Fig. 3.11. (a) Rheological curve of fine-grained soil and (b - c) diagrams of deformation of bodies: (b) elastic (Hooke's law), (c) elastoplastic; (d) non-linear-elastic, (e) viscous (Newton's law), (/) viscoplastic (Bingham's law), (g) non-linear viscous).

mation rate" dependence is normally applied. As noted by S.S. Vyalov (4), this seems more reasonable, because there is an analogy between the diagrams of deformation of elastic and viscous bodies (Fig. 3.11), which allows application of viscosity theory and of plasticity theory for problems of viscous flow, i.e. linear in the former case and non-linear in the latter. These solutions, with appropriate assumptions, can be used by formal substitution of the deformation value s by its rate s = de/dx.

The graphic dependence between the stress and the rate of steady flow is called the rheological curve and is described by Newton's or Bingham's equations (Fig. 3.11e,f). For thawed and frozen fine-grained soils however, the rheological curve is more complicated (Fig. 3.1 la). The flow of such soils at constant rate starts only after the critical crcr is exceeded. Up to that limit the deformations usually attenuate. When the stress crcr<a<a'cr, the rheological curve approaches a straight line, i.e. the flow in this segment of curve develops with constant maximal viscosity, called the Shvedov viscosity: t]sh = (<7 — <Jcr)/s = tan a. When <r'cr < a < a'^, there appears another linear segment on the rheological curve of frozen soils, where deformation (flow) occurs with constant minimal viscosity, called the Bingham viscosity: t]h = (cr — <r'er)/E = tan a'. Therefore, the deformation (flow) of frozen soils at constant rate has two critical values of viscosity, i.e. the highest f/sh viscosity, which corresponds to a practically undisturbed structure, and the lowest rjb viscosity, corresponding to the ultimately destroyed soil structure.

Specific ice-cementing bonds and cryogenic textures and structures are of fundamental importance in the development of rheological processes in frozen soils. Deformation of frozen soils due to displacements of individual soil particles or microaggregates in relation to each other takes place in the films of bound water and in the ice inclusions dividing them; most of these films and inclusions are actually areas of lower strength, i.e. 'defects' in the body of frozen soils. Further development of the 'defects' and their transformation into microcracks or local dislocation zones, should play the principal role in frozen ground destruction and cause weakening of inter-particle and interaggregate ties and lower local structural strength in some of its parts.

When ice content is high in frozen soils, then in the course of different types of deformations (shear, compression, extension) both momentary and long-term strength are reduced and reach the critical strength of ice. Consequently, during long-term deformations of frozen soils in the zones of displacement, microdislocation or extension, the local strength should decrease with time as a result of the supply of migrating unfrozen water and the increase of the ice content. The orientation of the forming ice microschlieren and the reorientation of soil microaggregates along the planes of displacement and microdislocation also cause reduction of resistance to dislocation, tension or compression in frozen soils locally. This process causes development of such deformations as unattenuating creep, flow or progressive creep, which terminate in destruction of the continuity and stability of the soil. In other words, a load which is constant in time causes greater deformations due to progressive reduction of frozen ground strength.

Concurrently with processes of structural transformation (weakening) during slow deformation of frozen soil described above, counter-processes and events develop in it. Among them are 'healing' of structural defects, closing of microcracks, reduction of interaggregate and aggregate porosity, rearrangement and denser packing of ground particles and aggregates, re-establishment of ties and greater molecular and cementing adhesion, etc. This combination of processes naturally results in strengthening of the frozen soil and its decreased deformation. According to S.S. Vyalov, N.A. Tsytovich and other researchers, the generation and development of rheological processes (creep and stress relaxation) in frozen soils are determined by two concurrent counter-processes of structural transformation: strengthening and weakening. If strengthening prevails, then creeping deformation attenuates. When weakening and strengthening deformations are mutually compensated, then the deformation develops continuously at a constant rate (viscoplastic flow). If weakening prevails over strengthening, then the deformation grows and unattenuating (progressive) creep develops.

The character and mechanism of slow deformation (creep) in frozen soils are different at different stages of creep (Fig. 3.10b). At the first unstable stage (attenuating creep) only small changes in the structure of frozen soil are observed, such as lesser inter-aggregate porosity, squeezing out of the air, a certain redistribution of ice content and moisture, healing of old and newly formed defects in structure and, as a result of displacement and denser packing of ground particles and aggregates, restoration of old and the appearance of new ties between particles. On the whole, the frozen ground is strengthened and deformations attenuate.

The second stage of deformation shows greater structural changes in frozen soil. The aggregates begin to disintegrate and fall into fragments, their basal planes start to reorient in the direction of the vector of dislocating tangential stresses or normal to the compressive stresses. This process reduces the resistance of the frozen soil to applied load. Destruction of structural bonds increases in the weakest areas of the frozen soil and structural defects increase. In this case the processes of formation of structures which strengthen the soils are subordinate. The principal role at this stage of deformation belongs to unfrozen water migration to the zones of concentration of dislocating or extending stresses. In the course of this process, the segregational ice schlieren, lying along the planes of dislocation (microdislocation) or tension, encourage sliding or fracture of the material and accelerate the flow process, which results in gradual and regular reduction of resistance of frozen ground to loads, i.e. the monotonous relaxation and deformation of ground at a constant rate.

Finally, a sufficiently long application of load creates areas in the ground with a maximum ice content, in fact an ice body with soil inclusions and the properties not of ground but of ice. With this kind of transformation of frozen soil structure its strengthening becomes practically impossible. Therefore, the deformation process passes to the stage of progressive flow which terminates with plastic loss of soil stability.

Not only the time period of load effect but also its value should be always taken into account when analyzing the mechanism of frozen soil deformation. For example, the creep curves (Fig. 3.10a) show that with the increase of applied load the area of constant deformation rate gradually disappears being transformed into the stage of progressive creep. Under the effect of high loads the unfrozen water migration and ice content redistribution in frozen soil are obviously insignificant.

If we disregard the cases of limited lateral deformations (triaxial test) or completely impossible lateral deformations (compression) of frozen soils under the effect of external loads, then the behaviour of ground in all other cases, i.e. during displacement, compression and extension (with free lateral deformation), will have a number of similar features. All kinds of deformations may in this case be classified as momentary, long-term, and destructive. Of momentary deformations in frozen soils the elastic deformations have the most practical significance, and of long-term deformations the attenuating creep and viscoplastic flow, degenerating under certain conditions into progressive flow, are the most important from the practical point of view. Among destructive deformations the brittle deformations are usually recognized as important, because they destroy the continuity of the frozen soil, and consequently inadmissible plastic changes of shape occur, resulting in the loss of the bearing capacity and stability of soils. These deformations are closely related to the ability of frozen soils to resist external load, i.e. resistance (momentary and long-term) to compression, extension, dislocation, etc.

The long-term deformations of frozen soils are of particular importance in both theoretical (geological) and economic aspects. These deformations develop under conditions of free deformation, and the longest of them and of the most practical significance is the settled or viscoplastic flow with constant deformation rate. The curves of creep during compression, dislocation and extension have on the whole a similar character (all three stages of creep and transitions from one stage to the next are clearly outlined), the difference is only in the quantitative property of the process. These conclusions were derived from the experimental data obtained by S.S. Vyalov (4) for frozen soils (Fig. 3.12), showing that, in the case of dislocation and compression, the transition from attenuating to unattenuating creep occurs during stresses which comprise 25-50% of the conventional-momentary strength of the frozen soil and, in the case of extension under loads, 8 10% of cmom. The stage of unstable flow can develop during several hundreds of hours and longer, the stage of the viscoplastic flow for several thousands of hours, and the stage of progressive flow (until the moment of destruction) from a few to hundreds of hours and more, depending on the amount of applied load.

For practical purposes, the effect of composition, cryogenic structure and properties (including temperature) of frozen ground on long-term deformations is of the greatest interest. In plastic frozen clayey soils with high contents of unfrozen water and ice, high negative temperatures and aggrega-tional and ice-aggregational types of contacts, the stage of the steady flow can continue for a long time, and it passes into the stage of progressing or 'secular' creep at a « 0.1 — 0.5 cmom. In solid frozen soils with low ice and unfrozen water content, low negative temperatures, ice-crystalline, coagulation and ice-coagulation contacts, the stage of attenuating deformation a

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Fig. 3.12. Creep curves for frozen soils (4): (a) - silty clay (dislocation along a cylindrical rod frozen at t = -0.4°C); (b) - sandy silt (dislocation on shearing device at t = - 10°C); (c) - sandy silt (uniaxial compression at t = — 20°C); (d) - polymineral clay (uniaxial compression at t = -20°C). A/i = deformation, s = strain).

Fig. 3.12. Creep curves for frozen soils (4): (a) - silty clay (dislocation along a cylindrical rod frozen at t = -0.4°C); (b) - sandy silt (dislocation on shearing device at t = - 10°C); (c) - sandy silt (uniaxial compression at t = — 20°C); (d) - polymineral clay (uniaxial compression at t = -20°C). A/i = deformation, s = strain).

usually dominates; it often transits immediately (omitting the stage of steady flow) into the stage of progressive flow. The progressive deformation develops at loads a « 0.5-0.7 amom, continues for a relatively short time and results in mostly friable destruction.

The deformation of frozen soils during the stage of visco-plastic flow with constant rate can be well traced on rheological curves (s =f(a))\ it is determined by the coefficient of viscosity t]. The presence of film unfrozen water in the soil is a determining factor in the development of creep and viscosity in frozen ground. According to N.A. Tsytovich (20), during experiments at f = — 0.8°C, the viscosity coefficient in frozen sandy silty material at Wtot « 19% was rj x 1.9 x 10nPa s; and in frozen clay at Wtot « 28%, t] « 0.9 x 10nPa s; this is almost an order of magnitude less than the viscosity coefficient of pure ice, which at t x — 0°C is rj x 1.2 x 10nPa s. These results can be, apparently, attributed to the fact that in the region of considerable phase transitions frozen clay contains much more unfrozen water, which causes greater rate of flow of clay compared to that of sandy silt and of ice. For this reason, as the negative temperature falls, the viscosity of the frozen soil grows. In this case, the viscosity coefficient is not a constant of the frozen soil but it is characteristic of the deformation process, essentially dependent both on the previous history of the stress-deformation of the soil and on the nature of the development of deformations, and on the kind of load (compression, dislocation, extension, torsion) and the method of load application (uniaxial, diaxial or triaxial tests) and conditions of loading.

The behaviour of frozen soils under external load in compression and triaxial tests essentially differs from their behaviour under conditions of free lateral deformation. For example, the creep deformation (without the possibility of lateral expansion of the frozen material) will always be attenuating under compression or under the effect of continuous load regularly distributed over the ground surface. As shown, however, by Brodskaya, Vyalov and Tsytovich, practically all frozen soils and particularly soils at high-temperature or with high ice content, experience considerable compressibility (densification) under load with time. This occurs owing to elastic deformation and closing of empty pores, cracks and other defects in frozen soil and also as a result of the lower porosity of the organic-mineral skeleton, as the unfrozen water and ice are evacuated from the frozen soil. Experimental research shows that compaction (consolidation) of frozen soils is inherently connected with the development of several extremely complicated physico-chemical processes. The most important are phase transitions of ice into bound water, migration of unfrozen water, redistribution of ice content in soil and transformation of microstructure, dislocation of ground particles and their aggregates, etc. On the whole, the pressure transmitted to ice-saturated ground is distributed between the mineral skeleton, ice and unfrozen water, which behave differently with time under load. Therefore, consolidation and compression of frozen soils largely depends on their composition, cryogenic structure, ice content, degree of filling of the pores with ice, and on the negative temperature and the active load (Fig. 3.13).

Fig. 3.13. (a) Curves of consolidation of frozen soils with time (b) compression of the same frozen soils for various loads (with load increments of 0.3 MPa): 1 and 2 - under temperatures of - 3 °C and -1.5 °C, respectively; 3 - 5 - polymineral clay: 3 - ice-saturated (G = 1); 4 - salt added (Z = 1.5%), 5 - not saturated with ice (G = 0.6).

Fig. 3.13. (a) Curves of consolidation of frozen soils with time (b) compression of the same frozen soils for various loads (with load increments of 0.3 MPa): 1 and 2 - under temperatures of - 3 °C and -1.5 °C, respectively; 3 - 5 - polymineral clay: 3 - ice-saturated (G = 1); 4 - salt added (Z = 1.5%), 5 - not saturated with ice (G = 0.6).

Transportation of unfrozen water and its evacuation from the ground system play an important role in frozen ground deformation under compression; as a result of this process the total water and ice contents in soils decrease. The deformation of frozen soils by compressional compaction due to seepage-migration in the frozen soil is often called initial consolidation, because it is assumed that deformation is the greatest in the initial period after application of load. In the course of time, its share in the total (stabilized) deformation of the consolidation of frozen soils becomes increasingly less. On the whole, seepage-migrational deformation is most

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