## 3 Simulating HMAC Pavement Deformation in Curved Ramp
### Influential Factor Analysis Using Orthogonal Design Method  
This section presents the discussion on the influence of different factors on the deformation developed in the HMAC pavement with sloped and horizontally curved road alignment. In view of the massive calculating runs resulting from full factorial design (5\({}^{6}\) = 15,625), the Taguchi array was employed to reduce experimental run. The Taguchi method or orthogonal design method (ODM) developed by Dr. [PERSON] in Japan is a partial fraction experiment and has found wide use in many regions [29]. This method uses a special set of arrays called orthogonal array (OA) to choose the level combination of the variables for each experiment and to determine the minimal number of experiments to give full information of the factors that affect the objective index [30]. This research considered the permanent deformation as the objective index and chose six main factors each with five levels to reflect their influence. The factors and their levels are shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multicolumn{5}{c}{**Level**} \\ \cline{2-5}  & **1** & **2** & **3** & **4** & **5** \\ \hline P1-tire pressure (MPa) & 0.4 & 0.7 & 1.0 & 1.3 & 1.6 \\ P2-ESAL (10\({}^{4}\) times) & 200 & 700 & 1300 & 2000 & 2800 \\ P3-top layer thickness (cm) & 3 & 4 & 5 & 6 & 7 \\ P4-middle course thickness (cm) & 4 & 5 & 6 & 7 & 8 \\ P5-binder course thickness (cm) & 5 & 6 & 7 & 8 & 9 \\ P6-base thickness (cm) & 16 & 20 & 24 & 28 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Six factors and the corresponding levels. An OA is usually denoted by \(L_{\text{N}}(l^{k})\), where \(N\) is the number of performed experiments, \(l\) is the number of levels per factor and \(k\) is the number of factors. This study selected the \(L_{25}(5^{6})\) OA (shown in Table 6) to design factor-level combination and to conduct trial calculations, which needs 25 experimental runs to give necessary data for further analysis. The calculated deformations under each of the 25 experiments are shown in the rightmost column of Table 6.  
The Taguchi method usually uses intuitive analysis to analyze experimental data since it could give an explicit depict of the influence of different factors. The result of intuitive analysis in this study is also shown in Table 6. To guide the readers, several supplementary instructions to this table are presented as follows. In Table 6, \(K_{ji}\) is the sum of the deformations with factor \(j\) at \(i\) level (\(j\) = P1 to P6, \(i\) = 1 to 5) out of all trials. In addition, the average value of \(K_{ji}\) and the range of each parameter is calculated as follows. \[\overline{K}_{ji}=\frac{1}{5}K_{ji},\ Range_{j}=\max_{i}\{\overline{K}_{ji}\}- \min\{\overline{K}_{ji}\} \tag{3}\]  
According to the Taguchi method, the range of a factor could reflect its influence on the objective index. The larger the range value of a factor, the greater its effect on the process [31]. Based on  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Experiment** & \multicolumn{6}{c}{**Factor**} & \multicolumn{1}{c}{**Deformation (mm)**} \\ \cline{2-7}
**No. ** & **P1** & **P2** & **P3** & **P4** & **P5** & **P6** & \\ \hline
1 & 1 & 1 & 1 & 1 & 1 & 1 & 1.308 \\
2 & 1 & 2 & 2 & 2 & 2 & 2 & 3.894 \\
3 & 1 & 3 & 3 & 3 & 3 & 3 & 6.350 \\
4 & 1 & 4 & 4 & 4 & 4 & 4 & 7.13  
the intuitive analysis, the ranking of factors according to their effect on pavement deformation in descending order is P2 \(\rightarrow\) P1 \(\rightarrow\) P3 \(\rightarrow\) P4 \(\rightarrow\) P6 \(\rightarrow\) P5. According to Table 5, this indicates that ESAL and contact pressure showed greater impact on the deformation developed in special road, and the thickness of upper and middle asphaltic layers were also crucial to the pavement deformation whereas the binder asphalt layer and semi rigid base demonstrated less influence.