Limit analysis approach for the in-plane collapse of masonry arches

This paper deals with the numerical evaluation of the in-plane collapse behaviour of unreinforced masonry arches and portals characterised by different geometries subjected to several loading conditions and modelled as assemblages of rigid blocks in contact through no-tensional and frictional interfaces. This study has been conducted using a new in-house code, which represents the updated version of the numerical procedure presented in the pioneering work of Baggio and Trovalusci). The minimisation problem corresponding to the upper-bound (or kinematic) approach of limit analysis is written as a linear programming problem solved taking advantages of the algorithms nowadays available. An important feature of the code is the capability to provide information about the sliding collapse of masonry structures, adopting the assumption of dilatancy in the analytic description of the yielding surface, permitting to overcome the classical Heyman's hypothesis, which limited the investigation of collapse to only hinging modes. A key contribution of this study is the comparison of results in terms of collapse multipliers and collapse mechanisms, considering different literature contributes as benchmark references. This research reveals the suitability of approaches based on mathematical programming and the crucial role played by sliding.