Issue 31

A. Abrishambaf et alii, Frattura ed Integrità Strutturale, 31 (2015) 38-53; DOI: 10.3221/IGF-ESIS.31.04 44 compared (see Tab. 2). On the other hand, when the notch plane was parallel to concrete flow direction, a higher orientation factor observed comparing to specimens with θ =9 0 ° . Therefore, in θ = 0 ° series, a higher number of the effective fibres in the fracture surface was appeared which increased the concrete fracture parameters. Regarding the fibre segregation factor, the obtained average values of seg  were insignificantly higher than 0.5 meaning that a slight fibre segregation occurred through the panel’s depth. This could also justify the asymmetric crack opening width observed in the splitting tensile specimens. θ= 0 ° θ= 90 ° Specimen Distance [cm] f N [fibres/cm 2 ] f eff N [fibres/cm 2 ] η θ [-] seg  [-] f N [fibres/cm 2 ] f eff N [fibres/cm 2 ] η θ [-] seg  [-] B3 20.0 2.071 1.291 0.827 0.580 1.557 0.405 0.688 0.476 A4 23.5 1.889 1.356 0.855 0.518 1.430 0.506 0.737 0.510 C4 32.0 2.036 1.430 0.851 0.555 0.665 0.133 0.630 0.597 D3 32.0 1.913 0.853 0.775 0.491 1.436 0.415 0.666 0.586 B4 40.0 1.956 0.851 0.773 0.530 0.506 0.074 0.561 0.643 A5 46.5 2.220 1.212 0.814 0.479 1.097 0.311 0.672 0.725 A6 69.5 2.304 1.803 0.866 0.557 0.967 0.132 0.604 0.539 C6 77.5 2.142 1.303 0.818 0.600 1.232 0.541 0.756 0.485 D1 77.5 1.921 1.089 0.795 0.532 1.355 0.631 0.760 0.594 Average 2.050 1.24 0.820 0.538 1.138 0.35 0.675 0.573 CoV (%) 7.16 23.74 4.15 7.33 31.98 57.11 10.20 14.00 Table 2 : Fibre distribution parameters. 102 60 110 Figure 8 : Localization of the plane surface considered in the fibre distribution assessment (units in mm). Fig. 9 illustrates the orientation profiles obtained for each average orientation factor in comparison to both the two- dimensional ( 2D ) distribution,   = 2 /π , [18] and the three-dimensional (3 D ) isotropic uniform random fibre distribution,   = 0.5, [19]. It was shown that the fibre orientation profile followed a Gaussian distribution [20, 21]. The orientation profile for θ= 0 ° series was represented by a distribution shifted to the left side, while for θ= 90 ° series the distribution profile tends to the right side. Therefore, within the specimens of θ= 0 ° series, fibres have a tendency to be aligned more perpendicular to the studied plane. The obtained distribution profile for the θ= 0 ° series was completely distinct from either the 2 D or 3 D theoretical isotropic uniform random distributions. Meanwhile, the distribution obtained for the θ= 90 ° series was very similar to the 2 D theoretical distribution. In conclusion, for SFRSCC laminar structures, assuming a 2 D or 3 D uniform fibre random distribution may be far from the reality, since the influence of fibre orientation due to the concrete flow also needs to be taken in to the account. Fig. 10 shows the exponential relationship between the number of fibres, f N , and effective fibres, f eff N .