62 D. La Mazza et al. Fig. 7.6 Spectrogram of the frequencies registered by one of the sensors installed on the central spans average vibration levels, highlighted through an exceedance of thresholds preliminarily fixed on vibration control parameters (STD and peak-to-peak – Fig. 7.5). In the end, the third dynamic condition, hereinafter defined as “winter condition,” was observed in cold weather. When temperature decreases, the bridge natural frequencies change again, showing a new longitudinal mode of vibration (3 Hz), highlighted in Fig. 7.4c, with prominent peaks in the PSDs calculated on acceleration data recorded along the y-axis, i.e., the direction parallel to the deck longitudinal axis. If the first lateral mode is considered, this remains the same as that of the baseline condition, while the first flexural mode frequency now lies between baseline and summer condition. The bridge vibrational response globally increases during winter condition for all the spans close to the southern joint, with respect to what was observed in the previous two dynamic configurations: in this state, the monitoring system detected an exceedance of the threshold levels on the group of sensors close to the joint. In Fig. 7.6, it is shown a spectrogram of the frequencies registered by one of the sensors installed on the central spans, where it is evident the seasonal frequency shift of the lateral mode described above. 7.5 FE Numerical Digital Twin The purpose of the FE modeling is to create a digital twin of the structure to support the monitoring system and simulate what, at a first glance, could have been considered as damage. Numerical models have been developed to compare and validate the data from the sensors. In fact, without a numerical simulation, it would be difficult to characterize the expected structural behavior in “standard” conditions and consequently to identify the onset of any anomalies. The first step in the development of the digital twin is to model the structure, considering the available historical information; the second step involves the static and dynamic updating of the model to simulate the structural behavior at the time the monitoring started; this constitutes the initial state to which refer any future changes in behavior recorded by the sensors. Model updating is an essential activity since, especially in the case of existing structures, the response can differ significantly from the behavior that the viaduct had at the time of construction or was originally designed for. Once the updated model has been defined, this can be used as a support tool to simulate the behavior recorded by the sensors (e.g., by simulating local damage to structural elements, by modifying the behavior of joints and supports, etc.) and to investigate the reasons that have produced the change in the structural response. This is the procedure followed also in the case of the viaduct in question, schematically represented in the following figure. The model was developed in SAP2000, by means of “beam” elements (1D) spatially connected to each other and having non-linear behavior based on a formulation of concentrated plasticity; each element is associated with a fiber hinge to which the corresponding cross section, discretized into fibers, is assigned so that each fiber has a reference material (i.e., concrete or steel); once the strain of each fiber is obtained, the software is able to calculate the corresponding stress level and, by means of numerical integration, can define the behavior of each beam element and then of the entire structure. In this case, considering the static scheme of the viaduct and the anomalies recorded, it is necessary to give particular emphasis to the modeling of the structural joints: in fact, analyzing the seasonality of the measured changes, it was assumed that the response variations could be determined by a particular behavior of the joints rather than by a damage to structural elements (Fig. 7.7). Starting from the updated model defined “baseline,” sensitivity studies have been undertaken to justify the summer and winter conditions identified with the data analytics, in which the behavior of the structural joints has been investigated. For this purpose, NL-Links able to simulate the behavior at the interface between the initially assumed independent deck portions
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