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Fig. 3.7. (a) Dependence of coefficient of volumetric thermal expansion avon temperature, various rocks (1 - granite, 2 - diabase, 3 - limestone, 4 - tuffolava, 5 - sandstone). (b) Dependence on mineral composition (1 - orthoclase, 2 - zircon,

3 - sillimanite, 4 - bytownite, 5 - labradorite, 6 - topaz, 7 ± albite, 8 - augite, 9 - hornblende, 10 - quartz, 11 - corundum, 12 - rutile, 13 - hematite,

14 - magnetite, 15 - sphalerite, 16 - pyrite, 17 - chalcopyrite, 18 - halinite, 19 - gypsum, 20-sylvite, 21 - halite), (c) Dependence of coefficient of linear thermal expansion a on silica content in rocks (1 - dunite, 2 - gabbro, 3 - diorite,

soil particles, microfissuring, migration and redistribution in the volume of individual components of the ground system, changes in porosity, etc.

The resulting effect of the change in the frozen soil volume, caused by the changes in its temperature, does not, therefore, amount simply to the sum of temperature deformations of individual components, but varies greatly in soils with different chemical-mineral composition, dispersion, ice content-humidity, cryogenic structure and texture, because the soils have a strikingly varied development of structure-forming processes. For example, in the temperature interval from -1 to - 10°C, the coefficient a in frozen clay will be 1 x 10"2 - 1 x 10~4 °C"\ in frozen sandy silts and silty clays 1 x 10"3 - 1 x lCT^C"1 and in sands 1 x 10"4 - 1 x lCT^C"1, whereas the coefficient of thermal expansion of the basic rock-forming minerals mainly keeps within (1 to 10) x 10" 6 °C_1 and of ice within (3 to 6) x Kr5oC_1. In other words, the mechanism of temperature deformation in frozen soils is much more complex than in continuous solid media. In sandy soils a values are additive and can be obtained as a sum of the deformations of the frozen soil components, except deformations appearing during phase transitions of water when its volume changes by 9%. In clayey frozen soils when negative temperatures change slowly and local temperature gradients appear in soil the unfrozen water is redistributed through the sample volume. For example, during all-round cooling the central part of a sample shrinks and dehydrates due to migration of unfrozen water into the peripheral parts. At the initial stage of water filling the pores (G = 1), the frozen soils heave, while at G < 1 their volume remains practically unchanged. The thermal deformations of soil components are secondary, while the values of thermal deformation of frozen soils can be several times as large as, and even exceed by several orders of magnitude, the values of the thermal expansion or contraction of its components. That is why the fall of temperature in non-ice saturated soils (G < 1) causes considerable reduction in the volume of frozen clay soils as a result of redistribution of water and of shrinkage. In ice saturated clay soils (G = 1), contraction deformations are essentially reduced, and the volume of soil can even grow due to the dominance of heaving. During this process, the stabilization of temperature deformations of frozen clay soils takes place rather slowly over several days (and even tens of days) after the samples have acquired an equilibrium temperature. This process is probably associated with the inertia of internal structural transformations of soil. This phenomenon was called the consequential effect of temperature by I.N. Votyakov and S.Ye. Grechishchev.

The basic factors determining the values and progress of temperature deformations of frozen fine-grained soils with concurrent contraction and expansion of their components are, therefore, the phase transitions of water, the presence or absence of free air porosity, and water exchange during temperature changes. The intensity of water exchange depends on the type of soil, its composition, structure and ice saturation as well as on external thermodynamic conditions (Fig. 3.8).

Development of thermal stresses in frozen soils depends on irregular changes of volume of soil elements. Therefore, these stresses should be grouped as volumetric-gradient stresses which are functions of restricted deformations in the volume of frozen soil. The authors of several works on that problem conclude that the value of these stresses may change within a wide range depending on temperature interval, composition and structure of frozen soils and conditions of cooling. It has been established that with

Fig. 3.8. Deformations of sandy silty material (1 and 4) and of polymineral clay (2 and 3) during cooling from + 20°C to — 30°C with water saturation G equal to 0.8(1 and 2) and 1.0(3 and 4).

the fall of negative temperature (from —2 to — 15°C) in frozen soils the stresses grow, and their maximal values are reached at the lowest negative temperatures. With an increase in the content of fine material and of the content of montmorillonites in soil, the thermal stresses also increase (Fig. 3.9a). It is obvious that if the frozen soil samples (or, more strictly, the ground mass) are sufficiently large, the stresses, totalled along the length of the cooling mass, will always exceed the resistance of frozen soil to rupture, thus causing frost cracks and relaxation of stresses.

Temperature cracking of earth materials is particularly evident in frost shattering of rocks at low temperature in natural conditions under seasonal and diurnal variations of negative temperatures. The temperature changes in the ground may reach 100°C, and annual temperature variations may penetrate tens of metres.

The diurnal and annual temperature fluctuations in the upper layer result in irregular extension or compression deformations which attenuate with depth. Due to its lesser deformation, the lower layer at a relatively lower absolute temperature holds back the complete development of deformations in the upper layer with large temperature deformations. In this way, in these layers 'unallowed' deformations appear, related to the temperature gradient with depth, which finally cause volumetric tensile stresses Pf or compression stresses Ptc (Fig. 3.9b). When these stresses exceed the local resistance of ground to rupture (Pf >arup), then temperature cracks, mostly vertical, appear and develop.

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