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Fig. 12.4. Graph of the variations of depth of ground freezing with time under 100000-year temperature fluctuations on the surface (after V.A. Kudryavtsev) for (1-3) moisture contents Wof 10,15,20%, respectively.

centimetres per year. When phase transitions of the water in the ground take place, the freezing rate is two to three orders of magnitude lower than the rate of penetration of the thermal wave into the permafrost where phase transitions are absent. Actually, as mentioned above, the temperature wave of period T = 300 years in dry ground reaches a depth of about 180 m, while freezing of moisture-rich rock of the same thickness takes 33 000 years, when the period of fluctuation (J) is equal to 100000 years.

The effect of the amplitude Aper and the mean (for the period Tpet) temperature (tper) on the depth of perennially frozen ground in the context of thermal physics are similar to their effect on seasonal freezing and thawing.

An increase of amplitude Aper of the temperature fluctuation on the surface of a frozen rock unit under a fixed value (for the fluctuation period) of the mean temperature tper causes deeper perennial freezing of the ground and formation of permafrost of greater thickness (Fig. 12.5). The dependence of permafrost thickness on variations of amplitude of the temperature wave, presented in the diagram, was obtained by Kudryavtsev using the formula (1.45) and computer computations, given the following input parameters: Tper = 100000 years; g = 0.01 °C m"1; fper = 1°C;1 = 2.89 kJ (mhr.°C)_1; <2ph = 52 375kJ m~3. According to the calculations, the increase by each 2°C of Aper in the range of amplitudes from 2-8 °C causes the thickness of permafrost to build up by 43, 28 and 23 m, respectively.

The dependence of the change of permafrost thickness ¿;per on the mean temperature iper (for the period of fluctuation) has also been obtained by Kudryavtsev from the calculations (Fig. 12.6), using the same values of input parameters as in Fig. 12.4. The maximum permafrost thickness appeared to be: £per = 130 m under f^ = 4°C; £per = 90 m under Ca„2 = 2°C; £Per = 45 m under tmeran3 = 4°C all other things being the same. Thus with the increase of mean perennial temperature, for every 2°C in the range of fPeeran from 0 to 4°C, permafrost thickness decreases by 40 and 45m

Fig. 12.5. Variation of the permafrost thickness depending on the amplitude of many-year temperature fluctuations on the surface at fPeeran = 1 C (after V.A. Kudryavtsev).

-t -6 -4 -2 0 2 4 6 8 10 + i ° C

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