Different Modeling of Ring Flexibility in Limit Analysis of Masonry Arch Bridge Considering Backfill

This paper proposes two alternative deformable elements to model the ring of masonry arch bridges in the limit analysis. Basic formulations for both elements are deduced from the kinematic view. The velocity field of the two elements is first constructed based on classic beam theory and elastic homogenous deformation, respectively, and the corresponding compatibility conditions are then put forward. After that, the constitutive model and flow rule applicable to the two deformable elements are investigated. Eventually, we give the updated formulation of upper bound limit analysis for the new elements. As an implementation, two proposed elements are applied to analyze the collapse of Prestwood Bridge, which is a practical bridge tested in-situ. In this analysis, arch-fill interaction is explicitly considered. We also provide the results of the bridge with rigid ring modeling for further comparison. The results indicate that when conducting the limit analysis of masonry arch bridges, suitable modeling of ring deformability is critical. Employing the rigid ring modeling will bring about an overestimated load prediction (about 46.3%) while the prediction from the axial-only deformable brick element perfectly agrees with the previous test results (bias within 1%). The homogenous deformable element could give rise to an accurate load prediction after the calibration of the material parameters but the predicted mechanism deviates from the experimental results due to the incorrect assumption of dilation mode.