The principle of information entropy for the description of fracture at multiple dimensions in real materials (concrete, rock) of buildings and rock seams^*

Abstract

The paper describes the generation of results from research into patterns of cracks forming in massive concrete and reinforced-concrete structures and rock. In the stage of pre-failure the massive over-sized solids (concrete, rock) transmute into a hierarchy of unitized solids, each enclosed in other blocks divided by long and broken cracks. Research in structural geophysics by M.A. Sadovskiy, V.A. Petrov, A.V. Drumya and N.V. Shebalin has indicated that sizes of rock blocks between cracks vary widely, but on average by 3.5 times. Taking into account the magnitude of the `jump' of 3.5, we shall have the nominal size of concrete block and levels of the hierarchy. Disclosing indeterminacy in a pattern of cracks, from the beginning and up to the end of loading, is for the first time described here with the help of information entropy under multi-step independent communications from many sources (signals of ruptured links between blocks). The concept of obtaining a stage of a structure under every degree of loading includes the parameter of reserve of serviceability for a structure. The curve of the parameter of serviceability coincides with the curve of the information entropy by the character of change. This permits the use of the scale coefficient in design. Using the criterion of serviceability means a design on a new state, i.e., the longitudinal crack resistance. This determines an assessment of expedience rehabilitation of a structure's damage with unknown load.