b-value of plain concrete beams based on AE Quanta

Abstract

In seismology, Gutenberg-Richter relationship $\log_{10} \ N = a - bM$ is an empirical relationship between the magnitude of earthquake and its recurrence frequency. The constant ‘b’, is called the b-value and is the log linear slope of frequency-magnitude distribution. An analogy is drawn between earthquake and failure process in concrete. During the failure process of concrete, Acoustic emission (AE) energy is released in the form of energy waves having certain peak amplitudes. While estimating the b-value during fracture in concrete, peak amplitudes of the AE signals are used. Right from the onset of micro-cracks till failure, the AE events are recorded with their peak amplitudes and AE energies. Interestingly, the AE energy release has been observed to be in “packets” or bursts. These energy packets have been called by the authors as AE quanta. In the estimation of b-value, peak amplitudes of events of groups having a definite number are used. Instead of using amplitudes of arbitrary group of events, quanta are utilized as groups for obtaining the b-value,. Unlike in seismology, wherein the b-value could be nearly unity, it is found that the b-value from quanta is much less than that obtained from the amplitudes.