# Influence of the Microwave Heating Time on the Self-Healing Properties of Asphal Mixtures
## 3 Results and Discussion
### Influence of Fibres and Heating Time on the Asphalt Self-Healing Properties
In addition, mixtures with 2% and 4% of fibres, registered similar values on their healing levels (55% on average), which can be related with the fact that their air void content and fibres distribution inside them are similar. Finally, mixtures with 8% of fibres presented the lowest healing levels (40% on average) after microwave heating during 30 s. This can be mainly attributed to the fact that higher fibres content produce higher air void contents in the mixtures, that consequently produced a decrease on their flexural resistance (see Figure 8a), and an increase on the formation of fibre clusters (see Figures 4d and 5d), which means that the use of asphalt mixtures with elevated contents of fibres is not recommended. Moreover, analysing the error bars obtained from the healing level results (see Figure 6), it can be observed that, regardless the healing cycle, the variability of the results obtained from samples with different fibres content was similar for all the heating times. This suggests that there is not a significant difference between healing levels of asphalt mixtures with different fibre contents. However, the influence of the fibres content on the healing levels reached by the asphalt mixtures has not been proved. Due to that, the Cycle Reduction Ratio (_CRR_) has been defined in this study with the purpose  
Figure 7: Optical microscope images of the crack produced on an asphalt sample with 4% of fibres, in different stages of the cyclic healing process: (**a**) before healing; (**b**) after the 2 nd healing cycle; (**c**) after the 5 th healing cycle; (**d**) after the 10 th healing cycle. Image dimensions are 8 \(\times\) 10 mm, approximately. of evaluating if an increase on the fibres content has an effect on the healing level of asphalt mixtures, according to the following Equation:  
\[CRR=\left[\frac{HL_{i}}{HL_{max}}\right]_{n} \tag{2}\]  
where \(n\) is the studied healing cycle, \(HL_{i}\) is the healing level of an asphalt sample with \(i\%\) of fibres and \(HL_{max}\) is the maximum healing level within the cycle \(n\) (considered as the average healing level obtained from the samples with the fibres content that reach the maximum value). This ratio represents the variation of the healing level of asphalt mixtures within a specific cycle, with different fibres contents. With the aim of demonstrating that the difference between \(CRR\) values is due to the scatter of the results (see Figure 6), the Weibull probability of all \(CRR\) data has been calculated and presented versus the data percentiles in a probability-probability plot, see Figure 8b. This probability function was used considering that the cyclical process of cracking-healing fits to a fracture process of materials, idealized by means of a damage function of Weibull type [26]. Figure 8b represents all the \(CRR\) data regardless the healing cycle and fibres content, for all the studied heating times. The results show that \(CRR\) values are aligned to a straight line with a slope 1:1, thus fitting to the Weibull distribution function. This means that the differences between healing levels reached by the asphalt mixtures within a specific cycle can be attributed to statistical variations, which implies that the maximum healing levels in a cycle are not statistically significant and that these values are not produced by the influence of the fibres or the number of cycle. Consequently, it can be stated that the variable that has influence on the healing level is the heating time. Besides, the goodness of fit of the CRR data series to the Weibull distribution function can be observed in Figure 8b, for the different heating times. In this context, it can be stated that the better is the data fitting, the higher is the influence of heating time on the healing levels of asphalt mixtures. As can be seen, \(CRR\) data corresponding to 30 s and 40 s heating times fit better to the probability distribution function, while \(CRR\) data corresponding to 10 s and 20 s heating times are more dispersed, see Figure 8b.