# High-Frequency Fatigue Testing of Recycled Aggregate Concrete
## 2 Materials and Methods
### Fatigue Tests  
The influence of conducting trials at a very high frequency was analyzed. For this purpose, the reference was tests carried out at moderate frequency, i.e., usual test frequencies, namely 10 Hz. For very high frequency tests, the highest possible test frequency was used, namely, tests were performed on a resonant fatigue machine. This machine carried out the tests at the resonance frequency of the set test machine and the specimen. In the specific case of the resonance machine used and the specimens used, these resonance frequencies were in the range of \(90\pm 5\) Hz. An explicative scheme of the fatigue tests that were carried out can be found in Figure 2a. Fatigue tests at both a moderate frequency (10 Hz) and a very high frequency (90 Hz) were performed using cylindrical specimens of 200 mm in height and 100 mm in diameter in all tests when these specimens were older than 90 days; this was done to ensure that the properties of the concrete had reached a stationary state. All the tests carried out recorded both the load applied to the specimen and the evolution of the strain suffered by the specimen. The strain was recorded by means of two strain gauges fixed to the specimens in two diametrically opposed generatrixes by considering the mean of the values provided by both gauges as the strain value of the specimen. In the high-frequency tests, the frequency at which the system was located was recorded, noting that the resonant frequency of the system will evolve with the variations in its stiffness. For each of the fatigue test types, two specimens were tested, ensuring that similar results were obtained in both. Fatigue characterization at a moderate frequency was performed using the Locati method [39; 40]. The Locati methodology consists of applying increasing steps of sinusoidal loads, maintaining a constant ratio \(\sigma_{\text{max}}/\sigma_{\text{min}}=0.1\) over a constant number of cycles, in this case \(2\times 10^{5}\) cycles (Figure 2b). These tests were performed on a servo-hydraulic machine with a maximum capacity of 1000 kN (Figure 2b). The criterion used to determine the fatigue limit using this type of test was that followed by [PERSON] in his PhD thesis [41], which obtained the fatigue limit stress range to be 80% of the stress range of the  
Figure 2: (**a**) Experimental fatigue campaign. (**b**) Locati methodology description. MF: moderate frequency, HF: high frequency. step in which the breaking occurs. The stress range was the difference between the maximum and minimum stress, i.e., \(\Delta\sigma=\sigma_{\text{max}}-\sigma_{\text{min}}\). This method is called method-1. In order to analyse whether an increase in frequency had an influence on the concrete fatigue limit, tests were performed under identical loads at a moderate frequency and a very high frequency. A 400-kN capacity machine was used to perform fatigue tests at the resonance frequency of the test set. This resonance frequency was found in all cases to be in the range \(90\pm 5\) Hz (see Figure 3b). In this case, in addition to analysing the results following the procedure followed by [PERSON] in his PhD thesis [41], an additional failure criterion was introduced, namely, to define the stress range of the step prior to a resonance frequency drop as the stress range of the endurance limit. This method was denominated as method-2. In order to analyse the influence of the number of cycles in the Locati tests, very high frequency tests were performed with the same stress values but applying \(5\times 10^{5}\) cycles per step instead of \(2\times 10^{5}\) cycles. For these tests, the same testing machine was used, and the same criteria were used to define the endurance tension range. The common objective of all these studies was to determine the step associated with the fatigue limit of the concrete in each case. In order to be able to compare the results as directly as possible, it was decided to fix the load steps based on the compressive strength of each material.