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internal friction and can be expressed by the equation S = C = tg <f> P, where C is cohesion; </> is the angle of internal friction.

In the majority of cases the total strength of the frozen soil increases with lower temperature. This is valid for practically all types of soils under all types of tests (Fig. 8.13). It is explained first of all by the smaller amount of unfrozen water due to the lower temperature and the simultaneous increase of close-contact ice, intensified ice-cement cohesion and strengthening of the ice itself.

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Fig. 8.13. Temperature dependence of strength of frozen soils: (a) - compression strength (1 - ice, 2 - sand, 3 and 4 - clay, with natural and with disturbed structure respectively; according to Ye.P. Shusherina, I.N. Ivashchenko, V.V. Vrachov); (b) - tensile strength (1 - ice, 2-5 - sand with moisture contents respectively 10,12,15,18%; 6-9 - silty clay material with moisture contents respectively 12,15,18, and 20%; according to E.P. Shusherina); (c) - shear strength (1,1' - silty clay instantaneous strength and long-term resistance, respectively; 2,2' - clay, the same; according to N.A. Tsytovich).

Fig. 8.13. Temperature dependence of strength of frozen soils: (a) - compression strength (1 - ice, 2 - sand, 3 and 4 - clay, with natural and with disturbed structure respectively; according to Ye.P. Shusherina, I.N. Ivashchenko, V.V. Vrachov); (b) - tensile strength (1 - ice, 2-5 - sand with moisture contents respectively 10,12,15,18%; 6-9 - silty clay material with moisture contents respectively 12,15,18, and 20%; according to E.P. Shusherina); (c) - shear strength (1,1' - silty clay instantaneous strength and long-term resistance, respectively; 2,2' - clay, the same; according to N.A. Tsytovich).

The strength of frozen soils increases going from clay to sand. However, this applies only to a certain temperature point. Thus, strength of the frozen clay begins to exceed that of the frozen sand at a temperature of — 50°C and lower. The nature of the dependence a (i) for the frozen sand is to a greater extent dictated by ice content which is shown by similar curves (see Fig. 8.13a, curves 1 and 2, and 8.13b, curve 1, and curves 2 to 5). The higher strength of the frozen sand compared to ice is explained by more intensified adhesion bonds of unfrozen water, strengthening of the ice due to reduced defects and development of close-contact ice, as well as the hampering of the growth of microstresses in microfissure openings in the strong sand particles and viscous films of unfrozen water.

At a temperature below — 30°C, when the role of phase transformations is reduced, a drastic increase of strength in clay-rich ground is observed which is due to a qualitative transition of coagulation-condensation bonds into crystallization ones as a result of cementation of contacts between particles of different chemical compounds. The ion-electrostatic interaction is likely to exert influence in the latter case. With higher total moisture content in the region of W« W0 (where W0 is full saturation with water) resistance to compression for all frozen soils increases, whereas in the case of full saturation with ice and frost heave of the soil this value, as a rule, diminishes (20). The nature of the dependence of shear resistance on total moisture content at low temperatures (from —10 to — 55 °C), thoroughly studied by Ye.P. Shusherina, is essentially the same for all types of frozen soils, namely: shear resistance increases when saturation with water is not complete and structure is loose, which is explained by the development of ice-cement cohesion. In the case of full saturation with ice and where WQ is exceeded, the frozen soil resistance diminishes approaching the shear resistance of ice.

The salinity of frozen soils causes substantial reduction of their strength. This is explained by the greater amount of unfrozen water and reduced ice content of the frozen soils caused by the greater concentrations of dissolved salts (at a given temperature). In addition the structure and strength of the ice formed are dependent on the concentration of the pore solution.

Cryogenic structure has a fundamental effect on mechanical properties. At high negative temperatures, frozen clay, having a great amount of unfrozen water and massive cryotexture, is characterized by lower values of shear resistance, cohesion and friction compared to that with cellular cryotexture, for which it is typical that strength increases with greater thickness of ice schlieren if the shear plane is perpendicular to the lamination. Shear resistance of the soil with laminated cryogenic texture is greater, the larger the portion of the shear going through ice.

Frozen ground strength is to a significant extent dependent on time of loading, diminishing as it increases. Thus, at t = — 10°C, St of a particular clay was 1.8 MPa, while Slon = 0.68 MPa, i.e. one third. Shear resistance is reduced mainly because of reduction of cohesion forces of the frozen soil and, partially, by reduction of the internal angle of friction. Strength diminishes to a certain limit, the so-called limit of long-term strength.

As shown by experiments, the long-term resistance limit is much lower than, sometimes a fifth or a tenth of, the short-term resistance to compression. Thus, according to the data of S.Ye. Grechishschev, at a temperature — 3°C, frozen sand (Wtot = 19.8%), C7tc0m = 75 x 105Pa and aion = 6-5 x 105 Pa, (i.e. one eleventh), frozen silty clay material (WM = 31.8%), actom = 35 x 105 Pa and = 3.6 x 105 Pa.

Experiments determining long-term resistance to compression of frozen ground under long-term load action showed that with greater load, deformation subsides more slowly: for example, at 0.25 MPa, deformation of silty-clay material ceased in 3 days; at 0.5 MPa, only in 10 days. Experiments by S.S. Yialov confirmed that frozen and permafrost ground possess long-term tensile strength. Thus, frozen silty sandy material at 31% moisture content and t = — 4.3 °C, having er™p = 2.0 MPa, was not broken during 6 years under a stretching stress of 0.18 MPa.

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