# Safety Assessment of Masonry Arch Bridges Considering the Fracturing Benefit
## 3 Masonry Arch Bridge Assessment: Elastic-Fracture-Plastic Transitions
Then, increasing the live load to 20 kN/m, the fracturing processes at the springings present a crack closure (Figure 5) equal to \(\xi^{*}\) = 0.03, i.e., \(a^{*}\) = 4.5 cm, which remains stable until four cross-sectional failures (blue circles in Figure 8c) due to compression in the arch ligament arise at \(q_{line}\) = 870 kN/m. For these reasons, the positions of the brittle hinges (cracked cross-sections) differ from those of the plastic hinges due to the fact that the real fracturing process is taken into account. Note that the aforesaid crack closure condition entailed a re-centering of the line of thrust, resulting in an improved bearing capacity of the arch structure. The total fracturing benefit computed by fracture analysis points out an increase in the arch bearing capacity from null value to 870 kN/m. As a second case study, the structural behavior of the Limyra bridge is described. The Limyra bridge is a late Roman monumental arch bridge located in the ancient protectorate of Lycia, in modern West Turkey (Figure 9), and it represents one of the oldest and longest segmental arch bridges in the world, spanning over a length of 360 m on 26 shallow arch structures [33]. This monumental bridge, crossing over the Alakir river, connected the ancient cities of Limyra and Pambylia, along the imperial road of Lycia. Before its restoration, the bridge had been totally sunken in alluvial soils for years, and only a few spans were accessible. Figure 8: Mosca bridge: (**a**) Elastic, (**b**) plastic, and (**c**) fracture analyses. The main geometrical and mechanical characteristics of the Limyra Bridge are reported in Table 1. Also for this case study, the elastic-fracture-plastic transitions return an effective comparison about the different values of maximum live load, as uniformly distributed over the whole bridge deck, and the positions of the critical sections representing the brittle hinges (cracks) within the fracture analysis, or the plastic hinges within the limit analysis (Figure 10). Figure 10: Limyra Bridge: (**a**) Elastic, (**b**) plastic, and (**c**) fracture analyses. Figure 9: Limyra bridge (Turkey): Overview (**a**); Single arch sketch (**b**) [34]. A Limyra bridge elastic analysis (Figure 10a) presents a line of thrust outside the central kern (middle third) for a uniformly distributed live load equal to zero, since tensile stresses in the masonry arise immediately. The elastic limit is overtaken in the two arch section at the springings, suddenly concluding the elastic analysis. In Figure 10a, red circles represent the points where the line of thrust exceeds the middle third of the arch cross section. Limit analysis (Figure 10b) shows that the uniformly distributed maximum live load affordable for the arch structure is 3490 kN/m, a value for which the masonry compressive strength in four points is reached. In these positions, plastic hinges (red circles in Figure 10b) due to compressive failure take place triggering the kinematic collapse of the arch bridge. Also in this case, the line of thrust remains within the arch volume, the ultimate structural behavior of the arch being characterized solely by the masonry compressive strength. On the other hand, fracture analysis (Figure 10c) allows the uniformly distributed live load to reach the value of \(q_{live}\) = 480 kN/m, for which four cracked arch sections, or brittle hinges, appear (blue circles in Figure 10c). In particular, for the maximum live load \(q_{live}\) = 480 kN/m, in the abovementioned four cross-sections the crack length \(\xi\) = 0.7, i.e., \(a\) = 70 cm, is reached, leading to the fracturing failure due to the complete inefficiency of the arch ligament. In this case, the compressive stress level in the arch ligament for the four cracked cross-sections is lower than 10 MPa, whereas the masonry compressive strength is equal to 50 MPa. Therefore, a consistent fracturing process is taken into account, contrary to what is accomplished by plastic analysis.