PSI - Issue 78

Mattia Zizi et al. / Procedia Structural Integrity 78 (2026) 1721–1728

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a Dynamic analysis, where horizontal movement was allowed at the base nodes of the movable supports (see Fig. 3a). A low and steady horizontal velocity of 0.1 mm/s was then applied. Using this low-velocity dynamic approach helped to avoid convergence problems by ensuring the load transfer remained close to quasi-static conditions. 3.3. Results Fig. 4 shows the results of the analyses in terms of force-displacement curves. As can be seen, the vault thickness strongly influences the capacity of the system, both in terms of peak and residual forces. The maximum lateral forces resulted in the range 90-135 kN and served as a reference for selecting the appropriate jack actuator for the test.

Fig. 4. Result of the numerical analyses in terms of force-displacement curves

All curves displayed a peak force at a displacement of approximately 4 mm, followed by a softening branch. Most retained a residual force of about 80% of the maximum value. However, in the case with a thickness of 6 cm, the residual force remained relatively comparable to the peak force, indicating a distinct structural response. This behaviour aligns with Heyman’s assumptions for masonry structures, where the tensile strength is not mobilized. The reduced thickness appears to lead to premature damage in the masonry elements, even at low displacement levels. This outcome suggests the need to construct a real specimen with a greater vault thickness to prevent unexpected early damage during the test. The damage patterns, represented by the tensile damage parameter at a displacement of 12 mm, are shown in Fig. 5. As observed, in all the analysed cases, damage was concentrated along the compressed ribs, indicating detachment of the vault. Additionally, diagonal cracking was observed in the vaults, particularly in the cases with lower thicknesses. In contrast, a four-hinge mechanism appeared to be activated along the tensile ribs.

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Fig. 5. Damage pattern (tensile damage) of the vaults at an horizontal displacement of 12 mm (deformed shapes amplified 50 times)