PSI - Issue 44

Micaela Mercuri et al. / Procedia Structural Integrity 44 (2023) 1276–1283 Author name / Structural Integrity Procedia 00 (2022) 000–000

1279

4

respectively. All the vaults have a constant width of 500 mm, representing the out-of-plane dimension. The preliminary operation related to all numerical simulations consisted in applying the gravity load with the vaults extremities being fixed. Afterward, two opposite velocities are applied to the two bottom surfaces of the vault in order to simulate the spreading of its supports. 3. Results and discussion 3.1. The progressive fracturing behavior of thrusting systems: from the trigger of the crack to the collapse state To point out the progressivity of the fracturing process of a vaulted structure under spreading supports, a barrel vault of slenderness ratio λ=0.2 is considered. The gravity load has first been applied to a vault configuration with the two extremities fixed. Thus, at zero displacement, the load is negative, corresponding to the reaction at the left support (or equivalently on the right) that counterbalances the self-weight of the structure (see Fig. 1a and Fig. 1b). When supports move horizontally, the load-displacement curve is characterized by two distinct phases (see Fig. 1a), i.e. an initial fracturing phase up to the activation of the mechanism, and a subsequent rigid-body-motion phase up to the complete structural collapse. It is worth observing that during the first phase (shown in detail in Fig. 1b), the arch exhibits an evolving fracturing behavior, providing the progressive formation of three cracked surfaces: the first crack appears at the crown of the arch (see Fig. 2a), the second and third cracks (see Fig. 2b and Fig. 2c, respectively) form in the lateral sides of the arch. It is important underlying that, although the structure and the loading are both symmetric, the second and third cracks do not appear simultaneously because of material heterogeneity. Once the abutments achieve a certain displacement, the second phase starts: the arch is in a condition of limit equilibrium, a kinematic mechanism is activated and the minimum value of the horizontal thrust F x is reached (see Fig. 2d). This condition does not imply the global failure of the arch because the horizontal thrust can still increase (in negative values) up to a maximum value F xu corresponding to the collapse state (see Fig. 2e).

Fig. 1. Force versus displacement curve related to the left bottom extremity of a barrel vault with slenderness ratio λ=0.2: (a) two distinct phases: initial fracturing and subsequent rigid-body-motion phases; (b) zoom of the first phase, three peaks corresponding to the formation of three cracked surfaces.