Upgraded formulations for the onset of local mechanisms in multi-storey masonry buildings using limit analysis

Unreinforced stone masonry (URSM) buildings without a box-like behaviour are very vulnerable to out-of-plane failure modes in seismic prone areas. These may involve partial or total collapses of walls with severe civil protection implications in terms of hazard to people, structures, and road network in the surroundings. In this paper, an advanced macro-block model accounting for frictional resistances is used to calculate the onset load factors for two classes of local mechanisms in multi-storey URSM buildings: the rocking-sliding and the flexure mechanisms. Based on the application of the kinematic approach of limit analysis, the presented formulations are an upgrade of the load factors identified within the FaMIVE (Failure Mechanism Identification and Vulnerability Evaluation) procedure existing in the literature and developed by the last author. These take into account a revisited evaluation of the in-plane frictional forces for the rocking-sliding mechanisms and the torsion-shear-flexure interactions for the horizontal flexure mechanisms. Moreover, the position of the hinge along the height of the building is identified more accurately, since it can be found at the story level or between two storeys, depending on the accounted mechanism. Other innovative issues concern upgrades of the former formulations for the vertical and horizontal flexure mechanisms. The final perspective of the presented abacus of local mechanisms in multi-storey URSM buildings is the next implementation of the proposed formulations in the FaMIVE procedure, after a sensitivity analysis of the main physical and geometrical parameters affecting the "hierarchy" among the all possible mechanisms. The identification of the most probable mechanisms, through a comprehensive but at the same time relatively rapid assessment, can be very useful for civil protection purposes.