## 4 Conclusions  
In northeast China, the sandstone-covered mudstone layer is a slide-prone stratum, and rainfall infiltration is the primary factor inducing cutting slope landslide. In this paper, the causes of landslide as well as the characteristics and process of mudstone softening are recorded and analyzed in the expansion project of Heishan village to Jixi section of Dan-A highway. The landslide mechanism and instability state of the study area under different working conditions are studied by finite element numerical analysis, and the following conclusions are drawn. 1. Rainfall duration, rainfall intensity, and rainfall lag condition will decrease the stability of the cutting slope in study area. When the precipitation is the same, the duration of rainfall is positively correlated with the change of pore water pressure and the rise of phreatic line. However, rainfall intensity is negatively correlated with pore water pressure and phreatic line change. When the rainfall intensity is the same, the change of pore water pressure will increase with the extension of rainfall time, and the maximum change rate of pore water pressure is in the initial rainfall stage. In addition, the influence of rainfall on the slope has a lag effect, which may be related to the hydraulic conductivity of sliding zone soil and mudstone creep. 2. It is concluded that the critical state of slope instability in the study area is when the rainfall intensity is 80 mm, the rainfall intensity is 1d, and the stagnation is 5 h. It is primarily caused by rainfall intensity being greater than the infiltration rate and hysteresis effect. 3. In the slope stress analysis, the first instability is the front slope toe of the landslide. The maximum strain at the critical state of slope instability is 0.078. The first reason is that rainfall makes mudstone soften and strength attenuate, so the stress gathers here. Second, improper excavation makes the toe of the cutting slope locally free, resulting in a decrease in the stability coefficient. In the X-direction displacement analysis at the top of the slope, the maximum displacement decreases with the increase in rainfall, indicating that the slope is prone to local instability. In addition, with the increase in rainfall infiltration time, the plastic strain penetrates from the mudstone softening layer to the whole slip surface, which verifies that the mudstone is extremely easy to soften and disintegrate in water. 4. The analysis of the influence of different rainfall factors on slope stability and the critical condition of slope instability in this study can provide an effective basis for landslide early warning work in sandstone-mudstone interbedding areas. Take the rainfall value under the critical condition of slope instability, as the rainfall threshold can effectively prevent the occurrence of such landslide disasters. **Author Contributions:** Conceptualization, Y.G. ; formal analysis, Y.G. and W.S. ; methodology, Y.D. and M.L. ; writing--original draft, Y.D. and M.L. ; writing--review and editing, Y.G., Y.D., W.S., M.L. and C.Z. ; supervision, Y.G. ; funding acquisition, Y.G. and W.S. All authors have read and agreed to the published version of the manuscript. **Funding:** We thank the National Natural Science Foundation of China (Grant No. 41641024) and Carbon Neutrality Fund of Northeast Forestry University (CNF-NEFU) and the Science and Technology Project of Heilongjiang Communications Investment Group (Grant No. JT-100000-ZC-FW-2021-0182) for providing financial support and the Field scientific observation and research station of the Ministry of Education-Geological environment system of permafrost area in Northeast China (MEORS-PGSNEC). **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** All data generated or analyzed during this study are included in this published article. **Acknowledgments:** We would like to thank all staff members who contributed to this study who are not named here.