Assessment of masonry structures subjected to foundation settlements using rigid block limit analysis

In this paper, a three-dimensional rigid body model is implemented to investigate the behaviour of masonry block structures subjected to foundation settlements. The structural behaviour is investigated formulating a limit analysis problem for the calculation of the base reaction and the associated failure mode once the settlement is introduced in the model. The structural model is an assemblage of rigid blocks which interact at contact interfaces. The latter are modelled as concave-contacts, using contact points located at the corners of the interface to represent interactions. A no-tension and non-associative frictional behaviour with infinite compressive strength is considered for joints. The limit analysis problem is formulated as a second order cone programming problem (SOCP) and an iterative procedure is adopted to take into account non-associative frictional behaviour. A computer program has been developed for applications of the proposed procedure. Two simple numerical examples are presented with the aim to verify the obtained results against analytical solutions. Applications to a set of experimental tests and to a 3D building model are introduced for validation and to evaluate the computational efficiency of the model. Finally a dissipation index is defined in order to give a quantitative estimation of the consequences related to the foundation settlement.