The effect of freeze-thaw cycles on the unfrozen water content in cohesive soils was examined. The freeze-thaw effect on the unfrozen water content in bentonites is not statistically significant. The unfrozen water content was found to be best correlated to the specific surface area and the clay content as measured by the laser diffraction method.
The effect of freeze-thaw cycles on the unfrozen water content in cohesive soils was examined. The freeze-thaw effect on the unfrozen water content in bentonites is not statistically significant. The unfrozen water content was found to be best correlated to the specific surface area and the clay content as measured by the laser diffraction method.
The unfrozen water content in frozen soils strongly influences heat and mass transport processes. Despite massive research work, the actual implications of the freeze–thaw process on unfrozen water still remain unknown. The main objective of this study was to examine the hypothetical effect of a number of previous freeze–thaw cycles on the unfrozen water content during the current cycle. Several bentonites (Stx-1b from Wyoming, SWy-2 from Texas, as well as Ca, Na, and K forms of bentonite from Chmielnik) with different water contents were subjected to repeated freezing to −90°C and thawing at 20°C in a differential scanning calorimeter (DSC). The total number of cycles was five. The unfrozen water contents were determined on warming during each cycle by the use of the stochastic deconvolution of the DSC signal. According to the ANOVA results, the freeze–thaw effect on the unfrozen water content wu in the bentonites was not statistically significant. A clear pattern of alterations of wu with the number of consecutive cycles could be distinguished, however, depending on the major exchangeable cation. The kind of exchangeable cation played a predominant role in the temperature dependence of the unfrozen water content. The specific surface area strongly affected the unfrozen water content at lower temperatures, i.e., at −5°C and below. Closer to 0?°C, the effect of the specific surface became absolutely insignificant, and the clay fraction content determined by the laser diffraction method proved to be the soil property best correlating with the unfrozen water content at −1°C.
The frost phenomena in soils play an important role in many types of problems in such varied fields as civil engineering, road geotechnics, agriculture, and meteorology. Many aspects of “frost geotechnics” have been being analyzed by many researchers for >100 yr. These include a general physics of the process, i.e., the freezing point depression and the water remaining unfrozen under the freezing point, frost heaving and the associated phenomena of mass transport, the mechanical properties of frozen soil, and many others. The cycling of freezing and thawing can be seen in this context in two ways. First, the freeze–thaw cycles generate their own specific phenomena, such as the resulting alteration of the soil structure and microstructure. Second, the history of previous cyclic freezing and thawing may affect the frost phenomena and soil properties as observed in a current freezing cycle or in the thawed state. Hence, an experimental design can be planned with the object to determine and, in some cases, explain the extent and kind of possible impact.
The alteration of the soil microstructure and fabric due to cyclic freezing and thawing seems to have been confirmed by many researchers by the use of scanning electron microscopy. Kujala and Laurinen (1989) observed that as a result of repeated freezing and thawing, the plate-like clay particles of their soil samples became aggregated in a random manner. The spaces between the ice lenses, which formed in the course of the freezing process, were filled with clay horizons in which the structural parts arranged themselves into parallel aggregates. This implied that consolidation had taken place in the soil, which was observable in terms of a decrease in porosity. Stępkowska and Skarżyńska (1989) observed the microstructure of several soils of different origin and of varying content of clay minerals. In all cases, the cryogenic microstructure was similar and consisted in a parallel particle arrangement as well as in an increase in the grain size and particle thickness, which testified to an intensive aggregation process during the freeze–thaw cycle. Similarly, Kumor (1989) observed a transformation of the initial microstructures of the tested kaolin and bentonite into new type of microstructures, called “quasi-parallel” and “lens-type” for kaolin and bentonite, respectively. These new microstructures were characterized by a more parallel orientation of clay particles and increased aggregation, together with an increase in the average particle thickness. Similarly, Hohmann-Porebska (2002) observed cryogenic alterations within clays, particularly close to the shearing plane. These modifications of fabric were progressive and occurred before their transition to the frozen stage and in the negative temperature range. The aggregates of fabric created by the ice lensing were generally stable.
An elaborated study of the behavior of soils subjected to freezing and thawing in a laboratory was done by Yong et al. (1985). The purpose of their research was to determine the effects of cyclic freeze–thaw on the liquid limit, the specific surface area, the cation exchange capacity, and the percentage finer than 2 μm of high-moisture-content, sensitive, natural clayey soils not previously subjected to freezing. Testing involved two freeze–thaw systems, closed and open, the former without and the latter with a drainage facility provided. The initial properties and composition of an unfrozen sample were established as a reference. Artificial soil samples were prepared to assess the influences of composition on cyclic freeze–thaw effects. The samples were subjected to one, two, four, eight, 16, and 32 freeze–thaw cycles to examine the extent of changes effected at each stage. The results obtained indicated a significant decrease in the liquid limit of the samples after only the first four freeze–thaw cycles and in the undrained shear strength after only one freeze–thaw cycle. Such pronounced changes were not apparent in prolonged freezing and thawing. Decreases in the specific surface area, reduced ability for moisture retention, and changes in grain size curves after the freeze–thaw cycles provided an idea of the significance of ice crystals in the alteration of the soil structure and the promotion of particle aggregation. The significance of the mineralogical factors was demonstrated by using two different “pure” soils, a kaolinite and Avonlea bentonite. In their opinion, correlations between the changes in the surface area and the undrained shear strength indicated the role of aggregation and its effect on the soil strength and thixotropy. Their study also indicated the enduring effect that desiccation in the open system of freeze–thaw can have on the mechanical properties of the soil. Based on such findings, a scheme of the influence of the freezing mechanism on soil behavior was proposed. In our opinion, however, the mechanism that takes into account only the ice pressure as the main factor involved is not fully reasonable. The changes in the salt concentration in the pore solution associated with the formation of ice crystals should also affect the processes of aggregation and disintegration of the soil particles.
The effect of the freeze–thaw on the other soil properties has been investigated most often with reference to the shear or compressive strength (Baykal and Türe, 1998; Ogata et al., 1985; Yong et al., 1985; Cokca and Yilmaz, 2004; Ghazavi and Roustaie, 2010) and permeability (Hohmann-Porebska, 2002; Baykal and Türe, 1998; Chamberlain and Gow, 1979; Nagasawa and Umeda, 1985; Cokca and Yilmaz, 2004; Fall et al., 2009). While the strength characteristics principally deteriorate as a result of cyclic freezing and thawing, results referring to permeability are inconsistent, with both increases and decreases reported, depending on the soil characteristics, the experimental conditions, and other factors.
Unfortunately, in all the studies mentioned above, no statistical analysis was given, which makes it difficult to critically assess the obtained results. Freeze–thaw experiments usually yield scattered data and the mean values obtained after the consecutive freezing cycles do not differ noticeably. In such a situation, tests for significant differences between means seem essential.
A few more recent studies have substantiated the significance of the effect of cyclic freezing and thawing in terms of statistics. Oztas and Fayetorbay (2003) studied the effect of freezing and thawing on the wet aggregate stability of soils formed in different parent materials, with different water contents, and for various freezing and thawing cycles (three, six, and nine) and freezing temperatures (−4 and −18°C). The ANOVA results indicated that all the treatment effects were statistically significant at P < 0.001. The results showed that freezing and thawing decreased the aggregate stability. The percentage decrease in the aggregate stability was dependent on the soil type, the initial aggregate size and stability, the soil moisture content at freezing, the number of freezing and thawing cycles, and the freezing temperature. Kværnø and Øygarden (2006) investigated the effects of freeze–thaw cycles and soil moisture conditions on the aggregate stability of three cohesive soils. The general linear model procedure was used to determine the treatment effects, including the soil, the matric potential, the number of freeze–thaw cycles, and the interactions between the matric potential and the number of freeze–thaw cycles. The decrease in stability after the first freeze–thaw cycle was significant for all three soils, but the effect was more severe on the silt soil. There was no evident effect of water content on the stability.
Despite massive research work, no general rule has been found and the actual implications of the freeze–thaw process in soils still remain unclear for many reasons. First of all, the presented results are partially incomparable and mutually exclusive. Such parameters of the experiments as the number of freeze–thaw cycles, the subfreezing temperatures, the duration of freezing and thawing in each cycle, and, of course, the properties of the soils used as the material have been different in individual cases (Henry, 2007).
This brief overview allows formulation of the following conclusions:
Generally, cyclic freezing and thawing seem to change the soil properties. Most of the reported results, however, lack a more sophisticated analysis to able to provide statistical evidence that the number and the duration of freeze–thaw cycles really are related to the tested soil parameters.
Any comparisons should be made between the results of experiments performed under similar conditions (open or closed systems, freezing temperatures and their duration in each cycle, the way of freezing and thawing the samples).
There is the necessity for a strict distinction between the isotropic soil parameters, such as consistency parameters, specific surface area, or cation exchange capacity, and the anisotropic parameters, such as water permeability and strength characteristics. The latter are strongly dependent on the size and shape of the sample and, generally, on the test procedure. Moreover, any references of the results to natural conditions may prove difficult or, in some cases, impossible.
The effect of cyclic freezing and thawing on some significant soil parameters connected with the freezing process, such as the freezing point depression and the unfrozen water content, has probably not been investigated by any researcher. Without any knowledge on this topic, however, our understanding of freeze–thaw phenomena will remain incomplete.
It has been widely understood for many years that the presence and phase changes of unfrozen water strongly influence heat and mass transport processes in frozen soils and other porous media. Nevertheless, the nature of the unfrozen water phenomenon deserves further investigation. Many researchers have dealt with this topic during the last decade experimentally, using nuclear magnetic resonance (Turov and Leboda, 1999; Watanabe and Mizoguchi, 2002; Darrow et al., 2009), calorimetry (Bronfenbrener and Korin, 2002; Kozlowski, 2003), time domain reflectometry (Yoshikawa and Overduin, 2005), and the dielectric capacity method (Fen-Chong and Fabbri, 2005; Fabbri et al., 2006). This study dealt with the problem of a probable effect of the previous freezing and thawing cycle on the phase composition of frozen soil. Anderson et al. (1978, p. 79 denoted factors such as clay mineral type, the nature of the cation complex, and the previous freeze–thaw history as being “of secondary importance” regarding the unfrozen water content, yet with the reservation that “this is not to say that these effects are negligible.”
These statements have not been supported, however, by any results of experiments performed with the object of determining how and to what extent the freeze–thaw history affects the phase composition of frozen soil. As stated above, a reasonable answer should be formulated in terms of statistics, otherwise the conclusions may prove baseless. Freeze–thaw experiments are very time consuming, however, and statistical analysis requires repeated determinations, which makes such a research project strenuous. This is the probable reason for the noticeable lack of studies on the topic.
Materials and Methods
The five tested soils are characterized in Table 1. Five model clays were used, including three homoionic forms (Ca, Na, and K) of bentonite from Chmielnik, Poland. This natural Ca-bentonite is characterized by a high montmorillonite content exceeding 96%. The forms were obtained by repeated saturation of the <0.063-mm fraction and subsequent purification from solutes by diffusion. The soil pastes were then air dried at room temperature. The other two clays were obtained from the Source Clays Repository of The Clay Minerals Society and included STx-1 (a natural Ca-bentonite from Texas) and SWy-2 (a natural Na–Ca-bentonite from Wyoming). No laboratory processing was done on the delivered air-dry material with the exception of mixing with distilled water to obtain soil pastes with various water contents.
Because the effect of the repeated freeze–thaw cycles on the unfrozen water content was expected to be relatively small, the bentonites selected had a high content of montmorillonite and were characterized by a relatively high specific surface area. It is widely known that phase change effects are particularly significant in soils of this type.
The plasticity characteristics were determined by the use of normal procedures (Casagrande’s cup device and the rolling test for the liquid limit [LL] and plastic limit [PL], respectively). The specific surface area determinations were based on the results of the water sorption test (WST) according to Stępkowska (1977). This method, although probably less reliable in terms of absolute values than the ethylene glycol monoethyl ether (EGME) adsorption or Brunauer–Emmett–Teller (BET) methods, has its own advantages. First, only the surface area available for water is measured, which agrees with the natural conditions in soil–water systems. Second, it is precise enough to make comparisons between different states of the same sample, which is of importance in freezing cycle investigations.
Homogenous soil pastes of various water contents were used in the experiments. Because of the DSC requirements, the sample masses were relatively small and ranged between 4 and 20 mg, with a mean of 8.03 mg and standard deviation of 2.77 mg. The water content (measured as a percentage by dry mass) varied from 25 to 154%, with an average value of 71.59% and standard deviation of 27.26%. The overall descriptive statistics are shown in Table 2.
A TA DSC Q200 differential scanning calorimeter with an RCS90 refrigerated cooling system was used in the experiments. The RCS90 enables cooling within an operating range of −90 to 550°C. The maximum rate of cooling depends on the temperature range of the experiment. The TA Q200 provides an expanded four-term heat flow that accounts for the imbalances and for heating rate differences during major thermal events (e.g., melting). The resulting heat flow signal provides a more accurate representation of the actual heat flowing to and from the sample. A special technology enabling it to account for the cell resistances and capacitances is referred to as Tzero.
The basic calibrations, including the baseline slope and offset calibration, were conducted according to the instrument manual. The enthalpy (cell) constant calibration was based on a run in which a sample of water was heated from −30 to 20°C through its melting transition at 0°C. The warming rate (5 K/min) was the same as in subsequent experiments. The calculated heat of fusion was compared with the reference value 333.67 J/g. The cell constant was calculated as the ratio between these two values.
In contrast to these mentioned calibrations, the temperature calibration was done using a procedure presented by Charsley et al. (2006). Several samples of water were heated at different scanning rates (10–0.1 K/min). Then the corresponding extrapolated onset melting temperatures were plotted against the heating rate. There was a clear linear relationship between the calculating melting temperature and the heating rate. From this plot, an intercept corresponding to a zero heating rate of T0 = 0.23°C was determined and applied as the temperature shift factor.
Aluminum hermetic pans and aluminum hermetic lids were used in the experiments. Each pan was weighed together with the lid and filled with a soil sample, sealed hermetically using a special sample encapsulating press, and weighed again. The masses of the soil samples were determined by subtraction and were approximately 10 mg. The sample pans were 6 mm in diameter and 3 mm high, which yielded 85 mm3 in volume. The total volume of a soil sample with a bulk density of, e.g., 2 g/cm3, is 20 mm3. Hence, there was enough space for swelling due to the volume expansion of the water on freezing and, ipso facto, the experiments were conducted at constant pressure. A thin layer of the soil sample covered only the bottom of the pan, which ensured a good exchange of heat and a quasi-uniform thermal field within the sample. During the experiment, the calorimetric cell was purged with dry N2 at a flow rate of 50 mL/min. Each sample was subjected to five cycles. One cycle included cooling with a scanning rate of 2.5 K/min to −90°C and then warming with a scanning rate of 5 K/min to 20°C. It must be stressed that the sensitivity in DSC investigations strongly depends on the warming and cooling rate. Because the total heat flow increases linearly with the heating rate, high heating rates should be used when trying to measure small transitions because they provide larger heat flow signals (Thomas, 2001). On the other hand, the temperature lag, leading to smearing of the observed DSC peaks, increases with an increasing cooling or warming rate due to the increasing difference between the temperatures in the center and at the surface of a sample. For these reasons, a cooling and warming rate in a given experiment is always a compromise. In a DSC investigation conducted on similar soils with a scanning rate one order of magnitude lower, the phase changes during warming were not detected before −15°C (Kozlowski, 2007), while, in contrast, the first thermal events during warming were observed at about −40°C in the present investigation.
The application of the DSC technique forced a closed system, in which no drainage was allowed during the test at any time, thereby maintaining a constant average water content. Such a system simulated the situation where a low-permeability soil underwent freezing without access to a free water source and thawed subsequently without any drainage (Yong et al., 1985).
After the experiment, pinholes were punched in the sample lids and the total water content was determined by drying to a constant mass at 110°C.
Calculating the Unfrozen Water Content
The value of Dk reaches a minimum for the best approximation of q(Ti). The computations are very time consuming because of n nesting loops involved in Eq. . In our investigation, the broad endothermic peak during warming usually began between −42 and −38°C and ended between 5 and 10°C. Because for n > 40 the computations take >1 wk just to calculate one case, the width of the temperature increment was assumed to be equal to 1°C.
Equation  only is valid above −46°C, at which temperature it yields a zero value of latent heat. Similarly, a formula for supercooled water, based on the differences in the densities of liquid water and ice, presented by Nevzorov (2006) predicts the vanishing of the latent heat at −39°C. According to Nevzorov (2006), such behavior may be attributed to the state at the temperature of homogenous nucleation, at which the internal energies of liquid water and ice become equal. A detailed discussion indicated that Eq.  can be applied to calculate the latent heat of water in porous systems above −46°C (Kozlowski, 2011). Notice that in the present investigation, the first exothermic events during warming were observed at about −40°C.
In addition, the so-called unfreezable water content wunf, i.e., the unfrozen water content at the temperature at the beginning of the observable process of melting, can be determined by the use of Eq. .
Results and Analysis
Plots of the unfrozen water content vs. temperature obtained in the first freeze–thaw cycle are shown in Fig. 1. In Fig. 2, the variation of the unfrozen water content with temperature in a typical sample is shown for all five cycles. It is apparent that the kind of soil and the temperature strongly affected the unfrozen water content, which obviously conformed to the known behavior of frozen soil–water systems. In contrast, the effect of the cyclic freezing and thawing seems not very significant at first glance.
To test for significant differences between mean values of the unfrozen water content observed in consecutive freeze–thaw cycles for different soils and at individual temperatures, an ANOVA was applied to the results. Additionally, interaction effects between variables were tested to test more complex hypotheses.
The following categorical predictors (factors) were distinguished: soil (bc, bn, bk, st, and wy), cycle (1, 2, 3, 4, or 5), water content (six ranges denoted as W = 30, 50, …, 130, where W is the water contents w in the range W ≤ w < W + 20), and temperature (−40, −5, −2, and −1°C). The temperature −40°C refers to the state when only the unfreezable water is present in all samples, i.e., directly before the start of the melting process with warming. Statistica 8.0 software was used in the calculations.
The results of ANOVA for temperature, soil, and the number of cycles are shown in Table 3. The effects of temperature and soil were highly significant statistically, similar to the temperature × soil interaction (P < 10−6). In contrast, the effect of the number of cycles was insignificant, although more significant than its interactions with soil, temperature, and temperature × soil.
In Fig. 3, the plot of means for the temperature × soil two-way interaction is shown. The graph indicates a clear increasing trend; the means became gradually higher with increasing temperature. Notice the similar behavior of both of the Na-bentonites (bn and wy): their unfrozen water contents were the highest of all at −1°C, in contrast to the unfreezable water contents at −40°C. This is particularly striking in the case of the Wyoming bentonite (wy). In Table 4, the average relative increments of the means between −40 and −1°C as well as between −2 and −1°C are shown in relation to the temperature increment and to the initial value of the unfrozen water content (i.e., the beginning of the corresponding temperature range). It can be seen that the highest increment per 1°C between −40 and −1°C occurred in both of the Na-bentonites, yet in relation to the initial value at −40°C (the unfreezable water content), this increment was highest in wy and, surprisingly, in the K-bentonite (bk). In turn, the Ca form of the Chmielnik bentonite exhibited an unexpectedly small increment at the “final” stage between −2 and −1°C; however, this increment was relatively small also in the Na bn and relatively high in the Ca st. Apparently, the kind of exchangeable cation plays a predominant role in the temperature dependence of the unfrozen water content, but the effect of the origin, which affects the type of montmorillonite and microstructural parameters, remains significantly large.
Comparing the graphs in Fig. 3 with the data in Table 1, a conclusion can be drawn that the specific surface area may significantly affect the unfrozen water content. To explore this hypothesis more closely, we calculated the correlation coefficients between the total specific surface area and the unfrozen water content at individual temperatures. In the same way, the correlation coefficients were calculated for some other properties, such as the limits of consistency and the clay fraction content, the latter determined by the hydrometer or laser diffraction methods.
The results are shown in Table 5. Regarding the specific surface area, the correlation, being significantly high at low temperatures (R = 0.918260 at −40°C and R = 0.838624 at −5°C), fell dramatically closer to 0°C, reaching R = 0.110305 at −1°C, which means there is no relationship. In contrast, the correlation between the unfrozen water content and the liquid limit and between the unfrozen water content and the clay fraction (determined by the laser diffraction method) were relatively high at −1°C and were completely not significant at −2°C and below. Notice that the correlation only relates to the clay fraction determined by laser diffraction and does not concern the clay fraction determined by the hydrometer method.
The corresponding plots for the best correlations (i.e., with the specific surface area, the liquid limit, and the laser diffraction clay fraction) are shown in Fig. 4.
The effect of the freeze–thaw cycle is shown in Fig. 5. It is apparent that this factor is statistically insignificant, although a slight effect on the unfrozen water content can be observed, particularly at −1°C. In Fig. 6, graphs for the unfrozen water content at −1°C are shown. Apparently, the kind of major exchangeable cation affects the way in which the unfrozen water content alters due to the freeze–thaw process. Both of the Na-bentonites, i.e., bn and wy, exhibited the same pattern, with an increase in Cycle 2, decrease in Cycles 3 and 4, and repeated increase in Cycle 5 (-^vv^). A similarity between both of the Ca-bentonites (bc and st) can also be observed (-v^v^). It can be calculated that the probability that in the set of five different soils, the two soils with the Ca cation will exhibit the same characteristic pattern and, simultaneously, the two soils with the Na cation will exhibit some characteristic pattern equals 1:4096 (162/165). Hence, the observed behavior cannot be accidental, independent of the fact that it remains statistically insignificant.
The effect of the interaction of the water content with the other grouping factors is presented in Table 6. As can be seen, only the interactions with soil and temperature are statistically significant, of course due to the high statistical significance of these factors themselves.
The results obtained definitely negate the hypothesis that freeze–thaw cycles significantly affect the unfrozen water content. The tested soils were bentonite pastes, traditionally regarded as typical frost-susceptible soil material. Moreover, the samples were frozen right down to −90°C. Hence, the most extreme possible impact of freeze–thaw was expected. It must be stressed, however, that the investigation was performed under closed system conditions, in which water uptake is impossible. On the other hand, relatively small values of permeability coefficients are expected in bentonites. In such soils, the differences in behavior between open and closed systems are usually small. Hence, the conclusion that the effect of cyclic freezing and thawing is less dependent on the freezing conditions in bentonites than in our types of soils seems reasonable. A question arises to what extent our findings would remain valid in other clay–water systems, with kaolin or illite as the predominant mineral, and in non-clay soils like silts or fine sands. On the one hand, the unfrozen water content is considerably smaller or almost zero in such soils; on the other hand, however, the pore structure of some of these soils may be more frost susceptible than that observed in bentonites.
For obvious reasons, it might be expected that cyclic freezing and thawing would strongly interact with the water content, i.e., the higher the water content, the more dramatic the change in the unfrozen water content determined in the subsequent cycles because of the higher ice pressure induced. Our results do not substantiate such a hypothesis. The effect of the interaction of water content and the number of freeze–thaw cycles proved statistically insignificant, although a detailed analysis, not presented here, indicated an interesting fact that the extreme values of water content, both the lowest and the highest, induced an increase in the unfrozen water content. An effect of lesser degrees of saturation was observed by Asare et al. (1999), who reported that changes in the saturated hydraulic conductivity by the impact of continuous freeze–thaw cycles was most severe at a lower degree of saturation and was reduced in severity as the degree of saturation increased. This topic deserves further investigation.
Similarly, the interaction of cyclic freezing and thawing with temperature was insignificant, although we initially assumed that the effect of the cyclic process would more visibly manifest itself at higher temperatures, when the influence of the pore distribution predominates over the specific surface. Such an influence was analyzed in more detail for −1°C. The characteristic patterns of alteration of the unfrozen water content with the number of a subsequent cycle were observed for pairs of bentonites with the same major exchangeable cations. Because the probability of an accidental conformity was estimated as very low (P = 0.00024), we conclude that physicochemical transformations in the soil–water system due to cyclic freezing and thawing are not a chaotic process, yet the corresponding changes are too small to be definitely differentiated from background factors such as a local microstructure of a sample (and, consequently, to become statistically significant).
In contrast to the number of freeze–thaw cycles, the effect of the major exchangeable cation and of the geologic origin, the latter affecting the type of montmorillonite and the type of microstructure, proved highly significant. The effect of the exchangeable cation was recently reported by Svensson and Hansen (2010), who studied Ca and Na forms of Wyoming bentonite with time-resolved synchrotron x-ray diffraction. Completely different textures of ice diffraction rings were observed, with a more dispersed texture for Na-montmorillonite and a more coarse texture for Ca-montmorillonite. Such a behavior could explain the current observations, according to which the unfrozen water content in the Na forms became significantly higher than in the Ca forms above −2°C. In this temperature range, the size of the remaining ice crystals begins to play a predominant role according to the rule that the smaller the crystal, the lower is its melting temperature.
The very fact that the clay fraction determined by the use of laser diffraction correlates with the unfrozen water content even better than the liquid limit is a bit surprising. Theoretically, such a relationship was expected by many researches in the past because the closer the temperature is to 0°C, the more water remains unfrozen due to confinement in the mezopores rather than due to adsorption on the planar surfaces. The clay fraction seemed a perfect candidate to describe the contribution of the mezopores to the overall soil porosity; however, all the attempts to find a significant correlation between the unfrozen water content and the clay fraction have failed. In the present investigation also, such a correlation was very weak for the clay fraction determined by the traditional hydrometer method, yet became significantly higher when calculated using the clay fraction determined by laser diffraction. Evidently, the results obtained by laser diffraction more correctly refer to the actual pore geometry.
The parameter estimates and the overall characteristics of the model are presented in Table 7. For the purpose of comparison, the model given by Eq.  is also given, but its parameters have been recalculated using the present results, ipso facto its chance to be well fitted has been increased.
All the parameter estimates are statistically significant at P = 0.05. The intercept, originally present in Eq. , has been skipped in the new model because of its small significance. Thanks to this, the new model has only one parameter more than the old one. The standard errors of the estimate have been calculated for both models at four individual temperature levels. It is apparent that, according to expectation, the model with the laser diffraction clay fraction better describes the unfrozen water content, particularly close to the freezing point.
It is very likely that an empirical model in a form similar to Eq.  could be a useful tool to calculate the unfrozen water content in frozen soils, yet its parameters should be estimated based on the results obtained for a set of various soils, including silts and clays with a significant content of illite and kaolinite.
1. In light of the obtained results, the freeze–thaw effect on the unfrozen water content wu in bentonites frozen in a closed system was not statistically significant; however, a clear pattern of alterations of wu with the number of consecutive cycles can be distinguished, depending on the major exchangeable cation.
2. The effect of the kind of bentonite was observed to be highly significant. Of the two possible factors, i.e., the origin and the kind of major exchangeable cation, the latter seems to be more important and the curves of the unfrozen water content for the two Ca and the two Na forms with different origins are strikingly similar by pairs.
3. The specific surface area strongly affects the unfrozen water content at lower temperatures, i.e., at −5°C and below. Closer to 0°C, the effect of the specific surface becomes absolutely insignificant, and an important part is played by such parameters as the clay fraction and the liquid limit. Such results confirm that the unfrozen water content can be categorized into unfreezable water, identified with the water adsorbed on the planar surfaces of clay minerals, and “freezable” unfrozen water, the quantity of which strongly depends on the pore distribution.
4. The clay fraction, as determined by the laser diffraction method, proved to be the soil property best correlating with the unfrozen water content at −1°C. In contrast, the clay fraction obtained by the hydrometer method did not exhibit any correlation, which probably shows that the latter method does not properly describe the actual soil granulation.
5. An empirical model with specific surface area and laser diffraction clay fraction exhibited significantly better correspondence with the measurement output than that of the known model of Anderson and Tice (1973), which uses the specific surface as the sole soil parameter.
This work was supported by the Polish Ministry of Science under Grant N N525 349538.