## 4 SPI Prediction and Application  
### Analysis of the SPI  
According to the AHP method, we issued an electronic questionnaire to 10 experts and scholars of highway maintenance management, aiming to quantitatively rank and analyze the importance of each index. Since the importance of index judgment given by individual respondents is different, it is necessary to calculate all the values of each index separately and take the weighted average value as the element in the initial judgment matrix to obtain a reasonable judgment matrix after multiple consistency tests and adjustments [43]. The weights of the five assessment objects in the second-level indexes are first obtained by establishing a judgment matrix. Then, the first-level judgment matrix is established for the specific subgrade distresses, which appear in the second-level objects. Finally, the assessment system of the subgrade distress is shown in Table 2. A landslide not only interrupts traffic for a long time, but also directly causes casualties and property losses. Therefore, \"landslide\" is the distress type with the highest weighting value among all the distress types. Through the assessment system, the SPI results of twenty sites spread over four highways from March 2016 to March 2019 are obtained (Figure 6). As shown in Figure 6, subgrade distress is an irreversible process that, like the evolution of a landslide, exhibits an open state [45], and the development of cracks ranges from small-scale local cracks to large-scale regional cracks [46]. Therefore, the subgrade distress of the twenty test sites accumulated on top of the previous ones, resulting in the decrease in the SPI. Additionally, the rate of SPI decline was generally the highest from March to September, which was the most concentrated and abundant period of rainfall. From October to February of the following year, the SPI of most test sites remained stable, which indicated that the change in the SPI was highly correlated with rainfall. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Second-Level Indexes** & **Index Weight** & **First-Level Indexes** & **Index Weight** & \begin{tabular}{c} **Second-Level** \\ **Indexes** \\ \end{tabular} & \begin{tabular}{c} **Index** \\ **Weight** \\ \end{tabular} & \begin{tabular}{c} **First-Level** \\ **Indexes** \\ \end{tabular} & \begin{tabular}{c} **Index** \\ **Indexes** \\ \end{tabular} & \begin{tabular}{c} **First-Level** \\ **Indexes** \\ \end{tabular} & \begin{tabular}{c} **Index** \\ **Indexes** \\ \end{tabular} & \begin{tabular}{c} **Index Weight** \\ **Index Weight** \\ \end{tabular} \\ \hline \multirow{3}{*}{\begin{tabular}{c} Embankment and \\ roadbed \\ \end{tabular} } & \multirow{3}{*}{0.27} & \multirow{3}{*}{\begin{tabular}{c} Uneven settlement \\ Pumping \\ Cracking and sliding \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} Road shoulder \\ 0.403 \\ \end{tabular} } & \multirow{3}{*}{0.08} & \multirow{3}{*}{0.36} & \multirow{3}{*}{\begin{tabular}{c} Shoulder defects \\ Blocked drainage \\ Uncleanliness \\ \end{tabular} } & \multirow{3}{*}{0.255} \\ \cline{1-1} \cline{5-5}  & & & Blocking & 0.441 & & & \\ \cline{1-1} \cline{5-5}  & & Damage & 0.347 & & & Slope erosion & 0.135 \\  & &adequate drainage facilities & 0.212 & & & Cracking & 0.065 \\ \hline \multirow{3}{*}{Reinforced structures} & \multirow{3}{*}{0.19} & \begin{tabular}{c} Blockage of drainage holes \\ Damages to the structures \\ Abnormal structural stress \\ \end{tabular} & \
\begin{tabular}{c} 0.153 \\ 0.505 \\ \end{tabular} & \multirow{3}{*}{Slope} & \multirow{3}{*}{0.36} & \multirow{3}{*}{
\begin{tabular}{c} Local collapse \\ Rockfall \\ Landslide \\ \end{tabular} } & \multirow{3}{*}{0.078} \\ \cline{1-1} \cline{5-5}  & & & & & & Landslide & 0.439 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The assessment system of the subgrade distress. The five test sites selected from the same highway have a similar investigation duration and frequency. Additionally, different test sites on the same highway exhibit similar rates of SPI decline (Figure 6).