## 3 Results and Discussion
### Discussion  
Fiber-reinforced concrete proves highly suitable for withstanding dynamic forces owing to its heightened ductility and increased ability to dissipate energy during fractures. Over the past few decades, research has extensively addressed the initiation and progression of mode I fracture cracks in plain Portland cement concrete, employing both experimental and numerical approaches. As concrete is inherently prone to damage and fracture, the loading rate plays a pivotal role in influencing its strength, failure mode, and ultimate crack patterns [42; 43; 44; 45]. This response may be attributed to various factors, including the growth of micro-cracks associated with loading rate, the viscous behavior influenced by water content, or the Steffan effect [46], and the impact of structural inertia forces. These forces, stemming from crack propagation, inertia activated by material hardening or softening, and inertia due to crack bifurcation, can alter the stress-strain state.  
The first two factors dominate at lower loading rates, while the third becomes more significant at higher loading rates. Concrete properties, such as bending [47; 48; 49], have been demonstrated to be rate-dependent. Consequently, applying quasi-static mechanical properties to structures becomes inappropriate when dynamic effects are significant. The introduction of fibers enhances the material's toughness by improving the stitching capacity of fibers for developed cracks through the pullout mechanism [50; 51]. Simultaneously, the dynamic fracture of fiber-reinforced concrete in mode I becomes more intricate. [PERSON] et al. [45; 52] conducted a study on the dynamic fracture of fiber-reinforced concrete, shedding light on these complexities.  
Therefore, characterizing these properties under dynamic loading conditions becomes imperative. In particular, the findings from this study are consistent with the existing scientific literature on Portland cement concrete. However, this work represents a relevant and novel contribution to fiber-reinforced lime concrete knowledge. Indeed, restoration and repair elements in heritage structures may need to sustain wind loads, earthquakes, cyclic loads, impacts, etc. Therefore, the reinforcement of natural hydraulic lime concrete with flexible fibers (in this case, PVA) is beneficial from multiple perspectives for use in heritage restoration and repair elements regarding strength, durability, and sustainability (economic, social, and environmental). It is noteworthy that one of the limitations identified in this study will be addressed in a subsequent article, where the results under impact loads will be analyzed. Therefore, for a proper interpretation of the findings in this study, it is crucial to bear in mind this important consideration.  
Figure 9 depicts the typical cracking pattern in a three-point bending test under mode I fracture on a specimen with a central notch. Upon dynamic loading, the initial observation is the development of the primary crack extending from the notch tip towards the loading point (Figure 10). In the dynamic regime, failure occurs along the intergranular regions of the fractured surface (Figure 11). Additionally, it is noted that the fibers predominantly fail through pullout, occasionally experiencing breakage (Figure 11). These characteristics of inter-granular fracture mode and predominant fiber pullout are similar to those observed in the quasi-static regime.  
Figure 9: Typical crack patterns for quasi-static three point bending test: (**a**) \(\phi_{f}\) = 0%, (**b**) \(\phi_{f}\) = 0.3%, (**c**) \(\phi_{f}\) = 0.6%, (**d**) \(\phi_{f}\) = 0.9%, (**e**) \(\phi_{f}\) = 1.2%.  
Figure 11: Perceivable inter-granular failure of fracture dynamic tests: (**a**) \(\phi_{f}=0\%\), (**b**) \(\phi_{f}=0.3\%\), (**c**) \(\phi_{f}=0.6\%\), (**d**) \(\phi_{f}=0.9\%\), (**e**) \(\phi_{f}=1.2\%\), (**f**) detail of inter-granular fracture in hydraulic lime fiber-reinforced concrete with \(\phi_{f}=0.9\%\).