Itc

n where Ç is depth of seasonal freezing or thawing of the ground; ^4mean is the average amplitude of annual temperature fluctuations in layer ç; C is volumetric heat capacity; X is thermal conductivity coefficient of the soil; gph is heat of phase transitions of moisture in the soil; i^eran is mean annual temperature of bare surface of ground; ris a period equal to one year; n is a coefficient approximately equal to 2 at low values of gph and ^Jl with greater gph and X.

Since the mean annual temperature of a bare surface can differ greatly from that of soils at the base of the seasonally freezing layer i^ean owing to the warming effect of snow At™ean and vegetation Ai*ee8an cover and infiltrating rainfall Afj^an, on account of the temperature offset in the layer of seasonal freezing Af^ean, then the thermodynamic condition for the development of perennially frozen strata should be represented as follows:

fi _ fSurf , i,in + Aiveg + Afinf — Afsh ^ 0°C no 101

'mean 'mean ^ "'mean ^ "'mean ^ "'mean "'mean ^ u ^ liu.iu;

The equations above (10.8-10.10) show that the temperature regime of the ground is determined by the incoming amount of solar radiation and structure of the radiation-thermal balance (proportions of its components), but it is also dependent on composition and thermal-physical properties of the underlying earth materials, on heat cycles, temperature shift and phase transitions of moisture, as well as on surface cover, ground water regime, etc. In other words, the thermodynamic conditions of perennially frozen strata are determined by geographical, geological and hydrogeological conditions.

Of paramount importance is the determination of the thermodynamic conditions for the development of perennially frozen strata as well as of the thermodynamic conditions for the formation of seasonally freezing and seasonally thawing soil layers and thus of the conditions enabling or making impossible their co-existence. Account should be taken of the mean temperature of the bare surface f^eran and the temperature deviation from the mean value during a year, i.e. the amplitude of temperature fluctuation at the surface of the ground A0. For the sake of convenience let us assume that CerL = ^mean = ¿mean- In such a case four essentially different situations can be analyzed concerning development of the seasonally freezing and perennially frozen soils (Fig. 10.1).

For condition fmean > 0, and A0 < |fmean|, only unfrozen ground can exist (situation I), as for the whole year the soil surface temperature does not go through 0°C into negative temperatures. In the case fmean>0, but for a certain time (the cold period of the year) surface temperature and that of the ground beneath is negative due to A0 > fmean, then there is seasonal freezing of ground and formation of the seasonal freezing layer (situation II). In the case when fmean < 0 the surface and underlying soil have a positive temperature during the warm period of a year (due to A0 > |fmean|). As a result, partial thawing from the surface of perennially frozen ground takes place with formation of the seasonal thawing layer (situation III). Finally, when during the whole year mean surface temperature does not exceed 0°C (fmean < 0, A0 < |fmean|) there is perennially frozen ground without seasonal thawing from the surface (situation IV).

Thus, the indispensable condition for the existence of perennially frozen ground is fmean < 0. The occurrence or absence of the processes of seasonal freezing and thawing and, accordingly, seasonally frozen or seasonally i n in ir i n in ir

Fig. 10.1. Conditions for formation and existence of seasonally and perennially frozen ground: A - expressed in terms of amplitude A0 of temperature and mean annual temperature rmean at the ground surface; B - by following the envelope of temperature fluctuations in the layer of annual temperature variation iian; clr and £th - depth of seasonal freezing and thawing of soils, Hp - lower boundary of permafrost; z - depth, t - temperature, i-time; 1-2 - layers of seasonal freezing and thawing, respectively; I-IV - for different values of A0 and fmean.

Fig. 10.1. Conditions for formation and existence of seasonally and perennially frozen ground: A - expressed in terms of amplitude A0 of temperature and mean annual temperature rmean at the ground surface; B - by following the envelope of temperature fluctuations in the layer of annual temperature variation iian; clr and £th - depth of seasonal freezing and thawing of soils, Hp - lower boundary of permafrost; z - depth, t - temperature, i-time; 1-2 - layers of seasonal freezing and thawing, respectively; I-IV - for different values of A0 and fmean.

thawed layers are determined by the relation of mean annual temperature and amplitude of temperature fluctuations at the surface of the ground. They exist if |fmean| < A0 and they are absent if |fmean| > A0. All the above cases (situations) can be shown in a diagram of A0 versus fmean (Fig. 10.2). The bisectors correspond to the condition |fmean| = A0 and therefore serve as boundaries of the likely existence of seasonal freezing or thawing.

Of paramount importance in geocryology is the concept of potential thawing or freezing. Potential thawing is possible when f^eran > 0 in the case of seasonal freezing of ground. The term refers to the depth of thawed ground developed during the summer period under the conditions fmean > 0 and |fmean| < A0, when, at the commencement of thawing the whole ground mass is frozen. This can be explained by an example: in an area of unfrozen ground (fmean > 0), there was excavation of material in winter to make an embankment of great thickness. The ground used was in the frozen state. Then in summer time this embankment thaws from the surface and, since it is rather thick, it will not thaw completely during the summer. Thickness of the layer thawed during the summer will correspond to potential seasonal thawing. A similar example can be given for the case of potential seasonal freezing (tmean < 0).

With ground temperature near to 0°C episodic increases of seasonal

Fig. 10.2. Diagram showing conditions for development and occurrence of seasonally and perennially frozen soils for various values of A0 and fmean: A - perennially frozen soils and seasonal freezing are absent; B - perennially frozen soils are absent, seasonal freezing occurs; C - perennially frozen soils and seasonal thawing occurs; D - perennially frozen soils occur, seasonal thawing is absent.

freezing that exceed the depth of potential thawing for the given ratio of ¿mean and A0, can give rise to a thin frozen layer existing for more than one year. Such frozen layers are called pereletok (short-term permafrost). It is distinguished from the short-term existing perennially frozen ground by the inconsistency of its freezing.

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