Soil Freezing and Soil Water Characteristic Curves1

R. W. R. KOOPMANS AND R. D. MlLLER2

ABSTRACTAn earlier paper suggested that the soil water characteristic

(SWC) of soil should have an analogue to be called the soilfreezing characteristic (SFC) that could be obtained by freezingsaturated soil in an apparatus functionally related to the pressureplate apparatus. The analogy for granular soil, free of colloids, ison a different basis (capillary effects) than for soil that is whollycolloidal (absorption effects). Different rules are needed to de-monstrate the analogies for the respective types. Apparatus wasdevised to permit SFC and SWC data to be obtained, in turn,with each material placed in the apparatus. Two silt fractions, asodium-montmorillonite paste, and a whole soil were used. Theresults confirm the expected analogies and indicate that in theseexperiments, the ratio of the specific surface energy of an air-water interface at 20C to that of an ice-water interface nearOCjWas as 72.7:33.1. The results demonstrate significant mobilityfor unfrozen water at temperatures as low as — 0.15C even in cleansilt fractions. It is concluded that the inherent instability of someof the residual water in soils during drying does not significantlyaffect the SWC in the range O to 4 bars of matric suction.

THIS PAPER presents experimental data to support anhypothesis given in an earlier paper by one of the authors

(11) and discusses implications of the results with respect topotential errors in the interpretation of soil water characteristicmeasurements.

The hypothesis was based on developments in the theory offrost heaving in soils (1, 5, 6, 8,10,12,15) and in effect statedthat qualitative parallels between the drying and wetting ofsoil, on the one hand, and freezing and thawing of soil, on theother, can be stated quantitatively if, but only if, the soil isknown to be one of two extreme types and if the conditionscorrespond in a prescribed manner. Most natural soils haveattributes of both of the extreme types, and the analogies canbe stated , quantitatively only to the extent that the soilapproaches one of the two extremes.

SS, SLS and SSLS SoilsOne of the two extreme types of soil to be considered is free

of colloidal material, for example, sand, silt, or coarse clayfractions, separately or in combination. These will bedesignated "SS soils" to imply direct solid-to-solid contactsbetween particles. Each particle is wedged among its neigh-bors and the pore geometry is fixed. A change in watercontent causes a displacement of the air-water interfacewithin the pore system, but no change in the bulk volume of

1 Contribution from the Department of Agronomy, CornellUniversity, Ithaca, New York, as Agronomy Paper no. 692. Thiswork was supported in part by USA Cold Regions Research andEngineering Laboratory, Contract DA-11-190-ENG-23 and in

Eart by Regional Research Project NE^tS. Presented before Div.-1, Soil Science, Society of America, Nov. 18, 1964. Received

Dec. 4, 1965. Approved Aug. 15, 1966.2 Ingenieur, Dienst der Zuiderzeewerken, Den Haag, Nether-lands, and Professor of Soil Physics, Cornell University, respec-tively.

the soil. The configuration of the air-water interface obeysthe surface tension equation and reflects the differencebetween the pressure in the air and the pressure in the water,the pore geometry, the surface tension, wetting angle, andprevious history of wetting and drying.

At the other extreme is soil in which the particles are alwaysseparated by liquid water, as in a suspension of sodium-saturated montmorillonite clay. These will be designated"SLS soils." A change in water content of SLS soil is accom-panied by corresponding changes in particle spacings and inthe bulk volume. Macroscopic cracks may open or close, butotherwise, the air phase does not penetrate the spaces betweenthe particles.

Since most soils combine both types of behavior in somedegree, they may be designated "SSLS soils." Given asufficient change in water content, SLS soil may become SSLSor even S S soil.

The Soil Water Characteristic (SWC)The affinity of soil for water depends upon water content in

a complicated way. A graphical representation of this iscalled the soil water characteristic (SWC) but usually includesonly some of the possible relationships. We will apply theterm to the drying curve of an initially saturated soil plus are wetting curve, if determined.

The affinity of soil for water will be expressed as thequantity (AP0 — APro), sometimes called "matric suction",where AP0 is the gauge pressure of the soil atmosphere andAPro is the gauge pressure of an external body of water inequilibrium with the soil water but separated from it by aporous membrane that is pervious to water and its solutes butis impervious to soil particles and to the gaseous phase. Asmentioned in the earlier paper (11), the external water is in ametastable state whenever (AP0 — APW) > 0; it is super-saturated with dissolved air whether AP0 > O or &PW < O,or both.

The Soil Freezing Characteristic (SFC)The concept of the soil freezing characteristic (SFC) is like

that of the SWC except that ice is substituted for air, air beingexcluded from the system. In graphical form, it shows therelationships between the unfrozen water content of the soiland the quantity (AP; — APJ where AP< is the gauge pressureof the ice. APro has the same meaning as before. Theexternal water is again metastable; this time it is supercooled.

The temperature of the soil-water-ice system may be usedinstead of the quantity (AP< -AP») if either AP< or AP» isknown. If this is done, the effect of solutes on freezingtemperature must be taken into account.

In the absence of solutes, the equilibrium temperature andthe pressures in the respective phases are related by anequation given in standard textbooks (9):

AT1 = - (Ft-AP< - [1]

680

KOOPMANS AND MILLER! SOIL FREEZING AND SOIL WATER CURVES 681

where AT7 is the deviation from the ice point, T0, in degreesKelvin; V is the specific volume, and AH is the specific heatof transition. Subscripts i and w refer to ice and water phases,respectively. This equation is an approximate form that issatisfactory when AT" is small. If solutes are present, asecond term ( — 1.86 S c,, where c,-.is the molal concentrationof the jth species) must be added to the right hand side. Inour experiments, APW was always zero and AT was controlledat various values. AP,- was computed using [1] with the solutecorrection if appropriate.

SWC and SFC for SS SoilFor SS soil, the analogy between the SWC and the SFC is

based on the following assumptions :1) The surfaces of soil particles exposed to soil air retain an

adsorbed film of mobile water and a similar film exists at thesurfaces of particles in contact with ice as proposed by Taber(15). The films may not be of equal thickness or identicalproperties, but if the specific surface of the soil is not largeneither film makes a significant contribution to the (unfrozen)water content.

2) The pore geometry is stable.3) The contact angle between (unfrozen) water and a soil

particle is about the same whether the complementary phaseis air or ice.

4) The specific surface energy (surface tension) of theice-water interface is independent of crystallographic orienta-tion of the interface, or nearly so.

5) The pressure discontinuity, (APa — APJ, at a curvedair -water interface is given by 2<rau,/r where <raw is the specificenergy of the interface and r is the mean radius of curvature.The corresponding expression for a curved ice-water interfaceis (APi - APJ = 2<riu/r.

6) Stresses in the ice phase are isotropic and can beexpressed by the quantity AP,-. This can be rationalized byassuming that when the interfacial curvature changes fromplace to place, there is a corresponding change in the pressurein the liquid phase so that the stresses in the ice remainisotropic. Since this condition must exist at an air-waterinterface (stresses in the air phase are isotropic) it can beassumed to hold when the ice phase is substituted for air.

If the assumptions are valid, it follows that any configura-tion of an air-water interface within the pore system of SSsoil can be reproduced by an ice-water interface, and the(liquid) water content will also be reproduced. When themean curvatures of the respective interfaces are the same,we find that

[2](APa - APtt) = (<raw/o-iw)

SWC and SFC for SLS SoilThe analogy between the SWC and the SFC for SLS soil is

based on the following assumptions:1) All of the water present is "absorbed" water which

completely surrounds every particle. The air phase isexcluded from the spaces between particles except in macro-scopic cracks that may form as a result of aniso tropic expansionor contraction of the soil mass.

2) The water present is mobile.' 3) The affinity of SLS soil for water depends upon water

content, wetting and drying history, and on solutes thatappear in the external water.

If these assumptions are valid, it is immaterial whether SLSsoil is confined by ice, air, or any inert substance. All thatmatters is the pressure exerted on the soil mass relative to thepressure in the external water. At corresponding points onthe SWC and the SFC, the water contents will be the same and

(AP0 - (AP( - APB) . [3]

The Ratio oaw/iwaTo demonstrate the expected analogies between the SFC

and the SWC for SS soil, it is necessary to know the ratio ofthe specific surface energies of the air-water and the ice-waterinterfaces, cr^/o-.-^, (see [2]). As a rule, actual values of <raware slightly below the handbook values owing to unavoidableimpurities. It is more difficult to know what value to use for<JiW since estimates given in the literature are in pooragreement.

If the hypothesis being tested is correct, it is possible toobtain an estimate of the ratio by pooling all data from SSsoil measurements. At any stage in the measurement of theSWC, with APB = O, we find from [1]:

AP,- = -(AH/T0Vi)AT = -11.1 AT bars. [4]

Follow ing a corresponding path to the same water content inthe SFC measurement, we find from [2]:

[5]

[6]

Eliminating APt- from [4] and [5] we have :

= 11.1 (<raw/<riw) bars/degree .

Hence by finding values of AP0 and AT that produce equalwater contents on corresponding legs of the SWC and the SFCfor each SS soil and plotting them (see Fig. 1), they shouldconform to a single straight line passing through the originwith slope 11.1 (<7aw/aiw) bars per degree, despite hysteresiseffects. If the points do conform to a single straight line, thisis a functional test of the hypothesis, and the observed slopecan be used to compute the apparent value of the ratio.

A different result is expected for SLS soil (see Fig. 2). Withthis soil, one expects points conforming to a straight line tofit the relation:

AP«/(-AT) =11.1 bars/degree [7]

obtained using [3] in place of [2].

EXPERIMENTALSFC and SWC data were obtained, in turn, from each of a

series of samples placed in an apparatus that served first as adilatometer and then as a pressure plate apparatus (R.W.R.Koopmans, 1965. Soil freezing and soil water characteristic curves.Ph.D. thesis, Cornell University, Ithaca, N. Y.). Soil saturated

682 SOIL SCI. SOC. AMEH. PROC., VOL. 30, 1966

c/1£_03.Q

4.0

3.00)

2.0 •4-8/i Experiment I• 2-4c Experiment .1o4-8"ExperimentIIQ2-4c Experiment!!V4-8c ExperimentHI

O -0.10Temperature

-0.18°C

Fig. 1—Relationship al equal (unfrozen) water contents of freez-ing temperature in SFC measurements to air pressure in SWCmeasurements for SS soils. Half-shaded symbols are forrewetting and thawing stages.

with de-aired water filled a cylindrical chamber of brass or stain-less steel with an internal diameter of 1.2 cm and a length of 4or 10 cm. A tubular tensiometer cup with an outside diameter of0.45 cm was mounted at one end and extended almost to the other.As ice formed in the soil, the volume change forced water throughthe tensiometer cup into a calibrated capillary. The volume of iceformed was computed, and the volume of unfrozen water in thesoil was found by difference.

Freezing was initiated in a small chamber connected to thesoil chamber by a metal tube soldered into a threaded plug thatserved as the end of the chamber opposite the tensiometer mount-ing. To start an experiment, the assembly was immersed in abath and brought to a temperature slightly below OC. The as-sembly was raised until the nucleating chamber was above thesurface of the bath, but the soil chamber remained submerged.The nucleating chamber was touched with dry ice for a momentand the assembly was again submerged. The following day, thevolume of water in the capillary was recorded. The temperaturewas lowered slightly and the capillary was read again the nextday. This process continued until the temperature reached about— 0.15C. The bath temperature was then raised slightly eachday, until all ice had melted.

When SFC measurements were complete, the soil chamberwas removed from the bath and brought to room temperature,20 ± 1C. The nucleating chamber was disconnected and an airline attached in its place. A larger calibrated capillary and abubble trap were connected to the tensiometer, with the chamberoriented to give a vertical channel from the tip of the tensiometercup to the bubble trap. The volume of water released as air wasintroduced at controlled pressures was measured, the pressurebeing increased by steps to about 4 bars and then decreased bysteps to zero. The equilibration periods used are described underResults. The initial volume of water in the sample was found byadding the volume of water remaining in the soil at the end of theexperiment to the net volume of water that remained in thecapillary. Corrections for evaporation from the capillaries wereobtained from a set of dummy capillaries. A correction was foundfor the volume of ice formed in the nucleating chamber. Correc-tions for differential thermal expansion were found to be negligible.

Materials for all but one of the experiments were obtained froma laboratory stock sample of New Hampshire silt (approximately7, 85, and 8% sand, silt and clay, respectively). The whole soilwas used to simulate SSLS soil. SS soils were simulated by 2-4juand 4-8M silt fractions isolated by repeated sedimentation anddecantation following pretreatment with H2O2 and a dispersingagent (Calgori).

One experiment used a sodium-saturated Wyoming bentonite(KWK montmorillonite) to simulate SLS soil. After removingparticles coarser than 2/x by gravity sedimentation, the clay wasalternately mixed with 0.1M NaCl and concentrated by centri-

(fl<D

CL

3.0

20

1.0

icorrected curve

O . -0.10 -Q20Temperature °C

Fig. 2—Relationship, at equal (unfrozen) water contents offreezing temperature and air pressure for SLS soil (cf Fig. 2).

fuging. Excess NaCl was removed by substituting distilled waterfor the NaCl solution and continuing the process until the Cl~content was <10~5M. Soil materials were stored under water,and before use were thoroughly de-aired by boiling at reducedpressure. The soil chamber was filled by slowly decanting aslurry into the chamber, allowing time for the sediment to settle.Some of the excess water overflowed; the rest was drawn throughthe tensiometer by gentle section. This was continued until thesediment reached a level that would leave no free space in thechamber when the threaded plug was in place. No air remainedin the chamber when the plug was seated.

RESULTSSWC and SFC data obtained with each sample are plotted

in Fig. 3-7, but it was necessary to find the value of the ratio(cTaw/^iw) before plotting the data for SS soils in Fig. 3, 4,and 5. The ratio was evaluated in the manner describedabove using points obtained by interpolation of the raw dataand plotting these in Fig. 1. Preliminary inspection suggestedthat SWC data at low water contents shown in Fig. 3 and 4were not equilibrium points. The time allowed for equilibra-tion was about 24 hours for each point in both SFC and SWCmeasurements shown in Fig. 3 and 4. The freezing and thedrying stages were repeated (Fig. 5) with a fresh sample of oneof the SS materials (4-8/Li). This time, the equilibrationperiods were increased to 8 days in the SWC measurements assoon as a significant release of water had been observed. Therest of the time, 24-hour equilibration periods were used, asbefore. The longer equilibration times brought the SWC datainto close agreement with the SFC data. It is reasonable toexpect more rapid equilibration in the SFC measurementssince only about one-tenth as much water actually leaves thesample, the rest merely changes to ice in situ.

In Fig. 1, points judged to be nonequilibrium points arerepresented by miniature symbols. A least-squares fit of theremaining points yields the relation: APa = 24.4( — AT) +0.018 bars with a standard error of 1.6%. Substituting theobserved slope into [6] yields the apparent value of the ratioffaw/viw = 24.4/11.1 = 2.20. If ff aw had its handbook valueat 20C (72.7 dynes/cm) the apparent value of <riw would be33.1 dynes/cm. The actual value of aau, was probablysomewhat less than 72.7, owing to impurities, so that theactual value of a,w was probably less than 33.1. For compari-son, Hesstvedt (7) has recently computed a^ = 31.7(1 +0.93 X 10~2 AT) dynes/cm using data for the homogeneousnucleation of ice. The value of aiw is uncertain, but the value

KOOPMANS AND MILLER: SOIL FREEZING AND SOIL WATER CURVES 683

AIR PRESSURE, bars2 3

I,40

o ,

I 30

20OOQL

10

o freezing• thawingV dryingT wetting

0.5TEMPERATURE,

1 U1 1.5 2C, & ICE PRESSURE, bars

-0.2°

Fig. 3—Soil freezing characteristic (SFC) data for second freezesthaw cycle and soil water characteristic (SWC) data for SSsoil, 4-Sfi. fraction.

AIR PRESSURE, bars2 3 4

0.5 f Q1° 1.5 • 2TEMPERATURE, °C & ICE- PRESSURE, bars

-0.2°

Fig. 5—SFC data for second freezing, and SWC data for drying(with prolonged equilibration periods at low water contents)for SS soil, 4-8ji fraction.

AIR PRESSURE, bars2 3

o freezing• thawingV dryingT wetting

0.5 I'0'1" 1.5 2TEMPERATURE,°C.& ICE PRESSURE, bars

-0.2°

Fig. 4—SFC data for second freeze-thaw cycle and SWC datafor SS soil, 2-4/i fraction.

of the ratio, 2.2, is probably a good working value. Tempera-ture and pressure scales in Fig. 3, 4, 5, and 7 have beenconstructed using this value.

Equilibration times for SWC measurements with SLS soilranged from 2 to 5 days, and with SSLS soil from 1 to 3 days.Both of these soils contained relatively large proportions of(unfrozen) water at the lowest temperatures and the highestpressures used in these experiments.

For SLS soil, the analogue of Fig. 1 is given in Fig. 2. Theobserved slope, by least-squares fit, is 10.7 bars- per degree,very close to the expected value of 11.1. The line should passthrough the origin, but has an intercept at —0.014C. This isattributed to solutes formed by hydrolysis and decompositionof the homoionic clay. Solutes would tend to decrease theslope if they are concentrated in the unfrozen water as iceforms. The maximum effect would be obtained if the effect onfreezing temperature, with zero ice present, increased ininverse proportion to the fraction of the water that is convertedto ice. "Corrected" points were calculated on this basis,

n 1st freezingo 2nd f reezing• 1st thawing• 2nd thawingv dryinT wetting

1 2TEMPERATURE, °C, & PRESSURE, bars

Fig. 6—SFC and SWC data for SLS soil, Na-montmorillonite.

AIR PRESSURE, bars2 3

o freezing• thawingv dryingT wetting

-O 2°

O 1 2TEMPERATURE,°C, & ICE PRESSURE, bars

Fig. 7—SFC data for third freeze-thaw cycle and SWC data forSSLS soil, New Hampshire silt. Data have been plotted as ifthe soil were an SS soil.

684 SOIL SCI. SOC. AMEH. PROC., VOL. 30, 1966

yielding a line with slope 11.5, only slightly greater than theexpected slope. Thus the expected relationship for SFC andSWC data "has been demonstrated for SLS soil, and is verydifferent from the relationship for SS soil.

SFC and SWC data are plotted in Fig. 6 using the theo-retical relationship [7] between temperature and pressurescales but with the temperature scale displaced by 0.014C tocompensate for the initial solute content of the sample.

Data for SSLS soil have been plotted in Fig. 7 as if thiswere SS soil. The agreement between SFC and SWC data inthe ranges measured indicate that the water frozen, ordisplaced by air, in this soil was "capillary" as opposed to"adsorbed" water. Nothing can be said, however, about thestatus of the water that was neither frozen nor displaced.

DISCUSSIONThe results shown in Fig. 5 demonstrate that discrepancies

between SFC and SWC data in Fig. 3 and 4 are not a fault inthe hypothesis being tested, but represent an error in estima-ting the time required to reach equilibrium in fine silt fractionsthat are devoid of clay. Shorter equilibration periods wereevidently sufficient when some clay was present (Fig. 7).Equilibrium was evidently approached rapidly in SLS soilalthough longer times might have been desirable for some ofthe large steps used in the rewetting stages.

We conclude that the hypothesis being tested was correct,and the assumptions behind the hypothesis are presumablycorrect. If so, the results have other implications.

For many years, soil physicists have wondered if the SWCdetermination might be affected by spontaneous nucleationof air bubbles in relatively large pores that remain filled athigh values of suction because surrounding pores are too smallto permit entry of the air-water interface. It is well knownthat bubbles appear spontaneously inside tensiometers, whichcan be viewed as extreme examples of such pores. As a result,tensiometers must be de-aired at regular intervals, but if AP^falls below about —0.8 bar, the problem becomes acute.A similar situation occurs with pressure plate and pressuremembrane extractors; bubbles form in the supersaturatedwater beneath the plate. The question is, do isolated bubblesalso form in some soil pores as APW decreases, or as APaincreases?

Since we obtained substantially the same results from SFCand SWC measurements at suctions up to about 4 bars, weconclude that isolated bubble nucleation did not occur to anysignificant degree in the SWC measurement. If it had, thenit would have been necessary to assume that bubble nucleationwas matched, pore-for-pore, by ice nucleation in the SFCmeasurement. Since it is easy to supercool water in soil byseveral degrees without nucleating any ice crystals at all (2).we are confident that it did not occur in these experiments.The data for SSLS soil (Fig. 7) are the most significant, sincethis soil undoubtedly had a wider range of pore sizes and atleast some metastable water at any given point on the SWCcurve.• The results clarify long-standing questions in the interpreta-tion of freezing point depression measurements of soils.Schofield, 'in proposing his pF scale for soil water (13), gave arelationship between pF and the freezing point depression

which is equivalent to our equation [1] if AP; is taken to bezero. Edlefsen and Anderson (4) regarded this assumption asplausible, but unproved, and developed an alternate modelinvolving hypothetical force fields that attract the watersubstance, whether in the vapor, liquid or solid state, towardsoil particles to explain why the freezing point was depressed,rather than elevated when APW < 0. They might havedropped this idea had they recognized two things: (i) The roleof surface energy and curvature of the ice-water interface insustaining water and ice in equilibrium at unequal pressures,and (ii) the significance of Taber's observation that ice tendsto form in large masses (ice lenses) when the soil is not rigidlyconfined (frost heaving). These lenses must form at ambientpressure, i.e., at atmospheric pressure in an unconfined sample.Our results demonstrate that the force-field model of Edlefsenand Anderson can be replaced by a much more straightforwardmodel that introduces no unknown phenomena and givesquantitative agreement between theory and experiment.

If our results clarify the freezing point depression phenome-non in soil, they also reveal a new problem. The Beckmanmethod as adapted to the measurement of the freezing pointdepression of moist soils normally involves inducing freezingin a slightly supercooled sample (14). The temperature risesto a point taken to be the freezing point of the sample andthen declines toward the bath temperature. The amount ofice formed during the period of rising temperature is estimatedand subtracted from the initial water content of the soil toobtain the water content that corresponds to the observedfreezing point depression. Aside from experimental uncer-tainties in this procedure, there are theoretical complications.Since the surface tension of the air-water interface exceedsthat of the ice-water interface, ice can enter some pores fromwhich air may be excluded at the prevailing suction, if thesoil is SS or SSLS soil. Thus a finite volume of water couldfreeze even if the curvature of the air-water interface weresomehow kept unchanged. This volume should not besubtracted from the initial water content, and the undercoolingcorrection may be larger than it should be by an undeterminedamount. This may explain the anomalies that led Campbell(3) to abandon attempts to apply undercooling corrections.

Our results also explain, qualitatively, discrepancies ob-served by Williams (16) in his attempt to relate the unfrozenwater content in saturated soils at various temperatures tothe pF (SWC) curves for those soils using Schofield's equation.According to our findings there should be no discrepancies forSLS soil, but there would be an error factor of (aaw/ffiw), orabout 2.2 for SS soil. For SSLS soil, the factor should bebetween 2.2 and unity, and might vary with the pF. Thediscrepancies observed by Williams are consistent with theseremarks.

MURTI ET AL : SOIL ADSORPTION OF LINEAR ALKYLATE SULFONATE 685