Modelling crushing failure in 3D limit analysis of masonry block structures by mathematical programming

In rigid block limit analysis of masonry structures, an infinite compressive is usually assumed at contact interfaces. This assumption is generally suitable to model unreinforced masonry structures with dry-joint or poor quality mortar joints, such as historical buildings, whose behaviour is mainly governed by nil or low tensile strength, sliding and rocking failure. Nevertheless, crushing could significantly affect the collapse behaviour of masonry structures, as it is the case of strengthened masonry. Indeed, the use of strengthening devices, such as metal ties or composite strips, may produce stress concentration in compression and, as a consequence, crushing failure of masonry panels. In this paper an efficient iterative solution procedure is presented to model crushing failure in 3D limit analysis of masonry block structures using mathematical programming. A concave contact model is adopted for interfaces, with contact points located at the corners of the interface to represent interactions. A no-tension and non-associative frictional behaviour with limited compressive strength is considered for joints. The limit analysis problem is formulated as a second order cone programming problem (SOCP). The accuracy and the computational efficiency of the proposed formulation are evaluated comparing the results of the proposed formulation with those obtained from experimental tests and alternative formulations from the literature.