## 3 Results
### Tensile Strength  
The tensile strength of UHPC specimens is directly determined using a specialized measuring device. The system consists of components installed on the machine, including a load cell, LVDT, and a datalogger system, aiding in the experiment to ascertain the stress-strain response during tensile deformation of the samples (Figure 2). The results in Figures 7 and 8 demonstrate that the tensile strength of UHPC increases when using RHA as a substitute for SF, with quantities ranging from 5 to 15% in both the 5-day and 28-day stages. The elimination of Ca(OH)\({}_{2}\) components is a critical factor to improve the concrete tensile strength. The ultrafine particles of SF and RHA not only assist  
Figure 6: Effect of SF and RHA on flexural strength of UHPC. in the pozzolanic reactions of cement but also initiate secondary reactions that consume Ca(OH)\({}_{2}\). These effects contribute to the improvement of the C-S-H gel and transition zones between the matrix and high-strength steel fibers, particularly evident in the early-age stage. The size of RHA falls between cement particles and SF, which also plays a significant role in creating a mixture with higher compactness. This aspect has also been addressed in studies by [46]. Additionally, the tensile strength of UHPC is enhanced by the stronger bond between the concrete matrix and high-strength steel fibers. The stress-strain relationship was obtained from the UHPC samples at the 5-day age stage (Figure 9) and 28-day age stage (Figure 10). From Figure 10, the samples with a combination of SF and RHA show significant improvement in ductility and deformation capacity, which is in line with current similar research [48]. Notably, the SF10 RHA10 sample maintains a good balance between tensile strength and deformation, suggesting an optimal mix of SF and RHA. The SF15 RHA5 sample has a tensile strength close to SF15 but with better deformation capacity, indicating that RHA improves the ductility of UHPC. Using too much RHA (RHA20) may reduce  
Figure 8: Effect of SF and RHA on tensile of UHPC at 28 days. Figure 7: Effect of SF and RHA on tensile of UHPC at 5 days. tensile strength but significantly improves the ductility of UHPC, which can be beneficial in applications requiring high ductility. This graph provides crucial information on how the ratios of SF and RHA affect the mechanical properties of UHPC, guiding the design and application of these high-performance concrete types in practical scenarios. The curves effectively illustrate the behavior of UHPC samples corresponding to varying levels of SF and RHA usage. Based on the chart, we can determine the strength at which the first crack appears for different UHPC mixtures when normalized to the ratio of initial crack strength to ultimate strength. The post-peak curves of samples using RHA (5-15%) exhibit different slopes compared to those using only SF; they have higher ductility and a lower slope, resulting in a larger area under the curve, indicating higher fracture energy. Therefore, it can be concluded that the fracture characteristics of UHPC will be enhanced by combining RHA and SF at appropriate levels. The utilization of fine particles can enhance the fracture properties of both concrete as well as UHPC, as evidenced by prior studies [49, 50]. Figure 10: Tensile stress–strain relationship of UHPC at 28 days. Figure 9: Tensile stress–strain relationship of UHPC at 5 days. Along with the above results, it is noteworthy that an emphasis on the analysis of the microstructure is necessary. The incorporation of RHA into UHPC enhances tensile strength by refining its microstructure. RHA, rich in amorphous silica, actively participates in the pozzolanic reaction, consuming calcium hydroxide (Ca(OH)\({}_{2}\)) and producing additional calcium silicate hydrate (C-S-H) gel. This process not only densifies the matrix but also reduces porosity, particularly in the interfacial transition zone (ITZ), which is typically a weak point in concrete.