# Modeling of Fatigue-Strength Development
## 3 Results and Discussions  
### Fatigue-Age Relationships  
Fatigue strength, in terms of number of load cycles to failure, \(\text{N}_{\text{f}}\), was determined for each of the cold-emulsion reclaimed asphalt pavement specimens as described in Section 2.3 and the results plotted in Figures 4-6 for specimens cured at 5 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 40 \({}^{\circ}\)C, respectively. Results for specimens cured at 50 \({}^{\circ}\)C were reserved for model validation purposes. As can be seen in Figures 4-6, the number of load cycles to failure are expressed in terms of natural logarithms.  
To study the combined effects of cure temperature and cure duration on fatigue strength development of the cold-emulsion reclaimed asphalt pavement mixture, fatigue strengths at each of the 6 test strain levels in Figures 4-6 for specimens cured at 5 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 40 \({}^{\circ}\)C, respectively, were plotted against the cure duration, as shown in Figure 7. Evolution of fatigue-strength was observed by fitting a general logarithmic curve to the data. Although it does not provide the best fit to the fatigue-age data, a logarithmic plot has been found to give a good indication of strength trends in cold-mix asphalts [28].  
Figure 4: Fatigue strengths for cold-emulsion asphalt specimens cured at 5 \({}^{\circ}\)C.  
Figure 5: Fatigue strengths for cold-emulsion asphalt specimens cured at 25 \({}^{\circ}\)C.  
It can be observed, in Figure 7, that fatigue strength in the cold-emulsion reclaimed asphalt pavement mixture generally decreased with increase in cure duration. This observation implies that as curing proceeds, the cold-emulsion asphalt mixture experiences continued reduction in its ability to resist flexure and a corresponding increase in its sensitivity to change in load strain levels. This behavior is attributed to a continued increase in asphalt stiffness, as emulsification and pre-mix water is progressively lost by the specimens through evaporation. An increase in asphalt stiffness is associated with increased brittleness, the property responsible for low fatigue resistance. It can also be noted that specimens cured at higher temperatures consistently achieved higher fatigue strengths than their counterparts cured at lower temperatures. An increase in cure temperature is expected to enhance adhesion of the binder film to the aggregate surfaces, leading to an increase in fatigue resistance and a reduction in sensitivity to change in load strain levels.  
It is evident from Figure 7 that specifying a curing protocol solely on the basis of cure temperature and duration will not suffice in the prediction of strength development in a cold-mix asphalt. The continued decrease, with time, of fatigue-strength of the cold-emulsion reclaimed asphalt pavement mixture will have some implications on the design of cold-emulsion asphalt pavements to resist fatigue cracking. There is a need for a model that predicts the ultimate fatigue strength of the cold-emulsion asphalt mix, for the avoidance of overestimation of fatigue performance during design. These observations lend credence to the choice of maturity method as an option to account for the combined effects of time and temperature on fatigue strength development of the cold-emulsion reclaimed asphalt pavement mixture.  
Figure 6: Fatigue strengths for cold-emulsion asphalt specimens cured at 40 \({}^{\circ}\)C.  
Figure 7: Fatigue strength development in cold-emulsion reclaimed asphalt mix.