Simple modeling of reinforced masonry arches for associated and non-associated heterogeneous limit analysis

This paper proposes a limit analysis heterogeneous model for masonry arches in presence of innovative strengthening, rigid blocks, and joints reduced to interfaces. The reinforcement is considered in a simplified but effective way in the context of limit analysis, suitably modifying the admissibility conditions of the constitutive law that governs the behavior of contact joints. First, the force resultants at the interface after the reinforcement is investigated. Based on that, the yield condition and flow rule in the standard heterogeneous limit analysis formulation are updated. This approach is applied to solve both associated and non-associated sliding cases. For benchmarking purposes, the collapse of a 2D arch with both-side Fiber Reinforced Polymer (FRP) reinforcement is analyzed, followed by several parametric studies and a cost-benefit study. Collapse analysis of a real arch tested in-situ is also presented for further verification. The results show that in some cases an incorrect collapse mechanism and an overestimated ultimate load would be obtained through associated limit analysis. Such overestimation may become very significant once the reinforcement is taken into account. The presented cases illustrate that the maximum overestimation of the load could reach in meaningful cases of technical interest 91% of the associated prediction. This suggests the use of a non-associated flow rule to accurately predict the collapse load increase of reinforced arches. According to the cost-benefit study, it is recommended to strengthen at least half of the joints to guarantee an acceptable effect of the strengthening. The simulation of the collapse of the in-situ tested arch further proves the reliability of the proposed approach.