Seismic collapse of vaulted structures: unreinforced quasi-brittle materials and the case study of the Basilica of Maxentius in Rome
Keywords: Vaulted structures
Experimental dynamic tests
Masonry structures
Basilica of Maxentius
Damage assessment
Seismic behaviour
Seismic collapse

Seismic loading is one of the biggest threats to the stability of masonry architecture is many parts of the world. Buildings that have stood for centuries under their self-weight, could suffer collapse in an unprecedented seismic event. The current research aims at furthering our understanding of how masonry vaulted buildings behave in earthquakes. Our ability to anticipate damages or collapse of existing structures will depend on this understanding.
Based on the study of ancient Roman buildings, this work focuses on types of masonry that exhibit cohesive behaviour due to the presence of strong mortar or to the interlocking between the components of the material matrix. Roman concrete is one of those materials.
The idea behind this work is to be able to base the experimental and theoretical work on real buildings, and vice-versa, to be able to relate any experimental and theoretical findings to real buildings. Hence the work has evolved around the case study of the Basilica of Maxentius in Rome.
The Basilica of Maxentius is a valuable case study for the study of the seismic behaviour of vaulted structures: not only does it feature the largest barrel and cross vaults known to have been built by the Romans, but it also underwent partial collapse, believed to have been triggered by an earthquake at some unknown point in the middle ages.
A detailed survey of the Basilica of Maxentius has been carried out to obtain a geometrical model of its current state; to study the deformations as a source of information for exploring the mechanical history of the structure; and to obtain a geometrical model of the original geometry of the building. The main techniques used in the survey were total station surveying and 3D photogrammetry. The foundations of the south nave of the Basilica, built over the remains of earlier ruins, were also surveyed to assess their quality and to look for potential signs of seismic damage. No clear signs of structural damage were observed on the foundations themselves, but some of the earlier remains featured clear signs of damage under the effect of lateral loads.
Shaking table tests on continuous circular arches and cross vaults constructed in lime mortar, a quasi-brittle material like Roman concrete but with weaker strength, have yielded interesting results that demonstrate that the dynamic behaviour of these structures is different to that of structures made of discrete blocks. Arches collapse by forming a four-link mechanism, but the hinge position is different to that observed in block arches: hinges are placed symmetrically about the mid-span axis. Only 2 cracks formed in all arches, leading to collapse by four-link mechanisms with hinges at the 2 cracks and at the 2 supports. Hinges were observed to remain fixed at these positions during rocking. When inwards sliding of supports is possible, the first crack typically forms by mobilising a slider-crank mechanism, the final crack forming a four-link mechanism in the reversed half-cycle.
It was also observed that pre-existing cracks in the arch had a very significant effect: these cracks become hinges and only 1 more crack is needed to form a four-link mechanism. The common crack at mid-span frequently found in real arches caused by spreading of the supports leads to mechanisms that require higher accelerations than a pre-existing crack offset from midspan. It is arguable that many real masonry structures will feature a degree of cohesiveness, and thus this observation opens a path for further investigations into the need to consider pre-existing cracks.
The formation of cracks has been analysed using limit and quasi-static linear elastic approaches. These analyses have been unsuccessful in predicting the formation of the first crack in undamaged arches (hyperstatic arches with hinges at the supports). Conventional limit analysis cannot be used because of the quasi-brittle nature of the material, while the elastic analysis fails to capture the behaviour observed in tests. The formation of the fourth hinge in pre-cracked arches has been analysed by application of equilibrium equations alone to the three-pin statically determinate arch. Good correlation has been obtained between experimental results and this analysis.
Finally, discrete element modelling code LMGC90 has been validated for analysis of dynamic behaviour of block arches, by comparison with experimental results.