From criticality to final collapse: Evolution of the “b-value” from 1.5 to 1.0

Extensive research and studies on concrete fracture and failure by means of the acoustic emission (AE) technique have shown that fracture and damage growth can be characterized through a single synthetic parameter, namely the b-value, which changes systematically during the different stages of the failure process, as shown by several AE tests carried out from the specimen to the structural scale [Sammonds PR, Meredith PG, Murrel SAF, Main IG. Modelling the damage evolution in rock containing porefluid by acoustic emission. In: Proceedings of the Eurock’94; 1994; Colombo S, Main IG, Forde MC. Assessing damage of reinforced concrete beam using “b-value” analysis of acoustic emission signals. J Mater Civil Eng ASCE 2003;15:280–6; Carpinteri A, Lacidogna G, Niccolini G. Critical behaviour in concrete structures and damage localisation by Acoustic Emission. Key Eng Mater 2006;312:305–10]. This parameter can be linked to the value of the exponent α of the power-law distribution of the crack size in a damaged structure. In this paper, we propose a statistical interpretation for the variation of the b-value during the evolution of damage, based on a treatment originally proposed by [Carpinteri A. Mechanical damage and crack growth in concrete: plastic collapse to brittle fracture. Dordrecht: Martinus Nijhoff Publishers; 1986; Carpinteri A. Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics. Int J Solid Struct 1989;25:407–29; Carpinteri A. Scaling laws and renormalization groups for strength and toughness of disordered materials. Int J Solid Struct 1994;31:291–302]. The proposed model captures the transition from the condition of criticality, in which α = 3, to that of imminent failure, characterized by α = 2, in terms of damage localisation.