f A

Fig. 3.9. Development of stresses and strains due to temperature in frozen soils, (a) Change in stress with time on reduction of t from — 2CC to — 15°C:

1 - montmorillonite, 2 - kaolinite, 3 - sandy silty material; 4 - sand. (¿) Change of temperature f, all-round stresses of distension PJ1 and linear dimension of frozen soil sample, I, against height, /?. 1 - unallowable temperature deformations of soil,

2 - actual deformations, l0 — l3- boundaries of soil sample; A-D -conventionally identified layers).

A striking manifestation of frost shattering in fine-grained soils is the formation of polygonal (in plan) nets of cracks and systems of intersecting wedgelike-vein underground ice. B.N. Dostovalov (17) has estimated the sizes of the polygons of cracking from data on temperature stresses developing in frozen soils. The distance between the vertical cracks (the size of polygons) can be determined using the equation:

o.G grad t where Ptd is the rupturing stress (volumetric-gradient tensile stresses equal to the instantaneous resistance of frozen soil to fracture); a is the coefficient of linear temperature deformation of the ground; G is the elasticity modulus during displacement; grad t is the temperature gradient with depth of the frozen soil. If the temperature gradients in homogeneous materials are small, then large rectangular blocks are formed. As these gradients grow, the rectangular cleavages are split consecutively by frost cracking of the second and higher generations, thus producing progressively smaller blocks. In heterogenous frozen soils, the process is more complicated, and frost clefts cannot be strictly parallel, but are mostly tetragonal and polygonal varieties.

The system of general temperature cracks, which break up frozen ground into rather large blocks and lumps, can be combined with smaller frost cracks (microcracks), which break up minerals and fracture rocks (up to the silt fraction). Temperature disintegration, or temperature destruction of fragments of rocks or minerals, is produced by different values of thermal expansion of the components of frozen rock, causing 'unallowed' deformations, and, consequently, volumetric-gradient stresses Pa on the boundaries of these components. Macrocracks occur when these stresses exceed the local strength of the rock or mineral fragment (Pa > crcoh). Naturally, rocks will disintegrate not momentarily, but gradually as microcracks appear, develop, merge, and grow due to repeated heating-cooling cycles.

Disintegration and fragmentation of debris of polymineral rocks are determined by volumetric-gradient stresses related to the maximum difference between thermal expansion coefficients of the components and minerals constituting the rock (A a = amax — ocmin). The greater this difference, the greater, evidently, will be the 'unallowed' temperature deformations and, consequently, the volumetric-gradient stresses Pa in the rock, i.e.

where kt is the coefficient of proportionality, or transition of 'unallowed' deformations into stresses, Pa°C.

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