Structural analysis of unreinforced masonry spiral staircases using Discrete Element modelling

Abstract

Unreinforced masonry spiral staircases have been built for more than two thousand years in castles, churches and palaces, and these staircases require structural assessment. For a few decades, the structural behaviour of “cantilever” staircases has been debated among scholars. Several structural methods have been used, but due to the complex 3D geometry and the substantial number of treads, a priori assumptions have been made about the magnitude and point of application of the contact forces between the treads and the wall-tread connections. These assumptions influence the calculation of torsional moment, which, in some methods, reaches high values that could generate shear stresses greater than the material's strength. In this paper, a 3D model based on one helix of the “cantilever” spiral staircase of San Domingo de Bonaval, in Spain, has been analysed using the Discrete Element Method. The entire stair is analysed without making assumptions on the magnitude and location of the resultant contact forces, which are calculated for each tread using customised Python-based functions. The wall-tread connections have been modelled using rigid blocks, and several contact conditions have been investigated. Moreover, different friction angles and the influence of geometrical imperfections are analysed to simulate material tolerances and assembly imprecisions. The simulation results indicate that perfect wall-tread contact conditions lead to conservative predictions of the torsional moment. Instead, gaps and imperfections allow small displacements, which reduce the torque and increase compression forces in the inner helical ring of the stair. Low friction angles could increase the torsional moment values, while vertical settlements do not cause a significant effect. Cantilever situations could still occur due to not perfect contact conditions between consecutive treads, which suggests that the tread-tread contact area should be carefully inspected during restoration. More generally, this paper demonstrates the potential variability of the structural behaviour of highly indeterminate structures when boundary conditions are uncertain, while providing valuable context to inform restoration strategies.