# Fatigue Behaviour of Concrete Using Siderurgical Aggregates
## 3 Results
### Fatigue Test
In the case of the LLC mix, the mean strain grows more during the first four steps, after which the SLC mix deforms more and more quickly. Figure 9 shows the evolution of the strain range with the passing cycles for the two mixes. The strain range was defined as the difference between the maximum and minimum strain registered by the strain gauges. Good coupling can be observed between the specimens of the same mix and the increase in range with the level of the applied load. The specimens of the LLC mix show a lower range, which becomes more distant between the two mixes as the steps progress. Irregular peaks generated by the strain of Specimen 1 of the LLC mix can be observed. This effect is due to noise in one of the strain gauges attached to the specimen during the first three load steps, after which it has disappeared. Figure 6: Evolution of the maximum and minimum strain for the LLC mix. Figure 7: Evolution of the maximum and minimum strain for the SLC mix. The range is notably higher in the case of the SLC mix, which may be due to the fact that the corresponding loads with the same step are 30% higher, due to the superior compressive strength of the SLC mix. After checking in which step the resonant frequency decreases and observing in which step it triggers, the fatigue limit step can be defined (criterion of the Frequency Droop). Table 6 shows the properties of the step prior to the frequency drop for the LLC and SLC mixes, defining the fatigue limit as the range of that step. The LLC mix managed to resist two more steps for the reasons explained above. Although the fc (%) of the LLC mix step is 10% higher, in absolute terms the range of the fatigue limit step is higher for the SLC mix. Figure 8: Evolution of mean strain for LLC and SLC mixes. Figure 9: Range evolution for mixes LLC and SLC. A second criterion was described in the methodology that defines the fatigue limit as 80% of the stress range of the step in which the specimen breaks. Table 7 shows the characteristics of the failure step as well as the fatigue limit associated with the stress range of the step. Making a comparison with the high-frequency fatigue limit values obtained by [PERSON] et al. [27], it is observed that the behavior of the SLC mix is similar to that of the RC-M mix (ballast aggregates with a small replacement of recycled Sleeper aggregate) for either of the two criteria used. As explained in the methodology, during the tests, the temperature of the outer surface of the test pieces was recorded. Figure 10a shows the evolution of the temperature for the LLC and SLC mixes. The increase in temperature is considerable and is associated with the high friction between the particles once the first micro-cracks appear and due to the high frequency at which the loads are applied. The high test frequency does not enable timely heat dissipation, as happens in low-frequency tests [34]. Figure 10b shows the range of strain in the specimens' gauges where the temperature was measured. A priori, it could be thought that the specimens of the LLC mix will suffer lower increases in temperature because the resonant frequency of the system is lower; however, there is an evident relationship between strain and temperature, in which the effect of friction is due to the amplitude of displacement rather than the speed of the displacement (frequency). The higher temperature in the SLC mix could also be favored because the siderurgical aggregates have a higher coefficient of thermal conductivity, due to the presence of iron, so the temperature increase occurs more quickly. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Mix** & **Step** & **\% f\({}_{\text{c}}\)** & **Min [MPa]** & **Max [MPa]** & **Mean [MPa]** & **Fatigue Limit [MPa]** \\ \hline SLC & 5 & 50\% & 4.2 & 42.4 & 23.3 & 38.2 \\ LLC & 7 & 60\% & 3.8 & _37.7_ & 20.8 & 34.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Fatigue failure step for LLC and SLC mixes: frequency reduction criterion. Figure 10: Evolution of maximum temperature (**a**) and average strain (**b**).