Macro and micro-block modelling for limit analysis of masonry structures with non-associative frictional joints Casapulla Claudia 1 , Portioli Francesco 2 , Maione Alessandra 3 , Landolfo Raffaele 4 ABSTRACT This paper presents a comparison between the macro and micro-block modelling for the assessment of the lateral capacity of masonry walls loaded in-plane. The macro-modelling is based on the assumption that the failure involves a single crack which separates the structure in two macro-blocks and all the possible relative motions among micro-blocks are concentrated along the crack. By using a limit-state analysis approach and assuming that the interaction at surfaces is governed by Coulomb friction, two limiting conditions for the ultimate load factor are kinematically computed with simple formulations in closed form, by use of minimization routines. The macro-block model and the solution procedure are validated through three illustrative examples of shear walls existing in literature and comparisons against a micro-block model from a recently proposed strategy, herein revised, show a good agreement of the results in terms of both the ultimate load multiplier and the crack slope. The analysis of the influence of the overload on the ultimate load factor is also presented both to validate the procedure and compare the two models. Keywords: Limit-state analysis, Non associative frictional joints, Macro and micro-modelling 1. INTRODUCTION Many works on limit-state analysis of masonry block structures can be found in literature, starting from Kooharian [1] and Heyman [2], but most of them are related to the Heyman’s assumption of failure modes only governed by overturning mechanisms or to the assumption of sliding in presence of associative friction ([3], [4], [5], [6]). Actually, i.e. for lateral loaded masonry walls with failure modes modelled as macro-block mechanisms, pure rotation of a whole portion with respect to the other is consistent with the discrete model assumptions only when the crack line has the same inclination as the staggering between the units, usually defined by their shape ratio. Some authors [7] have adopted this limit crack slope in the macro-block analysis of shear walls so that no resisting force due to friction may be exploited, because of the uplift during overturning and others [8] have proposed a similar simplification through a homogenisation procedure. This means that the inclination of the crack is assigned as a given parameter instead of being considered as a variable of the problem. Nevertheless, when non-standard frictional resistances are considered in the macro-block analysis the computed multipliers generally overestimate the true ones, as shown by a recent comparison between 1 Assistant Professor, University of Napoli “Federico II”, casacla@unina.it 2 Assistant Professor, University of Napoli “Federico II”, fportiol@unina.it 3 Research Fellow, University of Napoli “Federico II”, alessandramaione@tiscali.it 4 Full Professor, University of Napoli “Federico II”, landolfo@unina.it