The minimal thickness of masonry pavilion vaults

The aim of this study was to determine the minimally necessary uniform thickness of cloister vaults to carry their self-weight. First, preliminary numerical simulations (using well-calibrated DEM models to simulate strong limestone masonry with dry contacts) were done on the simplest geometries, to gain a first insight into the failure modes and into the internal stress states. By applying the experiences gained this way, analytical predictions were then derived for the minimum thickness in two alternative ways, i.e., using the two theorems of Limit State Analysis, for the full range of reasonable opening angles. After this, numerical simulations were done on various opening angles again, determining the minimal thickness for each. The comparison of the results from the three approaches revealed that while the predictions provided by the Kinematic Theorem were in excellent agreement with the numerical simulation results, the Static Theorem with the assumed stress distribution yielded overly conservative predictions, due to the oversimplification of the applied internal stress system. Specifically for a 2 × 90° opening angle, the minimal thickness is 4.28% of the radius of the middle barrel surface, decreases with decreasing opening angle, and becomes zero at 2 × 54°.