Why do we need probability distributions with fat tails to describe the surface strain evolution in reinforced concrete flexural members?

This paper, for the first time, justifies the use of alpha-stable distribution (a fat tailed distribution) for describing the statistical variations in surface strains in reinforced concrete flexural members. Justification is provided by viewing the cracking process in these members, that affects the strain evolution, as an emergent structure (in thermodynamical sense, Prigogine and Stengers in Order out of chaos: man’s new dialogue with nature, 1984; Carpinteri in J. Mech. Phys. Solids 37(5):567–582, 1989; van Mier et al. in Comput. Meth. Appl. Mech. Eng. 142(1–2):189–201, 1997). The proposal of the alpha-stable distribution is checked by comparing the estimated relevant parameters (namely, location and scale parameters which are representative of mean and dispersion) with the mean and standard deviation of experimentally measured surface strains both in extreme compression fibre and at the level of reinforcement (in the flexure zone), at different stages of loading. A satisfactory agreement is obtained between the respective experimental and estimated values. Also, comparison of the tails of estimated CDFs of normal and alpha-stable distributions with the cumulative distribution functions of experimentally observed strains suggested that alpha-stable distribution is able to fit the tails of compression and tensile strains better than normal distribution. For the purpose of the present study, the experimental results of three beams are considered. Also, in the present investigation the strains at the level of reinforcement and at the extreme compression fibre are considered. The practical consequence of the use alpha stable distribution in performance based design and future direction of research are also included.