Multi-Objective Optimization of UHPC Infill Strengthening for Arch Bridges Based on Finite Element Response Mapping and NSGA-III

To address the difficulty of coordinating structural performance improvement, material consumption control, and construction feasibility in the strengthening design of existing small-span concrete arch bridges, this study proposes a multi-objective optimization method for determining the ultra-high performance concrete (UHPC) infill strengthening thickness based on finite element response mapping and non-dominated sorting genetic algorithm III (NSGA-III). An existing multi-rib concrete arch bridge is taken as the engineering case. Field inspection, load testing, finite element model calibration, and comparative analysis of typical strengthening configurations are first conducted to clarify the applicability of the overall UHPC infill strengthening scheme. The maximum control thickness of UHPC infill between arch ribs is then selected as the primary design variable. A three-objective performance–material-consumption optimization model is established by minimizing mid-span deflection, maximum compressive stress at the arch springing, and UHPC consumption. The non-dominated candidate solution set is obtained using the NSGA-III algorithm combined with finite element response mapping. Representative finite element results show that the mid-span deflection and arch-springing compressive stress of the unstrengthened structure are 12.59 mm and 10.33 MPa, respectively. When the UHPC infill thickness is controlled within the range of 230.90–251.00 mm, the mid-span deflection decreases to 7.38–7.77 mm, and the arch-springing compressive stress decreases to 6.64–7.36 MPa. The optimization results indicate that structural deformation and critical-section stress generally decrease with increasing UHPC consumption, whereas the mechanical benefit gradually diminishes in the high-consumption range. Among the six reported cases, the 241 mm case represents a compromise between calculated structural responses and UHPC consumption under the modeled loading condition. This scheme corresponds to a mid-span deflection of 7.52 mm, an arch-springing compressive stress of 6.82 MPa, and a UHPC consumption of 19.83 m3, representing reductions of approximately 40.27% and 33.98% in deflection and stress, respectively, compared with the unstrengthened state. The findings provide a case-specific quantitative basis for the strengthening design of the investigated bridge and may serve as a reference for similar small-span multi-rib concrete arch bridges under comparable conditions.