Application of generalized logistic equation for b-value analysis in fracture of plain concrete beams under flexure

Abstract

This work investigates the effect of finite size and evolution of fracture process zone on b-value of acoustic emission in concrete beams. It is shown that the AE b-value determined using the Gutenberg-Richter (GR) law varies with beam size and invalidates universality. Since GR law fits the frequency-magnitude curve partially, a recently proposed Maslov’s generalized logistic equation (GLE) is used for b-value analysis. The existence of cut-off magnitude and nonlinearity of frequency-magnitude distribution is explained through crack interaction mechanisms occurring within the FPZ. The growth of micro and macro cracking in concrete is observed to follow logistic or sigmoid growth law rather than the power law. The b-values obtained from GR and GLE are compared and it is found that the b-value of GLE correlates well with the effective crack length during damage process of plain concrete thereby exhibiting damage compliant behavior which could be used in health monitoring of structures.