XWm ~1K"1

Fig. 7.4. Dependence of the temperature coefficient of linear expansion a, thermal conductivity A, and molar heat capacity Cm of ice on temperature t, and of its thermal conductivity on porosity n (according to B.S. Rachevskiy et al).

terized by the specific latent heat of fusion Lp diminishes with higher pressure. A certain quantity of heat is absorbed during ice sublimation; this value is the specific latent heat of ice sublimation. For nonsaline ice this value is 2834 J g-1, while for saline ice it varies between 2500 and 3000 J g~1.

Under the influence of external forces (loads) different properties - fragility, elasticity and plasticity of ice can manifest themselves. At certain conditions within the interval of temperatures from —3 to — 4°C ice behaves as an elastic body, according to Hooke's law. This takes place at compressive stresses up to 0.1 MPa, with the time of load application less than 10 s.

When the plastic limit of ice is exceeded its degradation begins. The maximum stress at which ice degradation begins is much dependent upon the rate of load application and conditions of deformation, because simultaneously with stress increase ice begins to creep. The strength of ice increases with lowering of temperature, nonlinearly with a diminishing rate of deformation.

When a load is acting on the ice causing plastic deformation there is no change in volume and no degradation. Ice plasticity depends on temperature, the nature of load and the rate of deformation. Ice resistance to flow is in direct proportion to the rate and is determined by ice viscosity. The data available show a wide spread in values of viscosity coefficient (from 103 to 108 MPas). This is likely to be associated with growth of stress in time and deviation of ice properties from those of a viscous (Newtonian) fluid. It is often assumed that ice possesses a yield strength of 0.1 MPa. Actually, creep is observed in ice with stresses less than the yield strength.

The structure, composition and properties of unfrozen water in the frozen soils have not been explored thoroughly, having a complex nature. Therefore their consideration is to a great extent based on the knowledge of the nature and properties of bound water in unfrozen fine-grained soils as well as on the hydrophilic model systems.

It was found experimentally that the amount of unfrozen water in the frozen soil is a function of the soil composition and structure which, in turn, are determined by the origin and age of deposits. Phase equilibrium of moisture in the frozen soils is also influenced by the thermodynamic conditions (temperature and pressure) as well as various physical fields. A variety of characteristics of the composition of the frozen soil and structure that determine phase composition of the moisture can be reduced to a few physical-chemical factors such as specific active surface, structure of void space, concentrations and type of ions in the pore solution, as all these factors are in functional dependence.

Specific active surface Ssp reflects not only surface area, but also the energy factor of this surface onto which a conventional monolayer of water molecules is adsorbed. Accordingly, Ssp is a composite value and is a function of both the grain size and the water receptive capacity of its surface. Specific active surface increases in the series sand - kaolin - hydromica clay

The unfrozen water in the frozen soils can fill the capillaries and be in the form of liquid films. At lower temperatures film water prevails, while at higher - capillary water does. Therefore, specific active surface serves as a key factor in the formation of unfrozen water only at temperatures below

— 5 °C and determines the total quantity of unfrozen water of island-like and multilayer adsorption and, partially, of the osmotic variety.

Assuming that thickness of the adsorbed layer is dependent on specific surface of soil and does not depend on its curvature, one may obtain a direct ratio fVunf = WunfSsp where Wunf is the quantity of unfrozen water per unit of Ssp. The presence even of a small amount of clay and colloidal, especially, montmorillonite, particles causes an increase of Ssp and, accordingly, increase of the liquid phase component. Thus, for example, at — 6°C the content of fVun[ in clays of different mineral composition increases in a series kaolin (3.5%) - hydromica-montmorillonite clay (9%) - bentonite (26%). Specific active surface in this case makes up 30, 109 and 560 m2 g"1, respectively.

With higher temperature (above — 2°C) the content of osmotic and capillary unfrozen moisture increases and a greater role in the phase composition is played by the structure of void space of the frozen soil, which it is convenient to express quantitatively through distribution of void volumes with radius. Fig. 7.5 shows typical curves of the A F/Algr relationship for soils of different composition. A distinct pattern is discerned: in the range of

Fig. 7.5. Curves of differential distribution of void volumes by radius (a, b) and dependence of the unfrozen water content on temperature (a', b') in soils of different granulometric (a) and mineral (b) composition: 1-2 - silty-clay material (1 - heavy, 2 - light); 3-5 - sandy clay-silt (3 - heavy fine, 4 - light, silty; 5 - light coarse, 6-8 - clay (6 - montmorillonite, 7 - hydromica, 8 - kaolinite).

Fig. 7.5. Curves of differential distribution of void volumes by radius (a, b) and dependence of the unfrozen water content on temperature (a', b') in soils of different granulometric (a) and mineral (b) composition: 1-2 - silty-clay material (1 - heavy, 2 - light); 3-5 - sandy clay-silt (3 - heavy fine, 4 - light, silty; 5 - light coarse, 6-8 - clay (6 - montmorillonite, 7 - hydromica, 8 - kaolinite).

high negative temperatures even for the same total porosity, the finer the pores, the larger is the liquid component.

The unfrozen water content in frozen soils usually follows the additivity rule which is confirmed, for example, by the linear dependence of Wunf on peat content. This principle applies because mechanical mixing of aggregates and particles of different composition does not, in effect, alter the main factors (Ssp, differential porosity, salinity) which are responsible for the contribution of each component of the frozen soil to phase composition of the moisture. Comparison of physico-chemical properties of frozen soils with different granulometry shows the expansion of the specific active surface of the mineral skeleton in going from sandy silty materials to clays, which is accompanied by an increase of the volume of fine pores and capillaries leading to a general increase in the unfrozen water content (see Fig. 7.5a).

Mineral composition is to a great extent a key factor determining the ratio of liquid and solid phases in the frozen soil. The manner of variation of composition within the range of negative temperatures (0 to — 6°C) has a complex nature (see Fig. 7.5). Thus, at low temperatures (— 1 to — 6°C) Wunf increases in the order kaolin - hydromica clay - bentonite. At high temperatures (— 0.3 to — 1 °C) the liquid phase increases in the order hydromica clay - bentonite - kaolin. In explaining this one must resort to results of investigations concerning void space and specific active surface.

Thus, for very dispersed montmorillonite clay with available hydrophilic internal basal surfaces in the fine pores, there are two peaks on the differential porosity curves, i.e. pore distribution by size has a bimodal nature (see Fig. 7.5b, curve 6). The first peak in the differential porosity curve corresponding to the finest pores of less than 8 nm, is determined by inter-crystalline porosity of minerals and inter-particle porosity. The second peak corresponding to pores of 30 nm is assumed to occur on account of interaggregate porosity.

Although there is no bimodal distribution of void space by radius of pores for hydromica and kaolinite clays, there are certain differences. Hydromica clay contains a greater amount of fine colloidal particles compared with kaolinite which predetermines its finer granular structure (curve 7), despite the fact that as regards average size of fine particles kaolin is more disperse. The homogeneous granulometric composition and regular shape of kaolinite clay particles leads to a higher monoporosity in kaolin among the soils compared (curve 8). Change in mineral composition brings about changes in the volume of ultra-capillary pores from, for montmorillonite clay, 0.3 cm3 g~ \ to 0.07 cm3 g~1 for hydromica clay and 0.02 cm3 g"1 for kaolinite clay.

Specific surface and pore structure of clays being the function of their mineral composition determine the course of both quantitative and qualitative changes of the unfrozen water content at negative temperatures. Thus, at temperatures lower than — 1 °C kaolinite clay contains a tenth of the unfrozen water content of montmorillonite and much less than hydromica clay (Fig. 7.5 b).

Within the temperature interval from — 1 °C to the freezing point of clay the pattern of variation of unfrozen water content with mineral composition is quite different. In this case the greatest amount of the liquid phase is observed in kaolinite clay, the smallest in hydromica clay, in between being bentonite. This pattern is also explained by the structure of void space. Kaolinite clay contains a big volume of pores sized about 100 nm in which unfrozen water is found. A highly homogeneous structure of the kaolin void space gives a sharp variation of the unfrozen water content in going from

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