PSI - Issue 62

Francesco Mariani et al. / Procedia Structural Integrity 62 (2024) 955–962 Mariani et al / Structural Integrity Procedia 00 (2019) 000 – 000

961

7

T3 T4 T5 T6 T7 T8 T9

-0.70 0.02 2.85 3.46 5.41 7.89 10.30 12.38 13.40

-1.44 -0.72 2.12 -7.13 4.69 7.18 9.59 11.68 12.71

0.01 0.74 3.58 4.19 6.16 8.66

1.05 1.84 4.94 5.62 7.77

1.64 2.43 5.52 6.19 8.34

0.92 1.15 3.80 5.32 6.47 9.07

10.52 13.20 15.53 16.67

11.08 13.75 16.08 17.21

11.10 13.22 14.25

11.59 13.78 14.85

T10 T11

6.3 Combined error The mean error resulting from the comparison of displacements and frequencies is aggregated by defining function (3). The coefficient α is considered the reference and set equal to 1, while the coefficient β varies from the limit case when experiment al results about the static behavior are not available (β=0) to a value chosen based on the difference in dimension of the two error types. The graph in Figure 5 illustrates the variation of the value E to minimize the objective function J(E) as the ratio α/β changes. The green area represents results obtained when the β coefficient is greater than α (i.e., when static tests are more reliable than dynamic ones). In this scenario, models T0 and T1, with an elastic modulus close to that noted from the specimens C0 compression (see Section 3.1), exhibit the minimum errors. For the case study, the blue area is more representative, defining the zone where the α coefficient is higher than the β coefficient. The reliability of dynamic results is given precedence over static ones. Indeed, the Ambient Vibration Tests (AVTs) conducted in 2022 utilize high-accuracy instrumentation and involve a thorough experimental campaign. Furthermore, the results obtained from the five accelerometer configurations, as detailed in Section 3.2, are combined returning a significant level of agreement. Conversely, the cores extraction campaign provided only two specimens with disparate results, making the construction of a statistical sample impossible. Nevertheless, the long-term viscoelastic model construction requires specifical considerations about both load, construction stages, and parameters influencing the rheological properties. The values of Young’s modulus that lead to a minimum error in J(E) range from 23000 MPa to 25000 MPa. These results exclude values of Young’s modulus under 21891 MPa and over 25500 MPa, confirming a significant difference between the elastic modulus of design, of about 32836 MPa, and the real one. 7. Conclusions This paper has presented a methodology for evaluating the long-term conditions of a full-scale post-tensioned concrete box girder bridge through a detailed time-dependent modeling of the structure and the calibration of the elastic modulus of concrete. Utilizing a specific case study modeled based on the design reports and drawings, the methodology also considers the results of an experimental campaign involving concrete cores extraction and compression tests, prompting the adjustment of the Young’s modulus of concrete used in the Finite Element model. A central role is associated to the static and dynamic tests. The former allow to update the model parameters such as Young’s modulus of concrete, while the latter allow to validate the model by checking its modal response. The approach relies on minimizing errors derived from the comparison between models and experimental measurements, encompassing both static and dynamic analyses. It enables the selection of a realistic value for the elastic modulus, even when limited information is available. In future, enhancing error estimation can be achieved by increasing the quantity of data compared and by fine-tuning coefficients in the objective function based on the number, reliability, and dispersion of tests results. This iterative process ensures a more accurate representation of the bridge’s long term behavior, contributing to the structural reliability assessment.