Soil Freezing and Soil Water Characteristic Curves1
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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, Cornell
University, 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 inEart by Regional Research Project NE^tS. Presented before Div.-1, Soil Science, Society of America, Nov. 18, 1964. ReceivedDec. 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< - 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  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
682 SOIL SCI. SOC. AMEH. PROC., VOL. 30, 1966
2.04-8/i Experiment I 2-4c Experiment .1o4-8"ExperimentIIQ2-4c Experiment!!V4-8c ExperimentHI
Fig. 1Relationship 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 underResult