PSI - Issue 44

Mattia Zizi et al. / Procedia Structural Integrity 44 (2023) 673–680 Mattia Zizi et al. / Structural Integrity Procedia 00 (2022) 000–000

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view of the bridge, together with the location of cracks and hinges obtained at the end of the test are shown, while in Fig. 1b a transversal section of the bridge is reported. On the other hand, in Fig. 2 the response in terms of force versus radial displacement of the intrados point of the arch under the load application is plotted.

Fig. 1. (a) main geometrical features of the bridge sample and location of the cracks exhibited at the end of the test; (b) transversal section AA’ of the bridge sample (measures in millimeters). Adapted from Melbourne et al. (1997)Melbourne et al. (1997).

Fig. 2. Force versus radial displacement curve of the test.

2.2. The numerical model To reproduce the experimental response of the reference test, a three-dimensional nonlinear numerical model was created in Abaqus software. The FE Model was composed of 3D eight-node solid elements with reduced (C3D8R) and full (C3D8) integration for backfill and masonry elements, respectively. An average mesh size of 100 mm was adopted for the elements of both materials, after a preliminary sensitivity analysis. Moreover, backfill and masonry interacted to one another by means of a Contact formulation of “hard” type in the normal direction (preventing interpenetration in compression) and with a Friction behavior in the tangential one. Given the symmetry of the investigated problem with respect to a vertical plane passing by the bridge axis, a reduced half-model was created and a symmetry boundary condition was applied to the nodes lying in the cutting plane. To simulate the presence of the additional walls introduced in the test to constrain the backfill in the transversal direction, the nodes of the backfill were restrained in the transversal direction. The base nodes were considered fully fixed. Such boundary conditions were assigned to reference points rigidly connected ( Rigid body ) with the nodes of the base surfaces. Also, longitudinal translations of the lateral external nodes of the backfill were restrained. The analysis was phased in two separate steps. During the first step gravity loads were applied, while in the second step the bridge was loaded until the collapse. To improve the convergence of the analysis, a Dynamic/Implicit analysis was performed in the second step. In particular, a constant vertical velocity of 0.01 mm/s was assigned to a reference point, which was in turn linked by means of a Continuum distributing Coupling to the loaded surface. Moreover, to limit the release of elastic energy due to abrupt loss of resistance (typical of brittle materials), a 20% damping ratio