PSI - Issue 44

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

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3.3. Symmetry/asymmetry and simultaneity/non simultaneity of the cracked surfaces According to the limit analysis, the cracks formed during the spreading of vault’s supports are located in predefined positions and they are always symmetric respect to the vertical plane. The limit analysis is allowed to ignore the evolution of the intermediate stress state because it assesses the safety levels of the structure in ultimate conditions. Conversely, the comprehension of the cracking process becomes of paramount importance if one wants to analyze intermediate damage states of vaulted structures for the check of serviceability limit states, or if the aim is to individuate a more realistic structural crack distribution in ultimate conditions and, most importantly, to capture the size effect. The LDPM analysis of masonry vaulted structures captures the development in time and space of the complex fracturing process. In fact, from the observation of the results related to the numerical simulations performed on groin, barrel and depressed vaults, it is important highlighting that most of the cracked surfaces do not appear simultaneously, that the lateral cracks are not perfectly symmetric with respect to the vertical axis and, more importantly, that not all the cracked surfaces form in predefined positions. In particular, the cracked surfaces do not appear simultaneously in 88.8\%, 80.5\% and 66.7\% of the cases for depressed vaults, barrel vaults and groin vaults, respectively. Moreover, the lateral cracks are not symmetric with respect to the vertical axis in 75.0\%, 80.5\%, 83.3\% of the cases for depressed vaults, barrel vaults, and groin vaults, respectively. These results let us infer that that the features of non simultaneity and symmetry of the cracks is correlated to the geometry of the vaulted structures. In fact, Fig. 4 illustrates that both the characteristics of simultaneity and asymmetry of the cracked surfaces increases (from 11.2\% to 33.3\% and from 75.0\% to 83.3\%, respectively) as the distance between the crown of the vault and the imposts increases, i.e. going from depressed vaults to groin vaults. Therefore, we can conclude that the evolution of the fracturing process occurs more progressively and exhibits less pronounced asymmetry in the case of depressed vaults as compared to groin vaults for which, in turn, the damage appears to be more brittle and characterized by asymmetry in the cracks distribution.

Fig. 4. Simultaneity and Symmetry of the fractured surfaces in LDPM simulations related to: (a) groin vaults; (b) barrel vaults; (c) depressed vaults. 4. Conclusions This study presents an in-depth analysis of the damage and collapse behavior of masonry vaulted structures under spreading supports. For this purpose, the so-called Lattice Discrete Particle Model (LDPM) was used. The ability of LDPM to reproduce realistic failures of a variety of vaulted structures was shown. On the basis of the obtained results, the following conclusions can be derived. ● LDPM is able to capture the damage evolution and the fracture propagation phenomena to assess intermediate states of stress of unreinforced irregular masonry vaulted structures ● LDPM can be used as an alternative tool to perform typical limit analysis for the assessment of safety of arches and vaults in ultimate conditions

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