# Safety Assessment of Masonry Arch Bridges Considering the Fracturing Benefit
## 3 Masonry Arch Bridge Assessment: Elastic-Fracture-Plastic Transitions
Finally, the fracturing benefit here computed points out an increase in the arch bearing capacity from null value to 480 kN/m. The last case study object of this work is related to the Vittorio Emanuele I bridge, erected in Turin by [PERSON]'s government after 1810 (Figure 11). Initially known as the \"Stone bridge\", after the return of the [PERSON] royal family to Turin in 1814, it was renamed \"Vittorio Emanuele I bridge\", the name that it still retains. At the time of its construction, this monumental arch bridge constituted the main entrance to Turin from Genoa and its harbor [32]. Figure 11: _Cont._  
The main geometrical and mechanical characteristics of the Vittorio Emanuele I bridge are reported in Table 1, whereas the elastic, plastic, and fracture analyses results are summarized in Figure 12.  
An elastic analysis (Figure 12a) returns a null value of the uniformly distributed live load, the arch structure showing the line of thrust outside the middle third for the most part of the bridge span. On the contrary, limit analysis (Figure 12b) allows the live load to reach the value of 725 kN/m. However, for this value, the compressive strength of the masonry is exceeded in four points (plastic hinges), the line of thrust remaining within the arch bulk. Also for the Vittorio Emanuele I bridge, the line of thrust remains within the arch volume for the whole bridge span, the ultimate structural behavior being characterized solely by the masonry compressive strength. Figure 11: Vittorio Emanuele I Bridge, Turin (Italy): Overview (**a**); Sketch of the polycentric arch (**b**). Figure 12: Vittorio Emanuele I bridge: (**a**) Elastic, (**b**) plastic, and (**c**) fracture analyses. The analysis of the fracturing process of the Vittorio Emanuele I arch structure (Figure 12c) returns a maximum live load \(q_{live}\) = 500 kN/m, when the formation of four cracked sections is acknowledged, triggering the global cracking failure of the bridge. In particular, up to \(q_{live}\) = 350 kN/m, two cracks of length \(\xi\) = 0.1, i.e., \(a\) = 10 cm, characterize the springing ligaments. Then a complete crack closure (Figure 5; \(\xi^{*}\) = 0.0) sets in, with a consequent re-centering of the line of thrust, and four cross-sectional failures (blue circles in Figure 12c) take place at \(q_{live}\) = 500 kN/m, due to high compression stress in the arch ligament. Also for the Vittorio Emanuele I bridge, a consistent fracturing process is taken into account for the arch structure, complying with the crucial need of a more accurate global assessment of the load carrying capacity of masonry bridges. Moreover, a comparison between the structural behaviours shown by the three analyzed bridges leads to the following comments. The three ultimate structural behaviours appear to be very diversified in terms of damage mechanisms and maximum live loads affordable by the three arch structure. This is due to the fact that the three bridges present two different main geometrical characteristics affecting the structural behavior: the arch shallowness ratio, and the arch depth (see Table 1). The Mosca bridge shows a shallowness ratio equal to 1/8 and arch depth of 1.5 m, whereas Limyra bridge is less shallow (1/5 in shallowness ratio) but thinner (1.0 m in arch depth). It has been demonstrated above that when the arch structure is more shallow, it tends to assume the ultimate structural behavior of a rectilinear beam, showing its cracked sections at the abutements (see Mosca bridge, Figure 8c). On the contrary, when the arch is less shallow, it tends to assume the structural behavior of a round arch (shallowness ratio: 1/2) with the cracked sections at the haunches (see Limyra bridge, Figure 10c). Furthermore, besides the different shallowness ratios, Mosca bridge and Limyra bridge show also a difference for the second main geometrical parameter: the arch depth, which contributes to the arch ultimate bearing capacities, in addition to the mechanical parameters of the masonry.