Tilting plane tests on a small-scale masonry cross vault: Experimental results and numerical simulations through a heterogeneous approach

• A heterogeneous non-linear Finite Element model is validated by experimental tests.
• The results of experimental tests on a scale model of cross vault are presented.
• Two types of displacement/rotation controlled tests (seismic actions), are simulated.
• Numerical results simulate very well experimental tests.

The seismic response of masonry vaults is discussed by presenting the results of an experimental campaign on a small-scale model and their numerical simulation though a heterogeneous full 3D non-linear Finite Element (FE) approach. The model relies into a discretization of the blocks by means of few rigid-infinitely resistant parallelepiped elements interacting by means of planar four-noded interfaces, where all the deformation (elastic and inelastic) occurs. In the framework of a heterogeneous approach, two typologies of interfaces are present, namely internal brick–brick interfaces, here assumed elastic, and mortar joints with zero thickness, behaving as a frictional (Mohr–Coulomb) material with infinite strength in compression and almost vanishing tensile strength. The model is incremental, non-linear elasto-plastic and exhibits softening at mortar interfaces. Each load step is solved by means of mathematical programming, i.e. through the formulation of a suitable constrained minimization problem where the objective function is represented by the energy of the mechanical system. The experimental and numerical results are compared and discussed in terms of both collapse mechanisms and force/displacement capacity.