## 3 Results
### Tensile Strength, Stress Causing First Crack Appearance, and Ultimate Tensile Strain
The following equation is proposed for prediction of tensile strength development of CSFRC over time based on the tensile strength at the age of 28 days:  
\[f_{ct}(t)=\left\{e^{0.025\cdot[1-(2/t)^{1.40}]}\right\}\cdot f_{ct}(28). \tag{1}\]  
The following equation is proposed for the same prediction but at the age of 21 days:  
\[f_{ct}(t)=\left\{e^{0.035\cdot[1-(2/t)^{1.50}]}\right\}\cdot f_{ct}(21). \tag{2}\]  
The parameters for Equations (1) and (2) are as follows:  
\(f_{ct}(t)\)--tensile strength of CSFRC at the age (\(t\));  
\(f_{ct}(28)\)--tensile strength of CSFRC at the age of 28 days;  
\(f_{ct}(21)\)--tensile strength of CSFRC at the age of 21 days. The prediction results calculated using Equations (1) and (2) are shown in Figure 2 and clearly show good agreement with the experimental results. The disagreement in the results for the ages of 14, 49, and 70 days is 4%, 1.8%, and 1.45% and can be ignored. As the tensile strength is around 3 MPa [36] for specimens manufactured from normal concrete and around 8 MPa [37] for those manufactured from ultra-high-performance concrete (UHPC), it is evident that the tensile strength of CSFRC is about 400% higher than that of normal concrete and about 88% higher than that of UHPC. An important parameter in the analysis of CSFRC behavior is the stress at the time of appearance of the first crack (nonlinearity), also referred to as the first crack strength. Table 3 and Figure 3 show that this value increases with aging. Figure 2: Temporal development of tensile strength. In doing so, Equation (3) aims to predict the stress development of CSFRC over time based on the tensile strength at the age of 28 days:  
\[\sigma_{cr}(t)=\left\{e^{0.38\cdot[1-(2^{8}/t)^{0.20}]}\right\}\cdot\sigma_{cr}(2 8), \tag{3}\]  
whereas Equation (4) intends to predict the stress development based on the tensile strength at the age of 21 days:  
\[\sigma_{cr}(t)=\left\{e^{0.64\cdot[1-(2^{8}/t)^{0.50}]}\right\}\cdot\sigma_{cr }(21), \tag{4}\]  
where  
\(\sigma_{cr}(t)\) is stress causing crack formation at age (\(t\)). In Figure 3, good agreement is observed between the experimental results and those obtained through Equations (3) and (4). The highest disagreement (not considering the age of 9 days) is about 10% at the age of 35 days. At the age of 9 days, the disagreement is about 26%, but the material at this age is not yet ready for exploitation, so these equations can be reliably used for prediction in the exploitation period. To ensure the possibility of comprehensively defining the constitutive law of material behavior, ultimate tensile strain is also an important parameter to consider. This strain is present in CSFRC immediately prior to failure. Table 3 and Figure 4 show that the value of this parameter decreases with aging. Reasons for this decrease will be explained later in this paper. Based on the fib Model Code 2010 [36], modified equations are proposed for prediction of this ultimate tensile strain. In doing so, Equation (5) aims to predict the ultimate strain development of CSFRC over time based on the ultimate tensile strain at the age of 28 days:  
\[\epsilon_{ul}(t)=\frac{\beta(t=28)}{\beta(t)}\cdot\epsilon_{ul}(28), \tag{5}\]  
Figure 4: Temporal development of the ultimate tensile strain. whereas the intention of Equation (6) is to predict the ultimate strain development of CSFRC over time based on the ultimate tensile strain at the age of 21 days:  
\[\varepsilon_{ul}(t)=\frac{\beta(t=21)}{\beta(t)}.\varepsilon_{ul}(21), \tag{6}\]  
where  
\(\beta(t)\) is temporal coefficient calculated according to Equation (7):  
\[\beta(t)=1-e^{-0.25.t^{0.5}}, \tag{7}\]  
and  
\(\varepsilon_{ul}(t)\) is ultimate tensile strain at the age ( _t_). Good agreement is observed when comparing the experimental results with those obtained through Equations (5) and (6) (Figure 4). The disagreement in the results is lower than 2% at the ages of 9, 21, 28, and 91 days but about 16%, 15%, and 12% at the ages of 35, 49, and 70 days, respectively.