## 3 Experimental Results and Discussion
### Correlation between the Pore and the Fiber Orientation  
Since voids are not rounded, but elongated, it is possible to obtain their orientation. Additionally, in the case of steel-fiber-reinforced concrete, it is possible to obtain the fiber orientation. By correlating the orientation of both voids and fibers, it is possible to check if the fibers influence in any way the  
Figure 11: Histograms of shape factor along the depth: (**a**) SFRC moist-cured, (**b**) SFRC air-cured, (**c**) PC moist-cured and (**d**) PC air-cured. orientation of the voids. Again, this information is obtained from the CT scanner and the post-processing and the image analysis software. In order to analyze the voids' and fibers' orientation, the following angles are used: \(\theta\) (theta) and \(\varphi\) (phi) (Figure 12). Theta is a polar angle, i.e., the angle between the main axis of the void or fiber (the one containing its length) and the Z axis. Phi is the azimuthal angle, i.e., the angle between the projection of the main axis on the XY plane and the X axis. Theta varies from \(0^{\circ}\) to \(90^{\circ}\), while phi varies from \(-180^{\circ}\) to \(180^{\circ}\). Next, the histograms of voids' and fibers' orientation are shown for the different mixtures and the different curing conditions (Figures 13 and 14). Figure 14: Fibers’ orientation: (**a**) phi and (**b**) theta. Figure 12: Identification of \(\theta\) (theta) and \(\varphi\) (phi) angles. Figure 13: Voids’ orientation: (**a**) phi and (**b**) theta. Figure 13 reveals that, in all cases, voids are mainly oriented in the XY plane, i.e., the horizontal plane, since Figure 13 reveals that the greater percentage of the pores shows a theta angle close to \(90^{\circ}\). Additionally, inside the XY plane, there is not a dominant direction, since Figure 13a reveals that, approximately, the phi angle is uniformly distributed. These tendencies can be observed in both plain concrete and steel-fiber-reinforced concrete mixtures and also in both air-cured and moist-cured concretes. In the case of the phi angle, it can be highlighted that, in all cases, there is a uniform distribution of the voids inside the XY plane. No relevant differences can be observed between plain concrete and steel-fiber-reinforced concrete mixtures, and there are also no relevant differences between air-cured and moist-cured concretes. In the case of the theta angle, it can be highlighted that pores belonging to steel-fiber-reinforced concrete mixtures tend to be more horizontal, since they show higher relative frequency in the range of \(70^{\circ}\)-\(90^{\circ}\) than plain concrete mixtures. Figure 14 reveals that fibers also show an orientation similar to the voids' one. Again, fibers are mainly oriented in the XY plane, since Figure 14b reveals that the greater percentage of the fibers shows a theta angle close to \(90^{\circ}\). Additionally, inside the XY plane, there is no dominant direction, since Figure 14a reveals that, approximately, the phi angle is uniformly distributed. In order to define numerically the orientation along Z axis (theta angle), the efficiency index (\(e_{i}\)) is used ([PERSON] et al. 2014) according to the following equation (Equation (2)):  
\[e_{i}=\sum_{i=1}^{n}f_{i}\cdot cos(\theta_{i}) \tag{2}\]  
where \(f_{i}\) is the relative frequency of each bar of the histogram, and \(\theta_{i}\) is the average value of the theta angle of each bar of the histogram. The efficiency index can show values from 0 to 1, where 0 means that all the elements (voids or fibers in this case) are oriented perpendicularly to the Z axis, and 1 means that all the elements (voids or fibers in this case) are oriented parallel to the Z axis. Table 4 shows the values of the efficiency index of both voids and fibers for all the mixtures and all the curing conditions. Table 4 reveals some significant results. First, it can be noticed that, in the case of the voids, the plain concrete mixtures show a greater value of efficiency index than the steel-fiber-reinforced concrete mixtures.