New Method for Obtaining the Homogeneity Index m of Weibull Distribution Using Peak and Crack-Damage Strains

Abstract

Heterogeneity is an intrinsic characteristic of rock and rock-like (brittle) materials. The statistical homogeneity assessment using Weibull distribution with a homogeneity index, m, is one of the most widely used methods for characterizing brittle material heterogeneity. The critical issue for this method is to obtain the m values. For previous studies, the linear least-squares (LLS) technique was used to obtain the m values during numerical modeling, which involves the ranking of failure strength data of the brittle-material model elements in ascending order. However, it is difficult to obtain the physical-mechanical parameters of the elements from laboratory experiments. Conversely, the macroscopic physical-mechanical parameters of brittle-material specimens in laboratory scale can be easily obtained. The objective of this paper is to present the creation of a practical method to obtain the homogeneity index m via the ratio of a macroscopic physical-mechanical parameter. According to the renormalization group theory and the acoustic emission (AE) technique, a new m-value-obtaining method, in which the peak strain is linked with the crack-damage strain (strain at the crack-damage stress threshold), is presented. To verify the feasibility of the proposed method, uniaxial compression tests on rock-like material (cement) specimens with different homogeneities were conducted. The specimen homogeneity was dominated by artificially created pre-existing flaws. In this paper, the effect of the geometries of the pre-existing flaws on the degree of homogeneity of the tested specimens and the influence of the homogeneity on the macroscopic mechanical properties are discussed according to the test results and proposed theoretical method.