Strength of ice in pores
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In the general problem of the strength of moist dispersed systems (soils, noncohesive rocks, granular loads, etc.) there are no concepts concerning the strength of the ice formed in the pores and the interstices between the solid particles. This is due to the difficulties of experimental determination of the strength of this ice. However, these concepts are necessary both for understanding the nature of the strength of dispersed systems and for solving various types of engineering problems in mining, construction, transporting of loads, etc. In this communication we give a theoretical estimate of the strength of ice in pores on the basis of present-day concepts of the physics of the strength of polycrystalline solids. In contrast to freely crystallizing ice, the ice which forms when the pore moisture in dispersed material freezes is produced in confined conditions. This confinement of crystallization which is due to the limited volume in the pores and interstices between the solid particles, must lead to the formation of fine-grained polycrystalline ice as a result of its growth from the mineral particle surfaces into the pore volume, because the formation energy of a nucleus on a thoroughly wetted surface is less than that of a free nucleus [i]. In this connection the shape of the ice crystals will be close to isometric, and their size will be determined by the degree of dispersion of the mineral particles. Clearly the strength of such ice will differ significantly from that of freely crystallizing ice. It is known that the strength properties of polycrystalline solids depend strongly on the size of the grains, and their components. Such a dependence has been established experimentally for metals and is known as the Perch--Hall formula [2]:
~=go+kd -I/~,
(i)
where g is the lower yield stress or breaking stress, go and k are constants, and d is the mean grain size. This dependence also governs the strength properties of polycrystalline bodies and other classes, e.g., cermet semiconductive compounds based on chalcogenides of lead, bismuth, antimony, etc. [3]. Thus, we can postulate that the equation holds for polycrystalllne ice also. The constants go and k are usually determined experimentally. However, their determination is extremely difficult in the case of pore ice. This means that theoretical determinations of go and k from the postulates of the dislocation theory of strength are of great importance. An attempt to give a theoretical explanation of the inversely proportional dependence of the breaking stress on the square root of the grain size was made by Cottrell [2] on the basis of the generalized Griffith crack theory. According to Cottrell
o
I
T2( )12. I
where g is the applied stress; gf, stress due to friction in the slip plane; and y, surface energy.
s , shear modulus;
Clearly the first term on the right-hand side of Eq. (2) does not depend on the grain size, and characterizes the strength properties of monocrystalline material. The "characteristic strength" of monocrystalline ice can be determi
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