# Modeling of Fatigue-Strength Development
## 3 Results and Discussions
### Prediction of Fatigue-Strength Development in Emulsion Asphalt.
#### 3.2.3 Temperature Sensitivity Factors for Modified Fatigue-Age Relationships  
The rate constants recorded in Tables 5 and 6 were fitted to the cure temperatures (5 \({}^{\circ}\)C,25 \({}^{\circ}\)C, and 40 \({}^{\circ}\)C) using the simplified Arrhenius function, Equation (3), to obtain slopes and intercepts of the Arrhenius  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Strain Level,** & \multicolumn{3}{c}{**5 \({}^{\circ}\)C Cure**} & \multicolumn{3}{c}{**25 \({}^{\circ}\)C Cure**} & \multicolumn{3}{c}{**40 \({}^{\circ}\)C Cure**} \\ \cline{2-7} \multicolumn{1}{c}{\(\varepsilon\) (\(\upmu\)m/m)} & **k (1/day)** & **F\({}_{\text{u}}\) (\(\times\)10\({}^{-3}\))** & **k (1/day)** & **F\({}_{\text{u}}\) (\(\times\)10\({}^{-3}\))** & **k (1/day)** & **F\({}_{\text{u}}\) (\(\times\)10\({}^{-3}\))** \\ \hline
125 & 5.57 & 103.06 & 4.89 & 100.57 & 27.13 & 87.80 \\
150 & 6.81 & 110.58 & 6.42 & 107.63 & 31.25 & 95.32 \\
175 & 8.50 & 117.84 & 8.49 & 114.62 & 35.04 & 102.96 \\
200 & 10.95 & 124.91 & 11.39 & 121.64 & 38.19 & 110.88 \\
225 & 14.72 & 131.87 & 15.65 & 128.77 & 40.32 & 119.19 \\
250 & 20.82 & 138.83 & 21.93 & 136.16 & 41.09 & 128.03 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Fatigue-age parameters for a parabolic hyperbolic model for emulsion reclaimed asphalt.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Strain Level,** & \multicolumn{3}{c}{**5 \({}^{\circ}\)C Cure**} & \multicolumn{3}{c}{**25 \({}^{\circ}\)C Cure**} & \multicolumn{3}{c}{**40 \({}^{\circ}\)C Cure**} \\ \cline{2-7} \multicolumn{1}{c}{\(\varepsilon\) (\(\upmu\)m/m)**} & **k (1/day)** & **F\({}_{\text{u}}\) (\(\times\)10\({}^{-3}\))** & **k (1/day)** & **F\({}_{\text{u}}\) (\(\times\)10\({}^{-3}\))** & **k (1/day)** & **F\({}_{\text{u}}\) (\(\times\)10\({}^{-3}\))** \\ \hline
125 & 3.33 & 93.81 & 3.36 & 90.63 & 7.23 & 83.93 \\
150 & 3.79 & 101.30 & 3.74 & 98.30 & 7.58 & 91.44 \\
175 & 4.38 & 108.67 & 4.15 & 105.97 & 7.85 & 99.06 \\
200 & 5.16 & 116.02 & 4.62 & 113.78 & 8.02 & 106.90 \\
225 & 6.27 & 123.43 & 5.16 & 121.78 & 8.08 & 115.09 \\
250 & 7.95 & 130.96 & 5.79 & 130.10 & 8.00 & 123.73 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Fatigue-age parameters for a linear hyperbolic model for emulsion reclaimed asphalt.  
function. The temperature sensitivity factors, B, for both linear hyperbolic and parabolic hyperbolic models were recorded in Table 7. A\({}_{\text{o}}\) is the rate constant at 0 \({}^{\circ}\)C, while B is the temperature sensitivity factor of the cold-emulsion reclaimed asphalt pavement mixture under variable temperature curing.  
There is a general increase in the temperature sensitivity factors with strain levels, in Table 7, implying that fatigue strength of the cold-emulsion reclaimed asphalt pavement mixture diminishes under variable temperature curing as the loading strains increase. This is a reflection of the conventional fatigue test, in which, the number of load cycles to failure decreases logarithmically with an increase in load strain levels. At high test strain levels, specimens experience a rapid reduction in stiffness leading to early failure.