Limit analysis of frictional block assemblies by means of fictitious associative-type contact interface laws

A new method for the limit analysis of discrete systems formed by dry rigid blocks with Coulomb-type (non-associative) contact interface laws is here exposed. The method resorts to a fictitious system whose cohesive-type contact interface laws depend on the axial forces of the real block system. Two theorems establish the connection between the collapse state of the frictional block assembly and that of the fictitious one. Based on this result, an original problem of mathematical programming is formulated to determine the minimum collapse load multiplier for block assemblies interacting through frictional interfaces. In the proposed formulation the complementarity condition is not introduced as constraint but is obtained as Karush–Khun–Tucker condition. Numerical applications demonstrate the potential of this approach for assessing the collapse load of masonry-like structures.