## 2 Methodology
### Determine Crash Risk Factors Using Fault Tree Analysis (FTA)
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Design Risk Factors**} & \multirow{2}{*}{**Risk Factor Ranges**} & \multirow{2}{*}{**Risk Factor Ranges**} & \multirow{2}{*}{**Distributing (RIN)**} & \multirow{2}{*}{**Receiving (\(RIN\))**} & \multirow{2}{*}{**Relative Influence (\(R_{j}\))**} & \multirow{2}{*}{**Net Effect (\(n_{i}\))**} & \multirow{2}{*}{**Weight (\(w_{j}\))**} \\  & & & & **(1-10)** & & & & & \\ \hline \multirow{4}{*}{2} & Horizontal Curve & \multirow{4}{*}{\(Ri\) (m)} & \(Ri\) \(<\) 600 & 10 & & & & & \\  & & & \(600\leq Ri<1000\) & 8 & \multirow{4}{*}{1.500} & \multirow{4}{*}{0.500} & \multirow{4}{*}{2.000} & \multirow{4}{*}{1.000} & \multirow{4}{*}{0.090} \\  & Radius & & \(1000\leq Ri<5500\) & 2 & & & & & \\  & & & \(Ri\geq 5500\) & 1 & & & & \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{Deflection Angle} & \multirow{4}{*}{\(D\) (\({}^{c}\))} & \(\lambda\) \(<\) 5 & 10 & & & & & \\  & & & \(5\leq\Delta<10\) & 8 & & & & & \\  & & \(10\leq\Delta<15\) & 4 & 0.000 & 1.833 & 1.833 & \(-1.833\) & 0.088 \\  & & & \(15\leq\Delta<25\) & 2 & & & & & \\  & & \(\Delta>25\) & 8 & & & & & & \\ \hline \multirow{4}{*}{4} & Horizontal Curve & \multirow{4}{*}{\(Lh\) (m)} & \(Lh\) \(<\) 200 & 10 & & & & & \\  & Length & & \(200\leq Lh<600\) & 8 & \multirow{4}{*}{0.833} & \multirow{4}{*}{0.500} & \multirow{4}{*}{1.333} & \multirow{4}{*}{0.333} & \multirow{4}{*}{0.081} \\  & & & \(600\leq Lh\leq 600\) & 2 & & & & & \\  & & & \(Lh\geq 2500\) & 6 & & & & & \\ \hline \multirow{4}{*}{5} & Vertical alignment & \multirow{4}{*}{\(A\) (\%)} & \(A<1\) & 2 & & & & & \\  & grade difference & & \(1\leq A<2\) & 6 & & & & & \\  & & & \(2\leq A<3\) & 8 & 0.000 & 1.833 & 1.833 & \(-1.833\) & 0.088 \\  & & & \(A\geq 3\) & 10 & & & & & \\ \hline \multirow{4}{*}{6} & Longitudinal grade & \multirow{4}{*}{\(G\) (\%)} & \(0\leq G<0.3\) & 6 & \multirow{4}{*}{2} & \multirow{4}{*}{0.667} & \multirow{4}{*}{0.500} & \multirow{4}{*}{1.167} & \multirow{4}{*}{0.167} & \multirow{4}{*}{0.078} \\  & & & \(0.5\leq G<3\) & 2 & & & & & \\  & & & \(G\geq 3\) & 10 & & & & & \\ \hline \multirow{4}{*}{7} & Slope length & \multirow{4}{*}{\(Lp\) (m)} & \(Lp\) \(<\) 300 & 6 & & & & & \\  & & & \(300\leq Lp\) \(<\) 700 & 2 & 0.000 & 0.500 & 0.500 & \(-0.500\) & 0.064 \\  & & & \(Lp\geq 700\) & 6 & & & & & \\ \hline \multirow{4}{*}{8} & \multirow{4}{*}{Crest curve parameter} & \multirow{4}{*}{\(kc\) (m)} & \(Ri\) \(<\) 7400 & 10 & & & & & \\  & & & \(7400\leq Ri<15,000\) & 6 & 0.333 & 0.000 & 0.333 & 0.333 & 0.060 \\  & & & \(Rci\geq 15,000\) & 1 & & & & & \\ \hline \multirow{4}{*}{9} & Sag curve parameter & \multirow{4}{*}{\(ks\) (m)} & \(Rsi\) \(<\) 5500 & 10 & & & & & \\  & & \(5500\leq Rsi<11,000\) & 6 & 0.333 & 0.000 & 0.333 & 0.333 & 0.060 \\  & & & \(Rsi\geq 11,000\) & 1 & & & & & \\ \hline \multirow{4}{*}{10} & Vertical curve length & \multirow{4}{*}{\(Lv\) (m)} & \(Lv\) \(<\) 70 & 10 & & & & & \\  & & & \(70\leq Lv<110\) & 6 & 0.000 & 0.667 & 0.667 & \(-0.667\) & 0.068 \\  & & & \(Lv\geq 110\) & 1 & & & & \\ \hline \multirow{4}{*}{11} & Flood Hazard & \multirow{4}{*}{\(H\) (\({}^{c}\))} & Table 2 & 0.667 & 0.000 & 0.667 & 0.667 & 0.068 \\ \cline{1-1} \cline{2-10}  & Road Infrastructure & \multirow{4}{*}{\(I\) (\({}^{c}\))} & \(I\geq 0.5\) & 10 & & & & \\  & Flood Hazard & & \(I\) \(<\) 0.5 & 5 & 0.667 & 0.000 & 0.667 & 0.667 & 0.068 \\ \hline \multirow{4}{*}{13} & Lithology Type & \multirow{4}{*}{\(Lh\) (\({}^{c}\))} & Table 3 & 0.667 & 0.000 & 0.667 & 0.667 & 0.068 \\ \cline{1-1} \cline{2-10}  & & & \(Lv\) \(<\) 70 & 10 & & & & \\ \cline{1-1} \cline{2-10}  & Vertical curve length & \multirow{4}{*}{\(Lv\) (m)} & \(\gamma_{0}\leq Lv<110\) & 6 & & & & \\ \cline{1-1}  & & \(Lv\geq 110\) & 1 & & & & \\ \hline \multirow{4}{*}{11} & Flood Hazard & \multirow{4}{*}{\(H\) (\({}^{c}\))} & Table 2 & 0.667 & 0.000 & 0.667 & 0.667 & 0.068 \\ \cline{1-1} \cline{2-10}  & Road Infrastructure & \multirow{4}{*}{\(I\) (\({}^{c}\))} & \(I\geq 0.5\) & 10 & & & & \\ \cline{1-1}  & Flood Hazard & & \(I\) \(<\) 0.5 & 5 & 0.667 & 0.000 & 0.667 & 0.667 & 0.068 \\ \hline \multirow{4}{*}{13} & Lithology Type & \multirow{4}{*}{\(Lh\) (\({}^{c}\))} & Table 3 & 0.667 & 0.000 & 0.667 & 0.667 & 0.068 \\ \cline{1-1} \cline{2-10}  & Linear Density & \multirow{4}{*}{\(LhD\) (\%)} & Table 4 & 0.667 & 0.000 & 0.667 & 0.667 & 0.068 \\ \hline \hline \end{tabular}
\end{table}