Fig. 1.13. Dynamics of the phase boundary movement under the changing temperature conditions on the surface: 1-111 - stages of the temperature change -in time (I - lowering; II - stabilization; III - rising); £ - position of the phase boundary; <jfr and <junf are the intensity of the heat flux from £ to the surface and from the unfrozen or thawed zone to £ respectively.

phase transitions and consequently on the temperature field. And finally, the increase of water volume in the course of freezing as well as its migration into the freezing zone can cause changes in the stress field in soils, associated inversely with the process of freezing (thawing). The fact that the depth of the phase transition zone is time-dependent is a vital particular feature of this zone in which the processes discussed above proceed. This boundary (zone) is moving and we can observe the sharp changes in the values of heat fluxes arriving at this surface and leaving it (Fig. 1.13). It is these abrupt changes which are responsible for the conditions of phase boundary movement in the ground.

Let us consider such a case (see Fig. 1.13). Assume that the temperature at the surface of the ground mass to the base of which the constant heat flux q arrived from the Earth's interior, had passed through 0°C at the initial moment of time q = 0 and the process of freezing had begun. The temperature on the surface fell further for some time and then became constant (negative). And finally, after a further period it began to rise, but remained negative. The process of freezing (thawing) of this mass has three clearly discernible stages (see Fig. 1.13). At the first stage the value of heat removal qir from the phase boundary turns out to be greater than that of heat arrival from the Earth's interior quni, i.e. qfr>qunf- Consequently freezing at the front occurs and the boundary moves downward, i.e. d^/dx = <f>0. At the second stage a balance of ingoing and outgoing heat is established at the phase boundary m, i.e. q[r = quni. The freezing boundary turns out to be fixed in this case, while = 0. And finally, in the third stage, warming on the surface results in the value of heat being removed from the boundary £ being less than that arriving from the Earth's interior, i.e. qir < quni. In this case the frozen body thaws from the bottom upwards. The thawing boundary moves upward while £'<0. It is precisely in this manner that the process of perennial freezing and thawing of strata proceeds, in many cases.

It should be stressed that the inequality between qit and qun{, i.e. qit — qun{ = Aq, with Aq is a necessary condition for the process of phase transition to proceed in freezing or thawing ground. At the same time for any period of time Ax, such a ground layer A£(A£ = £'At) freezes or thaws in which all the difference (AqAt) between the amounts of heat incoming to and outgoing from the front will be spent on the phase transition of water (2phA£). In other words, the heat condition at the mobile boundary of materials which are freezing or thawing can be written as: AT(qft — qunf) = QphAl The rate of ground freezing or thawing can be found from this expression, i.e. the velocity of movement of the boundary of moisture phase transition is as follows:

It follows from this that heating of ground below the phase front by phase transition heat being released in the course of freezing is impossible, as this heat can be released only when it can be removed, with the amount of released heat being equal to that of the heat which can be removed into outer space through the overlying layer of freezing ground.

Usually the previously obtained expression is written as Qtr ~ Qunt = or if writing the expression for heat fluxes:


unf d"

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