# Practical Application of Sustainable Road Structure: Mechanical and Environmental Approach
## 4 Mechanical Analysis  
### Laboratory Tests of the Complex Modulus and Fatigue Life  
The results of the tests are presented in Figure 3 in the form of the master curves of the stiffness module E, the components of the complex modulus-the elastic part E1 and the viscous part E2, and the phase shift angle. The graphs shown indicate that both mixtures have similar rheological characteristics. The greatest differences in the stiffness modulus and the components of the complex modulus occur at low and medium reduced frequencies, which corresponds to high temperature conditions and/or long loading times. The reference mixture has a higher stiffness under such conditions, with very similar phase shift angle values. As a result, both the component of the elastic part and the viscous part of the complex modulus are greater than for the APSE mixture. As the temperature decreases and the frequency increases, the differences disappear, especially in the range of the values of the stiffness modulus and the elastic phase. The phase shift angle values are slightly higher under these conditions, which also results in a higher share of the viscous phase. According to the results of the complex modulus of the tested mixtures, it can be concluded that the APSE mixtures show lower stiffness, despite the higher reclaimed asphalt content which potentially stiffens the mixture. This is the result of a refreshing effect of the BIO-additive. Differences in the rheological properties of mixtures can affect their functional properties, such as resistance to permanent strains, cracking or fatigue life. The analysis of fatigue life most often evaluates the \(\epsilon_{6}\) parameter (eps6), which determines the strain under the fatigue test, during which the life of 1 million load cycles is obtained. A higher value means potentially better fatigue properties. Additional information is provided by the fatigue characteristic, which is described by the equation:  
\[N=A\cdot\epsilon^{b} \tag{1}\]  
where: \(N\)--fatigue life, \(\epsilon\)--strain during fatigue test; \(A\), \(b\)--linear regression parameters, and \(b\) is the slope of the fatigue line. Moreover, the fatigue law was extrapolated to obtain fatigue endurance limit (FEL), which is defined as strain value in the fatigue test leading to 50 million cycles [18]. The results of the fatigue tests are presented in Figures 4 and 5 in the form of graphs of fatigue characteristics and a comparison of the values of parameters \(\epsilon_{6}\) and FEL. In general, it can be concluded that the d characteristics of the APSE and reference mixture are similar, showing a slightly better fatigue resistance for the reference mixture. Its fatigue characteristic line is shifted towards higher values. This results in differences in strain values \(\epsilon_{6}\) and FEL, where differences reach 10-20%, respectively. The fatigue life depends on many factors. In particular, considering the properties and composition of the bituminous mixture, the type of asphalt binder and its properties, as well as the content in the bituminous mixture and voids [19] are the main influencing factors. For the analysed mixtures, differences in their fatigue resistance may be due to at least two factors. The first is the use of the BIO-additive, which affects the properties of the asphalt binder. The second, probably the decisive factor, is the use of reclaimed asphalt pavement in a larger amount in the APSE mixture than in the reference mixture. Higher reclaimed asphalt content means above all a larger amount of the \"old\" asphalt binder, which may have inferior properties associated with possible stiffening due to aging and fatigue processes. The increase in the share of reclaimed asphalt can affect the functional properties of the mixture. Fatigue life and crack resistance may deteriorate if stiffness is increased, while resistance to permanent strains may increase [20]. Naturally, the effect of the use of reclaimed asphalt can vary.