Collapse Analysis of Reinforced Masonry Arches: A Comparison of Associated and Non-associated Sliding

In this paper, the standard formulation for rigid block limit analysis is extended to simulate the effect of innovative strengthening (FRP/FRCM), with a suitable modification of the constitutive constraint that governs the behavior of contact joints. The proposed modeling is applied to both associated and non-associated sliding. The change of the failure surface of a representative contact joint after the reinforcement is first derived. Casting it into a standard matrix form, the constitutive constraint in the lower bound theory is then modified to account for the strengthening effect. After that, the proposed technique is also extended to solve a non-associated problem. Utilizing this technique, the collapse of a 9-block 2D arch with FRP reinforcement is analyzed to compare predictions from associated and non-associated formulations. Detailed parametric studies are carried out to understand the influence of the critical parameters on the difference in the results from these two formulations. The results show that when analyzing the arch with reinforcement, the associated limit analysis may predict an incorrect collapse mechanism as well as an overestimated collapse load. Such overestimation could reach 70.5% in some cases. Employment of non-associated formulation is very necessary for more precise collapse analysis of reinforced masonry arches.