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Fig. 1.8. Dependence of the unfrozen water content (Wunf) on the negative temperature, showing the intensive (I), slight (II) and very little (III) phase transitions regions.

From this figure we note that successive changes of ground negative temperature by an equal value At causes freezing out of smaller and smaller amounts of unfrozen water and the decrease by smaller and smaller amounts in the thickness of the bound water film: hx — h2> h2 — h3 , resulting from a sharp increase in the value of energy of bonding between water molecules and mineral surface, with the unfrozen water film thinning in accordance with the curve Em — f(\/h"). Thus, it is this curve which determines essentially the trend of the curve Wun{ =f(t). Really, under high negative temperatures there is intensive freezing-out of the slightly bound water in soil systems for a drop in temperature of 1 °C, while in the region of low negative temperatures such a temperature fall is marked by an essential slowing down or, in effect, cessation of the transition of unfrozen water into ice (see Fig. 1.7). With allowance made for this and in line with the curve Wun{ =f(t), N.A. Tsytovich in 1973 proposed dividing the process of water phase transitions in soils into three categories or regions (see Fig. 1.8): I - the region of intensive phase transitions, when the unfrozen water content changes by 10% with a change of 1 °C in temperature, i.e. A Wun{ > 10%; II -the region of less intensive transitions, when A Wun{ changes in the range from 10 to 1 %, with Af = 1 °C; III - the region of virtual absence of phase transitions,when A Wuni < 1%,, with Af = 1°C.

The described patterns refer to chemically 'pure', bound water in soils. However under natural conditions the bound soil water is characterized by the presence of a significant amount of solute salts bonding the H20 molecules - and in so doing retarding the transition into ice of this osmoti-cally bound water. In line with this the condition of phase transition of bound water containing solute salts into ice (freezing-out of such unfrozen water in the range of negative temperature), given the film thickness h at its surface and the freezing temperature t, is described by:

where E0(t) is the energy of the bond between H20 molecules in the unfrozen water and the ions of solute salts at distance h from the mineral surface. It turns out in accordance with this condition (1.16) that the higher the concentration of the unfrozen water solution and, consequently, the energy of interaction between H20 molecules and ions, the lower is the negative temperature required to perform the phase transition of equal amounts of unfrozen water into ice.

The problem of the texture of the ice being formed may be of great interest when considering the phase transitions of unfrozen water in soils. It is assumed at the moment that the first type of ice (ice I) is formed in the soil when the greater part of the unfrozen water is freezing out. However it cannot be denied that the texture of the ice under formation must experience the effect of the mineral substrate surface forces. Such an effect can probably manifest itself (though very slightly) over a distance of the order of a few hundred nanometres, that is to say, at high negative temperatures. The effect will manifest itself most tangibly at a distance of tens and units of nanometers between the ice and the mineral surface, i.e. at low negative temperatures when the unfrozen water film thickness is rather small and completely under the effect of surface forces of the mineral particles (see Fig. 1.7, h « h3). Really, the energy of interaction between the unfrozen water molecules and the mineral surface is proved in this case to be essentially higher than that between the unfrozen water molecules and the ice surface, i.e. Els (t « t3) « Em (h « h3). At the same time distortions of hydrogen bonds in the unfrozen water by the mineral substrate surface forces turn out to be so strong that they are able to strain the hydrogen bonds in the ice texture, i.e. in essence to distort this texture. Thus the texture of the ice crystal accomodates itself to the texture of the mineral substrate under the effect of the mineral forces of this substrate (the phenomenon of pseudomorphism). According to the theory of pseudomorphism, propagation of stresses (on account of the distortion of hydrogen bonds in this case) inside the texture of the intergrow-ing bodies can extend tens of nanometers and depends on the size of the gap between the textures of the contacting bodies, on the energy of interaction between them and on the 'rigidity' or elasticity of their lattices. As this takes place, of two intergrowing bodies the crystals with the lower value of crystal lattice energy experience the greatest changes of volume under pseudomorphism. It is natural that the surface ice crystals will be more strained in conformity with the frozen soil system under consideration.

Experiments conducted by a number of researchers on the building up of ice on various mineral surfaces represent a certain experimental verification (if not a strict one, because the ice build-up was in the direction away from the mineral substrate, and not the reverse as would apply for the freezing of the unfrozen water). These experiments have shown that in the vicinity of the mineral surface the ice has a particular texture, different from the texture of the ice formed at a substantial distance from the surface. The thickness of such a contact layer of ice and the degree of its change of texture turn out to be essentially dependent on the particular texture of the crystal lattice of the mineral surface. Thus smaller ice crystals were formed on a polycrystalline base in the course of ice build-up. The extremely small crystals of the ice coating were formed on materials which were amorphous in structure. The mineral substrate of gypsum, which has a fibrous structure, caused the development of an oriented crystal lamination with the long axes of the crystals oriented transversely to the fibres of the base. It was found experimentally that there is a dependence between the orientation of the optical axes of the ice crystals in the contact ice layer and the value and direction of cooling. It is obvious that the effects of ice crystal texture distortion will manifest themselves less in the case of the freezing out of the unfrozen water because the mineral surface effect on the ice does not directly manifest itself through the film of bound water.

Using all the above-cited ideas on the freezing of unfrozen water in soils in the range of negative temperatures we can show that the reverse phase transition (ice melting and increase of the unfrozen water content on this account) will also not proceed at once and not at a constant temperature but gradually with the progressive raising of negative temperature in the thawing soil system. All the above is supported strongly by the results of experimental investigations (see Fig. 1.6).

Thus, the moisture phase transitions proceed in fine-grained soils not at 0°C and not at a particular constant negative temperature but in a range of negative temperatures. Freezing or frozen fine-grained soils always contains some amount of unfrozen water. Thus it has been established experimentally that even at a temperature of — 100°C there exists a thin film of unfrozen water of an order of 0.3 nm in thickness around the fine mineral particles. It must be stressed in this case that the unfrozen water should not be identified with bound water because the film of bound water of any thickness experiences the energy effect of mineral surface force only while the film of unfrozen water, being the same in thickness, experiences the effect of ice surface forces in addition. In other words, such a film of unfrozen water will be energetically bound and must be less mobile. At the same time the term 'unfrozen water in soils' includes practically all the types of ground moisture, as the situation may be: free water (freezing usually at 0°C and at temperatures much lower than 0°C in the conditions of high concentrations of pore solution); capillary water (freezing in the region of high negative temperatures, i.e. near 0°C); pellicular and adsorption water (freezing in a wide range of negative temperatures to —100°C and lower).

It should be stressed also that each negative temperature of a particular soil system in an equilibrium state must correspond to a strictly specified unfrozen water content or strictly specified thickness h of a water film. If this condition is violated, the thermodynamic state of the system will not be in equilibrium and the process of either freezing out of the excess (above the equilibrium value) moisture or of ice melting will proceed resulting in the unfrozen water content increasing up to its equilibrium value.

1.3 Sublimation and desublimation of moisture in frozen rocks

According to the thermodynamic viewpoint, ice sublimation represents the phase transition of a substance from the solid to the gaseous state without first forming a liquid and which occurs with heat absorption (the heat of sublimation is 2.83 kJ~ xg).

From the molecular-kinetic theoretical standpoint the mechanism of the sublimation and ablimation (desublimation) processes consists of the following. H20 molecules residing in the lattice structure of the ice surface and having the highest velocity of heat (kinetic, vibratory) motion (EK > Eb) escape into the gaseous surroundings, breaking free of the interaction with the rest of the molecules. Simultaneously with this process, there is the possibility of the process of the trapping of those individual molecules and chaotically moving groups in the gaseous surroundings which collide with the ice surface. These molecules lose the kinetic energy of their translational motion in the course of collision and are integrated into the crystal lattice of the ice surface. The process of ice sublimation proceeds in this case on condition that the process of abstraction of H20 molecules from the ice surface dominates over the process of their trapping from the gaseous surroundings, otherwise the process of ablimation (desublimation) of water vapour on the crystal ice surface occurs.

Based on the hypothesis of the presence of a quasi-liquid film on the ice surface, by the process of ice sublimation is meant the process of evaporation of this film with its restoration by ice melting. Microphotographic investigations show that the sublimation process proceeds not uniformly from the whole ice surface but from the individual most energetically unstable portions. These are various faults in the ice crystal texture as well as ice crystal edges and vertices on its surface.

The ice surface proves to be strewn with a great number of shallow recesses of a cup-like shape (cones) at the beginning of sublimation. The sublimation cones are characterized in this period by small cross-section and depth, forming a 'honey-comb' pattern on the ice surface. Furthermore, they become deeper, wider and coalesce together partially, resulting in the formation of oriented recesses and grooves.

Evidently, there exists a limitation on the development of concave microrelief elements after which the sublimation of protuberances begins with, at this moment, high energy instability. Large smooth microrelief forms appear and further development of small sublimation cones occurs again on this gentle wavy ice surface. Subsequently the ice surface is likely to be subject to cycles of simple microrelief evolution similar to the foregoing one, on the ice surface inherited from the previous cycle. Thus one can refer to the varied cyclic nature of the changes within the various parts of the sublimating ice surface, the areas of which can increase and decrease around a particular mean value. It is this fact which explains the scatter in the values of ice sublimation intensity Is, representing the ice mass loss in unit time for a constant cross-sectional area of the ice sample, determined by experimentation for various moments of time. However, by and large the experimental points are satisfactorily distributed about a constant (mean) value of the ice sublimation intensity (Fig. 1.9a). As the ice sublimation is developed only within the same energetically unstable portions on the sample surface initially, the minimum values of ice sublimation intensity occur then, increasing at first essentially with time and then stabilizing in response to the covering of the whole area of the ice sublimation surface by the processes of external heat-mass exchange. The sublimation process in samples with large- and small-crystal ice proceeds at different rates during the same time intervals. Thus this process proceeds faster in the samples of small-crystal ice on account of a great number of textural faults and high values of volumetric strain gradients as a result of small-crystal ice formation under conditions of low negative temperatures. Typically with such ice there is also less scatter about the mean value in the experimental data on the sublimation intensity.

The pattern of the ice sublimation process discussed applies also to ice occurring in macropores of soil systems. However it is complicated there by the presence of some amount of unfrozen water in dynamic equilibrium with ice. According to the principle of the equilibrium state of unfrozen water and ice in frozen soils, its amount must remain constant at a given temperature. Therefore by ice sublimation in soils can be understood not only the transition of ice from solid to gaseous state but also the evaporation of

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