**4. Analysis of Bridge Deflections**

From a practical point of view, it is important to know the maximum bridge deflections. Therefore, the authors decided to analyze the bridge behavior at selected points located at 1/4, 1/2, and 3/4 of the main bridge span. In total, 10 node points situated on the bridge deck were analyzed during the measurements (Figure 3a). In addition, two bridge towers were also observed. It should be emphasized that measurements using the tachymetry technique (the reference method) were conducted over a longer period of time. Nevertheless, the authors tried to record the data at a similar time as for other methods. The possible differences in the bridge deflections can be related to the insufficient synchronization of tests carried out with various techniques.

Figure 9 presents an example of the obtained bridge scans. The maximum deflection results for the selected bridge points are presented in Table 2. Other maximum deflections in each measurement series were similar to those presented in Table 2 (the maximum difference did not exceed 1–3% for considered load scenarios). Therefore, it can be assumed that the results obtained were relatively convergent in individual load cycles.

**Figure 9.** Bridge deflections under static loading (A) in chosen points received from the TLS technique (Trimble scanner).


**Table 2.** Results of the maximum recorded bridge deflections (in mm).

<sup>a</sup> Former TLS results [32] were considered uncertain (the quality of point cloud was weak); <sup>b</sup> bridge deflections under dynamic loading are not possible to extract at this stage (the next research are still required); A, B, and C mean the load scenarios according to static loading (with limestone), dynamic loading (without the limestone), and dynamic loading (with limestone), respectively.

The obtained results also show the bridge deflections for various load scenarios (A, B, and C), and it is easy to observe the differences obtained between applied measuring techniques. The presented results were calculated in relation to the dead load of the bridge (reference stage: static loading without the limestone). Maximum bridge deflections were 60 mm and 49 mm for the photogrammetry and TLS (Trimble scanner), respectively, which means that the TLS results are quite consistent with the reference method (tachymetry); in contrast, the maximum bridge displacements obtained from the photogrammetry technique are higher by 18–20% than those obtained from the tachymetry and TLS techniques. These differences are related to the pixel size of the applied digital camera (4 mm) in the photogrammetry technique. Generally, the maximum deflections were observed in the middle of the main span of the bridge. The bridge deflections at other points (at 1/4 and 3/4 of the bridge span) were much lower.

The obtained results expressly confirmed that the bridge deflections under the static loading (load scenario A) were greater than those received under dynamic loading (load scenario C). The obtained disparities differed depending on the bridge measuring points (17–37%). This is due to load scenario A, where the load (limestone) can be considered as a linear load, and it was positioned stationary on the bridge. The measurement under this load lasted at least 1 h. The bridge deflections according to the load scenario B (dynamic loading without limestone) were at a low level.

Generally, the bridge deflections received from the TLS and tachymetry techniques under the static loading (A) are quite close to each other (Table 2). The TLS method for the bridge deflection measurements requires application of an adequate scanner, i.e., Trimble TX8. The results are convergent with the reference: the tachymetry method. Using the FARO Focus 3D scanner was less precise. It was the result of the too-large distance between the apparatus and the bridge and too-small angular resolution of a laser scanner (point density). In addition, the fact that the suspension bridge has an openwork structure also affects poor results (scans of larger density than ones obtained from the FARO scanner are required). To verify the test, the same scanner (FARO) was used to conduct inventory work on a historic (the oldest in Europe) suspension cast-iron bridge in Ozimek on the Mala Panew river (Poland). The tests were conducted at a much shorter distance between the scanner and the bridge, i.e., 40 m. The recorded point cloud density allowed identifying the elements (details) of the bridge, and fully satisfactory bridge inventory results were obtained [32].

Additionally, the TLS results can be presented using a calibrated map of colors (Figure 10). This method of presenting the TLS result is helpful for determining the most strenuous bridge elements. In addition, it indicates the bridge elements (in colors) where the deformations can be exceeded due to damages (which are not visible from the bridge deck). In general, incorrect behavior of some bridge elements can be detected. With this information, the bridge inspector can pay more attention to these elements during inspections. Red indicates the largest deflections and navy blue indicates the smallest. Maximum deflections of 49 mm were obtained in the middle of the main bridge span (they were recorded in suspension cables and the upper parts of the transport gallery). Additionally, the deformations of the bridge pylons are small (Figure 10). However, due to the resolution of a single screen, Figure 10 presents an indicative image that shows the tendency of displacements of the entire bridge structure. For a more accurate reading of displacements, in software working with point clouds, it is necessary to enlarge the given bridge element (Figure 11) or to measure the location of the same point in two clouds, one representing different states of the structure and one that is georeferenced. Figure 11 shows the details of the bridge deflections under the static loads (load scenario A) in the middle part of the structure obtained using a Trimble TX8 scanner. This also presents the highest deflection of bridge elements (red—cables and upper elements of the truss).

**Figure 10.** Bridge displacements under load scenario A shown by means of color deviation maps (Trimble TX8 scanner).

**Figure 11.** View of bridge deflection details (in colors) using a Trimble TX8 scanner.

Considering the TLS measuring sessions and the TLS results analysis, it is not possible to distinguish the bridge deflections under the dynamic loading. This is related to relatively rapidly changing bridge deflections in relation to the rotation speed of the laser scanner. Further research is needed on this topic. The authors believe that using the "in-line scanning" function can give interesting results. Then, multiple one-line scans (for example, near the middle of the bridge span) may allow determining the bridge deflections under the dynamic loading.

Figure 12 shows the chosen bridge deflections received from the photogrammetry technique under the static loading (load scenario A). Well-identified points of the bridge structure were chosen for the measurements. Generally, the processing of the received photogrammetric results was based on overlapping the subsequent photograms (from the various load scenarios). For example, the first photogram came from the static loading scenario (without the limestone), and the next photogram displays two photograms superimposed (with and without the loads). On the images superimposed (presented in the small windows), one pixel has been rescaled to 10 mm. Next, the number of pixels of the tested bridge components moving to each other was determined (similar to in the lab tests mentioned earlier).

**Figure 12.** Bridge deflections under static loading (A) obtained from the photogrammetry.

The deflection of the bridge section (crossbeam) under the dynamic loading (load scenario C) using the photogrammetry technique is presented in Figure 13. The first photogram (Figure 13a) was made when the belt conveyor was stopped (without the load), and the next one (Figure 13b) presents the image with two photograms superimposed (static loading and dynamic with the limestone (influence of the service dynamic loads)). As during the static loading (A), Figure 13b presents the superimposed images in which one pixel means 10 mm. As a result, the change in the bridge deflections under load scenario C (effect of normal bridge operation) was obtained. The results obtained indicate that the long distance from the digital camera to the bridge (ca. 120 m) did not adversely affect the quality of the bridge deflection readings. It is important to choose the appropriate camera focus, which means that the pixel size should be as large as possible, e.g., 2 mm. A larger scale (larger camera's focus) of the photograms may permit obtaining detailed data on the observed bridge elements, e.g., cracks, corrosion, excessive distortions, etc. This can be useful for bridge managers and inspectors.

**Figure 13.** The analyzed detail in 3/4 of the bridge span: (**a**) without load, (**b**) images superimposed (without and with load) showing the scale of the bridge deflection under dynamic loads (load scenario C).

The obtained measurement errors in the case of the tested bridge are consistent with those reported by the manufacturers of the applied instruments. They were confirmed at reference points for multiple measurements of the measured quantity. The real measurement errors for the tested bridge were as follows: 2 mm for the tachymeter, 1 pixel (4 mm) for photogrammetry, and 2 mm for the TLS method.

The tested structure constitutes the technological bridge (without any specific requirements); therefore, the obtained results were compared to the regulations for railway and road bridges. The deflection limit of the steel railway bridges, in accordance with the bridge standard EN 1991-2 Eurocode [34], was calculated using the formula *l*/15*v*−400, where *v* is the maximum speed and *l* is the bridge span. The measured maximum deflection under the static loading in the middle of the main span is in the upper limit of permissible displacements (56 mm). However, considering the admissible deflections provided for the steel road bridges (PN-82/S-10052 [35]), the measured maximum test deflections are considerably below the admissible value (*l*/500 = 330 mm). To recap, the tested bridge (after repair) fulfills requirements for the steel road bridges.

It would be best to measure the bridge deflections with a few total stations and digital cameras at the same time. Then, it would be possible to control the selected points using various techniques. As a result, accurate bridge deflections would be achieved. This approach would allow a complete measuring synchronization, but this way is practically impossible to conduct. This is due to the need to monitor a dozen points on the bridge at the same time. The total station and scanner need some time to take the measurements. The full synchronization is possible only for photogrammetry method and requires using several cameras that would be simultaneously activated by radio waves.
