tube sections of the following diametersand lengths were used: 6.2 by 6.0 cm, 8.6 by 6.0 cm, and 9.8by 2.5 cm, respectively. These tube sections were inserted ver-tically into the respective horizons by means of a hydraulicjack, excavated out, and the excess soil trimmed to the tubevolume. Sampling was done at soil water contents experiencedin the profile after a few days of redistribution following infil-tration that moved the wetting front more than half way throughthe B2 horizon. Fifteen such samples or cores were taken fromthe C horizon and 19 from each of horizons Ap, Bl, B2, andB3. Each sample was wrapped in aluminum foil and stored atabout 1C until required for measurements. At the same time aquantity of soil was taken from each horizon with a shovel, airdried, and crushed to pass a 2-mm sieve.

The water content as a function of suction during the desorp-tion phase was determined on 6.2- by 6.0-cm core samples onsingle sample pressure plate apparatus. Plates with 2-bar air-entry values were used over the range 0.025 to 2 bars, while4- and 15-bar plates were used to appropriately extend therange to 15 bars. All samples were saturated under a vacuumof about 75 mbars. Water content as a function of suction dur-ing desorption was determined, with similar multiple sampleapparatus, on sieved soil samples placed to a depth of 1.5 to 3cm in retaining rings varying in diameter between 3.8 and 6cm. Sieved samples were saturated on the plate by maintaining

SOILWATER

CONTENT,9/9

.20 -

0.25 0.50 1.0SOIL WATER SUCTION, bar

2.0

Fig. 2—Soil water content, by weight, as a function of soilwater suction determined from sieved and core samples ofB2 horizon from Cecil loamy coarse sand.

excess water on the plate surface for about 24 hours prior toapplying pressure. The bulk density of such samples was esti-mated using the volume measured on samples at 1-bar equilib-rium. In all cases, equilibrium at the imposed pressure wasdeclared when no outflow was measured over an 8-hour period.

Soil water diffusivity was determined on the 8.6- by 6- and9.8- by 2.5-om core samples by the method suggested by Gard-ner (1962) and described by Doering (1964). Prior to mea-surement of outflow as a function of time, all samples weresaturated under a vacuum of 75 mbars. The 9.8- by 2.5-cmsamples were used to measure outflow when either a 4- or 12-bar pressure step was used. The 8.6- by 6.0-cm samples wereused for 1- and 2-bar pressure step measurements. In all casesthe air-entry value of the plate was only slightly greater thanthe pressure step applied. Following the saturation procedure apressure of 10 to 25 mbars was applied to each sample toremove free water from the system. When no outflow was mea-sured during a minimum period of 4 hours, a pressure of 1, 2,4, or 12 bars was applied and outflow as a function of time wasrecorded. Upon reaching a no-outflow condition the water con-tent of the sample was determined by oven drying at HOC.Outflow was recorded from at least two samples at each of theabove pressures. All outflow was measured with recording bal-ance systems in a constant temperature cabinet at 27C. Weightchanges of 1 mg were accurately measured by this balancesystem.

A mean diffusivity-water content curve was determined foreach soil horizon from the data for eight or more samples. Hy-draulic conductivity was calculated from the soil water diffu-sivity data by application of the appropriate water capacityvalues from water content-suction relations determined as pre-viously specified. The hydraulic conductivity at saturation wasdetermined on several core samples from each horizon by aconstant head procedure.

Procedures for calculating hydraulic conductivity from watercontent-suction data, suggested by Childs and Collis-George(1950), Marshall (1958), Millington and Quirk (1961), andLaliberte et al. (1966), have been applied. For the calculationsby Marshall method and Millington and Quirk method thecomputer program used by Green and Corey (1971) was used.

RESULTS AND DISCUSSION

Water Content-Suction Relation

In Fig. 1 and 2 the water content on a weight basis asa function of suction is shown for sieved and core samplesof the Ap and B2 horizons of Cecil loamy coarse sand. Thetwo kinds of samples give entirely different results forthe B2 while for the Ap significant differences appear only

BRUCE: HYDRAULIC CONDUCTIVITY EVALUATION OF THE SOIL PROFILE 557

,6

core

1= one sample2s mean of 2 samples

other points mean of 3 to 12 samples

Ap

.001 .01 .02 .03 .05 .1Soil Water Suction, bars

Fig. 3—Soil water content on a volume basis as a function of soil water suction determined from sieved and core samples of Ap, B2,and B3 horizons.

at very low suctions. It is reasoned that the sieving pro-cedure has markedly modified the pore volume of the B2horizon which retains water in this suction range, whereasthe effect on the Ap horizon pore volume is restricted tothe large pore range.

By applying the determined bulk density for each typeof sample the soil water content on a volume basis as afunction of soil water suction was obtained (Fig. 3). Thedetermined bulk densities, that were applied for the sievedsamples, are 1.39, 1.01, and 1.13 g/cm3 for the Ap, B2,and C horizons, respectively. The core sample bulk densi-ties are given in Table 1. Since the core bulk densities aregreater than the sieved sample densities, the core samplewater contents become greater than the sieved samplewater contents at all suctions greater than about 0.2-barsuction. However, this difference is not significant in thecase of the Ap horizon. At suctions less than about 0.1bar the water content of sieved samples is greater thanthat for core samples irrespective of horizons.

It is concluded from these observations, other evidencein the literature, and physical principles that samplemanipulation will significantly modify pore volume andpore size distribution. Consequently, soil water retentionand flow will be modified. Sandy, organic-matter-deficienthorizons are less affected, as demonstrated by the Ap hori^zon of the Cecil loamy coarse sand. Cultivated horizons

Table 1—Particle size distribution for Cecil loamy sand profileand bulk density of field core samples

are generally difficult to characterize, since tillage or othermanipulation modifies pore volume and pore size distribu-tion. If one really is interested in describing the nature andfunction of a field soil system, e.g. soil profile, then thereis no alternative to making measurements in situ or mak-ing measurements on samples that truly represent the realpore system. If manipulated samples are used, physicalprinciples operative in the field system are ignored andresultant measurements are largely irrelevant. Thus, inFig. 4 the water content-suction data from the measure-ments on core samples of each soil horizon describe thewater retention properties of the field system. These datawill be used for calculations of hydraulic conductivity bypreviously mentioned procedures.

Hydraulic Conductivity-Water Content Relation

LIMITED PORE-SIZE RANGE

The procedures for calculating hydraulic conductivityfrom the water contentrsuction relation have been appliedfor the most part to materials having a narrow range ofpore size. Water content-suction data from a drying cyclehave normally been used. Thus, results of calculations bythese procedures on such materials are first examined toprovide perspective. Figure 5 shows the hydraulic conduc-

Table 2—Particle size distribution of selected coarse grainedmaterial and some physical properties of packed samples

Particle size distributionHorizon

ApB,B2

C

Depthcm0-18

18-3333-8989-104

104-147+

Clay

532392619

Silt Sandby weight

1718192426

7850425055

Texture

Loamy coarse sandSandy clay loamClay loamSandy clay loamSandy loam

Bulkdensityg/cm>1.591.541.551.651.62

Material

SandGraded sandFine sandGlass beads

Particledensity

Samplebulk

densitys

2.66 1.732.68 1.682. 71 1. 57

Size class0.5-J

4.2

0.-0

53

1

25.5

.4

.0

(diameter in mm)0.1-0.25

by weig35.689.923.5

0.05-0.1

4.10.40.

.0

.1

.6

<0. 05

2.8

34.9

Saturatedconductivity,

Ks'cm/min

1. 14±2%8. 48 x 10-'±3%1.31 x 10-'±20%

1.49 35-105)i with 75% 60-95u 3.66x

558 SOIL SCI. SOC. AMER. PROC., VOL. 36, 1972

Cecil loamy land• Ap horizonO B,Q B2A B3X CPlot 4 Core Samples

10-3 10-2 10-1

SOIL WATER SUCTION, bars

Fig. 4—Soil water desorption curves for principal horizons of Cecil loamy sand.

tivity as a function of water content resulting from calcu-lations by the indicated procedures, using the desorptiondata in the graph of the sand listed in Table 2. Similar cal-culations made from desorption data (Bruce and Klute,1963) for the other sands and 75/x, glass beads describedin Table 2 yield a similar pattern. In Fig. 6 the hydraulicconductivity as a function of water content for gradedsand and fine sand, calculated by selected procedures fromdesorption data, is shown. When matched at the saturated

conductivity, Ks, the Marshall method gives values verysimilar to the Childs and Collis-George method and valueshigher than the Millington and Quirk method (M&Q)when matched at Ks (Fig. 5). The Laliberte et al. method(LBC) gave values similar to Millington and Quirkmethod, except near saturation, for all materials shownin Table 2, with the exception of the fine sand. In thecase of the fine sand (Fig. 6), LBC predicts lower values

o

•oa10-'

(Ks)c Ks/ (Ks)ccm/mln

® Childs and Collls-Georgex Marshall <m) O.93 1.222. MandQ(m) 1.88 0.605ALBC(m) 1 .17 0.97 .̂El Measured %f* /

S

10 0

1 lO

•a KT*

ICT=

Pb=42mb

.10 .20Water Content. cmVcm3

.30Q.I 0.2 0.3

Water Content, cm3/cm30.4

Fig. 5—Hydraulic conductivity as a function of water contentcalculated by several procedures from the plotted desorptiondata of the sand in comparison to measured values.

Fig. 6—Hydraulic conductivity as a function of water contentcalculated by several procedures from desorption data for agraded sand (upper curves) and a fine sand (lower curves)in comparison to their measured hydraulic conductivity.

BRUCE: HYDRAULIC CONDUCTIVITY EVALUATION OF THE SOIL PROFILE 559

-"

(Ksl̂ cm/min• Moreholl (m) 3.49 Millington ond Quirk (m) 6.3& Laliberte et ol 8.4El Measured

Pb=9.2mb

Cecil loamy sand

Ap cores

.05 .10 .15 .20 .25

Water Content, cm3/cm3.30

Fig. 7—Hydraulic conductivity of Ap horizon core samples ofCecil loamy sand calculated by several procedures over arange of water contents in comparison to measured values.

than M&Q matched at Ks in the low water content rangeas well as higher values in the range near saturation. TheLBC method gives about the same result unmatched asmatched for the sand, graded sand, and glass beads asevidenced by the very good prediction of Ks. The bubblingpressure, Pb, calculated according to Laliberte et al. forthe sand, graded sand, fine sand, and glass beads was 33,42, 164, and 83 mbars, respectively.

In Fig. 5 and 6 hydraulic conductivity calculated fromsoil water diffusivity measured by the method of Bruceand Klute (1956) on similar packings of these sands arecompared to hydraulic conductivity values calculated byselected procedures. In the case of the sand (Fig. 5), sixof the eight measured values fall on or very close to thecalculations by the Childs and Collis-George, and Marshallmatched (m) at Ks methods. The measured hydraulicconductivity values for the graded sand and fine sand gen-erally fall within the range of calculated values given inFig. 6. It seems that the LBC (m) calculations are mostclosely related to the measured values for the graded sandand perhaps the unmatched Marshall calculations are mostclosely related to the values for the fine sand. The un-matched M&Q represents the measured values quite wellfor both materials over a major part of the water contentrange.

As observed by others, (Ks,)c is usually significantlygreater than Ks and therefore KS/(KS)C« 1. However,for these materials KS/(KS)C was frequently > 1, e.g., finesand, or in the range 0.4 to 1.0. In spite of the error thatmay be associated with the measured values of both satu-rated and unsaturated hydraulic conductivity comparisonwith the calculated values indicates that these calculationprocedures are adapted to describing the operation of thesenarrow pore-size systems with varying degrees of reliability.

10-2

ID-'

E icr4

E

IQ-8

Cecil loamy sandBy cores

(Ks)e,cm/mln Ks/(Ks)c

Marshall (m) 3.2O .0022<s Millington and Oulrk(m) 5.57 .0013A Laliberte et al 0.15s Measuredx Millington and Quirk (M)

.26 .28 .30 .32 .34 .36 .38Water Content, cm'/crn3

Fig. 8—Hydraulic conductivity of B2 horizon core samples ofCecil loamy sand calculated by several procedures over arange of water contents in comparison to measured values.

Considerable uncertainty seems to exist in the estimates ofhydraulic conductivity in the range between saturation andPb. The Millington and Quirk unmatched method seems tomost closely match the measured values of all the materialslisted in Table 2 in spite of the fact that the Marshall (m)method fits the sand data in Fig. 5 better. It appears thata good estimate of Ks and conductivity in the wet rangecan be predicted by extrapolating the M&Q unmatchedcurve from about 0.90 of saturation to the saturated watercontent. If the M&Q method is matched at a convenientlymeasured value somewhat below Pb and extrapolated tosaturation as suggested above, an even more reliableestimate results.

SOIL HORIZON MATERIALSIn Fig. 7, 8, and 9, the results of calculating hydraulic

conductivity from water content-suction data obtainedfrom measurements during desorption of core samples ofthe Ap, B2, and B3 horizons of Cecil loamy sand areshown. These data are compared with values computedfrom soil water diffusivity measurements during desorptionon similar samples. From the standard deviation shownfor each mean of more than three samples, a rather largevariation is identified. This variation reflects real differ-ences in hydraulic conductivity among samples and errorassociated with measurements. A partitioning of the varia-tion has not been attempted. It was assumed, however, thatvariability among samples was major and that the proce-dure must allow relatively rapid and accurate measurement.The one-step outflow procedure was therefore selected.

In the case of loamy sand Ap horizon (Fig. 7), theMarshall and LBC method matched at Ks show goodagreement with the measured values. M&Q method pre-dicts values less than measured values by one standarddeviation. Since the measured values are in the range of

560 SOIL SCI. SOC. AMER. PROC., VOL. 36, 1972

oo

10rio

• Marshall (m)0 Millingtan and Quirk (m)ALaliberte et a I13 Measuredx Millington and Quirk (M)

(Ks)Ctcnytnin. Ks/(Ks)c

O.I barpressure

.22 .24 .26 .38 .40.28 .30 .32 .34 .36

WATER CONTENT, cmVcm3

Fig. 9—Hydraulic conductivity of B3 horizon core samples of Cecil loamy sand calculated by several procedures over a range of wa-ter contents in comparison to measured values.

0.06 to 2.5 bars, it is uncertain which method may betterpredict values between 0.06 bar and saturation. Of course,LBC assumes K=KS from P=0 to P=Pb. All of the. meth-ods, when unmatched, predict values that are too high.

The methods for calculating hydraulic conductivity whenmatched at saturation obviously do not reliably predictthat from measurements on B2 and B3 horizons (Fig. 8and 9). The Marshall and M&Q method when matchedat Ks predict values that are too low over the entire rangeof water content. The LBC method predicts values thatare too high in the wet range and too low in the dry range.The LBC method requires a great deal of "cut and try"in cases where the bubbling pressure is poorly defined andthe water content-suction curve is generally quite flat.When the Marshall and M&Q methods are fitted at awater content between 0.1 and 0.3 bar, there is satisfac-tory agreement with values in the range of greatest mea-surement confidence. As in the case of the Ap horizon theMarshall and M&Q methods yield values that are too highwhen unmatched.

If either the Marshall or M&Q curve of hydraulic con-ductivity when matched as in Fig. 8 at about 0.35 watercontent is extrapolated till it reaches the measured satu-rated hydraulic conductivity value, about 0.405 is read asan apparent saturation water content. If a similar pro-cedure is followed in the case of the B3 horizon in Fig. 9,an apparent saturation water content of about 0.36 is

Table 3—Hydraulic conductivity of Cecil loamy sand Ap hori-zon from samples at two sites by one-step outflow

measurements

Hydraulic conductivity at water content, cm'/cm8 ___0.12 0.15

-cm/mln-7.1 x 10-'5.2x ID"7

3.1 x !0-«1.3x 10-«

1.6x 10-5

1.8x 10-"1.6x 10-*7.1 x 10-'

found. By such manipulation the nature of the watercontent-suction relation near saturation is modified and theprocedure used in. its determination is questioned. In Fig.4 the nature of the desorption curves in this region isdetermined by a measurement at 25 mbars and the valueof total porosity calculated from measured bulk densityand particle density values. One has only to modify thecurves for B2 and B3 horizons in Fig. 4 in the less than15 mbars range to draw an acceptable curve to the appar-ent saturation water contents suggested above. Several ver-sions of the desorption curves between saturation and 15mbars suction have been used to calculate hydraulic con-ductivity by M&Q and the Marshall method. In Fig. 10three versions calculated by Marshall method are shownfor the B2 horizon. As expected, the measured values fitthe curve matched at 0.40 best with several points fallingbetween the 0.40 and 0.41 curves. The lower curve is cal-culated from the data in Fig. 4 and is the same as plottedin Fig. 8.

The comparisons of calculated and measured hydraulicconductivity evaluated from core samples of Cecil loamysand horizons, which vary in texture from loamy coarsesand in the Ap to clay loam in the B2, expose some dimen-sions of the problem encountered in adequately describingthe hydraulic conductivity water content relation for appli-cation to soil profile water transport. Although the tran-sient outflow method of determining soil water diffusivityhas recognized peculiarities that are not well understood,the one-step outflow procedure as used here to determinethe hydraulic conductivity-water content relation seemsadequate. To support this contention see the data in Table3 for samples taken from Ap horizon of two plots sampledat different times but which have very similar mechanicalcomposition and desorption curves over this range ofwater content. It therefore seems that the models examined

MUSTAFA & GAMAR: ADSORPTION AND DESORPTION OF DIURON 561

lo-1

ID'2

10-'

;i<r4

r io-5

la»

£io-7

I lO'8

10-9

X Marshalli_ Marshall_i Marshal0 Measuri

(m)(m)

i l l (m)

SaturatedWater Content

.400

B* coresy sand

.28 .30 .32 .34 .36 .38Water Content, cmVcm'

.44

Fig. 10—Hydraulic conductivity calculated by Marshall (m)method from three versions of the desorption curve between0 and 15 mbars for B2 horizon core samples of Cecil loamysand in comparison to measured values.

here for describing the pore transport system can be usedwith discrimination to calculate the hydraulic conductivityof many soil materials with adequate accuracy for manyapplications.

In the case of fine textured soils there seems to be aproblem associated with the description of the soil watercontent-suction relation near saturation, i.e. suctions lessthan 15 mbars. By matching the Marshall or M&Q calcu-lations at a conveniently measured hydraulic conductivityin the 0.1- to 0.3-bar range, the unsaturated hydraulicconductivity of these materials is adequately described.

For the coarser textured Ap horizon, matching the Mar-shall and LBC method at Ks gave acceptable agreementwith measured conductivities.