Generalized Stress Deviator and New Limiting State Criteria for Geomaterials
O. A. Mikenina, A. F. Revuzhenko
Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
Keywords: Rock pressure, stress tensor, deviator, limiting state, Mohr-Coulomb criterion
Abstract
The generalized stress deviator is introduced as a difference between a stress tensor and a unit tensor multiplied by an average normal stress non-reducible to an octahedral normal stress in a general case. From the condition that the average normal stress of the generalized deviator should be identically equal to zero, a functional equation relative to the average normal stress is obtained. The solution of the equation is given; it depends on one of the functions of two variables. The class of the limiting state criteria formulated relative to the average normal stress and the second invariant of the generalized stress deviator is discussed. It is shown that the von Mises-Schleicher and Mohr-Coulomb criteria belong in this class. Some intermediate cases are also discussed.
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