3D upper bound limit analysis for masonry arch bridges interacting with backfill

Limit analysis is a promising numerical framework for a rapid estimation of the collapse load of masonry arch bridges. However, the relevant approaches in recent literature were virtually limited to 2D. The consideration of backfill or spandrel was insufficient. This paper proposes a new 3D upper-bound limit analysis for masonry arch bridges featuring a blend of homogeneous and heterogeneous modeling strategies. Rigid blocks are employed to model the arch ring, considering the real bond pattern. The backfill and spandrel domains are discretized by the constant-strain elements applying 3D Drucker-Prager plasticity. The formulation is eventually stated as Second-Order Conic Programming (SOCP). The collapse of the straight Bolton Institute bridge is investigated for benchmark purposes. The results are compared to the numerical and experimental references. Then, the possible simplification of the spandrel in 3D analyses is explored. The results indicate a great necessity of using a 3D analysis when investigating the collapse of masonry arch bridges. The load predicted from the 2D approach is underestimated (about 40%) due to the absence of backfill-spandrel interaction. The 3D limit analysis also demonstrates better robustness in capturing the transition of the collapse mechanism when the material parameter varies. Based on the current results, the proposed 3D limit analysis modeling exhibits high reliability with an acceptable computational budget (within 1.5 minutes). The bias of the collapse load is only 2.5% compared to the experimental results. Additionally, it is not recommended to simplify the spandrel through boundary conditions because it usually leads to inaccurate load and mechanism predictions.