Adaptive NURBS limit analysis coupled with homogenization applied to sail vaults with orthotropy induced by variable brick arrangements

It is not uncommon to observe historical masonry vaults which were built with portions where bricks are laid in different preferential alignments, or even where different textures are used. Reasons stand in building technology needs. A stability assessment is a complex task, since irregular orthotropy at the macro-scale is induced by stereotomy, especially in the non-linear range. In presence of double curvature vaults, assessments are carried out by combining limit analysis and finite elements, the latter being needed to correctly reproduce complex crack patterns, which are triggering collapse. This leads to a linear programming problem, which can be similarly used to study the crack propagation in the case of springing settlement. Regardless of the source of degradation, when the vault is built by assembling portions with different textures, this may generate relevant computational issues, such as: analyses need a large number of finite elements, the numerical burden is not affordable and there is a high risk of premature halting. To overcome such problems, the present paper combines, in series, two steps: (i) a homogenization performed in the rigid plastic case with (ii) adaptive NURBS limit analysis. First, a viable homogenization approach, where blocks are assumed to exhibit an infinite compressive resistance and non-linearity is lumped on joints (reduced to interfaces) is proposed, to rapidly deduce homogenized masonry strength domains. Then the vaults are meshed with few NURBS and rigid-plastic spline interfaces, the latter obeying the homogenized failure resistance which was obtained in the first step. Mesh is intentionally rough and progressively adapted in shape to enforce at the converged iteration that some of the NURBS edges coincide with the active cracks, making sure, at the same time, to keep unchanged the edges of contiguous patches with different textures. The proposed methodology- here applied to a historical sail vault located in Sardinia, Italy - is characterized by a huge improvement in the analysis speed, providing realistic predictions of the load carrying capacity and feasible crack patterns (also in case of settlement), at a fraction of the time needed by heterogeneous approaches.