*6.2. Comparison of FEM Estimations and In Situ Measured Values*

Now comparisons of selected, representative results of the in situ measurements and corresponding FEM estimations are presented. Total deformations of the steel shell, measured by terrestrial laser scanning and total station are compared with the results coming from FEM calculations, in which different soil properties were assigned (refer to Table 2). These are shown in Figures 22–24, correspondingly, in 2-2 section under maximum load during S1 test, in 4-4 section under maximum load during S2 test and in 4-4 section during M24 moving load test configuration. It is worth mentioning that typically elastic displacements are analyzed during final acceptance tests. However, this is a specific case of a soil-steel structure. When the bridge was unloaded after S1 and S2 tests a slight change of shell shape was observed. Since point-cloud is created as a result of laser scanning, it is very hard to calculate elastic deformations coming from TLS. This is the reason why total deformations are compared in this chapter. Nevertheless in the case of moving load tests (refer for instance to Figure 24) the total deformation is nearly the same as the elastic deformation of the structure, because such a testing approach allows to significantly reduce this effect, as it was described in the Section 3. It has to be additionally noted that total station surveying was done in 9 points, as shown in Figure 6, in each cross section under consideration. In Figures 22–24, spline function was used to connect these 9 points and in effect deformed shape resulting from total station measurements was approximated.

It is seen in Figures 22–24 that the FEM estimations, even for different variants of the backfill elastic modulus, are generally in accordance with the measurements with regard to their quality and quantity. The backfill elastic modulus is an important parameter that affect the bridge response. It is a bit underestimated, when E = 170 MPa. Better quality results are obtained for E = 200 MPa and E = 230 MPa. In order to investigate displacements of the steel shell in detail, now, the extreme vertical displacements, that were obtained in the p4/2 point for the test S1, p4/4 for the test S2 and the corresponding FEM values (for different backfill material properties) are analyzed in Table 3. In Table 3 both total (Uin-situ,tot) and elastic (Uin-situ,el) in situ measured displacements are presented to highlight the issue of the shell shape change when the bridge was unloaded.

**Figure 22.** Comparison of the deformed shapes of the bridge in 2-2 section during the S1 test, when maximum load was applied, measured using terrestrial laser scanning, total station, and estimated by means of FEM (deformations in (mm) are 1000 times scaled).

**Figure 23.** Comparison of the deformed shapes of the bridge in 4-4 section during the S2 test, when maximum load was applied, measured using terrestrial laser scanning, total station, and estimated by means of FEM (deformations in (mm) are 1000 times scaled).

**Figure 24.** Comparison of the deformed shapes of the bridge in 4-4 section during the moving load M24 configuration, measured using terrestrial laser scanning, total station, and estimated by means of FEM (deformations in (mm) are 1000 times scaled).

In Table 4 vertical in situ displacements in the p4/4 point during the moving load tests M21–M26 are compared with the ones resulting from FEM calculations. Total displacement and the elastic values are not distinguished in Table 4, since they are almost the same.

The results from Tables 3 and 4 reveal that the response of the soil-steel composite bridge is underestimated, when the backfill elastic modulus is E = 170 MPa. In this case, the elastic displacement ratios Uin-situ,el/UFEM<sup>E</sup> <sup>=</sup> <sup>170</sup> for p4/2 and p4/4 locations, during S1 and S2 tests, are correspondingly 79% and 77%. The ratio between the biggest in situ vertical displacement during moving load test (M24 test configuration) and the corresponding FEM estimation Uin-situ,M24/UFEM,M24<sup>E</sup> <sup>=</sup> <sup>170</sup> equals 84%. Similarly, for the backfill elastic modulus equaling 200 MPa, the ratios Uin-situ,el/UFEM<sup>E</sup> <sup>=</sup> <sup>200</sup> in p4/2 and p4/4 points, during S1 and S2 tests are correspondingly 86% in both locations, while the ratio Uin-situ,M24/UFEM,M24<sup>E</sup> <sup>=</sup> <sup>200</sup> for the M24 test configuration is 94%. Finally the results are compared for the backfill having assigned E = 230 MPa. In this situation the ratios Uin-situ,el/UFEM<sup>E</sup> <sup>=</sup> <sup>230</sup> are 98% for p4/2 and 95% for p4/4 measurement point, whereas for the case of the moving load tests the ratio Uin-situ,M24/UFEM,M24<sup>E</sup> <sup>=</sup> <sup>230</sup> equals 104%. Based on these comparisons, it can be concluded, that from an engineering point of view, the response of the bridge is well recreated for the backfill with E = 200 MPa and E = 230 MPa. As the moving load test is probably the most effective way to examine and measure the bridge response (this issue has been already described in Section 3), it can be stated the real properties of the backfill regarding its elastic modulus are somewhere between 200 MPa and 230 MPa.


**Table 3.** Comparison of the in situ measured and estimated by means of FEM extreme displacements.

**Table 4.** Comparison of the in situ measured and estimated by means of FEM displacements in p4/4 measuring point during the moving load tests (M21–M26).


Nevertheless, the geometry of the shell at the beginning of the tests was slightly different than it was designed, as it had adjusted its shape during backfilling. Moreover, it continued to adjust its shape during final acceptance tests under different loading conditions and the whole bridge experienced some small permanent deformations. This is typical for soil-steel structures. In consequence, during static and moving loads tests, the loads caused by trucks were applied to the bridge having a bit different geometry. Ideal geometry of the structure, based on the technical drawings of the bridge, was defined in the numerical model. This could have caused the differences between the compared in situ and FEM values shown in Figures 22–24 and Tables 3 and 4. It is also worth to mention that the bridge shell is built of small corrugated steel sheets which are connected to each other with bolts (as shown in Figure 3). Such a connection technique requires the steel sheets to overlap each other. In effect, the whole shell is somehow locally stiffened, which may contribute also to the global stiffness of the whole system. A continuous shell without connections is created in the computational model. Therefore, one may expect that the structure has an internal margin of safety. Owing to the aforesaid considerations, we claim that the backfill properties are close to the ones represented by elastic modulus which is 200 MPa. In effect, we can say that the computational model has been calibrated with aid of the measurements. Thus, it reflects the real response of the analyzed structure. In effect it can be used for the purpose of the bridge diagnostics or support interpretation of SHM data.

Finally, the stresses calculated on the basis of strains, registered during the static tests S2 in t2/4 and t4/4 points, are shown together with corresponding FEM predictions in Table 5. The results presented in Table 5 were calculated assuming that the elastic modulus of the backfill is E = 200 MPa, which has been calibrated based on the displacement measurements, being the most reliable ones in this research. The points t2/4 and t4/4 were located approximately in the quarter-spans of the steel arch and extreme values were obtained there. Additionally, stresses in t3/4 point are also compared in Table 5. In Table 6 stresses calculated from strains in t2/4 point during the moving load tests M21–M26 are compared with the ones resulting from FEM calculations. Total and elastic values are not distinguished in Table 6, since they are almost the same.


**Table 5.** Comparison of the in-situ measured and estimated by means of FEM (for the backfill, having E = 200 MPa) extreme stresses.

**Table 6.** Comparison of the in situ measured and estimated by means of FEM (for the backfill, having E = 200 MPa) stresses in t2/4 measuring point during the moving load tests (M21–M26).


Similarly, as in case of displacements analysis, the stress ratios Sin-situ,el/SFEM for t2/4 and t4/4 from Table 5 are calculated and they are correspondingly 92% and 96%. The ratio between the biggest in situ stress during the moving load test (M24 test configuration) and the corresponding FEM estimation Sin-situ,M24/SFEM,M24 is 88%. It has to be emphasized here, that because of characteristics of the used devices (strain gauges) the accuracy of the calculated in situ stresses is ±1.2 MPa. The accuracy of displacements measure was way better than for the stresses, thus the displacements comparisons, presented in the preceding paragraph, seem to be more reliable and because of that were used for the purpose of the backfill stiffness properties calibration. From this reason the discussion about the cause of differences between measurements and numerical calculations has been done based on the registered displacements. Although the accuracy of stress measurements is not so good in relation to the values that were registered, which were relatively small and close to the device accuracy, it can be still concluded that there definitely is a correspondence between the in situ measurements and FEM estimations in the field of stress comparisons.
