## 5 Conclusions  
This study proposes a new computational model, namely the distributed steel fiber concrete arch (LSFRC), which considers the distribution of damage to the RC arch. The objective is to achieve a balance between the structural performance and economic benefit of the full-section steel fiber arch (FRC). The rationality of the LSFRC arch was verified through a numerical simulation of the concrete plastic damage model (CDP) in ABAQUS software. Furthermore, the influence of different steel fiber volume ratios and steel fiber  
Figure 17: Damage evolution trend of LSFRC arch spandrel with different steel fiber incorporation heights.  
layer heights on the performance of the LSFRC arch was deeply discussed. The research results are as follows:  
1. In the context of static arch loading, the damage to the RC arch section manifests as cracking at the lower edge of the arch crown, the foot edge of the arch, and the upper edge of the arch waist. The corresponding stress damage areas are [3L/8,5 L/8], [0, L/8], and [L/8, 3L/8], respectively.
2. A local incorporation of steel fibers can effectively increase the cracking load and bearing capacity of the RC arch, reduce the deflection of the arch waist and vault, and improve the damaged area of the section. The damage evolution rate of the LSFRC arch section slows down significantly with the increase in the steel fiber volume ratio and the height of the doped section, and crack propagation is effectively inhibited, thus improving the ductility and reliability of the failure stage.
3. In terms of a balance in performance, a local incorporation of steel fibers enhances the performance of RC arches while reducing the quantity of materials employed in comparison to the full-section incorporation of steel fiber (FRC) arch. Consequently, the LSFRC arch is more economical and practical. This research study offers a novel concept and methodology for the design and implementation of concrete arch bridges, which are anticipated to be widely adopted in future engineering practices.  
Conceptualization, Z.T. and Y.D.; methodology, Y.D.; software, Y.D.; validation, Y.D. and T.P.; formal analysis, Y.D.; investigation, Y.D., Z.Z., Y.C. and B.X.; resources, Y.D., T.P. and Z.Z.; data curation, Y.D. and T.P.; writing--original draft preparation, Y.D.; writing--review and editing, Z.T. and T.P.; visualization, Z.T.; supervision, Z.T.; project administration, Z.T.; funding acquisition, Z.T. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Nature Science Foundation of China, grant number 52078058; the National Nature Science Foundation of China, grant number 51478049; the Hunan Natural Science Foundation of China, grant number 2022 JJ50323; the Key Research and Development Project of Ningxia Hui Autonomous Region, grant number 2021 BEG0201; the Project Supported by Scientific Research Fund of Hunan Provincial Education Department, grant number 22C0164; and the Postgraduate Research and Innovation Project of Hunan, grant number CX2018B534.  
Not applicable.  
The data presented in this study are available in the article.  
The authors declare no conflicts of interest.