PSI - Issue 64

Antonino Maria Marra et al. / Procedia Structural Integrity 64 (2024) 2117–2124 Marra et al./ Structural Integrity Procedia 00 (2019) 000 – 000

2118

2

Nomenclature normalization constant distance between main steel beams elastic modulus ,0 median of the prior distribution of the elastic modulus natural frequencies ,1 , ,2 first and second natural frequencies 0 (⋅) prior probability density function ̅ (⋅) updated probability density function 1 horizontal displacement of the deck Power spectral density of the acceleration (first) natural periods ̅ measured (first) natural period 1 , 2 vertical displacements of the two main steel beams

1. Introduction Static and dynamic full-scale measurements are commonly used for updating the preliminary FE models of bridges through deterministic (e.g., Gatti, 2019; Marcheggiani et al., 2020; Zhang et al., 2021) or emerging probabilistic approaches (e.g., Bartoli et al., 2019; Marra et al., 2024), the latter should be recommended due to the non-negligible uncertainties present in both modeling and measurements. Friction of the supports, their behavior under traffic loads, out of plumb of piers and soil-structure interaction represent some of the main sources of uncertainties in modeling the response of existing bridges. In addition, the absence of analytical and numerical methods for damping estimation makes difficult preliminary evaluations of the dynamic response. Vibration measurements are an emerging technique to gain information for characterizing the global dynamic behavior of existing structures (Ko et al, 2005; Conte et al., 2008; Fraser et al., 2010; Cunha et al., 2013). Natural frequencies and modal shapes, together with estimations of the modal damping ratios, represent valuable information to calibrate FE models of bridges. The Bayesian FE-model updating procedure proposed by Marra et al. (2024) for updating the elastic modulus of RC deck slab is here applied to update the horizontal stiffness of the longitudinal restraints of a curved approaching span of the Indiano Bridge (Florence, Italy). The first natural period derived from ambient vibration measurements is employed for the model updating. The case study is represented by a steel/concrete composite deck slab bridge with a span of about 21 m. The procedure based on Bayes theorem incorporates both model uncertainties and measurement errors, which are integrated to obtain the likelihood function. The next section explains the Bayesian model updating (BMu) procedure. After, a section is dedicated to the description of the Indiano Bridge. The full-scale test results are shown in section 4. In section 5, the BMu procedure is applied to the case study for updating the horizontal stiffness of the restraints. Finally, some concluding remarks The procedure developed by Marra et al. (2024) to update the probability distribution of the elastic modulus of the RC deck slab, has been here employed to update the horizontal springs of the supports in the longitudinal direction, denoted by . The measurement of the first natural period, ̅ , is used as information gained from the ambient vibration tests. The posterior distribution of the horizontal stiffness of the supports can be derived from the following expression: ̅ ( ) = −1 [∫ ( ̅| , ) ⋅ ( | ) ⋅ ] ⋅ 0 ( ) (1) are reported at the end of the paper. 2. Bayesian FE-model updating