Simple Associated and Non-Associated Heterogeneous Limit Analyses for Reinforced Masonry Arches

A simple limit analysis modeling for masonry arches with innovative strengthening is proposed in this paper, where the arch ring is discretized by rigid blocks according to the real bond pattern and the reinforcement effect is modeled through updating the failure surface of the contact joints. Considering all the extra force resultants provided by the reinforcement layer, we have first derived the constraints for the new yield condition and flow rule, defining the failure surface after applying the strengthening, and the new limit analysis formulation with consideration of reinforcement effect is then given. Such modeling is also very convenient to incorporate with sequential linear programming to solve non-associated problems. Applying the proposed theory, collapse analysis of an FRP-reinforced arch in 2D is presented and the results predicted from associated and non-associated formulations are compared. The results show that when analyzing the arch with reinforcement, the associated limit analysis may overestimate the ultimate load, as well as produce an incorrect collapse mechanism. Therefore, it is necessary to employ the non-associated flow rule for an accurate prediction of the collapse performance of reinforced arches.