The search for reliable methods of forecasting macrofailure is one of the basic problems of modern geodynamics. This problem depends to alarge extent on the possibility of determining reliably defined precursors of failure (Sagiya 2011). Till now, these have been considered to be a rise in the acoustical activity of rocks and mass and large anomalous deformations of source areas and connected with formation of the area site for. However, restricting searches for precursors to field sites only for an area sharply narrows their nomenclature, and so also the quantity of independent information sources. There is a need to search for additional precursors that are closely connected with the formation of the source of the macro failure. Such precursors can be found in the area near the source which are directly bordering on the area site for. Attention to the reversible character of linear deformations of rock samples was presented, apparently, for the first time in (Seldenrath & Gramberg 1958). The authors did not research the mechanisms of the origination of the deformation anomalies, but already in subsequent works such attempts have begun to be undertaken. So the reversible character of the deformations of rocks was contacted with a barrel-shaped straining of samples at uniaxial compression (Tomashevskij & Khamidullin 1972). In the works of other researchers, residual stresses were proposed in the capacity of reasons for deformation anomalies of various types (Tazhibaev 1986). However, these hypotheses are not supported by critics on closer examination (Guzev & Makarov 2007). In this paper, based on specially developed complex research methods, including on deformation, acoustical and mathematical methods, the authors analyse deformation anomalies of reversible types in samples of rocks at uniaxial compression, define the mechanism of their origin, and develop a mathematical model of the phenomenon.

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