Full Modelling of Backfill in 3D Limit Analysis of Masonry Arch Bridges

Masonry arch bridges are valuable historical architectural heritage spreading over the Eastern and Western worlds, some of which are still in service with reliable structural performance. Before integrating them into the current infrastructural system, a prior assessment of their structural capacity is necessary. The limit analysis is a standard and fast approach to investigating the failure of masonry systems, which is thus promising to be employed in the safety assessment. However, current contributions that use limit analysis mostly ignore or implicitly consider the backfill upon the bridge. Some works employed deformable triangles to model the behaviour of the infill material, whereas the analyses remain in 2D. Once taking into account the spandrel part, simple 2D modelling will no longer be sufficient. This paper will generalise the limit analysis formulation of the 2D deformable triangles to the 3D polyhedral case, proposing a 3D limit analysis modelling for the backfill and spandrel of the bridges. The governing formulation will be established based on the Upper Bound theorem. The strain rate field of the deformable polyhedron is assumed to be constant, and the element flow rule is associated with 3D Drucker-Prager plasticity. Rigid block modelling is employed for the bridge ring, precisely accounting for the brick arrangement. Homogeneous techniques will be applied to the spandrel part to reduce the unnecessary computational cost. Finally, the limit analysis problem can be formalised as Second-Order Conic Programming (SOCP). The straight Bolton Institute bridge will be taken as a benchmark example to test the reliability of this approach. Then, parametric studies on the material parameters will be conducted to understand their sensitivity on the behaviour at collapse of the bridge.