# Resonance Fatigue Behaviour of Concretes with Recycled Cement and Aggregate
## 2 Materials and Methods
### Experimental Procedure
#### 2.2.1 Resonant Fatigue Test  
Resonant fatigue is a technique that allows fatigue testing at the resonant frequency of the system. This resonant frequency depends on the stiffness of the system, and, in the \begin{table}
\begin{tabular}{c c} \hline \hline
**Identification** & **Description** \\ \hline HP & OPC and 100\% NA \\ HR-25 & OPC and 25\% MRA \\ HR-50 & OPC and 50\% MRA \\ HP-R & OPC-25 CDW and 100\% NA \\ HRR-25 & OPC-25 CDW and 25\% MRA \\ HRR-50 & OPC-25 CDW and 50\% MRA \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Identification of manufactured concrete. Figure 1: Aggregate particle size distribution. Note: NA-S: natural sand (0/6 mm); NA-M: natural medium gravel (6/12 mm); NA-C: natural coarse gravel (12/22 mm). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Property** & \multicolumn{6}{c}{**Aggregates**} \\ \cline{2-7}  & **NA-S** & **NA-M** & **NA-C** & **MRA-M** & **MRA-G** & **EN 12620** \\ \hline Dry density (g/cm\({}^{3}\)) [47] & 2.73 & 2.71 & 2.72 & 2.28 & 2.32 & - \\ SSD (\({}^{1}\)) density (g/cm\({}^{3}\)) [47] & 2.76 & 2.74 & 2.74 & 2.42 & 2.45 & - \\ Water absorption 24 h (%wt.) [47] & 1.18 & 0.88 & 0.78 & 6.28 & 5.27 & \(\leq\)5 (\(\leq\)7) (\({}^{3}\)) \\ Open Porosity (volv.) [47] & 3.2 & 2.4 & 1.9 & 14.3 & 12.2 & \\ Los Angeles coefficient (\%wt.) [48] & - & 16 & 18 & 32 & 36 & \(<\)50 (\({}^{2}\)) \\ Flakiness index (\%wt.) [49] & - & 21 & 25 & 10 & 10 & \(<\)35 \\ \hline \hline \end{tabular} Note: \({}^{(1)}\) SSD: Saturated Surface Dry. \({}^{(2)}\) Concretes with a compressive strength of less than 30 MPa. \({}^{(3)}\) Mixture of recycled aggregate and natural aggregate.  
\end{table} 
Table 3: Physical properties of aggregates. case of concrete, the stiffness is highly dependent on both the load values between which it is being calculated and the degree of cracking of the specimens. The concrete's compressive resonant fatigue behaviour was studied using the Locati method, which enabled the estimation of the fatigue limit using a single specimen. For this purpose, the minimum stress value (\(\sigma_{0}\)), corresponding to the lower limit, was fixed, and the upper limit of the maximum stress range (\(\sigma_{j}\)) was varied in steps, where \(j\) represents the different steps. Six loading steps with \(1\times 10^{5}\) cycles each were established, and a sinusoidal wave was applied at resonance by means of load control. The specimens were instrumented with two 60 mm strain gauges to measure the strains. These were placed diametrically opposite to the central axis of the specimen and centred in height, and bonded with two-component epoxy resin. The strains recorded in both gauges were averaged for the calculations. The test programme for the determination of the resonant fatigue limits is shown in detail in Table 5. Based on the uniaxial compressive strengths (\(f_{cd,180}\)) of the set of specimens, the minimum stress, \(\sigma_{min}\), was defined as 2.5 MPa and the maximum initial stress, \(\sigma_{max}\), as 12.5 MPa, and an increase, \(\Delta\), in the maximum stresses of 5.0 MPa was considered in each successive step. The fatigue limit was established from Equation (1), which was determined by correlating tests on different types of concrete by applying the Locati and Staircase methods [53]. \[L_{F}=0.8*\ \Delta\sigma_{L} \tag{1}\]  
where \(L_{F}\) is the fatigue limit (MPa) and \(\Delta\sigma_{L}\) is the stress range of the Locati test rupture step (MPa). In addition, the influence coefficient (\(IC\)) was defined as the ratio of the fatigue limit to the compressive strength in percent. The resonance frequency tests were carried out with the Zwick/Roell Amsler 400 HFP 5100 Vibrophores (Figure 2), which have a maximum load capacity of 400 kN, maximum mean load of \(\pm\)300 kN, maximum force amplitude of \(\pm\)200 kN, and a test frequency range between 35 Hz and 300 Hz.