Numerical collapse load of multi-span masonry arch structures with FRP reinforcement

In this work, the rigid block method is used to estimate the collapse load of multi-span arch structures made of masonry and reinforced with externally bonded reinforcement (EBR), such as FRP. The considered arch structures are composed of an arbitrary number of spans with arches arranged in series and supported by piers and abutments. The interface between two adjacent masonry bodies (e.g. blocks, abutments, etc.) of the discrete model is characterized by no tensile resistance, finite compressive strength, which is modeled with interfacial penetration, and associative flow rule for frictional sliding. The crushing in the collapse mechanism is schematized by the interpenetration of the blocks with the formation of hinges at internal or boundary points of the interface. The collapse load is determined by solving the minimization problem obtained by applying the upper bound theorem of limit analysis. This represents the primal problem and provides a kinematic description of the collapse state. The corresponding dual problem is also formulated in order to provide the statics of the arch structure at the point of collapse. Finally, numerical examples are provided in order to show the applications of the proposed method and to investigate the effectiveness of the FRP strengthening the masonry arch structures.