Quadripartite vaults are found in many historic buildings and are often below ground level.ud When new infrastructure is developed above these structures it is necessary to assess theud strength of the existing vaults. A new formula for assessing the failure load of quadripartiteud masonry vaults under uniform loads is presented. The approach is based on the upperud bound solution from limit analysis of the elliptical arch defined at the intersection betweenud the cylindrical surfaces. The predictions from the analytical solution are consistent withud numerical results from a symmetrical 3D finite element analysis developed using a damagedud plasticity model with homogeneous material properties for the masonry. A case study is alsoud presented corresponding to the quadripartite vaults in the undercroft of London Bridgeud station. This case study is used to examine the effect of the presence of ribs and horizontalud movement restraint introduced by surrounding structures. The presence of ribs was found to have the largest effect on the strength of the vault. The non-linear FE analysis showedud that modifying the boundary conditions to restrain the edges of the vault from horizontalud movement increased the failure load by approximately 30% for a vault without ribs. Whenud ribs were included the introduction of horizontal restraint had a much larger impact and inud such cases a more refined model including explicitly the surrounding structure might beud needed.
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