PSI - Issue 44

Riccardo Martini et al. / Procedia Structural Integrity 44 (2023) 657–664 Riccardo Martini et al. / Structural Integrity Procedia 00 (2022) 000–000

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columns of fully loaded trucks over the deck) before the opening to traffic. In addition to that, some codes (AASTHO (2018), SIA (2011) and NTC (2018)) also prescribe a dynamic test, in order to investigate the fundamental frequency of the structure to increase the level of knowledge of the structure and to reduce uncertainties in the numerical model used to predict the structural behaviour during the static proof load test. Moreover, also mode shapes and damping ratios can be identified with the same tests providing the fundamental frequencies of the structure, with the advantage to have a greater number of data to assess the reliability of the model adopted for the bridge design. Recently, dynamic tests for the modal parameters identification are more and more widespread and the literature is plentiful of application examples to different structural schemes, such as arch bridges, cable-stayed bridges, and precast concrete bridges. (Ribeiro et al. (2021), Cachot et al. (2015), Innocenzi et al. (2022) and Chen et al. (2022)). The identification of the modal parameters is carried out by means of the Operational Modal Analysis (OMA), which is a well-known technique based on the post-processing of results obtained by performing the Ambient Vibration Tests (AVTs); the latter consist of acceleration recordings obtained from sensors suitably deployed on the bridge due to the environmental noise. The versatility of AVTs, which can be executed through light and portable instrumentation, allows the investigation of the dynamic of the bridge both in unloaded and loaded conditions. The dynamic identification of bridges at loaded conditions (i.e. performed during the static proof test, when stationary trucks are placed on the deck) can provide same advantages for both the construction check before the opening to traffic, and for long-term purposes, related to the Structural Health Monitoring (SHM) of the structure. In detail, the knowledge of the bridge dynamics at severe load conditions can support the choice of the Engineering Demand Parameters (EDPs) and the related Performance Levels (PLs) in a SHM system and it allows the determination of the modal participation factors according to procedures established in the literature (Parloo et al. (2002) and Heylen et al. (1997)), and consequently to define the receptance matrix of the bridge (Carbonari et al. (2022)). In addition, the evaluation of the modal parameters of the loaded bridge contribute to increase the control of the loading phases during the test; indeed, by monitoring the frequencies of the bridge, it is possible to check the consistency between the experimental frequencies and the numerical ones, the latter obtained from the numerical model used to design the loading tests. However, if the numerical model takes into account only the additional trucks masses, by neglecting their vertical stiffness, the interpretation of the frequencies consistency is not an easy task. As a matter of fact, depending on the case, dynamic interaction phenomena between the bridge and the trucks may occur and it may lead to unrealistic and unconservative conclusions (Carbonari et al. (2022) and Gara et al. (2020)). In this paper, the Bridge-Trucks Interaction (BTI) phenomena are investigated. Firstly, an analytical tool for the BTI analysis in case of single span bridges is presented, by reducing the problem to a 2 Degree of Freedom (DoF) system and by performing a set of application to explore the significance of the interaction; then, a real case study dealing with the interpretation of dynamic test results performed during a proof load tests is presented. 2. Bridge-truck interaction phenomenon The static proof load tests reproduce severe load conditions (i.e. the characteristic design load configuration) for the bridge by placing one or more stationary trucks over the deck. From a dynamic point of view, the bridge and trucks are not two independent systems, and the level of interaction depends on several factors, such as the bridge-truck mass ratio and the bridge-truck stiffness ratio. Therefore, with the aim to analyse the BTI phenomena, a simple 2 DoF system is presented, where, 1 and 1 represent the mass of the truck (or trucks) and the vertical stiffness of the tires and shock absorbers, respectively, and 2 and 2 are the bridge mass and the flexural stiffness of the loaded bridge span. In order to simplify the model, the damping of both the bridge and the vehicle are neglected, in order to formulate the eigenvalue problem; however, it is worth observing that the system dynamics is not influenced by damping because the magnitude of excitations is rather low in case of ambient excitations, and thus unable to activate significant dissipative mechanisms. The equation of motion for the undamped free vibrations of the proposed linear 2-DoF system is: � 1 0 0 2 � � ̈ 12 ̈ 22 � + � 1 − 1 − 1 1 + 2 � � 1 2 � = (1)