Numeric Analyses

Numeric analyses were carried out prior and after the experimental tests. Pilot analyses provided some useful information to guide the modelling and design of the experimental test. On the other hand, upon completion of the experimental test, the experimental results were used to validate the numeric model.

Figure 15. Mesh B. Contact elements are located aside each white element along the vault crown and the abutments, and along the vault-to-backfill and backfill-to-abutment interfaces.

The model validation is necessary, in order to extend the application of the numeric model to different case studies, geometries and load layouts. This way, the FE analyses can help practicing engineers in defining retrofitting strategies, and in testing their effectiveness.

Different numeric models were implemented. First, a pilot linear elastic analysis was performed for the general understanding of the structural behaviour (Mesh A). Once the governing mechanisms were identified, the model was further refined both in terms of modelling assumptions and material behaviour. A second model was developed by adopting contact elements to simulate and allow the onset and development of cracks in the structure (Mesh B) Finally, in a third model, non linear constitutive laws for masonry were adopted (Mesh C). Mesh B showed the best fitting of the numeric results and is discussed in the following. The complete discussion concerning the numeric study can be found in Giardina et al. (2007c).

Geometry as well as loading conditions are derived from the experimental tests. Therefore, the loads acting on the model are:

- dead load

- vertical point loads at the abutment top edges

- horizontal point loads applied at the springing.

The analyses is performed by incrementing the horizontal points loads.

Mesh A was used to identify the zones of weakness where tensile stresses concentrate, i.e. where cracks might develop. The results highlighted that higher tensile stresses occur along the vault ring, at the abutment base and, when horizontal loads are applied, at the vault springing.

In Mesh B masonry and backfill were modelled by means of 3-4 node plain strain elements (Fig. 15). The non linear behaviour ofthe structure was modelled

Table 1. Mechanical properties in Mesh B.

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