Limit analysis of masonry walls by rigid block modelling with cracking units and cohesive joints using linear programming

In this paper a rigid block model with cracking units and cohesive joints is developed for limit analysis of masonry structures using linear programming. The model is applicable to in-plane loaded unreinforced masonry block walls with regular textures and provides as output failure loads and collapse mechanisms. A simplified micro-modelling approach is adopted, based on the discretization of masonry units into triangular blocks separated by contact interfaces. Tensionless contact interfaces are used to model dry joints and cohesive contacts are introduced for mortar joints and internal unit interfaces. Failure modes at contact interfaces involve cracking, crushing and sliding. An iterative solution procedure is used to model non-associative flow rule in sliding and to take into account no-tension behaviour of cohesive joints in case of cracking. The modelling approach is validated and applied to different structural examples from the literature, including unconfined and confined masonry panels and a masonry beam. To show the accuracy of the proposed model and the improvement of the predicted response, the obtained results are compared with experimental tests and with the outcomes of standard rigid block models using a single block per masonry unit and tensionless interfaces