Simulating soil freezing conditions in the laboratory

Simulating soil freezing conditions in the laboratory Permafrost, Phillips, Springman & Arenson (eds) 2003 Swets & Zeitlinger, Lisse, ISBN 90 5809 582 7 K.S. Henry U.S.Army Corps of Engineers, Engineering Research and Development Center, Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire, USA R.D. Holtz Department of Civil Engineering, University of Washington, Seattle, Washington, USA ABSTRACT: We used a simplified energy balance to estimate the net heat flux from pavements that have been monitored for frost heave and frost penetration. The pavements are located in Finland, Sweden and the United States and represent a variety of climatic zones. A comparison of the thermal conditions experienced in the field to thermal conditions typically used in soil freezing tests indicates that freezing tests are often conducted at rates of heat extraction and temperature gradients that are high compared to those in the field. While this may be acceptable for frost-susceptibility index tests, some research requires a closer simulation of the thermal conditions experienced in the field. 1 INTRODUCTION Rate of heat extraction at the surface of and temperature distribution within a body of soil influence rate and amount of frost heave. Thus, to study the influence of factors other than these thermal conditions on frost heave, it is helpful to use thermal conditions that the soil will typically experience in the field. A capillary barrier can be constructed of a layer of coarse, porous material and placed in soil above the water table to prevent unsaturated water flow across the layer. Capillary barriers reduce frost heave in soils and pavements when they are located between the water table and the freezing front. Due to their large pore sizes, drainage geocomposites are capillary barriers. Research was performed to determine 1) the range of soil and thermal conditions under which geosynthetic capillary barriers reduce frost heave for a very high water table, and 2) material properties required for capillary barrier performance (Henry & Holtz 2001). In this paper, we present the technique and data used to select thermal conditions representative of field conditions to conduct research about the influence of capillary barriers on frost heave. 2 INFLUENCE OF HEAT FLUX AND TEMPERATURE GRADIENTS ON FROST HEAVE Loch (1979a) gave an excellent overview of the rate of frost heaving as a function of the net rate of heat extraction (i.e. heat flux) from a volume of saturated, freezing soil given that all other variables are held constant. Consider the hypothetical case that all heat extracted from the freezing zone comes from ice lens growth e.g., very low net heat extraction rate, unlimited water supply in a saturated soil, constant overburden pressure and constant end temperatures. There is no frost penetration, and the energy balance of the freezing zone indicates that rate of ice formation is limited only by the net rate of heat extraction, and that the velocity of water flowing to the freezing front v w is equal to the net heat extraction rate q net divided by the latent heat of fusion of water L f (L f 333.519 10 6 J m 3 ): v w q L net f (1) At higher freezing rates, the soil hydraulic conductivity limits rate of water flow to the freezing front, and at extremely high rates of heat extraction (imagine that the soil can freeze instantaneously), frost heave consists only of volume expansion of water. Figure 1 shows frost heave rate as a function of the rate of heat extraction for saturated soils. The upper straight line depicts the relationship between the rate of heave and rate of water flow when there is no frost penetration: v I ( v w 1.1) (q net /L f )1.1, where v I is the rate of frost heave. When frost penetrates into the soil, heave rate as a function of net heat flux deviates from a straight line. The vertical distance between the upper straight line and the curve represents the frost penetration rate. The lower dashed line represents the rate of frost heave due to freezing of in-situ pore water. The specific value of net heat flux at which maximum frost-heave rate occurs is a function of soil type and density, overburden pressure, and temperature distribution. Net heat flux is an important variable in capillary barrier testing. The vertical distance between the curve and 377

Figure 1. Rate of frost heave vs. net heat flux for a saturated soil at constant overburden pressure and constant temperature gradients (modified after Penner 1972). the lower dashed line in Figure 1 represents the maximum amount that the frost-heave rate can be reduced by the emplacement of a 100% effective capillary barrier (i.e. one that would prevent all water from migrating from below it to above it during freezing). For freezing rates occurring to the left of the maximum, the use of a capillary barrier will reduce frost heave significantly. If the soil freezes at rates that fall on the far right side of the maximum of the curve shown, a capillary barrier will not be very effective. Temperature gradients also influence rate of heave because temperatures control the amount of unfrozen water in soil and, therefore, they control the hydraulic conductivity of the frozen fringe. Konrad (1984) presented evidence that one rate of heat flux can be generated by a number of thermal gradients and that the thermal gradients also influence the heave rate. Therefore, in addition to reproducing net heat flux, it is important to simulate expected temperature distributions in soil-freezing experiments, if possible. Figure 2 presents curves developed by Konrad (1984) and Loch (1979a) for one-dimensional soil freezing. The curves from Konrad (1984) show the influence of the temperature gradients imposed on freezing soil specimens for one soil. For these tests, one end of a specimen was held at a temperature less than 0 C and the other end was held at a temperature greater than 0 C. The temperature gradients that both Konrad (1984) and Loch (1979a) imposed on soil specimens during soil freezing experiments were extremely high compared with temperature gradients that have been observed on freezing soils in the field, with the possible exception of the value of 25 Cm 1. Temperature gradients in freezing soil typically range up to 10 Cm 1 (e.g. Farouki 1981). Thus, although Konrad s (1984) and Loch s (1979a) experiments indicate trends in behavior, they do not necessarily represent field freezing conditions. Furthermore, with the exception of Loch Figure 2. Rate of frost heave vs. net heat flux for soils tested under different temperature gradients by Loch (1979a) and Konrad (1984). Figure 3. Simplified energy balance across zone of freezing for one-dimensional heat transfer in soil. (1979b), no estimates of field rates of heat flux have been made and compared with curves such as those shown in Figure 2. Thus we examined field data for freezing soil (including frost heave and frost penetration) and used these to estimate heat flux. We also noted temperature gradients in the field soils. We did this to obtain information on realistic soil freezing conditions so that we could simulate them as closely as practical for the research program regarding capillary barriers influence on frost heave. Figure 3 depicts a simplified energy balance at the freezing front, across the frozen fringe, bounded on the bottom by unfrozen soil and the top by frozen soil (i.e. all pore water is frozen). It is based on the assumptions that (1) one-dimensional heat extraction is occurring, (2) the heat flow across the boundaries is due only to conduction, and (3) the latent heat released by freezing of water between the two boundaries is the only heat generated within the volume. The net heat flux q net from the freezing front can be estimated either by knowing the temperatures and thermal conductivities of the soil above and below it 378

or by knowing the rates of frost heave and frost penetration (Equation 2 or 3): Tf qnet qout qin lf l z q net vi s Lf qw 11. t Tu z (2) (3) where is the thermal conductivity, T is temperature, q w is the volumetric water content, s/ t is the rate of frost penetration and the subscripts f and u refer to frozen and unfrozen soil, respectively. Equation 2 can be used to determine the heat flux in soil if the temperature distribution is known. This is known as the temperature gradient method (Kimball et al. 1976, Fuchs 1986). The difficulty with this approach is that, although soil temperature data are available for a number of paved roads and airfields, the thermal conductivities of those soils (which can range over an order of magnitude) at the times that the measurements were made are not known. Another approach is to use Equation 3 and evaluate field data for which rates of frost heave and frost penetration, soil layer density, and water content are well documented. We used this approach to estimate heat flux from soils in pavement systems because it is easy and does not require soil thermal conductivity determination. u Table 1. Locations for which net heat flux from pavement was estimated. Design/Mean Freezing freezing index for index year(s) Source Location Years ( C days) monitored Saarelainen Joensuu, 1982 83 1,670/Not 920 (1992) Finland available Vikstrom Lulea, 1995 96 Not available/ Not (1997) Sweden 1,100 available Henry Hamilton, 1985 86 420/Not 483 (1990) Montana available Henry Pittsburg, 1993 94, 1,100/Not 1,143 for (1998) New 1994 95 available 1993 94 Hampshire Table 2. Soil description, frost heave and penetration at Joensuu, Finland, point 14 (Saarelainen 1992) used in example. Gravimetric Volumetric Layer depth Dry density, water content, water content, description (m), d (Mg m 3 ) w(m w /M s ) q w (V w /V s ) 0.7 0.8, sand 1.8 0.154 0.277 0.8 1.1, silt 1.7 0.21 0.357 Days in Frost heave Frost penetration Date estimate (m) (m) 13 Jan 1983 0.0152 0.696 27 Jan 1983 14 0.0283 0.978 3 ESTIMATED RATES OF HEAT LOSS FROM PAVEMENTS Table 1 lists the sites used to estimate net heat flux from soils beneath pavement. A range of climatic conditions is represented, from the temperate region of Hamilton, Montana, to the subarctic of Luleå, Sweden. Freezing indices are provided to compare the locations tested. Soil density and water content information is provided along with frost penetration and frost heave records for each site for the years noted. The data from Pittsburg, New Hampshire, are reported in detail in Henry (1998). Table 3 provides detailed soil layer information used in the estimations of heat flux. We assumed that water contents in the winter were equal to those measured when the soil was unfrozen because at least one of the following conditions was met: 1. The water table level throughout the winter remained within 0.2 m of the water table in the summer (e.g. Henry 1990). 2. Frozen soil cores had water contents equal to or greater than the water contents measured in the summer (e.g. Saarelainen 1992). 3. The water table remained within 0.3 m of the location of the freezing front during the freezing season. The following procedure was used to estimate net heat flux from pavement sections: 1. We verified that the water contents measured were reasonable estimates of water contents during the freezing season. That is, we determined that at least one of the above three conditions was met. 2. If information was published as graphs of frost heave and frost penetration versus time, the graphs were digitized to develop tables of dates, frost heave, and frost penetration, estimated to be accurate to within 2% of the scales on the graphs used. This estimated error is about 1 day on the date scale, 0.003 m for frost heave, and 0.04 m for frost penetration. 3. Equation 3 was applied, using days between frostheave measurements to determine the length of the interval for which the net heat flux is estimated. Linear interpolation was used to estimate when the frost penetrated the identified soil layers. 4. An example is provided here (refer to Table 2): The freezing front crossed from the upper layer into the lower layer 5.2 days after 13 January (determined by linear interpolation). Thus, the weight given upper layer is 0.37 (ratio of time that frost was in upper layer), and that given lower layer is 0.63. The net heat 379

Table 3. Soil layer information used in estimates of heat flux. Gravimetric Volumetric Layer depth Dry density water content water content description (m), (Mg m 3 ) (M w /M s ) (V w /V s ) Saarelainen (1992), Joensuu, Finland, Point 14: 0 0.7, gravelly 1.9 0.08 1.152 sand 0.7 0.8, sand 1.8 0.154 0.277 0.8 1.1, silt 1.7 0.21 0.357 1.1, clayey silt 1.6 0.238 0.381 Saarelainen (1992), Joensuu, Finland, Point 33: 0 0.6, gravelly 1.9 0.05 0.095 sand 0.6 1.1, sand 1.8 0.15 0.270 1.1, clayey silt 1.7 0.18 0.306 Henry (1990), Montana, Station 6: 0 0.305, gravel 2.12 0.06 0.127 0.305 0.91, silt 1.58 0.25 0.395 0.91, gravel 1.96 0.04 0.078 Vikström (1997), Luleå, Sweden: 0 0.5, gravel 2.0 0.10 0.20 0.5 1.5, silt 1.85 0.38 0.70 1.5, silt 1.65 0.68 1.12 Henry (1998), Pittsburg, New Hampshire: 0 0.61, gravel 1.92* 0.05* 0.96 0.61 1.22, silt 1.96* 0.13* 0.25 (compacted) 1.22, silt 1.80** 0.15** 0.27 * Guess, based on preconstruction site investigation. ** Values obtained in preconstruction site investigation. flux during this 14-day time period that resulted in frost heave was determined as follows: 6 3 q heave 333. 519 10 J m 1 0. 0283 0. 0152 1 m s 11. 14 86400 or 3.3 W m 2. The net heat flux during the same time that resulted in frost penetration is given by: 6 3 q penetration 333. 519 10 J m (. 0 37[. 0 277] 0. 63[. 0 357]) 0. 978 0. 696 1 14 86400 m s 1 or 25.5 W m 2 for a total net heat flux of 28.8 W m 2. Henry (1998, Appendix B) contains detailed frost heave and frost penetration information used in the estimations. Net heat flux estimates are presented in Table 4 along with temperature gradient. Loch (1979b) measured heat flux from pavements with a heat flow meter for road sections in Norway from 1973 through 1975. Maximum heat extraction 1 rates from subgrade soil in Ostfold, Norway, measured in the winters of 1973, 1974 and 1975 were about 15, 42 and 124 W m 2, respectively. Thus, the values in Table 4 appear to be reasonable by comparison to Loch s (1979b) measured values. 4 COMPARISON OF FIELD ESTIMATES WITH HEAT FLUX VALUES USED IN FREEZING TESTS Heat flux rates and thermal gradients have been used in freezing tests that are somewhat higher than those that usually occur in pavement subgrades (Fig. 2). The maximum rate of heat extraction that we estimated was 66 W m 2 and the maximum heat extraction rate from a subgrade measured by Loch (1979b) was 124 W m 2. The maximum temperature gradient documented in the field data that we reviewed was 12 C m 1. For comparison, the ASTM standard test method for frost heave and thaw weakening susceptibility of soils (ASTM D 5918) imposes temperature gradients of 40 and 80 C m 1. Heat flux, assuming a thermal conductivity of 2.2 W m 1 K 1 for fine-grained soil at 15% water content and a dry density of 2.0 Mg m 2 (e.g. Chamberlain 1991) is about 88 or 176 W m 2 (Equation 3). It would be higher for higher water contents and for frozen soils. Thus, the ASTM thermal gradient is extremely high and the heat flux is somewhat high compared to field observations. We decided to match the thermal conditions that occur in the field more closely for our research rather than to use the ASTM standard, which is intended as an index test. 5 SUMMARY AND THERMAL CONDITIONS SELECTED FOR USE IN FREEZING TESTS Net heat flux and temperature distributions in freezing soil are important variables controlling frost heave. For a saturated soil with constant overburden pressure and constant temperature gradient, the rate of frost heave is a function of the net heat flux. Rate of heave initially increases with net heat flux, then it reaches a maximum and decreases until it reaches the rate of heave due to freezing of the in-situ soil water. For freezing rates that occur below the maximum heave rate, the use of a capillary barrier significantly reduces frost heave. If, however, the soil freezes at rates that fall on the far right side of the maximum of the curve shown in Figure 1, a capillary barrier will not be as effective. Temperature gradients also influence frost heave rate. Therefore, to test the effectiveness of capillary barriers, it is important to simulate conditions that soil will experience in the field. 380

Table 4. Estimated net heat flux based on frost heave and penetration measurements (q net q heave q penetration ). Temp. gradient Days in q heave q penetration q net frozen/unfrozen Date estimate (W m 2 ) (W m 2 ) (W m 2 ) soil ( C m 1 ) Saarelainen (1992), Joensuu, Finland, Point 14 1/13/83 64 0.83 6.37 7.2 NA 1/27/83 14 3.28 25.52 28.8 4.2/2.0 2/10/83 14 7.62 22.04 29.7 NA 2/25/83 15 7.63 14.91 22.5 5.0/3.3 3/10/83 13 8.21 19.67 27.9 NA 3/22/83 12 4.47 5.33 9.8 4.0/2.5 Saarelainen (1992), Joensuu, Finland, Point 33 1/28/83 14 2.12 44.71 46.8 3.0/0.0 2/09/83 12 5.77 28.20 34.0 NA 2/24/83 15 7.91 14.66 22.6 6.3/4.0 3/11/83 15 6.22 10.73 17.0 NA 3/25/83 14 5.34 4.93 10.3 2.0/2.4 Vikström (1997), Luleå, Sweden 11/13/95 12 7.79 10.23 18.0 NA 12/03/95 20 9.87 30.39 40.3 NA 12/17/95 14 5.20 00.00 5.2 NA 01/14/96 28 2.10 19.58 21.7 NA 01/29/96 15 0.70 62.05 62.8 NA 02/11/96 13 0.27 31.31 31.6 NA 02/29/96 18 1.15 45.14 46.3 NA Henry (1990), Hamilton, Montana 11/30/85 10/9 12/04/85 22 10.91 41.81 52.7 3/4 12/20/85 11/8 Henry (1998), Pittsburg, New Hampshire (four test sections, labeled 1, 2, 9 and 10) 12/30/93, 1 08 5.35 60.13 65.5 4.4/3.7 2 5.01 55.12 60.1 11.8/4.4 9 3.06 46.85 49.9 8.7/2.9 10 14.59 46.62 59.2 9.6/4.3 01/20/94, 1 21 3.82 36.66 40.5 2.6/n.a. 2 3.31 31.41 34.7 4.7/3.5 9 4.71 41.82 46.5 2.9/n.a. 10 3.56 30.41 34.0 4.9/3.1 12/21/94, 1 13 5.76 29.98 34.7 0.8/4.0 2 6.58 8.34 14.9 3.6/4.4 9 5.76 16.27 22.0 0.8/3.6 10 3.09 5.26 8.4 0.3/2.8 01/05/95, 1 15 2.14 23.35 25.5 3.9/2.7 2 0.53 14.44 15.0 4.4/3.8 9 0.89 3.89 4.8 2.6/2.5 10 0.00 10.89 10.9 4.1/3.8 01/26/95, 1 21 1.53 14.73 16.3 1.7/0.8 2 1.66 11.90 13.6 2.2/1.0 9 1.66 14.27 15.9 2.0/0.7 10 0.26 10.90 11.5 2.3/0.7 02/10/95, 1 15 4.10 11.15 15.3 3.5/1.9 2 4.99 10.74 15.7 4.5/2.5 9 4.10 10.41 14.5 3.3/2.0 10 3.57 17.32 20.9 2.4/2.4 Heat flux values calculated for pavements in a range of climates ranged from less than 5 W m 2 to more than 60 W m 2. Comparing these results with soil freezing tests conducted in the laboratory, we find that the laboratory tests use extremely high thermal gradients and the heat flux is somewhat high compared to field observations. Based on visual inspection of the results presented in Table 3, we selected 30 W m 2 as an approximate lower value of net heat flux for experiments conducted 381

and 55 W m 2 as an upper value. The length of specimens tested was 150 mm, and we could not increase the length of the specimens due to the fact that extensive modifications to the entire experimental setup would be required. Thus, temperature gradients for the selected heat flux values were about 10 2 C m 1 for the specimens tested at approximately 30 W m 2 and about 27 2 C m 1 in the specimens with larger heat flux. REFERENCES ASTM D 5918. 1998. Standard test method for frost heave and thaw weakening susceptibility of soils. ASTM, West Conshohocken, PA: 795 806. Chamberlain, E.C. 1991. Modified Berggren program for determining the depth of freeze or thaw in layered soil systems. PC version. U.S. Army Corps of Engineers Cold Regions Research and Engineering Laboratory, Hanover, NH. Farouki, O.T. 1981. Thermal properties of soils. CRREL Monograph 81 1. Hanover, NH: U.S. Cold Regions Research and Engineering Laboratory. Fuchs, M. 1986. Heat flux. In A. Klute, Ed., Methods of soil analysis, Part 1 Physical and mineralogical methods (2nd ed.). Madison, WI: American Society of Agronomy: Soil Science Society of America: 957 968. Henry, K.S. 1990. A case study of the potential causes of frost heave. CRREL Special Report 90-9. Hanover, NH: U.S. Army Corps of Engineers Cold Regions Research and Engineering Laboratory. Henry, K.S. 1998. The use of geosynthetics to mitigate frost heave in soils. Ph. D. Dissertation, Civil Engineering Department. Seattle: University of Washington. Henry, K.S. & Holtz, R.D. 2001. Geocomposite capillary barriers to reduce frost heave in soil. Canadian Geotechnical Journal 38: 678 694. Kimball, B.A., Jackson, R.D., Nadayama, F.S., Idso, S.B. & Reginato, R.J. 1976. Soil heat flux determination: Temperature gradient method with computed thermal conductivities. Soil Science Society of America Journal 40: 25 28. Konrad, J.-M. 1984. Soil freezing characteristics versus heat extraction rate. National Research Council of Canada, Division of Building Research, DBR Paper No. 1257, Ottawa, Ontario. Loch, J.P.G. 1979a. Influence of the heat extraction rate on the ice segregation rate of soils. Frost i Jord 20: 19 30. Loch, J.P.G. 1979b. Suggestions for an improved standard laboratory test for frost susceptibility of soils. Frost i Jord 20: 33 38. Penner, E. 1972. Influence of freezing rate on frost heaving. Highway Research Record 393: 56 64. Saarelainen, S. 1992. Modelling frost heaving and frost penetration in soils at some observation sites in Finland: The SSR model. VTT Publications 95. Espoo: Technical Research Centre of Finland. Vikström, L. 1997. A comparison between measured and calculated frost heave, frost penetration and formation of ice lenses. In Proceedings, International Symposium on Ground Freezing and Frost Action in Soils, Luleå, Sweden: 297 305. 382