## 4 Calculation of Damage to RC Arch
### Parametric Analysis of the LSFRC Arch  
A parametric analysis of the LSFRC arch was conducted, utilizing the volume fraction (\(v\)) and the height of admixture along the cross-section (\(l_{\text{2}}\)) as variables. The steel fiber coefficients were set to 1%, 2%, and 3%, respectively, and the height of admixture along the cross-section \(h_{\text{2}}\) was set to h/4, 2h/4, and 3h/4, respectively. The results of the calculations are presented in Figure 16.  
As illustrated in Figure 16a, the load-carrying capacity of steel fiber-reinforced lightweight concrete (LSFRC) arches was observed to increase with the height of doping across the cross-section. The ultimate load capacities at doping height positions of h/4, 2h/4, and 3h/4 were measured at 181 kN, 190 kN, and 206.5 kN, respectively. These results demonstrate that a gradient increase in the steel fiber concentration along the height of the cross-section significantly enhances structural stress performance, thereby improving the tensile strength and toughness of the reinforced concrete (RC) arch. Figure 16b presents the load-displacement curves for LSFRC arches with varying steel fiber volume ratios at 2h/4. While the differences in the load capacity are relatively minor, it is evident that increases in steel fiber volume enhance structural ductility during the post-peak phase, resulting in higher energy absorption during the damage phase. As illustrated in Figure 16a, the incorporation height of LSFRC arch steel fiber at h/4, 2h/4, and 3h/4 results in ultimate bearing capacities of 181 kN, 190 kN, and 206.5 kN, respectively. As the steel fiber content increases along the section, the ultimate bearing capacity increases by 5.6% and 14.7% compared to the LSFRC-h/4. This demonstrates that the addition of steel fiber along the section height can effectively enhance the mechanical properties of the structure, improving the bearing capacity and toughness of the RC arch. Figure 16b displays the load-displacement curves of the LSFRC-2H/4 arch at varying steel fiber volume rates of 1%, 2%, and 3%. As illustrated in Figure 1, the carrying capacity of the specimen was found to be 190 kN, 196.6 kN, and 198.8 kN, respectively. Upon reaching a volume rate of 3%, the lifting effect of the volume rate on the carrying capacity of the LSFRC  
Figure 16: Comparison of load–displacement curve parameters of LSFRC arch: (**a**) different heights along the cross-section; (**b**) different steel fiber volume rates. Figure 15: The region of arch intrados damage evolution. arch begins to diminish. Nevertheless, in the subsequent decline phase, following the peak load, an increase in the steel fiber volume rate is accompanied by a more ductile response of the LSFRC arch to failure, although this is accompanied by a greater energy consumption. As illustrated in Figure 17, this study comparatively analyzed the damage evolution of LSFRC-2h/4 and LSFRC-3h/4 arches at the location of the arch footing under the same load using the LSFRC-h/4 arch structure at a peak load of 181 kN. The analysis results indicate that at the initial stage of damage (damage state value of 0.2), the corresponding damage rates of each stage are not significantly different. Upon reaching a load of 181 kN, the degree of damage of the three components at the foot of the arch cross-section is 0.89, 0.76, and 0.61, respectively. The results demonstrate that, with the increase in the height of steel fiber doping, the cross-section damage evolution rate of LSFRC arches is effectively slowed down. This can inhibit crack extensions more effectively and slow down the process of structural attenuation. Consequently, an optimal increase in the cross-sectional height when incorporating steel fiber can markedly decelerate the process of RC arch damage and enhance structural reliability. As illustrated in Figure 17, the damage evolution of the arch foot position of the LSFRC-20/4 and LSFRC-3h/4 arches under the same load was compared and analyzed based on the peak load of the LSFRC-h/4 arch, which was found to be 181 kN.