STATISTICAL NATURE OF STRENGTH AND SCALE EFFECT IN MOUNTAIN ROCKS

Abstract

The theories and concepts of strength considered above are based on the model of a body either as a homogeneous structureless medium, or as a material having a structure, but uniform throughout its volume. Rocks are obviously not such bodies. They are composed of mineral grains of different properties, contain macrodefects in the form of pores and various inclusions, as well as objects of various aggregate states (gases, liquids). Under these conditions, deterministic theories of strength turn out to be clearly untenable. In particular, the use of the classical theory of Griffith cracks is complicated by the following circumstance. Since the rock is an aggregate of mineral grains, a microcrack developing inside the grain inevitably reaches its boundary and, consequently, the radius r of the crack mouth increases abruptly. Therefore, for the transition of a crack to another grain and its further development, a stress greater than that follows from Griffith's theory is required. Thus, there is some "barrier" stress, at which only the development of a crack in a real rock is possible. In addition, the development of cracks in the rock occurs mainly along the contact of mineral grains, i.e., along the cementing material, often of a clay composition. For such a material, the theory of brittle fracture is applicable. The destruction of the rock (from the standpoint of any theory of strength) is determined by the stresses acting in it. But due to the heterogeneous structure of the rocks, the local stress concentration centers are randomly distributed in its volume. Therefore, the strength and destruction of rocks must be considered from a statistical standpoint. This approach is justified for most other materials used by humans. The idea of the statistical nature of strength was first put forward in scientific terms by A.P. Aleksandrov and N.S. Zhurkov in 1933. Keywords: rock strength, constant material, scale effect, rocks, destruction probability, fractured, robustness theory, microcrack, mineral, experience constant, density of defects, displacement, compression.