Issue 10

M. Paggi, Frattura ed Integrità Strutturale, 10 (2009) 43-55; DOI: 10.3221/IGF-ESIS.10.06 53 The experimental data by Bažant and Xu [15] for normal strength concrete and by Bažant and Shell [16] for high strength concrete can also be used to assess the hypothesis of incomplete self-similarity in 3  and therefore the size-scale effect on the parameter C . Plotting the Paris’ law coefficient C vs. 3  in a bilogarithmic diagram and computing the best- fitting power-law regression curves, we find 2 4.7   for normal strength concrete and 2 1.1   for high strength concrete (see Fig. 8). Figure 8 : Size-scale effects on the Paris’ law coefficient C (evaluated using K  in MPa m and d a /d N in m/cycle) as a result of incomplete self-similarity in 3  for normal and high strength concretes (experimental data from [15,16] reinterpreted in [41]) . Incomplete self-similarity in 3  is also expected to occur in the Wöhler regime, as recently put into evidence for metals in [35] on the basis of fractal concepts. For concrete specimens, the experimental data by Zhang and Stang [9] a nd Murdock et al. [42] show that the S-N curves corresponding to two different sizes are almost parallel to each other and translate vertically. In particular, the larger the beam size, the lower stress range at static failure (see Fig. 8) . This result is in perfect agreement with the present theoretical predictions and with the numerical findings by Zhang et al. [11]. In this case, however, it is not possible to compute the incomplete self-similarity exponent 2  , since we have only two values of ( 1) u N       for different beam depths. Figure 9 : The effect of the structural size on the S-N curves (experimental data taken from [9, 42] ).