Rock as a medium with internal energy sources and sinks: Paper 1

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. 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\(\bar V\)(x1, x2) corresponds to the function F(x); the field\(\bar v\)(x1, x2) to f(x); the tensor ɛ to the derivative f'(x); and the remaining tensors to the “local derivative” g'(x). 3. Deformations and rotations at the microlevel are connected with macrodeformations and rotations by compatibility conditions (1.14), (1.20), (1.21).