## 4 SPI Prediction and Application
### Analysis of the SPI
Therefore, a typical section is selected to represent each highway in this study. The relationship between the extracted changes of the SPI and accumulated precipitation, maximum daily precipitation, and rainfall days over the past 6-month period are provided (Figure 7). Using the Pearson Correlations (\(r\)) analysis method to evaluate the strength of a linear relationship between two variables [47], the Pearson Correlation, \(r\), between the SPI changes and the impact factors is shown in Table 3. Generally, \(r\leq 0.39\) represents weak correlations, \(r\) between 0.40 and 0.69 represents moderate correlations, and \(r\) between 0.70 and 1 represents strong or high correlations [48]. The \(r\) between the SPI changes of G105 and the cumulative precipitation and maximum daily precipitation is above 0.8, demonstrating a strong correlation (Figure 7a and Table 3). During the investigation period, the maximum accumulated precipitation of G105 in half a year reaches 1694 mm. This occurs from March to September 2016. The maximum daily precipitation occurs in June 2017, reaching 146 mm. The rain intensity level is heavy rain ([[http://www.cma.gov.cn/](http://www.cma.gov.cn/)]([http://www.cma.gov.cn/](http://www.cma.gov.cn/))). Normally, the rainy season is from March to August every year and annual rainfall is mainly concentrated in this period. The accumulated precipitation in the rainy season is generally about twice as high as it is in other months. In addition, this highway is built along the mountainous area, where the integrated granite stratum is widely distributed, so that the decrease in SPI is small. As can be seen from Figure 7b,c and Table 3, the \(r\) between the SPI changes of S223 and S270 and the cumulative precipitation is above 0.8. The two highways are built along the river. Under the condition of extreme rainfall, the embankment along the river is prone to erosion, resulting in the overall sliding of the embankment [49; 50]. Additionally, the cracks caused by the uneven settlement of  
Figure 6: Accumulated precipitation, time, and SPI from the test sites: (**a**) K2451–K2456 of G105; (**b**) K91–K96 of S223; (**c**) K100–K105 of S270; and (**d**) K5–K10 of S356. the embankment and the shrinkage cracks during the summer months allow the formation of positive pore water pressure at a shallow depth and trigger embankment failure [51]. Figure 7d and Table 3 show that the correlation between the SPI changes of S356 and the cumulative precipitation and rainfall days is strong. Along the line of S356, there are many double-decked slopes, the surface layer is weathered residual soil, and the residual soil slopes are very sensitive to short-term heavy rainfall [52]. Moreover, this line is located in the coastal area, and there are typhoons throughout the year. Typhoons are often accompanied by short-term heavy rains, causing a large number of slope erosion and local collapse disasters. Again, the evolution of subgrade distress is not only affected by external rainfall factors, but also by internal time factors that affect subgrade ancillary structures (such as retaining walls, anchor cables, anti-slide piles, etc.). The same is true for the multi-stage characteristic evolution process shown by landslide disasters [19]. The response process of the subgrade distress evolution to the same external factors may be different. When the ancillary structures of the subgrade are in a stable stage, even a strong influence from external factors can hardly cause subgrade distress. In contrast, when the ancillary structures begin to age after a certain period of time, which leads to a decline in anti-sliding ability, even slight disturbances may cause subgrade damage. Therefore, the time factor is considered as the internal factor of the SPI.