Issue 30

A. Fernàndez-Canteli et alii, Frattura ed Integrità Strutturale, 30 (2014) 327-339; DOI: 10.3221/IGF-ESIS.30.40 328 ranges becomes unity. After this formulation, this rule is repeatedly tested for different materials under multi-step and variable amplitude loading programs. Though its applicability has been often questioned, it has been practically adopted by all standards related to structural and mechanical fatigue design. While Birnbaum and Saunders [1] tried to find a relation of the probabilistic distribution of the Miner number to the crack growth, Van Leeuwen and Siemes [2, 3] conducted series of tests on plain concrete and interpreted directly the scatter of the Miner number M by obtaining theoretical expressions for the mean and standard deviation values of M from the Wöhler curve. These formulae, initially derived for the simple case of constant amplitude cycling were then extended to the case of general loading. They showed that the Miner number M at failure is a stochastic variable with an approximate log-normal distribution and emphasized the importance of the study of the scatter of the Wöhler curve for constant amplitude cycling. Based on Holmen’s investigation on concrete [4], Fernández-Canteli [5] justified a generalization of the Van Leeuwen and Siemes work by considering a probabilistic S-N field providing a statistical distribution of the Miner number although based on a log-normal distribution. Some theoretical advances were performed in [6] and [7]. From this, it follows that the Miner number can be used to ascertain the probability of failure, as a more suitable design criterion, rather than as a measure of a problematic and abstract “degree of damage”. It can then be taken as a basis for a consistent life prediction in fatigue design, in accordance with the consideration of fatigue failure as limit state. R ESULTS FROM H OLMEN n this Section, the fatigue results for concrete specimens under compression provided in the study of Holmen [4] are introduced and eventually adapted in order to proceed to the probabilistic interpretation of the Miner Number. Figure 1: S-N field fitted with the Mc Call model [7] for the normalized fatigue results for concrete under compression from Holmen [4]. S-N fatigue results for constant stress level Fig. 1, shows the S-N field resulting from the fatigue data obtained in Holmen’s fatigue experimental program, according to Tab. 1, using the procedure proposed by Mc Call [8]. The tests were carried out for constant stress range S=S max - S min =(  max -  min ) /  R and constant minimum stress level ( S min=  min  R =0.05 ), where  max and  min are, respectively, the maximum and minimum stress applied during the test and  R is the fracture stress of the concrete This model, based on fitting a regression hyperbola linking the respective percentiles values resulting from the cumulative distribution functions I