Keywords: rigid block model, cracking units, masonry, limit analysis, linear programming.

In rigid block limit analysis by mathematical programming, masonry structures are idealized as an assemblage of rigid bodies interacting at contact interfaces. As for micro-modelling approaches, rigid blocks are used to model masonry units (i.e. stones or bricks) and contact interfaces are used to represent mortar and mortar-unit interface behaviour. Failure modes are generally restricted to mortar and mortar-unit interfaces, being neglected the potential failure of a masonry unit itself. With such assumptions, the application of limit analysis by mathematical programming of rigid block models to masonry shear walls may lead to the unreliable prediction of collapse loads and mechanisms if failure of the masonry unit occurs.

Following these considerations, in this paper a rigid block model which takes into account the possibility of local failure in masonry units is developed for the limit analysis of masonry structures. A simplified micro-modelling approach is adopted, based on the discretization of the single masonry unit in two blocks separated by a vertical interface which realizes a cohesive contact. Failure modes at interfaces involve crushing, cracking and sliding.

To take into account the nonassociative behaviour in sliding, the iterative solution procedure proposed by Gilbert et al. [1] was used to find the minimum collapse load, instead of solving the underlying mixed complementarity program.

Moreover, a specific iterative procedure was used to take into account the brittle behaviour of mortar joints and also unit interfaces undergoing cracking failure. The procedure is based on a different plastic behaviour of uncracked and cracked interfaces and it is organized in the following steps: (1) Limit analysis of the rigid block model with effective values of plastic strength based on yield functions related to uncracked behaviour; (2) Detection of contacts undergoing cracking failure; (3) Redefinition of mechanical properties at the selected interfaces according to cracked behaviour; (4) Repetition of steps from 1 to 3 until convergence.

The modelling approach is validated against a literature case study of unconfined masonry panel, where the collapse mechanism involves cracking of units.

To show the accuracy of the proposed modelling approach, the results obtained of the analysis are compared with experimental tests and with the outcomes of other modelling approaches used in the literature for limit analysis of the investigated panels [2].

1

M. Gilbert, C. Casapulla, H.M. Ahmed, "Limit analysis of masonry block structures with non-associative frictional joints using linear programming", Computers and Structures, 84, 873-887, 2006. doi:10.1016/j.compstruc.2006.02.005

2

A. Orduña, P.B. Lourenço, "Cap model for limit analysis and strengthening of masonry structures", Journal of Structural Engineering, 129, 1367-1375, 2003. doi:10.1061/(ASCE)0733-9445(2003)129:10(1367)

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