Arch bridges subject to pier settlements: continuous vs. piecewise rigid displacement methods

Settlements severely affect historic masonry arch bridges worldwide. There are countless examples of structural dislocations and ruins in recent years due to severe settlements at the base of pier foundations, often caused by shipworm infestation of wooden foundations or scouring and riverbed erosion phenomena. The present paper proposes an original way to approach the failure analysis of settled masonry arch bridges. The proposed method combines two different 2D numerical models for the prediction of masonry arch bridge capacity against settlements and for safety assessment. The first one is the Piecewise Rigid Displacement method, i.e. a block-based limit analysis approach using the well known Heyman's hypotheses; the second one is a continuous Finite Element approach. The case study of the four-span Deba Bridge (Spain, 2018) failure is presented with the aim to illustrate how the methods work. The failure analysis produced satisfactory results by applying both methods separately, in confirmation of their reliability. Their combination also allowed to obtain a significantly reduction in computational cost and an improvement of prediction accuracy. A sensitivity and a path-following analysis were also performed with the aim to demonstrate the robustness of the presented method. The obtained simulations highlighted that the results do not depend on the friction angle and that a proper prediction of the evolution of the structural behavior can be obtained only taking into account geometric nonlinearities. Such results demonstrate once again that in settled masonry arches geometry prevails over the mechanical parameters. The current study paves the way for the fruitful use of the proposed approaches for a wider range of applications, as, for example, the mechanism identification or the displacement capacity assessment of masonry structures under overloading as seismic loads