## 2 High-Performance Fiber Reinforced Concrete to Repair RC Components
### Concrete Mechanical Characterization
#### 2.2.2 Bending Tests  
Four-point bending tests on a notched concrete beam (Figure 2a) were performed to identify the load crack tip opening displacement (CTOD) curves. CTOD measures the relative displacement of two points on the opposite edges at the top of a notch created at the beam midspan, measured while the load is increased (Figure 2b). The bending tests were performed on beam specimens 100 \(\times\) 100 \(\times\) 400 mm\({}^{3}\) after seven days of curing. The tested concrete beams included: (1) Three beams for each fiber content (1, 2, and 3%) for concrete with steel fibers (UHS); and (2) three beams for each fiber content (2 and 4%) for concrete with polymer fibers (UHP). The beam dimensions followed the standards indicated in UNI-11039 [52] or RILEM TC162-TDF (2003) [53] and had a ratio of length/lateral side (h/L, Figure 2b) equal to four. Figure 1: Mean cube compressive strength variation increasing the fiber volume fraction: (**a**) concrete reinforced with steel fibers (UHS) and (**b**) concrete reinforced with polymer fibers (UHP) after seven days of curing. The notch size was determined by Equation (1), as suggested by CI-S-002-2003 [54], which was equal to 30 mm. \[\mathrm{a}_{0}=0.3\mathrm{h}\mp 0.01\mathrm{h} \tag{1}\]  
The four-points bending tests were carried out using the force-controlled method to test the UHS beams with a constant load rate of 0.07 \(\mathrm{kN/s}\) by the available test apparatus, and by the displacement-controlled method to test the UHP beams with a constant displacement rate of two mm/min using a new test apparatus. The opening velocity of the cracks and the load corresponding to different deformations were measured. The displacement-controlled method permitted us to observe the softening beam behavior, usually recorded for concrete with polymer fibers. The CTOD was measured by means of two linear variable differential transformers (LVDT) on each lateral side of the UHS beam at the notch, and the elaboration of the film recorded by a camera placed in front of one side of the beam that took photos automatically every five seconds starting exactly when the load control machine was turned on (Figure 3a). As a reference for both the crack opening and the deflection, two rules, one vertical and one horizontal, were applied. On the other side of the beam, a graded camera allowed us to detect CTOD with an accuracy of 0.5 mm by shooting a video of the notch. The frames obtained from the camera were processed and the CTOD was measured every five seconds. To synchronize crack opening data with the displacement-load data, the first crack opening was used as the reference time control, considering that the camera was always switched on at the same time of the displacement control machine. Figure 2: Bending test on high-performance fiber reinforced concrete (HPFRC) with different polymer fiber volume fractions: (**a**) Beam with notch and (**b**) four-points bending test scheme. The typical crack for the notched beam with fibers bridging effect after the test is showed in Figure 3b. The load-CTOD curves for the UHS beams with 2% and 3% fiber volume fractions are depicted in Figure 4 and the equivalent stress (feq2) and the ultimate residual tensile strength (fFlu), according Equations (5) and (6) in Section 2.3 (CNR-DT 204/2006 [55]), respectively, are shown in Table 2. The energy U2 in Equation (5) was calculated in the range of 0.6 mm to 3 mm below the mean experimental curve (red line in Figure 4) (mean of the applied loads on the tested beams) and below the minimum experimental curve (curve with lowest experimental loads). There was a modest variation in the tensile strength of the UHS beams when the fiber content increased from 2% to 3%. The maximum flexural strength of each beam corresponded to a CTOD value of about 1.5 mm for the 2% fibers fraction and may exceed 2.5 mm for the 3% concrete. This value is a little greater than the value expected for a beam with a notch of 2.5 mm and with a 2% fibers fraction, which ranged around 0.5 to 1 mm in [PERSON] et al. [56].