THE DETERMINATION OF MOISTURE IN UNDISTURBED SOIL1

N. E. EDLEFSEN AND W. O. SMITH2

WE SHALL discuss only two of the factors requiredto fix the physical state of the water in soils,

namely, the quantity of water in the soil, and thetightness with which it is held. Quantity of the soilmoisture will be expressed conventionally as a per-centage of the dry weight of the soil, but a quanti-tative measure of the tightness with which water isheld in soil is not so familiar and probably justifiesmore discussion.

A function, f, called free energy, serves admirablyto express the tightness with which water is held insoil and is defined by

f = e + Pv — Ts = h — Ts iwhere e, v, h, s, T, and P represent specific internalenergy, specific volume, specific heat content, specificentropy, temperature, and hydrostatic pressure, re-spectively. This quantity, f, has been called thethermodynamic potential but is more commonlyknown in this country as free energy. Discussion hasbeen made elsewhere (7, 12, 14)3 of the use of thisfunction in thermodynamic interpretation of soil mois-ture. We shall here confine our remarks on this func-tion to a discussion of methods of measuring soilmoisture. Although this discussion has to do withdetermination of moisture in undisturbed soils, it ispertinent that we review briefly those phases of labo-ratory studies that have a direct bearing on themeasurement of soil water under field conditions. Weare usually interested in the change in free energyof moisture in soil from some standard state, con-veniently taken as pure free water under a pressureof one atmosphere. Thus, we are interested in Afrather than f.

BEARING OF LABORATORY STUDIES ONFIELD DETERMINATIONS

The free energy of soil moisture in a given soildepends upon the moisture content. The questionas to whether in a given soil the free energy is asingle-valued function of the moisture content hasreceived much thought and has been the subject ofconsiderable laboratory experimentation. There istheoretical (28) and experimental (18, 22) evidencethat this function may be multiple valued. The dif-ference between a real hysteresis or multiple valueand a lag in equilibrium must be clearly distinguished.It is difficult to tell, in laboratory work, whether ornot there exists a multiple value for the free energyas a function of moisture content or whether there ismerely a lag in obtaining equilibrium. The existenceof hysteresis under field conditions will not be dis-cussed since field measurements indicate it to be oflittle importance.

METHODS OF MEASURING FREE ENERGY

The simplest way theoretically of measuring thefree energy of soil moisture is by means of vaporpressure since, regardless of the causes, the freeenergy is related to vapor pressure by

Af = RT InPo

While the determination of Af is simple theoreti-cally, practically it is difficult because the vapor pres-sure at the moisture content where plants wilt (per-manent wilting percentage) (31), at 30° C is only0.4 mm of mercury less than for free water. Since therange from field capacity down to the permanentwilting percentage is that range of the soil moisturein which agronomists are most interested, it appearsthat vapor-pressure methods are not the most suitablefor measuring free energy. Measurements made bythese methods, however, indicate magnitudes of thevariation of free energy over the range of moistureavailable to plants. Using the datum of 0.4 mm men-tioned above, the vapor-pressure measurements (10,29) indicate that at the permanent wilting percentagethe free energy of the moisture is approximately—17.7 X io6 ergs per gram. Plants having their rootsin sugar solutions (32) wilt when the water in thesolution has a free energy of approximately this samevalue which tends to substantiate the values obtainedby vapor-pressure methods. In interpreting laboratorymeasurements of this function, we must keep in mindthat free energy has a number of components (7,12, 14), thus

Af = Afp + Af0 + AfF 3

Under certain conditions, other components mustbe added to express fully the value of the free energy.The three given, however, are sufficient for ourpurpose.

The first component, that due to the pressure onthe liquid, is

Afp = v AP 4

where v is the specific volume of the water and APis the hydrostatic pressure on the water at the pointin question. Atmospheric pressure is usually takenas the datum. The value of AP may, of course, beeither negative or positive.

The second component is that due to material insolution and is

Af. = -v AP0 5

where v is the specific volume of the water and AP0

'This discussion was prepared at the request of the Executive Committee of Section I of the Soil Science Society of Americafor presentation at the Nov. 1943 annual meeting of the Society. The views expressed in this paper are necessarily limited, andthe authors accept responsibility for such errors as have occurred in the present appraisal of the problem.

"Associate Irrigation Engineer and Associate Professor of Irrigation, University of California, Davis, Calif.; and AssociatePhysicist, Bureau of Plant Industry, U. S. Dept. of Agriculture, Washington, D. C., respectively.

3Figures in parenthesis refer to "Literature Cited", p. 114.

EDLEFSEN AND SMITH: DETERMINATION OF MOISTURE IN UNDISTURBED SOILS

is the osmotic pressure in the water at the point inquestion.

The third component has to do with the force field.This field may be gravitational, adsorptive, or elec-trical. In any case, it is evaluated thus,

rBAfF = - K C o s t f d l 6

where K is the magnitude of the vector representingthe force at a point in the force field making an angle6 with the direction of the element of the path ofintegration dl ; A represents the zero point of ref-erence and B represents the point at which Afpis to be evaluated. Some parts of this third compo-nent are easily measured, such as the contribution ofthe gravitational field, whereas others are not.

Determination of the free energy of soil moistureby the freezing-point depression (26) involves someassumption as to the mechanism involved in thefreezing. Since the moisture in soil is in a field offorce, pressure is produced. Material is also in so-lution. The magnitude of the depression of the freez-ing point caused by each of these factors must bedistinguished. The thermodynamic interpretation offreezing-point measurements as conducted by theBeckmann technic have been discussed elsewhere(7. 14).

The dilatometer technic involving freezing pointscan also be used to measure free energy. Studies bythis method together with the theory for the thermo-dynamic interpretation of such measurements havebeen made (6) .

Tensiometers are satisfactory for measuring thepressure component of free energy over the rangeof tension o to ~o.&5 atmosphere. This tensionrange limits the use of this device to moisture con-tents well above the permanent wilting percentage.Recently, another promising method (21, 34) hasbeen devised for measuring the pressure componentof free energy. In this pressure-plate method themoist soil is placed on a porous membrane in a closedcontainer, and the pressure of the gas is increaseduntil soil water is forced through the porous mem-brane. The free energy of the moisture is thus raisedto approximately zero assuming that no material isin solution, by the increase of pressure on the gas.The information obtained by the use of these methodsfor measuring free energy gives a fairly satisfactorypicture as to the way the free energy varies in agiven soil with variation in moisture content.

FIELD STUDIES

Let us now turn to the application of this laboratoryinformation to field determinations of moisture insoils. All field measurements of soil moisture havebeen compared with the moisture content as deter-mined by the customary technique of sampling thesoil and drying it at a standard temperature, usually110° C.

All field measurements are indirect, that is, wemeasure some characteristic and then correlate itwith moisture content as determined by drying. Thesemeasurements may be divided into two classes, viz.A, those correlated with moisture content, and B,those correlated with free energy.

In class A are those measurements associated withthe amount of moisture in the soil but not governedby the free energy of the soil water. To make this_point clear, consider three soils of widely differenttexture and therefore different moisture character-istics. As pointed out above, we know from labora-tory measurements that the moisture of all three ofthese soils will have approximately the same freeenergy at the permanent wilting percentage. Someof these characteristics, for example, the electricalconductivity, will show different values for the threesoils when the soil moisture of each is.at the wiltingpercentage and yet changes in characteristics mayshow good correlation with changes in moisture con-tent above that percentage. Methods of this type areconvenient for measuring or for calibrating the soilas to its moisture content, but are of little use inevaluating the free energy or the tightness with whichwater is held in the soil.

Methods in which the electrical conductivity of asoil itself is measured, fall in class A. These methodshave received much attention (9, 13, 17, 20, 33) butdue to variations in salt content of the soil solution,to temperature effects, and to erratic variations incontact resistance, this method has not met with muchfavor. The four-electrode method (13, 20) seems togive fairly satisfactory results, that is, they are closelycorrelated with the moisture content of a particularsoil so long as the salt content is not materiallychanged. Caution must be exercised, however, sinceonly a limited range of soil types has been tested bythis method. The equipment used with this method isrelatively simple and the electrodes are rugged, thusthe method appears to have value for practical pur-poses.

Another measurement under class A involves thedielectric constant of the soil itself. Preliminary workonly, has been published on this method (n, 16).At present, therefore, it is impossible to estimate itspractical value.

A third type of measurement falling under class Ainvolves the heat conductivity of the soil (27). This,like the dielectric-constant method, has received onlypreliminary attention. The results available as yet areinsufficient to warrant its .appraisal.

The force required to push a standard point intoa given soil varies with the soil moisture. A studyhas been made of this method (i, 2, 3) and fairlygood correlations are reported for given soils.

The values obtained by each of the methods ofclass' A when plotted against soil moisture for aspecific soil give a curve that is characteristic forthat soil only. The value at the permanent wiltingpercentage of any one of these particular measure-ments will, in general, be different for different soils.

H4 SOIL SCIENCE SOCIETY PROCEEDINGS 1943

Those measurements involved in methods fallingunder class B are characterized by the fact that eachmeasurement is determined by the free energy of thesoil water. As pointed out above, the free energy atthe permanent wilting percentage is approximatelythe same in all types of soils. At the permanent wilt-ing percentage, therefore, the results obtained on dif-ferent soils by measurements of the class B oughtto be approximately the same. In most of the class Bmethods, a standard porous material is placed in thesoil and allowed to come to equilibrium with it, orapproximately so. Some measurement usually of thesame type as listed in class A is then made on thestandard porous material and its absorbed moisture,rather than on the soil itself. Since the quantity ofmoisture in the standard material is fixed by the quan-tity of moisture in the soil with which it is in contact,as well as the tightness with which it is held, thewater in the standard material has the same free energyas the moisture in the soils. Obviously, time is re-quired for moisture in the standard porous materialto come to equilibrium with that in the soil with whichit is in contact, and this is a serious difficulty. This is•especially true at the lower range of available mois-ture (5), the lag being very great. This difficulty,however, does not seem to be serious (5) when plantsare growing on the soil, that is, where plant rootspermeate the soil in the neighborhood of the block.The roots seem to create a steep gradient from theblock to the soil or from the soil to the block as thecase may be. In any event, the adjustment of the blockto any changes in soil-moisture content seems to bemuch more rapid when actively transpiring plants aregrowing.

Measurements now available (5, 8, 15) indicatethat the electrical conductivity of a given porousmaterial has approximately the same value at thepermanent wilting percentage in all of the soils thathave been studied. The same may be said of thethermal conductivity (19) and the dielectric constantmeasurements (4) falling in class B, although thesehave not been studied as extensively as the electrical•conductivity. All of these methods have been usedwith varying degrees of success to measure the tight-ness with which moisture is held in soils under field•conditions. Many aspects of these types of measure-ments must be worked out before they can be re-garded as completely successful from a practical view-point. The experimental work on the use of porousplaster of Paris blocks as electrical conductors hasbeen extensive and the result has been consideredsufficient by some commercial companies to warranttheir use as indicators for need of irrigation.

The use of tensiometers (23, 24, 30) is anothermethod that has been used in the field for measuringthe free energy or, at least, for measuring the pres-sure component of free energy. This component, how-ever, is perhaps the most important at high moisturecontents, and this is the only range of soil-moisture•content for which the tensiometer is capable of indi-cating readings. In the use of tensiometers, just as inthe case of the porous blocks, time is required for

equilibrium, and the instruments might give a veryerroneous reading if plants are not growing on thesoil so that moisture is reduced fairly uniformlythroughout the soil mass. One desirable feature aboutthe use of the tensiometer is that since the pressurecomponent of the free energy is usually the only oneof any practical importance, at a given horizontal levelin comparatively wet soils, the reading of the tensi-ometer gives us directly a reading of practically thecomplete value of the free energy. Whereas in usingporous blocks the measurements of electrical conduc-tivity, heat conductivity, or electrical capacity do notyield free energy directly, but instead the blocks mustbe calibrated. This may be done by use of a vapor-pressure chamber wherein the block can be placed inthe chamber in equilibrium with vapor at definitepressures. For practical purposes, however, we donot need to know the exact value of the free energy.The agronomist is largely interested in knowingwhether there is available water present for the plantsand if so how much, or what is just as good as faras he is concerned, how long will it be before themoisture will be depleted at a particular point in thesoil.

Only the general ideas of the use of these methodshave been discussed in this paper. Details can beobtained, however, from the references listed. Re-marks given here have been limited to two functions,namely the mass of moisture per unit mass of soil andthe free energy of that moisture. We have discussedthe aspects of laboratory measurements briefly sincethey have a direct bearing on the field measurementsand the interpretation of field data. Measurementsmade in the field have been classified into two groups,depending on whether they more nearly measure thequantity of water in the soil or whether they are morenearly associated with the free energy of that water.It is clear, of course, that if the free energy of the soilmoisture in a particular soil has been determined asa function of the moisture content, then any one typeof either class of measurements may be used to evalu-ate either the quantity of moisture per unit mass ofsoil or the free energy of the moisture.

In most of the studies referred to above, the num-ber of measurements made and the kinds of soils uponwhich they have been made are of necessity limited.

EDLEFSEN AND SMITH: DETERMINATION OF MOISTURE IN UNDISTURBED SOILS "5