# Mechanical and Microstructural Studies of High Performance Concrete with Condensed Silica Fume
## 3 Results and Discussion
### Flexural Strength and Fracture Properties
The characteristic length is determined in accordance with the below equation [55]:  
\[f_{t,fl}=\frac{3F_{p}l}{2b(h-a_{0})^{2}}\ (\text{MPa}\,) \tag{1}\]1  
where \(f_{t}\) is the splitting tensile strength. HPC flexural performance is critical for safeguarding infrastructure from severe weather conditions. The flexural strength of HPC containing CSF and its variability are given in \[f_{t,fl}=\frac{3F_{p}l}{2b(h-a_{0})^{2}}\ (\text{MPa}\,) \tag{1}\]2  
The replacement of cement by 5%, 10%, 15%, and 20% of the CSF content in HPC enhanced the flexural strength by 16%, 16%, 11%, and 7%, respectively, compared to reference specimens without CSF. However, strength decreased by 2% for 25% CSF content compared to control HPC. The average flexural strength increases from 0% to 10% and decreases from 10% to 25% of the CSF content. For HPC mixtures with a W/B ratio of 0.25, the compatibility between flexural and tensile splitting strength may affected by HPC brittleness. As will be exposed, the brittleness related to the characteristic length of HPC mixtures with a W/B ratio of 0.25 increases from 0% to 15% and decreases from 15% to 25%. This suggests a more fragile crack development, which may result in increased flexural strength. [PERSON] et al. [3] found that the flexural strength increased by about 11%,  
\[f_{t,fl}=\frac{3F_{p}l}{2b(h-a_{0})^{2}}\ (\text{MPa}\,) \tag{1}\]3 Differences in flexural strength with CSF substitution. 15%, 29%, and 18%, when 10%, 15%, 20%, and 25% silica fume were applied, respectively. [PERSON] et al. [56] stated that the substitution of fine aggregate with silica fume up to 10% in attendance of 2% nanosilica and 20% steel slag as a partial replacement of coarse aggregate exhibited the maximum flexural strength. It was found that the increase in the substitution of silica fume and steel slag above this value caused an insignificant decrease in the flexural strength. In addition, it was stated that the air holes were occupied by a greater content of silica fume and steel slag, and the reduced water availability may have limited the hydration reaction, adversely affecting the flexural strength of the concrete. The average values of the HPCs fracture properties determined based on Equations (2)-(8) are given in \[f_{t,fl}=\frac{3F_{p}l}{2b(h-a_{0})^{2}}\ (\text{MPa}\,) \tag{1}\]4  
Variations in fracture energy and characteristic length with CSF content are shown in Figure 9a,b, respectively. The fracture energy increased with the increase in the CSF content up to 5% and then gradually reduces. The use of CSF revealed an enhancement in fracture energy of approximately 30.5%, 28%, 19.5%, and 11%, respectively, compared to the reference specimen when it was 5%, 10%, 15%, and 20% of the applied CSF content. However, the fracture energy decreased by 2% for 25% CSF content in comparison with reference HPC. The higher fracture energy showed that more of it was needed to fracture the HPC, and thus HPC had better fracture characteristics. On the other hand, HPC had poor fracture properties with lower fracture energy. Consequently, variations in fracture energy also indicate that lower CSF content helps to improve fracture-related properties of HPC. [PERSON] et al. [14] described that the average fracture energy increased with increasing compressive strength. However, quite large scatters were obtained in the fracture energy results, and therefore any conclusions regarding the influence of strength and age are uncertain. Therefore, any possible impact of silica fume on fracture energy is not clear. \[f_{t,fl}=\frac{3F_{p}l}{2b(h-a_{0})^{2}}\ (\text{MPa}\,) \tag{1}\]5 Differences in (**a**) fracture energy; (**b**) characteristic length with CSF content.