Prediction of cracking evolution in full scale structures by the b-value analysis and Yule statistics

Abstract

Understanding and predicting the process of material fracture and failure in heterogeneous materials such as rocks, concrete, ceramics and other composites is an extremely challenging scientific problem, central to a large number of applications and crucial in predicting the long-term structural integrity of structures. The complex phenomena occurring at the micro- and mesoscale can be monitored by using acoustic emission techniques that reveal some universal features in the damage evolution and fracture. In particular, extensive research works and studies on concrete fracture and failure have shown that fracture growth and damage evolution can be characterized through a single synthetic parameter, namely the b-value of the Gutenberg-Richter law, which changes systematically with the different stages of fracture growth. In this paper, we propose two different interpretations for the variation of the b-value during the evolution of damage, focused on the spatial development of cracks in the material. The first one, called the self-similarity approach, is based on fractal geometry and the statistical characterization of the cracks inside a material by means of two power-law distributions: one for the spatial arrangement of crack barycentres, and the second for the crack length distribution. The second interpretation is based on the Yule process, originally proposed to explain the power-law size distribution of biological taxa. Both modelling idealizations capture the transition from the condition of criticality, in which b = 1.5, to that of imminent failure, characterized by b = 1.0, in terms of damage localisation. As a case study we present the method used by the authors to determine the conditions of the materials and the crack patterns in the structures of the Syracuse Cathedral, built in the 17th century on the structures of the ancient Greek “Temple of Athena” (5th century B.C.). In particular, the acoustic emission technique was used to evaluate the onset of critical conditions in a monitored pillar, which is part of the vertical load-bearing structures. The b-value trends are shown by several acoustic emission tests carried out on specimens of different dimensions extracted from the pillar. In addition, these results are compared to the acoustic emission data obtained from the in situ monitored pillar; it is shown that the b-value can be used both in the laboratory specimens and in the in situ measurements as a reliable indicator of the structural integrity.