Response of fiber reinforced concrete while entering into the critical stage: An attempt to detect pre-failure indicators in terms of non-extensive statistical mechanics

Abstract

The main goal of the present study is to explore the potentialities of Non-Extensive Statistical Mechanics (NESM) to provide signals that could be considered as pre-failure indicators. In this direction concrete beams, either unreinforced or reinforced with short fibers, were submitted to three-point bending. The acoustic signals detected during loading were analyzed in terms of their interevent time intervals and the respective cumulative probability. The experimental data were then properly fitted by means of the q-exponential function providing the temporal evolution of the entropic index q throughout the duration of each experiment. The evolution of q was studied in juxtaposition to that of the load applied as well as to that of some additional parameters used to describe the acoustic activity, namely the b-values and the F-, P- and d-functions. The analysis indicated that at load levels approaching the load-carrying capacity of the specimens, the response of both the unreinforced and the fiber reinforced beams corresponds to q-values approaching 2. It is thus highlighted that, according to NESM principles, the damage processes at the specific load levels are characterized by the existence of a number of non-independent subsystems with long-range mutual interactions and memory effects, which cannot be properly described by the concepts of the traditional Boltzmann-Gibbs Statistical Mechanics. On the contrary, description in terms of NESM provided useful information about the damage evolution during the very last loading stages before macroscopic fracture. In addition, the analysis provided indications that the onset of decrease of the q-values, towards the critical limit of 1, could be considered as a potential pre-failure index, warning about upcoming entrance of the system into its critical stage, namely that of impending fracture.