## 4 The Compressive Constitutive Relationship of Steel Slag Micronized UHPC  
### Stress-Strain Curves  
The stress-strain curves of the specimens were plotted based on the experimental results, as shown in Figure 5. Figure 5a-c show the stress-strain curves of the 1%, 1.5%,  
Figure 4: Relationship between peak strain and axial compressive strength. and 2% steel fibre content groups, respectively. Each graph has three levels of stress-strain curves and is compared with the P10 group without steel fiber control group. Figure 5 illustrates that during the initial loading stage of the test, the specimens were in the elastic phase, and the stress-strain curves exhibited an approximately linear upward trend. Although there were some variations in the slope of each curve, the overall slope increased with an increase in the coarse aggregate content while the steel fibre content remained constant. The curve had the highest slope when the coarse aggregate content was 20%, indicating that an appropriate addition of coarse aggregate can enhance the elastic modulus of steel slag micro-powder UHPC mixed with steel fibre. However, if the coarse aggregate content is increased to 40%, the volume of the cementitious material decreases, and the bond between the coarse aggregates formed by the cementitious material and steel fibres is reduced, leading to an overall decrease in the elastic modulus of the specimens. As the stress on the specimens approached 0.7 f\({}_{\text{c}}\) to f\({}_{\text{c}}\), the slope of the curve gradually decreased, and when the load reached 90% of the ultimate bearing capacity of the specimen, the curve started to level off. For specimens with a constant steel fibre content, when the coarse aggregate content was 40%, the curve showed a shorter plateau segment, and the strain of the specimen was also the lowest among specimens with the same steel fibre content. This indicates that the excessive addition of coarse aggregate to the specimens would reduce the ductility of steel slag micro-powder UHPC. After reaching the peak stress, the curve entered the descending stage, and the addition of steel fibres and coarse aggregates made the descending stage smoother. Among them, the addition of 20% coarse aggregate content resulted in the smoothest descending stage. Compared with P10 (the group without steel fibres), all nine groups showed a significantly smoother descending stage, indicating a good toughening effect. The stress-strain relationship model for uniaxial compression of ultra-high-performance concrete proposed in [28] was used for comparison. The model relationship is as follows:  
\[\sigma_{c}=E_{U}\varepsilon_{c}\ \ \ \ \ \varepsilon_{c}<\varepsilon_{c0}\]  
\[\varepsilon_{c}=f_{c}\ \ \ \ \ \ \ \varepsilon_{c0}\leq\varepsilon_{c}\leq \varepsilon_{cu}\]  
\[\varepsilon_{cu}=0.0034+(f_{cu,k}-120)\times 10^{-5} \tag{6}\]  
In the equation, \(\sigma_{c}\) represents the stress when the strain of ultra-high-performance concrete reaches \(\varepsilon_{c}\); \(E_{U}\) is the elastic modulus of ultra-high-performance concrete; \(\varepsilon_{\text{c},k}\) is the standard the design compressive strength of ultra-high-performance concrete; \(\varepsilon_{c0}\) is the strain corresponding to the peak stress fc of ultra-high-performance concrete; and \(\varepsilon_{cu}\) is the ultimate  
Figure 5: Stress–strain diagram of steel fibre-doped steel slag micronized UHPC. compressive strain of ultra-high-performance concrete, which is taken as \(\varepsilon_{c0}\) when under axial compression. The stress-strain relationship calculated using Equation (6) was compared with the experimental values, as shown in Figure 6. Figure 6a-c show a comparison of the 1%, 1.5%, and 2% steel fibre content groups, respectively. Each graph has three experimental stress-strain curves and three calculated curves using specifications for comparison.The slopes of the stress-strain curves obtained from the model in the code were generally greater than those of the experimental curves.