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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To guarantee robustness in the numerical solution, the backfill material was modelled assuming a Drucker-Prager Linear (DP) constitutive relationship with a perfectly-plastic post-linear law. Since the friction coefficient value provided by the experimental reference regarded a Mohr-Coulomb (MC) representation, some adjustments in the material parameters were needed given that DP was calibrated to approximate the outer cone of MC failure surface. A small cohesion ( c =0.001 Mpa) was introduced despite the incoherent nature of the material to avoid convergence issues, while friction φ DP and dilation ψ DP angles were both set equal to 50.5° (associated plasticity). It is important to point out that several mechanical parameters necessary for the numerical description were not reported in the experimental reference, and they were calibrated against the experimental response. In particular, a parametric analysis entailing 27 different simulations was performed in order to determine the effect of the following parameters on the response: i. the Elastic Modulus of the backfill E b ; ii. the tensile strength of the masonry f tm ; iii. the tangential friction of the contact law between structure and backfill μ . The best match was provided by E b =50 MPa, f tm =0.2 MPa and μ =tan(30°), which were selected as the sought material parameters. 2.4. Results of the reference numerical model At the end of the analysis, the implemented numerical model provided a very good agreement with the experimental test. The comparison in terms of force-radial displacement curve between the experimental test and the numerical analysis is displayed in Fig. 5.

Fig. 5. Comparison of numerical and experimental force-radial displacement curves.

As it can be seen, the two curves exhibited very similar trends, with minor differences in the first part of the nonlinear branch of the responses. Conversely, remarkable agreement is seen in terms of maximum strength and ductility. From a quantitative point of view, a relative error of about 3% between the experimental and numerical curves was estimated. Also, a very good agreement between the experimental and numerical failure modes can be noted by comparing the damage patterns of Fig. 6 and the crack positions of Fig. 1. Based on these results, the calibrated model was applied to investigate the seismic response of the bridge. 3. Seismic analysis 3.1. Numerical modelling The seismic response of the bridge was investigated by means of a push-over analysis. After a first step where gravity loads acted on the structure, monotonic, mass-proportional horizontal loads in the longitudinal direction were applied to the model to simulate the earthquake action in a second step of the analysis. Force-controlled static analyses were performed in order to estimate the seismic strength of the bridge. To improve the convergence of the analysis, a small value (i.e. 10 -5 ) for the viscosity parameter was introduced in the CDP material model. Also, a parametric study aimed at investigating the influence on the seismic capacity of the backfill quality, as well as its interaction with the masonry material, is proposed in the following.