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Fig. 3.5. (a) Development of heaving stresses Phea and (b) heaving /¡hea of the surface (isurf = -2°C) of soil samples, depending on depth of freezing £ 1-3 - clay (1 - kaolinite, 2 - polymineral, 3 - montmorillonite); 4 - peat, 5 - sandy silty material; 6 - sand).

point over the value at another point, as a percentage of the distance between them. In natural conditions, the values of this coefficient of irregularity of heaving may vary within the range 3-15%, while the change in absolute values of deformation over the area of heaving may change from fractions to tens of centimetres.

Heaving of freezing soils may occur in an 'open' system (with water supply from a water-bearing horizon) and 'closed' system (without external water supply) and when water is transported by injection to the front of ice segregation. In any one of these cases the mechanism of development of heaving deformations comprises several physico-chemical processes, the share of which in the total heaving value /jheav depends on the specific conditions of the freezing of the soil. The generalized value /jheav of the freezing layer may have the following expression:

where hho is the heaving of the soil as a result of increase of water volume by 9% in the freezing part of the soil in the process of its transition into ice; /i, is the heaving due to water supplied to the frozen part of the soil by migration or injection; /jshr is the deformation value of shrinkage of the soil in its frozen and unfrozen parts.

Numerous studies have revealed that ice accumulation due to water migration into the frozen part is the principal process in the formation of the total heaving value of freezing soil (90-95%). Therefore, when the intensity of the migration water flow in the freezing soil Im increases and the rate of

ground freezing falls, then ice accumulation and, consequently, the heaving value of soils, grows. This observation was used as the basis for practically all calculation schemes and methods of quantitative estimation of the heaving value of freezing soils (I. A. Zolotar, V.O. Orlov, N.A. Puzakov, and others). These methods allow us to determine the maximum possible heaving value, i.e. the actual value of total ice accumulation in the frozen zone of the ground.

In reality, the heaving value essentially depends not only on the total (summarized) ice accumulation value in soils but on the distribution pattern of ice content in it, on the type of the newly formed cryogenic structure, and on the shrinkage value hshT here of the unfrozen zone of freezing soils. For example, if a massive cryostructure (pore ice only) is formed, then heaving may be small. There is almost no heaving in the freezing of soil of a typically cellular ('bentonitic') cryostructure owing to the specific kind of growth of vertical and horizontal ice layers with a decrease of volume of soil cells. The maximum heave usually occurs when an ice lens cryogenic structure is formed and heaving largely depends on the total thickness of ice schlieren.

The increasing intensity of water migration flows into the zone of intensive phase transitions in the series 'sandy-silt - silty-clay' causes larger heaving values due to migration ice accumulation in the freezing clayey soils. For example, the share of migration ice accumulation in the heaving of freezing kaolinite clay is 80-95%, whereas in the freezing of sandy coarse-silty samples it is rarely more than 50-60%. In clayey soils the massive heaving is normally not more than 20%, in sandy silty materials it may often reach 70-80% and more. Concurrently the settling deformations grow in the order 'sandy-silt - silty-clay', and consequently the heaving deformations are compensated to a greater extent. The shrinkage deformation hshT depends on composition and structure of the soils and on freezing conditions and may reach a considerable value, sometimes in specific conditions even exceeding the value of hv Therefore, the lithological sequence of soils may change its heaving value, if the settling of the unfrozen part of the ground is taken into account. Though migration ice accumulation in clay has rather large values, the heaving value in it can be even less than in sandy silts as a result of large shrinkage deformations. For example, in montmoril-lonite clays shrinkage can reduce heaving by 80-90%.

Development of heaving deformations in freezing soils is largely dependent on freezing conditions, i.e. on the temperature gradient in the zone of intensive phase transition, on freezing rate and external water supply. For example, the higher temperature gradient usually coincides with the growth of intensity of the migration water flow and the total heave hheav. A higher freezing rate is in all cases associated with lesser total ice accumulation and heaving. Freezing of soils in an 'open' system, that is, with a supply of water from the water-bearing horizon (migration or injection), is almost always associated with a sudden increase in heaving deformation compared to the 'closed' system. A load on freezing soil, i.e. freezing under pressure, causes less heaving because the density of migration water flow in the frozen part of the soil is less.

Subsidence of thawing soils has a more complicated mechanism and several peculiar features, which are different from the heaving of freezing soils. In the general aspect the subsidence value Ssub in natural conditions (without external load) may be written as:

where Ssub is subsidence of the ground due to thawing of pore ice and ice layers; is shrinkage in the thawed dehydrated part of thawing soil; h{r is heave deformation due to water migration and ice accumulation in the frozen part of the thawing soil; h% is swelling deformation in thawing soil in its transition from the frozen to the thawed state. It follows from equation (3.2) that, in special cases, the resulting deformation Ssub of soil may acquire positive values; for example, during slow thawing of frozen soils with massive cryogenic structure and high density of the mineral skeleton, when the components Ssub and are rather small, and the components h{T and h^ are considerable (due to sufficiently high and prolonged water migration into the frozen part of the sample and a large swelling value). In other words, in this case the ground surface does not subside (sink) but rises (heaves).

In natural conditions, the subsidence deformations (sinking of the ground surface) are dominant in thawing soils as a result of thawing out of pore ice with reduction of its volume by 9% (Spor), and of ice streaks or schlieren (Sstr). In the course of quick thawing of ice schlieren, the cavities which appear in the ground do not always become fully closed and, therefore, the total Ssub value is often less (by several percent), than the total thickness of the thawing pore ice and ice schlieren (Spor + Sstr). Only the slow thawing of frozen soils with ice schlieren can cause complete closing of cavities filled with segregation ice, that is, in this case, S^ub = Sstr + Spor. On the whole, the total subsidence will be greater the greater is the ice content and the greater the content of ice schlieren, whose thawing makes up the greatest part of the Slsub component. Maximum subsidences are typical of frozen soils with laminated and meshy cryogenic structures.

Fig. 3.6. (a) Effect of external load P on development of deformations with time during thawing of clay (after Yu.G. Fedoseyev) and (b) on the relative settlement: 1-6 - loads P, MPa (1 -0.01; 2 -0.05; 3 -0.1; 4 -0.15; 5 -0.5; 6 -0.4). Dotted lines: samples previously compacted and frozen under pressure of 0.6 MPa, solid lines: 0.8 MPa. (b) Relative compaction (/tha = etha) of the thawing soils as a a function of external load P).

Fig. 3.6. (a) Effect of external load P on development of deformations with time during thawing of clay (after Yu.G. Fedoseyev) and (b) on the relative settlement: 1-6 - loads P, MPa (1 -0.01; 2 -0.05; 3 -0.1; 4 -0.15; 5 -0.5; 6 -0.4). Dotted lines: samples previously compacted and frozen under pressure of 0.6 MPa, solid lines: 0.8 MPa. (b) Relative compaction (/tha = etha) of the thawing soils as a a function of external load P).

For practical purposes Ssub « SgUb can be adopted for sandy and coarse clastic frozen soils. In most cases, however, Ssub is seldom equal to SgUb especially in clayey soils. In fact, swelling is typical of the mineral part of clayey frozen soils even without water migration into the frozen part of the thawing soil (when + Ssbr->0). In this case swelling deformations may reach considerable values (Fig. 3.6a), particularly in soils with a mobile crystalline lattice. In mining, cases are known when thawing of supersaturated frozen clayey sediments did not cause subsidence but a positive deformation of the surface due to swelling.

The cases of subsidence deformations of thawing soils described above belong to the so-called 'thermal' subsidence, when frozen soils were not subjected to any substantial loads (dwellings or engineering constructions). The notion of stabilizing subsidence, or Stha, is used in engineering practice; it takes place under the effect of a continuous load P on thawing ground until the moment of complete thawing and stabilization of subsidence due to consolidation. Stabilized subsidence in this case is composed of the thawing subsidence Ssub or 'thermal' subsidence unaffected by any external pressure, and subsidence by consolidation Scomp, which is a direct function of normal pressure, i.e. Ssub(P) = Ssub + Scomp. A comparison of compression curves of unfrozen and thawing soils shows that the greatest deformations and changes in the porosity coefficient e appear not in the process of consolidation of the thawed soil, but in the course of its thawing, i.e. in most cases Ssub > Scomp. The same dependence is shown by plots of changes in relative subsidence (etha = (Ssub + Scomp)/l = Ssub{P)/l, where / is the thickness of the thawed ground) of frozen soils during thawing and their concurrent densifi-

cation by the compressing-densifying load P (Fig. 3.6b). The equation of the straight line etha = f(P) will be etha = A + aP or

where A is the coefficient of thawing during thermal subsidence (P = 0); a is the coefficient of relative consolidation of the frozen ground on thawing.

The process of thawing in frozen ground greatly changes its texture and structure; adhesion becomes many times less in thawed soil (Ctha « Cfr), and permeability increases by several times compared even to unfrozen ground of the same composition. These effects determine the character and intensity of contraction of thawed soil, i.e. the consolidation subsidence value Scomp. The ice content i in thawing soils is an important index of estimation of their densification subsidence with time. The theory of filtration consolidation can be applied to ground with high ice content, and Scomp will be first of all determined by conditions of water filtration from the thawed zone of the ground. In the case of ground with low ice content, the theory of creep is primarily applied, and Scomp is determined by the structural transformations of soil as a result of visco-plastic displacement of particles and aggregates of the soil.

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