# Force Performance Analysis and Numerical Simulation of Assembled Ribbed-Slab Abutments
## 3 Assembled Ribbed-Slab Abutment Model Validation and Foundation Model Analysis
### FE Analysis of the Full Model of the Assembled Ribbed-Abutment  
In this section, we focus on the structural performance of the overall ARBA structure, and a footbridge abutment model is set up for force analysis. Notably, this analysis excludes the considerations of soil pressure at the back of the abutment. The following is a comparative analysis of cast-in-place ribbed-slab abutments and flanged assembled ribbed-slabutments. (1) Damage to concrete  
In the Abaqus FE simulation, two types of ribbed-plate bridge deck damage with concrete compression damage are evident, as depicted in Figure 10. For the two types of bridge deck compression damage, Figure 10 illustrates that the distribution area of the concrete compression damage was essentially the same, being largely distributed around the platform cap area near the rib plate. Among them, the concrete damage of the cast-in-place abutment exhibits an arch-shaped region, which corresponds to the distribution of crack development observed in the test. In contrast, for the ARBA model, where joint disconnection resulted in unconnected cracks, the concrete damage distribution aligns with the crack patterns observed during testing. The damage at the cap region in both structures was consistent with the mode of structural failure under compression bending actions. (2) Reinforcement Skeleton Equivalent Force Cloud  
Figure 11 depicts the equivalent stress cloud diagrams of the reinforcement skeletons for both structures. From the figure, it could be found that the two structures are part of the tensile area of the rebar fracture in the specimen damage to the reinforcing steel skeleton were deformed, the deformation of the ARBA was relatively small, the two groups of specimens in the area of the cap close to the ribbed plate, and the stress concentration was more obvious. Owing to the continuity of the overall cast-in-place abutment, the stress maps of the reinforcement still exhibited an arch-shaped region, and yielding did not occur at the flange of the ARBA. Figure 10: Damage to concrete under compression. Figure 9: Comparison of the total crack distribution. (3)  
Stress map of the connector  
Figure 12 presents the stress cloud diagram of the connection device of the assembled ribbed-slab abutment. Evidently, the flange in the ARBA structure, even at its ultimate bearing capacity, has not yielded. Moreover, its stress is largely concentrated in the L-type connection (table cap and back wall connection). This is because the flange is a steel structural member, and it experiences significant vertical loads in the discontinuous region due to its high stiffness, making the L-type connection a relatively weak point in the structure. In the assembly of the ribbed-plate bridge deck, the ultimate bearing capacity of the bolt group structure did not reach the yield state, and the stress was primarily concentrated in the lower bolt connection. This concentration of stress arises from the vertical load on the lower part of the cap, which induces tension. As a result, the bolts in the bolts in the lower joints bear relatively high stress. (4)  
Load-deflection curve for the midspan section  
The load-deflection curves of the FE calculation of the cast-in-place and ARBA specimens are presented in Figure 13. The initial stiffnesses of the two structures were essentially the same at the beginning of the loading. After the initiation of cracking, both structures experienced a reduction in stiffnesses. Notably, the ARBA exhibited a considerably higher stiffness compared to the monolithic cast-in-place ribbed-slab abutment. The ultimate bearing capacity of the ARBA during the late structural loading stage was slightly larger than that of the overall cast-in-place ribbed-slab abutment. Nevertheless, the deformation capacity of the ARBA was inferior to that of the overall cast-in-place slab abutment, largely owing to the high structural stiffness of the steel structure at the intermediate joints of the ARBA and the high strength.