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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Fig. 2. Fracture process in a barrel vault of slenderness ratio λ=0.2: (a) the first cracked surface triggers from the intrados of the crown and propagates to the extrados; (b) the second lateral fracture triggers from the extrados and propagates to the intrados; (c) the third lateral crack also triggers from the extrados and progressively reaches the intrados; (d) activation of the kinematic mechanism; (e) collapse state. 3.2. Collapse load and comparison with limit analysis Figure 3 shows the results of all simulations in terms of minimum horizontal thrust F x and for different slenderness ratios, corresponding to the activation of the mechanism for the three types of vaults. All the numerical data points represent the average of six simulations with different particle size distributions. Figure 3 also reports the values of the minimum horizontal thrust obtained by limit analysis (Coccia et al. (2015)). It is straightforward observing that, for all the types of vaults, the simulated responses are in good agreement with the limit analysis results. It is worth pointing out that F x increases by increasing the vault slenderness λ and that, for a constant slenderness ratio, F x decreases as the distance between the crown of the vault and the imposts increases, i.e. going from depressed vaults to groin vaults. This latter observation seems to justify the historical structural evolution of vaulted structures that occurred over the centuries, implying the progressive increase of the height of the arched structure measured from the imposts to the crown, aiming to reduce the horizontal thrust.

Fig. 3. Minimum horizontal thrust F x corresponding to the activation of the mechanism for: (a) groin vaults, (b) barrel vaults; (c) depressed vaults. LA = limit analysis prediction. The LDPM numerical simulations are in good agreement with the LA results for all types of vaults and all the slenderness ratios.