Structural appraisal of existing masonry quadripartite vaults

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 the\ud strength of the existing vaults. A new formula for assessing the failure load of quadripartite\ud masonry vaults under uniform loads is presented. The approach is based on the upper\ud bound solution from limit analysis of the elliptical arch defined at the intersection between\ud the cylindrical surfaces. The predictions from the analytical solution are consistent with\ud numerical results from a symmetrical 3D finite element analysis developed using a damaged\ud plasticity model with homogeneous material properties for the masonry. A case study is also\ud presented corresponding to the quadripartite vaults in the undercroft of London Bridge\ud station. This case study is used to examine the effect of the presence of ribs and horizontal\ud 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 showed\ud that modifying the boundary conditions to restrain the edges of the vault from horizontal\ud movement increased the failure load by approximately 30% for a vault without ribs. When\ud ribs were included the introduction of horizontal restraint had a much larger impact and in\ud such cases a more refined model including explicitly the surrounding structure might be\ud needed