# An Evaluation of the Efficiency of Compartmented
## Materials and Methods
### Testing
#### 2.4.3 4 PB Fatigue Test  
The 4 PB Fatigue test was employed as a third standard test for the evaluation of asphalt mix healing and asphalt healing system efficiency. The system does not allow for adequate crack propagation and monitoring as with the previous two test systems (ITS & SCB), but it is considered the most reliable means of evaluating asphalt pavement performance [21]. The authors believe that the healing system for an asphalt pavement is only effective for micro cracks, because large cracks, even if closed, will still deform the test specimen, thus rendering it useless and challenging the results. [PERSON] et al. [21] found that microcracks result in the creation of large cracks, leading to full pavement failure. Thus, a focus of the self healing system should be the prevention of large cracks and a test system able to insert fatigue loading, simulating repetitive wheel loading, with a deflection strain control allowing small deformations and small crack formation in the test specimen is most suitable for studying the asphalt mix healing and asphalt healing system efficiency.  
Figure 7a,b illustrate the 4 PB Fatigue test set-up. They show a prismatic beam, 50 \(\times\) 50 \(\times\) 400 mm, subjected to four point bending with supposedly free rotation and translation at all load and reaction points. The bending is realised by a sinusoidal movement of the centre bearings in a vertical direction. The vertical position of the end-bearings is fixed. The applied displacement was generated by means of a servo-hydraulic testing device and an Instron Labtronic 8400 controller, which used feedback control of the actuator and an NI DAQ system with LABVIEW software to control the loading process and to collect test data. The program enables full control of the test system. A displacement transducer for the measurement of the deflection, not shown in Figure 7b, is positioned at the middle of the upper surface of the test specimen, where the deflection is at a maximum (300 \(\upmu\)m). The measuring range of the displacement transducer was \(\pm\)1 mm, and its resolution, according to the specifications, was 1 \(\upmu\)m. The measuring range of the load cell for the measurement of the force was 2 kN. The maximum deflection amplitude was 300 \(\upmu\)m. The test temperature was 20 \({}^{\circ}\)C, and the frequency was fixed at 30 Hz. Figure 7c shows the continuous sine-shaped deformation in the four-point bending test when the load frequency was 30 Hz and the deflection was 300 \(\upmu\)m.  
Since the load and displacement are continuously measured during the test, the parameters, such as flexural stiffness (\(S_{mix}\)), can easily be calculated. By shifting the stiffness versus loading frequency curves at a reference temperature using the Arrhenius equation [22], a master curve for the stiffness can be determined (Equation (7)).  
\[S_{mix}=a_{0}\left\{1-e^{-\left[\frac{f_{ref}}{a_{1}}\right]^{a_{2}}}\right\} \tag{7}\]  
where:  
\(S_{mix}=\) stiffness,  
\(f_{ref}=\) reduced frequency (Hz) and  
\(a_{0}\), \(a_{1}\), \(a_{2}=\) material parameters.  
The fatigue life is defined as the number of cycles where the stiffness is half of the initial value. Fatigue relationships are described using Equation (8).  
\[N_{f}=c\epsilon^{k}\text{ or }logN_{f}=logc+klog\epsilon \tag{8}\]  
where:  
\(N_{f}=\) number of constant strain applications until the specimen reaches half of the initial stiffness, \(\epsilon=\) applied strain (\(\mu\)m/m) and  
\(c\) & \(k=\) material parameters.