# Automated Trucks' Impact on pavement Fatigue Damage
## 2 Materials and Methods
### Fatigue Damage Computation  
The initial stage of this study involved the computation of critical strain values that resulted from a dual type loading on each pavement structure composition mentioned above. Considering the traffic data used by [PERSON] et al. [17], the study assumes that the pavement structure would carry 30 million standard equivalent 80 kN single axle loads over a 20-year design period. This translates to each model dual type receiving a load of 40 kN, with each tyre of the dual tyre set receiving 20 kN. Specifically, the contact area of the dual tyre comprises two rectangles, each measuring 0.1981 m in length and 0.1930 m in width. The tyre pressure exerted on the pavement, consistently assumed at 523.31 kPa across the contact area, aligns with [PERSON]'s study, which standardises the pressure distribution over the tyre-pavement interface. Given that each dual tyre set supports 40 kN, an axle, which has two dual tyre sets, supports a total load of 80 kN. This load value represents the standard equivalent single axle load of 80 kN used in pavement design and fatigue analysis. The centre-to-centre distance of the rectangular areas is assumed to be 0.335 m. Since this study focuses on the bottom-up (BU) fatigue damage (i.e., fatigue cracking that begins at the bottom of the asphalt layer and propagates to the surface), the horizontal strain values at the bottom of the HMA layer are determined via the finite element method (FEM) using the commercial software ABAQUS 2020 [33]. The maximum horizontal tensile strains at the bottom of the HMA layer are the critical strain values for BU fatigue damage. This study used the method proposed by [PERSON] et al. [31] to incorporate wheel wander in fatigue damage computation. For this purpose, we determined the horizontal strains at the bottom of the surface layer in the centre of the loading area and 89 lateral points to the right and left of the centre point by the interval value of 30 mm. In the next step, the calculated strain values are considered to calculate the DI value in the assumed lateral points at the bottom of the \(HMA\) layer after one wheel pass. To this \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Layer** & **Thickness (cm)** & **Stiffness (MPa)** & **Poisson’s Ratio** \\ \hline HMA Layer & 10, 15, 20 & 3100, 6200, 9300 & 0.3 \\ \hline Base Layer & 20, 40 & 300, 600 & 0.35 \\ \hline Subgrade Layer & Assumed to be infinite thickness & 100 & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Flexible pavement cross-section combinations. end, the present study used [PERSON]'s rule concept proposed in the MEPDG [30], as shown in Equation (1):  
\[DI=\sum(\Delta DI)_{j,m,J,p,T}=\sum\left(\frac{n}{N_{f-HMA}}\right)_{j,m,l,p,T} \tag{1}\]  
where \(n\) is the actual number of axle-load applications within a specific period, \(j\) is the axle-load interval, as obtained from weight in motion (WIM) data, \(m\) is the axle-load type (e.g., single, tandem, tridem, quad, or any other particular configuration), \(l\) is the truck type, \(p\) is the month, \(T\) is the median temperature for the five temperature intervals or quintiles used to subdivide each month, and \(N_{f-HMA}\) is the allowable number of axle load repetitions.