*4.2. Array-Type Pulley-Group Loading System Test*

To verify the reliability and stability of the array-type loading system in practical applications, selected loading points during the external concreting stage of the model test were chosen, and their design load values are presented in Table 2. The Donghua DHDAS data acquisition system was employed to collect real-time counterweight data of the relevant loading points, and the results are shown in Figure 12.


**Table 2.** Design loading value of selected loading points.

**Figure 12.** Time load curve of each loading point.

As shown in Figure 12, approximately 5 min after each loading point has completed loading, the values of the tension sensors can reach the designed load and remain relatively stable. Moreover, the load value of the *i*th loading point is affected by the *j*th loading point. This is because the counterweight of the latter causes a vertical deflection at the loading position of the former. This deflection is transmitted to the movable pulley group, causing the movable pulley group and the fixed pulley group to move closer together, which results in a certain degree of slack in the steel wire rope and a decrease in the total load value. However, after about 5 min, the load at each point returns to the original load due to the equal tension of the steel wire rope on both sides of the same pulley, demonstrating that the self-stabilizing characteristic of the system causes the mutual influence between the loading points to diminish over time. This confirms that the array-type pulley-group loading system exhibits good stability and high reliability.

#### *4.3. Comparison of Finite Element Simulation Results*

To verify the correctness of the load optimization algorithm for the array-type selfbalancing pulley-group loading system, finite element models of the original bridge and the model bridge were established using the ANSYS APDL 18.0 software [30], as shown in Figures 13 and 14. In both cases, the rigid steel skeleton and internal concrete were simulated using Beam188 elements, while the external concrete was simulated using Shell181 elements. The displacement and rotation of both arch feet were constrained, and the construction process was simulated using birth and death elements. During calculations, only the self-weight load was considered for the original bridge, whereas the model test bridge considered not only the self-weight load but also the vertical load applied by each pulley-group loading device on the structure.

**Figure 13.** Finite element model of the main arch ring in the model test.

The stress values of the main steel tubes, internal concrete, and external concrete in the rigid steel skeletons of the original bridge and the model test bridge at key sections during the construction process were extracted and compared. Some of the results are shown in Figure 15.

**Figure 15.** Comparison of the theoretical stress results of different components of the original bridge and the model test bridge. (**a**) stress results of the upper chords of 3/16-span sections; (**b**) stress results of the upper chord of 1/4 span sections; (**c**) stress results of the roof concrete of 1/4 Spans sections.

In Figure 15, the stress results of different components of the model bridge and the original bridge exhibit similar trends at various construction stages. During the web concrete pouring stage, the stress results of the model bridge are slightly larger than those of the original bridge. This is because the web concrete thickness of the original bridge, which is 45 cm, was scaled down to only 45 mm, making it difficult to arrange the reinforcement. For construction safety, the web concrete thickness in this area was increased to 55 mm, resulting in an increased self-weight load of the scaled-down web concrete and, ultimately, slightly higher stress results for the model bridge during this construction process.

In Figure 15a, the stress of the rigid steel skeleton has a larger difference during the 2–3# construction stages, while the maximum difference in the other construction stages is 8.33%. This difference arises from the fact that, for safety reasons, the model test did not apply loads after the rigid steel skeleton was connected; instead, the counterweights were applied after the internal concrete was poured. Considering that the focus of the model test is on the structural state during the external concrete process, and subsequent construction stages show good agreement between the two stress results, the stress difference during the internal concrete pouring stage can be ignored. In Figure 15b, the maximum stress deviation between the model bridge and the original bridge for the main arch ring, excluding the web concrete pouring stage, is 9.34%. As shown in Figure 15c, the stress trends of the bottom slab concrete construction stages for the model bridge's and original bridge's main arch ring are essentially the same, with a maximum stress difference of 0.66 MPa. These results indicate that the model bridge's main arch ring can adequately reflect the stress state of the original bridge during construction, verifying the correctness of the load optimization algorithm for the array-type, self-balancing pulley-group loading system.
