TRANSPORTATION RESEARCH RECORD 1307 291

Measuring Negative Pore Water Pressures in a Freezing Environment

D. G. FREDLUND, J. K. GAN, AND H. RAHARDJO

The measurement of negative pore water pressures is essential more significant in and clays depending on the temper­ to the study of behavior in a freezing environment. Various ature gradients and the rate of freezing (2). The suction just devices are now available for suction measurements in unfrozen, below the frost front can range from 6 kPa in to 400 kPa unsaturated . The possibility of using these devices in the in Leda (3). The suction values in the frozen zone increase measurement of negative pore water pressures under freezing conditions is discussed. The thermal conductivity sensor appears with decreasing temperatures below 0°C. to be a promi ing device for suction measurement. The thermal Water can exist in three phases as shown by a phase diagram conductivity method of suction measurement in a freezing envi­ (Figure 2). The fusion curve, OC, is associated with the freez­ ronment is examined. The theory of freezing soil and the thermal ing and thawing processes. At a given temperature, T, ice properties of soil are presented. Suction mea ·urements in a freez­ and water can coexist under a specified pressure as determined ing environment u ing thermal conductivity ens rs from recent by the fusion curve, OC. The slopes of the curves on the tests conducted at the University of Saskatchewan are also pre­ sented. The results are interpreted using the theory of freezing phase diagram in Figure 2 are described by the Clausius­ soil and the thermal properties of soil. The latent heat of fusion Clapeyron equation (4) . For the fusion curve, OC, the slope associated with the water phase transformation of water has sig­ has the following relation: nificant influence on the thermal conductivity reading of the sen­ sor during freezing and thawing. The formation of ice on freezing dP L makes the interpretation of sensor reading difficult because of (1) dT the significantly higher thermal conductivity of ice than that of Tv.,. water. where

The negative pore water pressures in a soil or soil suctions dP = change in pressure; affect the moisture flow , volume change, shear strength, and dT = change in temperature; frost-heaving characteristics of a soil as it freezes. There is L = latent heat of fusion, which is the heat liberated when therefore a need for reliable techniques to measure negative water turns to ice or the heat absorbed when ice turns pore water pressures in a freezing environment. Various tech­ to water (i.e., 333 kJ/kg) ; niques are now available for measuring soil suction in un­ T = temperature (°Kelvin); and frozen soils. Of these techniques, the thermal conductivity v ... = specific volume of water [i .e., l ip... where p ... is the 3 sensor appears to be one of the most promising devices. The water density (1,000 kg/m )] . suitability of the thermal conductivity sensor for in situ suction Equation 1 has commonly been used to calculate the suction measurements in a freezing environment is evaluated. developed in the freezing fringe . Williams (2) defined the suction in the frozen soil as the difference between the ice

and the pore water pressures (u 1 - u,.,), where u1 = ice pres­ PHYSICS OF THE PROBLEM sure and u, ., = . The ice pressure, u1, is usually assumed to be constant (e.g., atmospheric pressure, As temperature drops below 0°C, some soil waters freeze or u1 = 0 gauge). This definition of suction is analogous to producing ice in the soil. Consider the situation of a thermal the matric suction definition in an unsaturated soil. The pres­ gradient with the coldest temperature at the ground surface. ence of suction results in a lower freezing temperature from Figure 1 (I) shows a typical temperature gradient in a soil that of the normal freezing temperature of 0°C or 273.15°K under freezing conditions. Water moves from the unfrozen (5). The suction in the frozen soil can be related to the low­ zone to the frozen zone through a thin partially frozen fringe. ering of the freezing temperature below 0°C (i.e., dT0 ) using The frozen zone slowly advances to a greater depth below Equation 1. the ground surface.

The ability of water to move upward to the freezing fringe d(u - u,..) L 1 (2) is attributed to the deve lopment of a negative pore water dT pressure (suction) gradient through the frozen fringe as shown 0 in Figure 1 (I). The suction can be negligible in , but where normal freezing temperature in Kelvin (i.e. , 273. 15°K D. G. Fredlund and J. K. Gan, Department of Civil Engineering, University of Saskatchewan, Saskatoon, Saskatche wan, Canada S7N or point 0 in Figure 2); and OWO. H. Rahardjo, School of Civil and Structural Engineerin g, Nan­ freezing point depression, either in degrees Celsius yang Technological Institute, Singapore 2263. or Kelvin. 292 TRANSPORTATION RESEARCH RECORD 1307

LOG APPLIED PRESSURE TEMPERATURE SOIL SUCTION HYDRAULIC Pa 0 CONDUCTIVITY

z l(<

Tw RATE• v0 Ku WATER AT P•O

FIGURE 1 Schematic description of a freezing system (1).

distribution, and (f) surface charged density. Generally, the c smaller the particles, the greater the amount of unfrozen water 22,090 ------present at any temperature below freezing (Figure 4) . As FUSION CURVE freezing progresses, it becomes increasingly more difficult to freeze the remaining water. The freezing point depression is SOLID caused by the increasing surface forces on the water as the 0 Q. freezing advances closer to the particle surface. .. LIQUID A. 101 ------l&I Thermal Conductivity er :J fl) fl) In a soil, heat is transferred by direct thermal conductivity, l&I er 0.61 k, which is defined as the amount of heat that is transferred Q. 0 VAPOR in a unit time through a unit length of the soil with a unit SUBLIMATION cross-sectional area under a unit temperature gradient. The CURVE thermal conductivities of the various constituents in a soil are 273.15 373.15 647.15 different and must be combined to give the apparent thermal TEMPERATURE,T (K) conductivity of the soil. As the proportions of the constituents are changed , the apparent thermal conductivity of the soil FIGURE 2 Phase diagram for water (not to scale). will also change. Typical values of thermal 1.:umludivilies of various constituents of a partially frozen soil are given in Considering a constant ice pressure (i.e. u; = 0) and rear­ Tables 1-3 (7) . For a given soil, the bulk density of the soil ranging Equation 2 yields an equation for the suction in the particles remains fairly constant. However, there are signif­ frozen soil: icant changes in the proportion of the frozen and unfrozen water contents as the water freezes. L The thermal conductivity of ice is approximately four times d(-u,v) = - -- dT 0 (3) greater than that of water (Figure 5). As the ice content in a To Vw soil increases, the unfrozen decreases. During The d( - uw) term in Equation 3 refers to an increase in freezing, it is anticipated that the apparent thermal conduc­ tivity of the soil will increase. suction as the freezing temperature is lowered by dT0 from 0°C. In other words, the suction increases as the temperature decreases below 0°C. Equation 3 is plotted in Figure 3 to­ gether with typical experimental data (2). Heat Capacity

The heat capacity of a soil refers to the quantity of heat that RELEVANT PROPERTIES OF PARTIALLY is required to raise the temperature of a unit mass of the soil FROZEN SOILS by l °C. The heat capacity of a partly frozen soil is simply the sum of the heat capacities of its constituents. When freezing Water in a porous medium, such as soil, does not all freeze occurs, the heat capacity appears to increase significantly be­ at a single freezing temperature (Figure 4) (6) . The freezing cause of the latent heat of fusion that is required in the water­ characteristics of the pore water are dependent on many fac­ ice phase transformation. The specific heat capacity, c, is the tors. Among these factors are (a) mineralogical composition, heat capacity of the soil per unit weight. Typical values of (b) specific surface area of soil solids, (c) surface forces, (d) specific heat capacities of soil constituents are presented in osmotic potential of soil solution, (e) grain size and grain size Tables 1-3 (7). Fredlund et al. 293

AT -4.~ °C • SUCTION• ~.6 MPa ~ -1 .0

'O II .u o LEDA CLAY KNB • IRON ORE w t NIAGARA SILT ~ - o . ~ o WINNIPEG CLAY 8 I- " LEDA CLAY GC "' <( a:: A w c.. ::!! w • 0 I- oL_~_jl,__-=:=:t-==:::r:=:I::..i.~~--1.~~--L~_L--L--L~~....J• 0 .1 0.2 0.4 o.6 o.e 1.0 2.0 4.0 6 .0 e.o 10 .0 20.0 SUCTION ( xlOO kPa l FIGURE 3 Theoretical and experimental relationships between temperature and suction at atmospheric pressure (2).

1.4 TABLE 2 PHYSICAL PROPERTIES OF LIQUID WATER (7) : A WYOMING BENTONITE, NATURAL Latent B KAOLINITE Specific Thermal Heal or "' 1.2 c RUST ( Fe, o.i Temp Dcnsily Heat Conductivity Evaporation ..... ~ l q ( kg/ m3 ) (kJ/kg° C) (W/m K) (kJ/kg) 0 0 LIMONITE c· £ E W. LEBANON GRAVEL< 1001' .10 997.94 4.268 2523 "' 1.0 FAIRBANKS SILT F -5 999. 18 a:: w 0 999.87 4.2150 0.561 2499 I- 0 El <( 4 100.00 j: . 999.99 4.1995 0.574 2487 ~ 0.6 10 999.73 4.1894 0.596 2476 N 15 999.13 4.1832 0.595 2464 0 J •A a:: ~~-- 20 998.23 4.1790 0.603 2452 u.. 0 .4 ...... \Aoy."'":-.. ... z I\ • 25 997.08 4.1769 0.611 2440 ::::> ,....; ,e 30 995.68 4.1756 0.620 2428 ~·, c ..... 35 994.06 4.1752 0.628 2417 E'I'?~ ...,,,."'" 40 992.25 4.1756 0.632 2405 ------0 ~1'"-···:: 45 990.24 4.1765 0.605 2393 o -2 -4 -6 -e -10 so 988.07 4.1777 0.645 2381 TEMPERATURE ( °C) FIGURE 4 Variation of unfrozen water content with temperature for six The phase transformation takes place without any change in representative soils and soils constituents (6). temperature.

TABLE 1 THERMAL PROPERTIES OF SOIL Thermal Diffusivity CONSTITUENTS AT 20°C AND 1 atm (7) Specific Thermal Thermal The thermal diffusivity, ct, of a soil is given by Density Heat Conductivity Diffusivity p c k a Material (kg/m3) (kJ/kg 0 c) (W/m K) (10-7 m2/s) k ct (4) Quartz 2650 0.732 8.4 43 pc Many soil minerals• 2650 0.732 2.9 43 • 1300 1.925 0.25 15 where Water 1000 4.184 0.6 1.42 k thermal conductivity, Air 1.2 1.004 0.026 0.21 c = specific heat capacity, and • Approximate average values p density. Thermal diffusivity controls the rate at which a temperature Latent Heat change spreads through a mass. The thermal conductivity of ice is approximately four times that of water. The specific The latent heat of fusion is the heat or energy that is required heat capacity of ice is approximately half that of water. Con­ in a phase change (e.g., from a liquid to a solid phase, or vice sequently, the diffusivity of ice is about eight times the dif­ versa). For water, the latent heat of fusion L, is 333 kJ/kg. fusivity of water. Therefore, in a frozen soil, temperatures This means that 333 kJ of heat is liberated when 1 kg of water can change faster and to a greater extent than in an unfrozen turns to ice, or is absorbed when 1 kg of ice turns to water. soil. 294 TRANSPORTATION RESEARCH RECORD 1307

TABLE 3 PHYSICAL PROPERTIES OF ICE (7) Specific Thermal Latent Latent Heat Conductivity Heat of Heat of Temp Density c (cal/cm s •c) Sublimation Fusion (•C) (.kg/cm 3) (kJ/kg•c J (W/m Kl (kl/kg) (kJ/kg) -20 920 1.958 2.433 2836 289 -10 919 2.029 2.319 2835 312 0 917 2.105 2.240 2833 333

"f s 30 '311 .. ICE I 'o I . ______1... ______1... ______I1... ______20 >­ I I I .... I > I 1I I' ;:::: I I u I I ::> c I I 1 z I J J 0 10 ------r------r------r------u 1 I .....J 1 WATER I :Ii a:: :r"' .... O +-r--.-.--.-...... ,...... ,,-n,.,.,,.,-,...... ,...... ,,-nn-r.-r.-.-r-r+-.....-.....-.....-,.-,-T+,.-,-,.-,-.,...,...,...,....-1 - 20 - 10 0 10 20 30 TEMPERATURE ("Cl FIGURE 5 Thermal conductivity of ice and water at various temperatures.

In a fine-grained soil, the water in the pores freezes grad­ 160 ually. Its latent heat is therefore released in stages (Figure 6) 140 (8). The rate of the heat released reduces with decreasing """' --A-w•lllO._ temperatures. The result of a release in latent heat is a sudden ..,' 120 --<>- w •100 .. change in the specific heat immediately below the temperature ...J 0 at which freezing begins (Figure 7) (9) . The latent heat acts I/) 100 similar to a large sink in which ht:al is rdt:ased or absorbed >- without any change in temperature. This sudden change in ~ BO the specific heat causes a corresponding sudden change in the '"' ....>- diffusivity (e.g., Figure 8) (10) . u 60 100 ~ FIGURE 7 Relationship between heat ..J 0 capacity and temperature of a partially 0 BO 0 frozen bentonite (9). >- Ill 60 0w SUCTION MEASUREMENT TECHNIQUES (/) <( 40 w Several techniques are available for suction measurements in w..J a:: 20 an unfrozen soil. These techniques include (a) tensiometers, ..... <( (b) psychrometers, (c) filter paper methods, and (d) thermal w conductivity sensors. Some of these techniques have also been :I: 00 - 2 - 4 -6 ·B - 10 used for frozen solids. The psychometric and filter paper tech­ TEMPERATURE ("C) niques do not require intimate contact with the soil. The other FIGURE 6 Latent heat released on cooling techniques require the use of a porous medium in intimate below 0°C (8). contact with the soil and allowing the suction in the medium Fredlund et al. 295

~ IOJfii'Jl!JiC:::~~,...--.-----.~"T"---.r--r--.---, limited to approximately - 90 kPa because of cavitation of ~:; 8 water in the tensiometer. :> ...... LL E Ingersoll and Berg (11) have used tensiometers for meas­ ~ u 6 c uring negative pore water pressures under freezing conditions. ..J70 4 The tensiometer cups were installed along a cylindrical soil

80 ~~r · ------" ,r'",,,, ~ 60 I ,. I I I I ~ 40 I i= I u I :> I ~ "' 20 m _J / 0.05 0 ! 0.10 m "' 28 30 2 MARCH 1980 + APRIL 1980 26 28 30 2 4 4~~~~~~~...-~_,..~~..-~--.-~~..-~~~~..-~-.

2 a.. ...i= 0 01---~~~~~,...-~~-"""--=-~~~~~~~~~~~~- a: "':> 1- : -2 a.. ::i:"'

I-"' - "' FIGURE 9 Suction measurements using tensiometers in a freezing environment (JJ). 296 TRANSPORTATION RESEARCH RECORD 1307 reduction in the relative humidity with decreasing tempera­ voltage output is a function of the electrical resistance, which tures below 0°C. in turn is a function of the temperature rise. The voltage outputs varies linearly with temperature and therefore the difference is not affected by the temperature of the sensor. Filter Paper Technique A single calibration is therefore adequate for all temperatures. In an unfrozen soil, a low water content in the sensor, or The filter paper technique has not been used to measure soil high soil suction, would result in a high temperature increase suction under frozen conditions. The vapor pressure associ­ in the thermal conductivity sensor. This high temperature ated with ice implies that there may be some possibility in increase indicates a low apparent thermal conductivity of the using this technique for frozen soils. Research is needed in sensor because of its low water content. In a frozen or partially this area. frozen soil, the thermal conductivity of the sensor is not only a function of the unfrozen water content, but it also depends on the ice content. Thus, in a frozen soil at a low unfrozen Thermal Conductivity Sensor water content, the temperature increase recorded by the sen­ sor would be expected to be low because of the high thermal The operation of a thermal conductivity sensor is based on conductivity of ice. the principle of heat dissipation in a porous material. The rate of heat dissipation is dependent on (a) the thermal con­ ductivity of the solid material and of the water, and (b) the RESULTS OF SUCTION MEASUREMENTS USING mass of the solid and the water. The thermal conductivity of THERMAL CONDUCTIVITY SENSORS air can be considered negligible. For a particular sensor, the mass of the solid is a constant and the rate of heat dissipated Lee (14) used heat dissipation sensors (MCS 6000) sensors in the solid will be constant. Therefore, changes in the rate both for in situ and for laboratory suction measurements. of heat dissipated in a sensor are directly related to the water MCS 6000 sensors were manufactured by Moisture Control content of the sensor. System Corporation, Findlay, Ohio. The results of in situ When a sensor is inserted into a soil, water will move be­ suction measurements conducted in a glacial till are shown in tween the sensor and the soil. The movement of water takes Figure 11. The results indicate that suction variations followed place until stress equilibrium is attained between the soil and closely the daily temperature variation. The soil suction in­ the sensor. The equilibrium water content of the sensor is an creased as the temperature approached 0°C. When the tem­ indication of the suction in the sensor and in the soil. The peratures dropped below 0°C, the sensor was not able to water content of the sensor can be calibrated against the ap­ record any suction reading. plied suction using a modified pressure plate apparatus (JJ). Van der Raadt et al. (15) used AGWA-II thermal con­ A typical sensor is made up of two parts, (a) a heating and ductivity sensors for monitoring suction changes below rail­ heat sensing device enclosed within, (b) a porous block (Fig­ way subgrades. AGWA-II sensors were manufactured by ure 10). The heater and the sensing devices are embedded Agwatronics Incorporated, Merced, California. Results of within a porous ceramic of low thermal conductivity. The suction measurements using the AGWA-II sensors from one porous ceramic should be relatively small to ensure a rapid site are shown in Figure 12. The results also show that the re ponse. However, the porou ceramic must be ufficiently suction readings increased as the temperature decreased be­ large so that the heat pulse generated is fully contained within low freezing. Several suction measurements were obtained the ceramic block. Otherwise, the thermal conductivity read­ for the soil in the frozen state. ing will be affected by the type of surroun

4LeadWires sensors. A soil column was prepared by compacting a glacial till into a PVC cylinder. The cylinder had a height of 300 mm and a diameter of 150 Epoxy Backing mm . A thermal conductivity sensor together with a thermo­ couple were embedded near the top, middle, and bottom sections of the soil column (Figure 13). The thermocouple was used to measure the temperature in the soil at the prox­ imity of each thermal conductivity sensor. The column was insulated on all sides except for the top face. The top of the Ceramic Porous column was subjected to temperatures ranging from 22°C down Media to - 20°C inside a freezing chamber. FIGURE 10 A cross-sectional diagram of The suction and temperature measurements with respect the AGWA-11 thermal conductivity sensor. to time are shown in Figures 14-16. All three sensors ap- Fredlund et al. 297

SHOWER SNOWING ~ 190 '''' ,, ' ' rr. 180 ' '' ... '""NO READING - 170 WHEN SOIL TEMPERATURE ~ 160 BELOW ZERO •c t- 150 u DEPTH • 0 . 15 m ~ 140

...J 130 ~ 120 ( 110 I

I ~ 20 ,u I • 16 .\,.I\ /\ /",.....-AIR TEMPERATURE w ."'"" '\...J \ I V"' a:: 12 -~ / •., ,, ·,1,. ,. /'--../ , .\ ,~ '\ ;:) t- 8 .,;"'-.;_;/'--·,"".... '-\ / \/ \

FREEZER UNIT 1070 mm 600 0 ~ 500 PVC CASING z 400 150 mm 0 I- 300 FIBREGLASS u ;:) (f) 200 ...J 0 100 E (f) e 0 0 NOV JAN MAR MAY JUL SEP "' 1984 19 85 FIGURE 12 Variation of soil suction with time of year for various depths of Regina clay in Saskatchewan {15). THICK STYROFOAM INSULATION peared to respond in a similar manner. As the temperature FIGURE 13 Setup for soil suction measurements using the decreased from above freezing to bel w freezing, the . ensor AGWA-11 sensor in a freezing test. reading dropped sharply. As freezing progresses, the sen or readings increased rapidly to approximately the ame readings before freezing ccur . The same b havi r was ob erved as in.crease produced by the heat pulse will be maller in a freez­ the temperature was increased from below freezing to above ing ens r a. compared to that regi tered in a nonfreezing freezing. All three sensors bowed that after thawing, the soil ensor. This phenomenon could be attributed to the tendency suctions dropped to a range of 0 to 40 kPa. of the water to maintain a con tant temperature during the pha ·e transformation. Tbe reduced temperature in.crca e in a freezing ensor would then be int rpreted from the ca li bra­ INTERPRETATION OF TEST RESULTS tion curve as a decrea ing oil suction. Thi situation i dem­ onstrated by the drops in soil suction readings as tbe tem­ As the water in the sensor begins to freeze, the apparent p rature decreases 10 0° . thermal conductivity of the sensor is affected by the latent After a major portion of the water in the sensor has frozen heat of fusion. During the freezing process, the latent heat the temperature increa e measured because of the heat pul e of fusion is released at a constant temperature. However, the depends on the proportion of ice and unfrozen water, and water in the sensor does not freeze simultaneously, but rather al o on the quantity of air bubbles pre ent. The higher ensor it freezes in a gradual manner. As a result, the temperature readings in the frozen tate are probal ly becau. e f the re- 298 TRANSPORTATION RESEARCH RECORD 1307

300 ,_ __ --. ,' I ,' ' POSTULATED ACTUAL SUCTION ~ 250 I a.... z 200 0 ;::: u ::> 150 (/)

...J 0 100 (/)

50

0

.u 25

...a: ::> I-

FIGURE 14 Suction and temperature measurements at the top section of the soil column.

300

250 a." .., 200 z ~ 150 u POSTULATED ACTUAL SUCTION ::> .r--- (/) 100 ... I ~ ...... J N z 0 ... ,/, i (/) 50 \ ...

w a: ::J ~ 0 -r-~~~~..,,__,.~~~-t-:...,.... ,.,..~ -t-~~~~ a: w a. 2 I-"' · 25 -+-r-n-rn-rn-rrrrrlTTTTTTTTTTrrrl+rT"TTrrrTTTn-rrlTTTTTTTTn""T"ri..+r-rn-rnTnTn'TI 0 7500 15000 22500 30000 37500 TIME (min.) FIGURE 15 Suction and temperature measurements at the middle section of the soil column. duced thermal conductivity caused by the presence of air The reduction in the sensor reading after a complete thaw­ bubbles. ing of the ice, is probably caused by the overwetting of the As the water in the sensor begins to thaw, the heat pulse sensor, which is followed by separation from the soil. The released in the sensor is again affected by the latent heat of separation of the sensor from the soil could be caused by the fusion. During the thawing process, the latent heat of fusion expansion of the frozen and the migration of melting is adsorbed at a constant temperature. The thawing process water upon thawing. In fact, the soil column was found to also occurs gradually within the sensor. The tendency to main­ have expanded vertically by approximately 5 mm at the end tain a con tant temperature will again reduce the temperature of the test. When the water at the contact between the sensor increase generated by the heat pul e. As a result, the suction and the soil thaws, a portion of the water may migrate into readings will drop again as the temperature increases toward the sensor pores. As a result, a gap develops between the ooc. sensor and the soil. Once the sensor has separated from the Fredlund et al. 299

~250 4-

z200 -H--'t---~~-+-­ o .... ~ 150 -tt~--T~~·-.:-ir "' =1 00 -l-l-~~~~-+-~~~-~~-1+~-1-~-~-+-~~~~-t-~~~~--t 0 "'

0 7500 15000 22500 37500 TIME (min.) FIGURE 16 Suction and temperature measurements at the bottom section of the soil column. soil, the sensor registers a suction reading depending on the 5. N. E. Edlefsen, and A. B. C. Anderson. Thermodynamics of remaining water content of the sensor. oil Moislure. flilgardia , Vol. 15, o. 2, 1943. pp. 31- 298. 6. D . M. Anderson and N. R. Morgensrcrn. Physics, Chemistry and Mechanic of Frozen Ground: A Review. Proc., 211d 111tema1io11al Conference on Pemiafrost, Yakutsk, U.S.S.R., North American CONCLUSION Contribution, National Academy of Sciences, Washington, D.C. , l973, pp. 257-288. Experimental evidence has identified the difficulties associ­ 7. W. R. Vall Wijk (ed.). Physics of Plant Environment, 2nd ed. ated with the measurement of negative pore water pressures Norlh Holland, Amsterdam, The Ne1herlands L963 , 382 pp. 8. 0 . Johan ·en. Thermal Co11d11c1i11iry of Soil . Ph.D. Oisscrta1ion, in freezing soils. In particular, the use of thermal conductivity Trondheim, Norway 1976. sensors in freezing environment is emphasized. Di tinct drop 9. P. F. Low, D. M. Anderson, and P. Hoekstra. Some Thermo­ in suction readings have been observed during the freezing dynamic Relationships for Soils a1 or below 1he Freezing Point. and thawing processes. These drops are attributed to the effect I. Freezing Point Depression and Heat Capacity. Wa1er Re­ source l~esearch Vol. 4, o. 2, 1968. pp. 379- 394. of the latent heat of fusion on the thermal conductivity mea­ .10. P. Hoekstra. Special Reporr 103: The Physics and hemi rry of surements. Also, as soil freezes, the proportions of unfrozen Frozen Soils. Effects of Tcmpera1ure and Heal on E ngineering and frozen water change. Ice and water have different thermal Behavior of Soils, HRB, National Research Council , Washing­ conductivities. As a result, the sensor readings are difficult ton, D.C., 1969, pp. 78-90. 11. J. Ingersoll and R. Berg. imulating Frost Action by u ing an to interpret and to converr lo . oi l suctions. In addition, the ln trumented Soil Column. Frost Action and Risk Assessment rigid , brittle ceramic used for the thermal conductivity ensor in Soil Medianic . In Tra11sporration Research Record 809, TRB, is susceptible to cracking caused by the expan on freezing, National Research Council, Washing1on, D.C., 1981, pp. 34- 42. especially under high water content conditions. , 12. B. P. Van Haveren. Measurement of Relative Vapor Pressure in Snow with Thermocouple Psychrometers. In Psycliro111e1ry in Waler Relmions Research, R. W. Brown and B. P. Yun Haveren (ed .). Proc., Symposium 011 Tltermocouple P ·ychromcters. Utah REFERENCES Srace University, Logan, 1972, pp. 178- 185 . 13. D. G. Fredlund, and 0 . K. H . Wong. Calibra1ion o( Thermal l. J. M. Konrad. egregation Potential- Pressure- aH nity Rela· Conduc1ivity Sensors for Measuring Soil Suction. Geo1ec/111ical tionship near Thermal Steady State for a l<1yey Silt. C01wdia11 Testing Joumal Vol. 12 No. 3, ept. 1989, pp. 18 - 194. Geoteclmical Joumal, Vol. 27, No. 2, 1990 pp. 203-215. 14. R. K. . Lee. Meas1m:mem of Soil S11c1io11 using rlie MCS 6000 2. P. J. William . The Surf"ce of the Eanli: An lmroductio11 ro Sensor. M.Sc. thesis. University of Saskatchewan, Saskatoon, G1101ech11ical Science . Longman, New York, L982, 212 pp. 1983. 3. P. J. Williams. Properries and Behavior of Freezing Soils. Pub­ 15. P. van der Raadt. Field Measurement of Soil Suction using Ther­ lication 72. Norwegian Geotechnical Institute, 1967, 120 pp. mal Conductivity Matric Potential Sensors. M.Sc. thesis. Univer· 4. B. P. Van Haveren, and R. W. Brown. The Properties and Be­ sity of Saskatchewan, Saskatoon, 1988. havior of Water i1' lhc Soil- Plant-Atmo phere ContiDuum. In Psychromerry i11 Warer Relario11s Resec1rch (R. W. Brown and B. P. Van Haveren eds.), Proc., Symposium 011 Thermocouple Psychrometers, Utah Stale University, Logan, 1972 pp. 1- 27. Publication of lhis paper sponsored by Commiftee on Frost Action.