# Evaluation of Fatigue Life of Asphalt Concrete Mixtures with Reclaimed Asphalt Pavement
## 5 Analyses of Pavement Design Life
### Numerical Method  
The mechanistic pavement design method consists of determining the fatigue life of the structure on the basis of a stress-strain state analysis. For this purpose, the surface is treated as a system of \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Mixture** & \begin{tabular}{c} **AC22P 35/50** \\ **50\%RAP** \\ \end{tabular} & \begin{tabular}{c} **AC16W 25/55-60** \\ **50\%RAP** \\ \end{tabular} & \begin{tabular}{c} **ACWMS16** \\ **25/55-60 50\%RAP** \\ \end{tabular} & \
\begin{tabular}{c} **AC115 45/80-55** \\ **30\%RAP** \\ \end{tabular} &
\begin{tabular}{c} **SMA11 45/80-55** \\ **15\%RAP** \\ \end{tabular} \\ \hline Stiffness (0.02 s, 13 \({}^{\circ}\)C) under & 13,900 & 10,600 & 9230 & 5900 & 4700 \\ \hline Stiffness (0.02 s, 10 \({}^{\circ}\)C) under & 15,600 & 12,300 & 11,300 & 7260 & 5880 \\ \hline Stiffness (10 Hz, 10 \({}^{\circ}\)C) under & 16,100 & 12,600 & 11,700 & 7700 & 6260 \\ \hline Stiffness (10 Hz, 10 \({}^{\circ}\)C) under & 15,716 & 14,690 & 12,722 & 9189 & 7853 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stiffness modulus. Figure 7: Upper layers of pavement structures for fatigue analyses for different traffic load categories. courses with specific thicknesses on the subgrade with infinite thickness. The most common model is the model of elastic layers located in the elastic half-space. The individual courses are characterized by thickness (h), the modulus of elasticity (stiffness) (E), and Poisson's ratio (v). The asphalt layers' stiffness modulus were adopted in accordance with the results of tests and calculations stated above. The remaining parameters were selected in accordance with the instructions specified in the Catalogue [30]:  
* subgrade modulus of elasticity G1 equal to 80 MPa, Poisson's ratio 0.35,
* modulus of elasticity of the cement treated sub-base 200 MPa, Poisson's ratio 0.3,
* modulus of elasticity of the unbound subbase 400 MPa, Poisson's ratio 0.3,
* Poisson's ratio of asphalt courses 0.3. In order to make the design life calculations of the analyzed flexible pavement structure, it is necessary to determine horizontal tensile strains in the bottom of the asphalt layers and the compressive vertical strains in the upper surface of the subgrade. Calculations of the stress-strain states in the structure were performed using the NOAH 2.0 software (Nynas NV, Stockholm, Sweden, 1996). The following assumptions were made in accordance with the provisions adopted during the development of the Catalogue [31]:  
* equivalent axle load 100 kN (wheel load 50.0 kN),
* contact pressure q = 850 kPa,
* equivalent temperature 10 (French method) or 13 \({}^{\circ}\)C (AASHTO method). Two criteria of pavement failure were considered; i.e., the criterion of fatigue of the asphalt layers and the criterion of the subgrade deformation. The calculations were carried out using the criteria recommended for use in Poland [31]; i.e., the 2004 AASHTO method in relation to the fatigue life of asphalt layers and the method of the Asphalt Institute with respect to the subgrade. The fatigue life of asphalt layers according to the 2004 AASHTO criterion is described with the following equations [32]:  
\[N_{asf}=7.3557\cdot(10^{-6})\cdot C\cdot k_{1}^{\prime}\cdot(\varepsilon_{f}^{- 3.9492})\cdot E^{-1.281}, \tag{2}\]  
where:  
\[C=10^{M}, \tag{3}\]  
\[M=4.84\cdot\left(\frac{V_{b}}{V_{a}+V_{b}}-0.69\right), \tag{4}\]  
\(N_{asf}\)--fatigue life (number of equivalent standard axles), \(\varepsilon_{f}\)--tensile strain (\(\upmu\)m/m), \(E\)--stiffness (MPa), \(V_{b}\)--asphalt content by volume (% \(v/v\)), \(V_{a}\)--air voids (% \(v/v\)), \(h_{ac}\)--total thickness of bituminous layers (cm).