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8 16 24u 102 cm hr"1

Fig. 3.4. (a) Relationships between volumetric stresses Pshr, gradient of stresses grad Pshr, rate of freezing and migration water flow I„, for freezing kaolinite clay; (b) between stress gradients grad Pshr, rate of freezing and frequency of horizontal ice layers I).

shrinkage deformations are recorded not in the unfrozen dehydrating part of the soil sample, but in its frozen part between the freezing front and the visually observed front of ice segregation £si, i.e. on the boundary where £def deformations change their direction in the freezing soil (Fig. 3.2b). In actual fact, in the lower part of the freezing zone, in a sample of kaolinite clay (between £fr and £def), where intensive phase transitions and stresses (though weak) of swelling Psw and of ice expansion Ph0 develop as a result of water migration, the deformation recorders also show the development of a shrinkage process, that is, Pshr — (Psw + Pho) > 0. But in the layer between the boundary where deformations £def change their direction, and the visual boundary of ice segregation or the boundary of transition of the freezing zone into the frozen, £si, where considerable water (ice) accumulation is already active, the swelling-heaving stresses exceed the now weak shrinkage stresses, that is, Pshr — (Psw + Pho)<0. As a result, in the segment of the freezing zone from £def to £si the swelling and heaving deformations develop, i.e. deformations with directions opposite to the directions of the shrinkage deformations (Fig. 3.2). It seems obvious that on the mobile and variable boundary, where the changes in the direction of deformations occur, the opposite forces should be equal, that is, Pshr = Psw + Ph0, and this boundary will be the plane of stresses of equal value but opposite sign.

Special experiments have established that the freezing of water in a confined volume, which could be the pores of the soil, may produce significant stresses, if heaving deformation is not allowed. These stresses, if approximately estimated using the Clausius-Clapeyron equation, will be about 13.4 Mpa for every 1°C of fall of negative temperature. Since natural soils cannot be 'closed' undeformable systems, the component of heaving stresses in the total stress and deformation value in freezing soils in most cases is not dominant, but occurs as a certain addition to swelling stresses, caused by the wedging effect of fine films of migrating water. The wedging activity of fine films of unfrozen water, at the same time also causing its migration, plays a large part in the formation of heaving stresses.

The amount of prevented deformation has a decisive effect on the heaving and settling stresses, i.e. the more the deformation is prevented, the higher are the stress values in the freezing soil. For example, results of a study of stresses using recorders with different rigidity values Kdef have shown that, with the growth of Kdef from 800 to 1700 MPam-1, the values of stresses in freezing soils almost double. The increase of rigidity value of the recorder in this case has reduced the allowed deformation of the sample.

The smaller size and compression of the unfrozen zone in a sample are significant in the development of the heaving stresses in soils. In fact at the beginning of freezing, as the unfrozen zone is dehydrated, it is easily deformed and becomes smaller. But later, the shrinkage deformations attenuate, whereas the general deformation of the ground system is reduced causing accumulation (growth) of unrelaxed stresses. This process is associated with the growth of heaving stresses with time (as the freezing front advances), which reach their largest values by the end of freezing (Fig. 3.5a).

The stresses and deformations in the freezing part of soils largely depend on their composition and structure. The greater the fine-particle content of soils and the more complete their water saturation, and the higher the initial water content, the more intensive are the stresses and the more active the migration water flows (Fig. 3.5).

The same relationship exists between the freezing conditions and the development of stresses and deformations in soils. For example, if there is an external supply of water to the freezing sample (an 'open' system), then it has higher values of heaving stresses. The same is observed during slow freezing of soils which is associated, as shown by experiment, with greater redistribution of water and ice accumulation in the freezing zone of the sample and, therefore, with a longer active deformation of the freezing soil due to wedging by the films of migrating water.

Heaving and shrinkage of freezing and thawing soils The freezing and thawing of soils often causes deformation (rising or sinking), i.e. heaving or subsidence of the ground surface. During the economic development of the country, engineering constructions are particularly threatened not by the absolute values of these deformations but by their irregular occurrence over the area. The criterion of irregularity of, for example, areal heaving, is normally expressed as the excess of heaving at one a

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