Novel block element with axial-only deformation for limit analysis of masonry arch bridges

This paper proposes a novel limit analysis block element to model the ring behavior in masonry arch bridges, with consideration of axial deformation induced by both bending and axial compressing motions. The governing formulation is established based on the kinematic theorem. After constructing the velocity field of the block element, the new compatibility condition is put forward, followed by a discussion of possible linearization for the element constitutive model. A new heterogeneous limit analysis formulation that accounts for the deformability of the elements is given at the end. For benchmarking purposes, the collapse of an 80-block arch is first investigated to understand the influence of using different constitutive linearizations. Then, the proposed element is applied to analyze the collapse of a practical bridge involving arch-fill interactions. The results indicate a great necessity of considering the deformability of the ring when analyzing the collapse of masonry arch bridges. Compared with previous experimental results of Prestwood Bridge, employing the rigid modeling for the ring will lead to a significantly overestimated load prediction (about 46.3%) while the proposed deformable brick element with quadrilateral-linearized constitutive can produce a very accurate prediction (bias within 1%). Adoption of the hexagon linearization will give rise to a comparatively inflexible block behavior and the corresponding ring performs analogous to the rigid case. Finally, the model proposed gets over the main shortcoming exhibited by a beam discretization of the ring, namely the potential over-flexibility of the bridge arch, induced by the simplification of the actual geometry.