## 4 Results and Discussion
### Tensile Tests  
Figure 6a shows the load-displacement curves of three specimens of each type of concrete under tensile testing. In all cases the cross-section was \(60\times 60\) mm\({}^{2}\). For the three concretes analyzed the load-displacement curve shows quite similar behavior: the first linear load branch until reaching the maximum load value (\(F_{LOP}\)), at which point the initial cracking of the specimens occurred. The second branch is a descending stretch with high negative slope to the minimum load point (\(F_{MIN}\)). From this point the remaining load increases as the displacement increases, up to the maximum remaining load value (\(F_{REM}\)). Figure 6b shows the detail of the load branch, associated with the uncracked matrix of the concrete up to a slip lower than 0.02 mm and the beginning of the load loss branch corresponding to the cracked concrete. The first branch is associated with the strength of concrete matrix, while the residual loads are governed by the resistant capacity of the fibers. Load variation in \(F_{MIN}\) ranged from 0.55 to 1.57 kN, while this difference significatively increased for \(F_{REM}\), with values of 3.02 kN for SCCP6, 5.19 kN for VCCP6 and 1.10 kN for VCLP6. As it can be seen, the length of the fibers and the compaction procedure employed considerably affected the remaining load strength of the fiber reinforced concrete. Figure 6c shows the influence of the coefficient of orientation of fibers in the minimum load value (\(F_{MIN}\)) and the maximum remaining load value (\(F_{REM}\)). The coefficient of orientation of the fibers is supplied by Equation (1) [32]. To this end, the number of fibers in the fracture section was counted and related to the theoretical number of fibers that should exist in that cross section. It can be concluded that the orientation of the fibers plays a primary role in the post-cracking behavior of the fiber reinforced concrete. \[\theta=\frac{n}{th}=\frac{nA_{f}}{V_{f}A_{c}} \tag{1}\]  
The random orientation of short linear elements and the geometrical probability problem is a longstanding question, which was possibly first posed in the celebrated [PERSON]'s needle problem that has also been shown to have a direct link with modern stereology and methodology and, therefore, with its applicability to modern concrete technology. The theoretical number of fibers that cross any section would, in the end, be that obtained by means of expression (Equation (1)). This number of fibers, which would enclose the theoretical number of fibers to be counted in any section, is termed in this research \(th\). Once the theoretical number of fibers in an idealistic positioning has been defined, the next step is to denominate the orientation factor (\(\theta\)) as the relation of the number of fibers counted in a certain surface over its theoretical number. That is to say, it is possible to obtain the orientation factor once it has been counted by using the expression (1), with \(A_{c}\) being the cross section of the sample, \(A_{f}\) the section of one fiber and \(n\) the number of fibers actually counted in situ. In addition, the experimental assessment of displacement, obtained using extensometers, are compared with the one registered by video extensometry. Figure 7a shows the linear variable differential transformer (LVDT) placed in the specimen surface in order to assess the relative displacements between the lips of the notch. White dots were painted on the area above and under the notch of the front face of the specimens, as shown in Figure 7a. Video-extensometry was able to measure the relative distances between the centers of gravity of the aforementioned white dots during the test. Figure 7b shows the evolution of the relative distance of the white dots during testing. In this image, the top points correspond to the position of the points drawn above the notch, while the vertical lines represent the displacement of the points marked right under the notch along the test.