Abstract: |
1. |
The analogy in the behavior of a rock mass and a granular medium is commonly used to build physical models of equivalent materials.
The analogy can be extended to mathematical models as well.
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2. |
An actual discontinuous velocity field can be described in terms of both an average smooth field (1.3) and kinematic tensors
(1.12). The tensor ɛ represents macrodeformations and rotations. The other tensors appear as additional kinematic variables
(microdeformations and rotations). The tensor ɛΠ describes deformation of the cement; ɛt, ɛτ describe deformation of particles; ɛR describes the relative slippage of particles. In a comparison with one-dimensional construct (1.1) the actual velocity field
(x1, x2) corresponds to the function F(x); the field
(x1, x2) to f(x); the tensor ɛ to the derivative f'(x); and the remaining tensors to the “local derivative” g'(x).
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3. |
Deformations and rotations at the microlevel are connected with macrodeformations and rotations by compatibility conditions
(1.14), (1.20), (1.21).
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Institute of Mining, Siberian Department, Academy of Sciences of the USSR, Novosibirsk. Translated from Fiziko-Tekhnicheskie
Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 14–21, July–August, 1990. |