###### Abstract  
To investigate the toughening effect and stress-strain relationship of steel fibre-reinforced steel slag micropowder ultra-high-performance concrete (UHPC), nine sets of specimens with coarse aggregate and steel fibre contents were prepared for axial compression and elastic modulus tests. This study examines the variations in compressive strength and peak strain of the steel slag micropowder UHPC specimens to determine the corresponding characteristics of the stress-strain relationship. The results indicate that the experimental groups mixed with 1%, 1.5%, and 2% steel fibre increased the peak strain by about 20.3%, 25.3%, and 26.2%, respectively, compared to the non-steel fibre specimens. It can be seen that the toughening effect of UHPC with steel fibre and slag micro powder is good. With a fixed steel fibre content, the compressive strength and peak strain of steel slag micropowder UHPC initially increase and then decrease as the coarse aggregate content increases. The maximum compressive strength is achieved when the steel fibre content is 1.5% and the coarse aggregate content is 20%. A constitutive equation suitable for steel fibre-reinforced steel slag micropowder UHPC was derived through curve fitting based on the experimentally obtained stress-strain curves. The calculated values from the equation show deviations within 10% of the measured values, indicating a good fit. Nonlinear analysis of the entire compression process of prismatic specimens using the finite element method confirms the rationality of the constitutive equation, as the simulated curve closely aligns with the experimental curve. This research findings provide a reference for the engineering application of steel slag micropowder UHPC. b +
Footnote †: journal: Medical  
ductivity [9]. Among fibre materials, steel fibres have the characteristics of high elastic modulus and high tensile strength, which have a particularly significant improvement effect on the toughness of concrete [10]. Therefore, a certain amount of steel fibre can be added to steel slag micro powder UHPC to improve its compressive strength and toughness and reduce the problems of early cracking and high brittleness of steel slag micro powder UHPC. At the same time, research has found that adding a certain volume of coarse aggregate to UHPC can further reduce the preparation cost without affecting its performance [11,12] and can also improve the elastic modulus and compressive strength of concrete to a certain extent. Therefore, it can be attempted to add a certain amount of coarse aggregate to steel slag micro powder UHPC to optimize its performance while reducing costs again. The stress-strain relationship reflects the fundamental mechanical properties of UHPC, and the study and analysis of its stress-strain curve equation are of significant importance. Many scholars have conducted relevant research in this area. [PERSON] [13] investigated the different fibre contents on the uniaxial compressive mechanical properties of UHPC specimens and derived the constitutive relationship for UHPC with various fibre additions. [PERSON] [14] established a constitutive model for restrained ultra-high-performance concrete based on theoretical analysis and regression analysis. This constitutive model, validated through plastic damage analysis and comparison with load-displacement curves, is suitable for finite element analysis. [PERSON] [15] studied the uniaxial behaviour of confined coarse aggregate ultra-high-performance concrete (CA-UHPC) under compression deformation and theoretically derived the constitutive model for CA-UHPC. [PERSON] [16] considered the multiaxial stress-strain behaviour of the cementitious matrix and the stress-slip response of fibres, proposing a triaxial constitutive model for fibre-reinforced cementitious material UHPC. [PERSON] et al.