On The Time Dependence, Probability Distribution, and Size Effect of Rock Strength

Abstract

Time dependence, probability distribution, and size effect have been investigated by many researchers and are still important issues in rock engineering. These seem to be different characteristics of rock but were found to be closely related to each other through laboratory tests with rock specimens in recent studies. In this paper, the theoretical aspects on the time dependence, probability distribution, and size effect of rock strength were explained, and some of the theoretical results were compared with the previous experimental results. The theoretical formulae based on the rate process theory that represent the failure progression of rock were introduced, and their relation to the theories of visco-elasticity and visco-plasticity was described. The exact solutions of the loading-rate dependence of strength and the creep lifetime were derived from the formulae and were compared with the experimental results of andesite. In addition, the exact solutions of the probability distribution of strength and creep lifetime and their relation to the statistics of extremes were described; the exact solutions of the size effect of strength and creep lifetime and their relation to the comminution theory were also described. The authors clarified what issues have been or have not been verified in previous studies and presented the subjects of future investigation.

Keywords

• rock
• strength
• loading-rate dependence
• extreme value distribution
• size effect