Keywords: close range photogrammetry, masonry arches, geometric model, discontinuous models, finite element analysis, failure load.

Many historic buildings and infrastructure constructions (historic bridges, tunnels, etc.) have been often built using masonry arches. Nowadays, a large number of masonry bridges remains in service, as part of the road and rail networks. Many of those bridges date from the roman and medieval periods. Others, date from more recent times, as the nineteenth or early twentieth century. These constructions, as an important part of our engineering´s works heritage, ought to be assessed and preserved.

This paper analyzes a method to determine masonry arch load failure using a micro-model where both the geometry and the behaviour of each individual voussoir are included. The arch geometry in the model is obtained for each individual voussoir from the identification of its contour obtained by close range photogrammetry. Three-dimensional high fidelity models can be obtained with actual geometry through the use of this technique.

An approach based on numerical methods is used to determine the failure load of discontinuous arch models [1]. This failure load can be estimated from the load-displacement diagram. This load can be obtained by varying the loads in an iterative process by determining the peak load. In each voussoir and for each analysed load level a finite element discretisation is performed and the inside stresss distribution at the interfaces can be obtained.

This load analysis has been carried out both on arch ring models obtained by photogrammetry from the actual geometry of existing bridges and on a total of three models of ideal regular geometry arches. These three models of regular arch (semicircular) differ in their thickness and density of backfill. This analysis has been performed in order to check the consistency of the results with those based on the rigid block limit analysis method by using a common geometric model in both cases.

Despite the greater consumption of computational and time resources, compared to other traditional methods such as thrust line, the proposed methodology provides the advantages of numerical limit analysis by finite elements in discontinuous models (e.g. the obtaining of the safety factor for load, or stress distribution at the interfaces and inside the voussoirs). The use of the precise geometric model has significant advantages when the voussoirs are substantially different in size or the geometry is irregular.

Additionally, the photogrammetry techniques used to obtain the geometry provide the following advantages over traditional techniques of measurement: they do not require direct contact with the arch for measurement; they do not require scaffolding so they are safer for workers, and provide a geometric model closest to reality.

1

P.B. Lourenço, "Computations on historic masonry structures", Progress in Structural Engineering and Materials, 4(3), 301-319, 2002. doi:10.1002/pse.120

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