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Volume 31 Issue 6
Dec.  2020
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Tingyao Wu, Jianhong Jia, Nan Jiang, Chuanbo Zhou, Xuedong Luo, Yuqing Xia. Model Test of Deformation Evolution and Multi Factor Prediction of Anchorage Slope Stability under Rainfall Condition. Journal of Earth Science, 2020, 31(6): 1109-1120. doi: 10.1007/s12583-020-1343-5
Citation: Tingyao Wu, Jianhong Jia, Nan Jiang, Chuanbo Zhou, Xuedong Luo, Yuqing Xia. Model Test of Deformation Evolution and Multi Factor Prediction of Anchorage Slope Stability under Rainfall Condition. Journal of Earth Science, 2020, 31(6): 1109-1120. doi: 10.1007/s12583-020-1343-5

Model Test of Deformation Evolution and Multi Factor Prediction of Anchorage Slope Stability under Rainfall Condition

doi: 10.1007/s12583-020-1343-5
More Information
  • The stability of the anchorage slope on the Baiyang Yangtze River Highway Bridge in Yichang,China,was investigated under different rainfall conditions using model test,numerical simulation,and factor analysis. The results of the study are as follows:(1) with the increase of rainfall intensity,the change of earth pressure can be divided into three stages. However,when the rainfall intensity was larger than a certain value,the change of earth pressure of cut slope became two stages; with the increase of rainfall intensity,pore water pressure increased with the increase of rainfall time,while at a certain stage after the rainfall,the pore water pressure in the cut slope did not decrease immediately,but increased for a period of time. (2) When the rainfall stopped,the stability coefficient of the anchorage slope continued to decrease,then slowly increased,and finally tended to be gentle. Meanwhile,when the rainstorm reached a certain intensity,the main factor that restricted the rainfall infiltration rate became the geotechnical permeability coefficient of the cut slope,which was no longer the rainfall intensity. (3) Factor analysis shows that the rainfall intensity and rainfall duration were the most important factors for anchorage slope stability,while earth pressure,pore water pressure and slope displacement were much less significant.
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  • Anderson, T. W., Laake, P., 1998. Exact and Approximate Distributions of the Maximum Likelihood Estimate in a Simple Factor Analysis Model. Scandinavian Journal of Statistics, 25(1):39–51. https://doi.org/10.1111/1467-9469.00162 doi:  10.1111/1467-9469.00162
    Atangana, A., Vermeulen, P. D., 2014. Analytical Solutions of a Space-Time Fractional Derivative of Groundwater Flow Equation. Abstract and Applied Analysis, 2014(1):1–11. https://doi.org/10.1155/2014/381753 doi:  10.1155/2014/381753
    Benson, J. D., Benson, C. T., Critser, J. K., 2014. Mathematical Model Formulation and Validation of Water and Solute Transport in Whole Hamster Pancreatic Islets. Mathematical Biosciences, 254:64–75. https://doi.org/10.1016/j.mbs.2014.06.003 doi:  10.1016/j.mbs.2014.06.003
    Biddoccu, M., Ferraris, S., Cavallo, E., et al., 2013. Hillslope Vineyard Rainfall-Runoff Measurements in Relation to Soil Infiltration and Water Content. Procedia Environmental Sciences, 19:351–360. https://doi.org/10.1016/j.proenv.2013.06.040 doi:  10.1016/j.proenv.2013.06.040
    Blake, J. R., Renaud, J. P., Anderson, M. G., et al., 2003. Prediction of Rainfall-Induced Transient Water Pressure Head Behind a Retaining Wall Using a High-Resolution Finite Element Model. Computers and Geotechnics, 30(6):431–442. https://doi.org/10.1016/s0266-352x(03)00055-7 doi:  10.1016/s0266-352x(03)00055-7
    Egeli, I., Pulat, H. F., 2011. Mechanism and Modelling of Shallow Soil Slope Stability during High Intensity and Short Duration Rainfall. Scientia Iranica, 18(6):1179–1187. https://doi.org/10.1016/j.scient.2011.09.010 doi:  10.1016/j.scient.2011.09.010
    Hamza, A., Bahar, R., Abrishami, J., 2008. Finite Element Modelling of a Two Dimensional Transient Flow Using Saturated and Unsaturated Theory. International Journal of Geotechnical Engineering, 2(1):69–76. https://doi.org/10.3328/ijge.2007.02.01.69-76 doi:  10.3328/ijge.2007.02.01.69-76
    Hossain, M. S., Lozano, N., Hossain, J., et al., 2011. Investigation of Geohazard Potential of Highway Embankment Slopes on Expansive Clay by Using Geophysical Method. In: Wardani, S. P. R., Chu, J., Robert Lo, S. C., et al., eds., Proceedings of the 3rd and 5th International Conference. Semarang, Indonesia, May 18–20, 2011. https://doi.org/10.1142/9789814365161_0073
    Hu, X. L., Tang, H. M., Li, C. D., et al., 2012. Stability of Huangtupo Riverside Slumping Mass II# under Water Level Fluctuation of Three Gorges Reservoir. Journal of Earth Science, 23(3):326–334. https://doi.org/10.1007/s12583-012-0259-0 doi:  10.1007/s12583-012-0259-0
    Huang, R. Q., 2009. Some Catastrophic Landslides since the Twentieth Century in the Southwest of China. Landslides, 6(1):69–81. https://doi.org/10.1007/s10346-009-0142-y doi:  10.1007/s10346-009-0142-y
    Huat, B. B. K., Ali, F. H., Low, T. H., 2006. Water Infiltration Characteristics of Unsaturated Soil Slope and Its Effect on Suction and Stability. Geotechnical and Geological Engineering, 24(5):1293–1306. https://doi.org/10.1007/s10706-005-1881-8 doi:  10.1007/s10706-005-1881-8
    Jiang, Q., Su, G. S., Feng, X. T., et al., 2019. Excavation Optimization and Stability Analysis for Large Underground Caverns under High Geostress:A Case Study of the Chinese Laxiwa Project. Rock Mechanics and Rock Engineering, 52(3):895–915. https://doi.org/10.1007/s00603-018-1605-z doi:  10.1007/s00603-018-1605-z
    Jiang, Q., Zhong, S., Pan, P. Z., et al., 2020. Observe the Temporal Evolution of Deep Tunnelʼs 3D Deformation by 3D Laser Scanning in the Jinchuan No. 2 Mine. Tunnelling and Underground Space Technology, 97:103237. https://doi.org/10.1016/j.tust.2019.103237 doi:  10.1016/j.tust.2019.103237
    Kawamura, M., Tsujino, K., Tsujiko, Y., 2003. Analysis of Slope Failures due to the 2000 Tokai Heavy Rainfall Using High Resolution Satellite Images. IEEE International Geoscience & Remote Sensing Symposium. Toulouse. 2413–2418. https://doi.org/10.1109/igarss.2003.1294459
    Kim, J., Kim, Y., Jeong, S., et al., 2017. Rainfall-Induced Landslides by Deficit Field Matric Suction in Unsaturated Soil Slopes. Environmental Earth Sciences, 76(23):808. https://doi.org/10.1007/s12665-017-7127-2 doi:  10.1007/s12665-017-7127-2
    Kimoto, S., Oka, F., Garcia, E., 2013. Numerical Simulation of the Rainfall Infiltration on Unsaturated Soil Slope Considering a Seepage Flow. Geotechnical Engineering Journal of the SEAGS & AGSSEA, 44(3):1–13 http://www.researchgate.net/publication/276301586_Numerical_Simulation_of_the_Rainfall_Infiltration_on_Unsaturated_Soil_Slope_Considering_a_Seepage_Flow
    Kundu, J., Sarkar, K., Singh, P. K., et al., 2018. Deterministic and Probabilistic Stability Analysis of Soil Slope—A Case Study. Journal of the Geological Society of India, 91(4):418–424. https://doi.org/10.1007/s12594-018-0874-1 doi:  10.1007/s12594-018-0874-1
    Kyngdon, A., 2004. Comparing Factor Analysis and the Rasch Model for Ordered Response Categories:An Investigation of the Scale of Gambling Choices. Journal of Applied Measurement, 5(4):398–418 http://www.ncbi.nlm.nih.gov/pubmed/15496747
    Lange, B., Bronstert, A., 2013. Rainfall-Runoff Relation: A physically Based Model to Investigate Interactions between Rainfall Duration, Slope Angle, Soil Depth and Bedrock Topography. EGU General Assembly 2013, 15: EGU2013-7076
    Li, A. G., Yue, Z. Q., Tham, L. G., et al., 2005. Field-Monitored Variations of Soil Moisture and Matric Suction in a Saprolite Slope. Canadian Geotechnical Journal, 42(1):13–26. https://doi.org/10.1139/t04-069 doi:  10.1139/t04-069
    Li, S. J., Gao, H., Xu, D. M., et al., 2012. Comprehensive Determination of Reinforcement Parameters for High Cut Slope Based on Intelligent Optimization and Numerical Analysis. Journal of Earth Science, 23(2):233–242. https://doi.org/10.1007/s12583-012-0250-9 doi:  10.1007/s12583-012-0250-9
    Li, Y. H., Tang, X. J., Yang, S., et al., 2019. Evolution of the Broken Rock Zone in the Mixed Ground Tunnel Based on the DSCM. Tunnelling and Underground Space Technology, 84:248–258. https://doi.org/10.1016/j.tust.2018.11.017 doi:  10.1016/j.tust.2018.11.017
    Li, Y. H., Zhang, Q., Lin, Z. B., et al., 2016. Spatiotemporal Evolution Rule of Rocks Fracture Surrounding Gob-Side Roadway with Model Experiments. International Journal of Mining Science and Technology, 26(5):895–902. https://doi.org/10.1016/j.ijmst.2016.05.031 doi:  10.1016/j.ijmst.2016.05.031
    Mazaeva, O., Khak, V., Kozyreva, E., 2013. Model of Erosion-Landslide Interaction in the Context of the Reservoir Water Level Variations (East Siberia, Russia):Factors, Environment and Mechanisms. Journal of Earth System Science, 122(6):1515–1531. https://doi.org/10.1007/s12040-013-0363-2 doi:  10.1007/s12040-013-0363-2
    Mein, R. G., Larson, C. L., 1973. Modeling Infiltration during a Steady Rain. Water Resources Research, 9(2):384–394. https://doi.org/10.1029/wr009i002p00384 doi:  10.1029/wr009i002p00384
    Pham, K., Kim, D., Choi, H. J., et al., 2018. A Numerical Framework for Infinite Slope Stability Analysis under Transient Unsaturated Seepage Conditions. Engineering Geology, 243:36–49. https://doi.org/10.1016/j.enggeo.2018.05.021 doi:  10.1016/j.enggeo.2018.05.021
    Rahardjo, H., Lee, T. T., Leong, E. C., et al., 2005. Response of a Residual Soil Slope to Rainfall. Canadian Geotechnical Journal, 42(2):340–351. https://doi.org/10.1139/t04-101 doi:  10.1139/t04-101
    Robinson, J. D., Vahedifard, F., AghaKouchak, A., 2017. Rainfall-Triggered Slope Instabilities under a Changing Climate:Comparative Study Using Historical and Projected Precipitation Extremes. Canadian Geotechnical Journal, 54(1):117–127. https://doi.org/10.1139/cgj-2015-0602 doi:  10.1139/cgj-2015-0602
    Take, W. A., Bolton, M. D., Wong, P. C. P., et al., 2004. Evaluation of Landslide Triggering Mechanisms in Model Fill Slopes. Landslides, 1(3):173–184. https://doi.org/10.1007/s10346-004-0025-1 doi:  10.1007/s10346-004-0025-1
    Taniguchi, J., Tabei, K., Imai, M., 1987. Profiles of Water and Solute Transport along Long-Loop Descending Limb:Analysis by Mathematical Model. American Journal of Physiology-Renal Physiology, 252(3):F393–F402. https://doi.org/10.1152/ajprenal.1987.252.3.f393 doi:  10.1152/ajprenal.1987.252.3.f393
    Trandafir, A. C., Sidle, R. C., Gomi, T., et al., 2008. Monitored and Simulated Variations in Matric Suction during Rainfall in a Residual Soil Slope. Environmental Geology, 55(5):951–961. https://doi.org/10.1007/s00254-007-1045-7 doi:  10.1007/s00254-007-1045-7
    Tu, X. B., Kwong, A. K. L., Dai, F. C., et al., 2009. Field Monitoring of Rainfall Infiltration in a Loess Slope and Analysis of Failure Mechanism of Rainfall-Induced Landslides. Engineering Geology, 105(1/2):134–150. https://doi.org/10.1016/j.enggeo.2008.11.011 doi:  10.1016/j.enggeo.2008.11.011
    van Genuchten, M. T., 1980. A Closed-Form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal, 44(5):892–898. https://doi.org/10.2136/sssaj1980.03615995004400050002x doi:  10.2136/sssaj1980.03615995004400050002x
    Xu, J. T., Jian, W. B., Wu, N. S., et al., 2018. Unsaturated Seepage Characteristics of Slope under Rainfall Infiltration. Earth Science, 43(3):922–932 (in Chinese with English Abstract) http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQKX201803023.htm
    Yan, B., Toda, S., Lin, A. M., 2018. Coulomb Stress Evolution History as Implication on the Pattern of Strong Earthquakes along the Xianshuihe-Xiaojiang Fault System, China. Journal of Earth Science, 29(2):427–440. https://doi.org/10.1007/s12583-018-0840-2 doi:  10.1007/s12583-018-0840-2
    Yeh, W. W. G., 2000. Optimal Management of Flow in Groundwater Systems. Eos, Transactions American Geophysical Union, 81(28):315. https://doi.org/10.1029/00eo00242 doi:  10.1029/00eo00242
    Zhang, T. T., Yan, E. C., Cheng, J. T., et al., 2010. Mechanism of Reservoir Water in the Deformation of Hefeng Landslide. Journal of Earth Science, 21(6):870–875. https://doi.org/10.1007/s12583-010-0139-4 doi:  10.1007/s12583-010-0139-4
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Model Test of Deformation Evolution and Multi Factor Prediction of Anchorage Slope Stability under Rainfall Condition

doi: 10.1007/s12583-020-1343-5

Abstract: The stability of the anchorage slope on the Baiyang Yangtze River Highway Bridge in Yichang,China,was investigated under different rainfall conditions using model test,numerical simulation,and factor analysis. The results of the study are as follows:(1) with the increase of rainfall intensity,the change of earth pressure can be divided into three stages. However,when the rainfall intensity was larger than a certain value,the change of earth pressure of cut slope became two stages; with the increase of rainfall intensity,pore water pressure increased with the increase of rainfall time,while at a certain stage after the rainfall,the pore water pressure in the cut slope did not decrease immediately,but increased for a period of time. (2) When the rainfall stopped,the stability coefficient of the anchorage slope continued to decrease,then slowly increased,and finally tended to be gentle. Meanwhile,when the rainstorm reached a certain intensity,the main factor that restricted the rainfall infiltration rate became the geotechnical permeability coefficient of the cut slope,which was no longer the rainfall intensity. (3) Factor analysis shows that the rainfall intensity and rainfall duration were the most important factors for anchorage slope stability,while earth pressure,pore water pressure and slope displacement were much less significant.

Tingyao Wu, Jianhong Jia, Nan Jiang, Chuanbo Zhou, Xuedong Luo, Yuqing Xia. Model Test of Deformation Evolution and Multi Factor Prediction of Anchorage Slope Stability under Rainfall Condition. Journal of Earth Science, 2020, 31(6): 1109-1120. doi: 10.1007/s12583-020-1343-5
Citation: Tingyao Wu, Jianhong Jia, Nan Jiang, Chuanbo Zhou, Xuedong Luo, Yuqing Xia. Model Test of Deformation Evolution and Multi Factor Prediction of Anchorage Slope Stability under Rainfall Condition. Journal of Earth Science, 2020, 31(6): 1109-1120. doi: 10.1007/s12583-020-1343-5
  • The main types of geological hazards in the Three Gorges Reservoir area are landslide, debris flow, collapse, land subsidence, earthquake, ground crack, immersion and karst collapse. According to incomplete statistics, there are more than 20 000 various types of geological disasters, among which the most harmful hazards with the largest number and the widest distribution are landslide, debris flow and collapse (e.g., Jiang et al., 2019; Yan et al., 2018; Huang, 2009). The terrain in this area is mainly mountainous and hilly, and geological disasters are triggered occasionally, such as debris flow and landslide. The types of geological hazards are basically shallow soil landslides induced by rainfall, with a thickness range of 1–3 m. Generally, the thickness of sliding bodies is less than 5 m. Rainfall- induced landslide disaster causes not only huge economic loss, but also casualties (e.g., Take et al., 2004; Mein and Larson, 1973). In this case, it is necessary to study the sliding mechanism of landslide under rainfall conditions. At present, the research on stability of rainfall-induced landslide mainly focuses on model test, numerical simulation and field monitoring. When the similar conditions are satisfied, the model test can reflect the internal interaction of landslide, consider the influence of various factors comprehensively, and simulate complex boundary conditions (e.g., Xu et al., 2018; Kim et al., 2017; Robinson et al., 2017). Furthermore, in order to reveal the rainfall-runoff relation, a physically based model was developed to investigate interactions between rainfall duration, slope angle, soil depth and bedrock topography (Biddoccu et al., 2013; Lange and Bronstert, 2013; Rahardjo et al., 2005). In terms of numerical simulation, Pham et al. (2018) and Blake et al. (2003) presented a numerical model to analyze saturated-unsaturated seepage problem of rock slope under rainfall infiltration. Besides, based on the saturated-unsaturated seepage theory and the effect of rainfall infiltration, coupled with two phase mediums of unsaturated soil and water, numerical simulation of soil slope under rainfall condition was carried out using the strength reduction finite element method (Kimoto et al., 2013; Hamza et al., 2008). In the field monitoring, according to the monitoring results of soil moisture probe, densitometer and water level, the surface infiltration process of unsaturated soil is revealed (Tu et al., 2009; Trandafir et al., 2008; Li et al., 2005). Moreover, considering Buckley-Leverett Equation, a new mathematical model for saturated-unsaturated seepage in rock and soil media was presented with the foundation of two-phase seepage equation of continuity and Darcy's Law (Benson et al., 2014; Taniguchi et al., 1987). In addition to the above research on the deformation characteristics of slopes under rainfall conditions, there are also some studies on the stability and formation mechanism of the landslide, for example, the stability of the slope was studied by field data and numerical simulation (Hu et al., 2012; Zhang et al., 2010). Similarly, mechanism and modeling of shallow soil slope stability during high intensity and short duration rainfall have also been studied, and main conclusion is that the mechanism of the failures was mainly due to the loss of matric suction of soils by rainwater (e.g., Egeli and Pulat, 2011; Hossain et al., 2011; Huat et al., 2006). However, in addition to shallow soil slope, in the western part of China, large-scale landslides are notable for their scale, complex formation mechanism, and serious construction, one of the main unstable factors of high cut slope is high rainfall (e.g., Huang, 2009). At the same time, the stability of shore high slope at home and abroad is also easily disturbed by abrasion of slope foot and inundation of the slide zone (Mazaeva et al., 2013; Li et al., 2012).

    To sum up, most of the research on the evolution process and failure mode of landslides under the rainfall condition in the existing literature is mainly based on the model test or numerical simulation to study the change laws of pore water pressure and displacement in the slope. The study of slope stability under rainfall condition mainly focuses on the study or prediction of slope stability with a single variable, neglecting that the cut slope stability under rainfall condition is based on the comprehensive influence of multi field coupling. It is worth noting that the stability of the cut slope is affected by many factors, and it is not reasonable to judge by a single variable for the failure mechanism and stability prediction of the slope.

    In this paper, the north bank slope of Baiyang Yangtze River Highway Bridge in Baiyang Town, Yichang City is taken as the engineering background. Based on the similarity theory of model test and numerical simulation software GeoStudio, the deformation evolution and failure law of anchorage slope under different rainfall intensity were studied by means of digital photography, pore water pressure sensors and earth pressure sensors. In order to establish a mathematical prediction model reflecting the multi factors of cut slope stability, the factor analysis method considering the coupling effect of many factors was applied to the stability analysis of anchorage slope, and the advantage of factor analysis was that it considered all the comprehensive factors and highlighted the effect of key factors on the results, and then the numerical relationship between the key factors and the comprehensive factors affecting the slope stability under the rainfall intensity was established, and the change of cut slope stability under different rainfall conditions was revealed. At last, the mathematical prediction model of cut slope stability under the action of multiple factors was obtained, and a prediction and analysis method of cut slope safety under the influence of multiple factors was put forward, which also provides research ideas for the prevention and control of landslide under such heavy rainfall conditions.

  • Baiyang Yangtze River Highway Bridge is a passage for Yichang Zhangjiajie Expressway to cross the Yangtze River in Yichang. The bridge site is located in the section from Yichang to Zhicheng in the Middle Reaches of the Yangtze River. Baiyang Town on the north bank is an anchorage of gravity. The foundation pit of the anchorage was constructed by direct excavation on the ground. In the construction site, earth pressure sensors, pore water pressure sensors and settlement displacement monitoring points were buried into the soil to monitor the deformation of the anchored slope, which also could ensure the safety of the cut slope. At the same time, combined with the layout of the site monitoring point, the same monitoring points are arranged on the test model. Schematic diagram of geological section and instrumentation details of actual field conditions is shown in Fig. 1.

    Figure 1.  Schematic diagram of geological section and instrumentation details of actual field conditions.

  • The model of cut slope was mainly used to simulate the cut slope of foundation pit with anchor block. In this study, the typical section of foundation pit excavation was selected and simplified as plane strain model. Rainfall played an important role in the weakening of the properties of rock and the seepage of water in the cut slope, which was also an important factor affecting the stability of cut slope (e.g., Jiang et al., 2020; Kundu et al., 2018). For the model of landslide induced by rainfall, the water softening properties of in-situ rock mass and material for physical model need to be similar. The similarity of mechanical properties of in-situ rock includes the weight, cohesion, internal friction angle and water softening effect; the similarity of seepage action for water includes cohesion, internal friction angle and the seepage path. In the model test of landslide, the permeability coefficient of similar materials for in-situ rock is usually increased properly, so as to increase the infiltration speed and the effect of groundwater. The density of in-situ rock mass was calculated by its mass and volume. The elastic modulus and uniaxial compressive strength of in-situ rock mass were obtained by uniaxial compression test of standard test block of rock and soil. The cohesion and internal friction angle of in-situ rock mass were obtained by shear tests under different normal stresses. The permeability coefficient of in-situ rock mass was obtained by observing the change of the pumping capacity and water level in the test well, while the permeability coefficient of material for the physical model was obtained by the conventional permeability test instrument. The water softening coefficient of rock and soil mass was the ratio of uniaxial compressive strength of rock and soil mass in two states, including the state after water saturation and dry state. At the same time, the values of all mechanical parameters of in-situ rock mass were obtained through the above mentioned tests, while the numerical value of the material for physical model was obtained by the similarity ratio and the mechanical parameters of in-situ rock mass. The correlation coefficient of key physical quantities in the model test is shown in Eqs. (1)–(3). Comparison of mechanical parameters of material used and in-situ rock is presented in Table 1.

    Medium Types of surrounding rock Density (kg/m3) Modulus of elasticity (MPa) Cohesive force (kPa) Internal friction angle Compressive strength (MPa) Permeability coefficient (cm/s) Coefficient of water softening
    Prototype Strongly weathered argillaceous sandstone 1.5 300 10 18° 8 2.0×10-6 0.67
    Moderately weathered argillaceous sandstone 2.0 1 500 34.5 20.7° 30 0.3×10-6 0.8
    Model Strongly weathered argillaceous sandstone 1.5 2.5 0.083 18° 0.067 2.0×10-7 0.56
    Moderately weathered argillaceous sandstone 2.0 12.5 0.288 20.7° 0.25 0.3×10-7 0.82

    Table 1.  Comparison of mechanical parameters of materials used and in-situ rocks

    where ρ is density, μ is poissonʼs ratio, φ is internal friction angle, ε is strain, g is acceleration of gravity, Kd is coefficient of water softening, E is elastic modulus, C is cohesive force, l is length, u is displacement, t is time, q is permeability coefficient.

    Combined with the physical material parameters of similar materials and in-situ rock mass, it can be seen that the similar material had a high correlation coefficient with in-situ rock mass, in terms of the effect for water softening, which also showed that the similar material can better effect the water softening characteristics of the in-situ rock mass. Among them, the main material of bedrock is moderately weathered argillaceous sandstone, and the main material of anchorage slope is strongly weathered argillaceous sandstone. According to the report of geological survey, rock samples were taken from the site, and then a large number of indoor tests were carried out. Moreover, the cut slope and bedrock of anchored slope were selected, and the physical properties of the model material were further determined. The similar material ratio of moderately weathered argillaceous sandstone was quartz medium sand : quartz fine sand : gypsum : water=5 : 1 : 1.21 : 0.72; the similar material ratio of strongly weathered argillaceous sandstone was quartz fine sand : gypsum : cement : water=21.4 : 1 : 0.07 : 4.1.

  • Considering that the deformation and stress of cut slope were caused by excavation of foundation pit, which were the same in the horizontal direction of anchor foundation pit, so the physical model was simplified as plane strain model. At the same time, since the section shown in Fig. 1 was a typical excavation section of anchor foundation pit excavation, the same geological section as Fig. 1 was selected as the prototype slope for indoor physical model test, then combined with the length similarity ratio mentioned above, the size of the model in the physical model test was determined. Therefore, based on the above analysis results, the length×width×height of the anchorage slope model was 115 cm×40 cm×50 cm, and the schematic diagram of test system for anchorage slope model is shown in Fig. 2. In consideration of the measurability of anchorage slope surface displacement, each grid node was marked with a red mark, and the digital Single Lens Reflex (SLR) camera was placed in front of the anchorage slope to take photos continuously at 2 s intervals, recording the deformation characteristics of red mark in the process of anchorage slope excavation, so as to prepare for the analysis of anchorage slope deformation by digital processing technology (e.g., Li et al., 2019, 2016). At the same time, four dial indicators were placed on the upper surface of the anchorage slope model to measure the surface settlement of anchorage slope, and earth pressure sensors and pore water pressure sensors were embedded in the slope. On the right side of the anchorage slope model, a total station was used to measure the displacement change of a point in the anchorage slope, and the instrument of static strain test system named DH3816 was used to measure earth pressure and pore water pressure of cut slope.

    Figure 2.  Schematic diagram of anchorage slope model test system.

  • First, the soil sample for model test was prepared, secondly, the soil was filled into the test equipment box, at the same time, the monitoring instrument was buried in the soil, thirdly, the instrument used in the model test was adjusted to the normal state, and finally the rainfall model test of cut slope was carried out by simulating the artificial rainfall. According to the statistics of rainfall parameters, for a heavy rainfall with a two year recurrence probability, the maximum rainfall intensity in this area is 50 mm/h, or 100 mm/2 h. In the model test, polyethylene plastic pipe was used to connect the water conveyance system at the beginning and the end of the artificial rainfall device was sealed with plug, which crossed over the model groove and was fixed on its crossbeam with iron wire, and a lot of small holes were inserted on the polyethylene plastic pipe to design and implement different rainfall processes. In order to control the pressure and flow of rainfall in the process of rainfall, the rainfall intensity of the rainfall system was mainly controlled by the height of the water tank and the rotation angle of the water valve. The orthogonal tests were carried out in 25 groups, in which the time of rainfall was divided into 5 levels, namely 10, 20, 30, 60, 120 min; and the rainfall intensity was divided into 5 levels, namely 10, 20, 30, 40, 50 mm/h.

  • The model test of anchorage slope under rainfall condition was carried out according to the following process: preparation of test framework→preparation of cut slope model for simulating anchorage slope→installation of test monitoring device→ connection and commissioning of rainfall device→rainfall test of cut slope was carried out→data collection of monitoring instrument and observation on the macro change of cut slope. Part of the rainfall test procedures is shown in Fig. 3.

    Figure 3.  Photographs showing the test procedures. (a) Test frame was prepared; (b) test model was made and monitoring points were arranged; (c) rainfall device was connected; (d) rainfall device was commissioned; (e) rainfall test was carried out; (f) view of the model test setup.

  • The change of earth pressure in cut slope with rainfall duration and rainfall intensity was counted and analyzed (Fig. 3). When the rainfall duration was 120 min, under different rainfall stages and rainfall intensity conditions, the change of earth pressure monitoring points (T1) with rainfall intensity is shown in Fig. 4a, and when rainfall intensity was 30 mm/h, the change of earth pressure monitoring points (T1, T2 and T3) with rainfall intensity is shown in Fig. 4b.

    Figure 4.  Diagrams showing the changes of earth pressure in cut slope with rainfall intensity. (a) The change of earth pressure monitoring points named T1; (b) the change of earth pressure monitoring points named T1, T2 and T3.

    It can be seen from Fig. 4a that with the increase of rainfall duration, the earth pressure of cut slope gradually decreases, and with the increase of rainfall intensity, the decrease range of earth pressure of cut slope gradually increases, including the following two forms: (1) when the rainfall intensity was small, the change of earth pressure was mainly divided into three stages with the increase of rainfall time, in the first stage (A1A2, B1B2, C1C2, D1D2), the earth pressure of cut slope decreased slowly and linearly with the increase of rainfall time, which was the stage of weakening and gradual development of earth pressure. In this stage, the earth pressure decreased gradually, the pore water pressure in the cut slope also increased gradually; In the second stage (A2A3, B2B3, C2C3, D2D3), the earth pressure in the cut slope decreased rapidly with the increase of loading time, in this stage, with the increase of rainfall intensity, the soil began to soften, the cohesion and friction angle of soil decreased rapidly. At the same time, cracks appeared in some parts of the cut slope and local collapse was formed. With the collapse of the overlying soil, the earth pressure of cut slope decreased rapidly.

    The third stage was the stable stage of change for earth pressure (A3A4, B3B4, C3C4, D3D4), in this stage, the pore water pressure in the cut slope has reached the saturation state. The weakening of the mechanical parameters of the soil did not depend on the rainfall intensity but on the permeability coefficient of the soil. In this stage, the change of the earth pressure tended to be stable, as the water on the surface of the cut slope mainly drained along the cut slope and did not penetrate into the soil, the change of the earth pressure of cut slope was not significant. (2) when the rainfall intensity was larger, that was, when the rainfall intensity reached 50 mm/h, the shear strength of the soil on the slope surface decreased rapidly, and the infiltration rate of the slope increased, so the sliding force of the potential slip surface in the slope increased, and resisting forces decreased. The infiltration rate of rainwater was far greater than the drainage rate of rainwater, and finally the cut slope collapsed locally, so the three-stage variation trend of the earth pressure attenuation became two stages. That is to say, when the first stage rapidly attenuated to a stable state (E1E3), and when it was the second stage (E3E4), the landslide surface has been destroyed and the earth pressure remains unchanged.

    It can be seen from Fig. 4b that the earth pressure monitoring points (T2, T3) inside the cut slope were increased first and then became stable, because the precipitation of water in the soil was affected by the resistance of soil particles, and the infiltration speed was very slow, in addition, the cut slope has a large gradient, and most of the precipitation flowed directly in the form of runoff, that is, there was no time to infiltrate into the depth of the soil. Therefore, only after a long time of rainfall, the moisture content of soil will increase greatly within a certain depth range, and then the earth pressure will increase greatly. Through the analysis, it can be concluded that the increase range of earth pressure in cut slope increased with the increase of buried depth of earth pressure, and the increase rate of earth pressure was about 12.61% to 15.97% more than before the rainfall.

  • In Fig. 3, with the change of rainfall duration and rainfall intensity, the change of pore water pressure monitoring point in the cut slope was analyzed, when the rainfall duration was 120 min, under different rainfall stages and rainfall intensity conditions, the change of pore water pressure monitoring points (P1) with rainfall intensity was shown in Fig. 5a, and under rainfall intensity was 30 mm/h, the change of pore water pressure monitoring points (P1, P2 and P3) with rainfall intensity is shown in Fig. 5b.

    Figure 5.  Diagrams showing the changes of pore water pressure in cut slope with rainfall intensity. (a) The change of pore water pressure monitoring points named T1; (b) the change of pore water pressure monitoring points named P1, P2 and P3.

    It can be seen from Fig. 5a that the pore water pressure increased with the increase of rainfall duration and rainfall intensity, at the same time, with the increase of rainfall intensity, the influence of rainfall intensity on the increase of pore water pressure gradually became significant. In the early stage of rainfall, the pore water pressure didn't change significantly, and then with the increase of rainfall time, the front edge of the cut slope was gradually flooded by rainwater. The values of the pore pressure sensors located in the front of the cut slope were significantly increased, and the closer to the surface of the cut slope, the greater the pore water pressure value increased. At the same time, in a certain stage after rainfall, the data of the monitoring points of pore water pressure near the surface of cut slope decreased rapidly, while the monitoring points of pore water pressure far away from the surface of cut slope gradually dissipated, and the pore water pressure decreased gradually. However, as rainwater intruded into the surface of the cut slope, the pore water pressure showed a certain lag, that is, the pore water pressure showed an appropriate increase after the rainfall. The increase percentage of pore water pressure in monitoring points (P3) was relatively small with the increase of rainfall time, which was far away from the slope surface. With the increase of rainfall time, the increase percentage of pore water pressure in monitoring points (P2 and P1) was relatively large, which was close to the cut slope surface. Meanwhile, the increase rate of pore water pressure in the cut slope was 6.2–9.32 times more than before the rainfall.

  • In the case of rainfall, the stability of cut slope changes with rainfall intensity and duration. Based on saturated-unsaturated theory and GeoStudio numerical simulation software, the change of cut slope stability during the whole rainfall duration has been analyzed, including the internal seepage and rainfall infiltration rate of anchorage slope under different rainfall intensity. Using the SLOPE/W and SEEP/W coupling modules in GeoStudio, the numerical model for analysis has been established as shown in Fig. 1, and the physical and mechanical parameters of rock and soil are shown in Table 1.

  • In order to calculate stability coefficient of the cut slope under rainfall conditions, it is necessary to obtain the water and soil characteristic curve first, which hads been obtained in the model test. The basic steps of numerical simulation include: (1) selecting the analysis module, which is seep/w module in this paper; (2) drawing the geometry to be analyzed, as shown in Fig. 1; (3) defining the material parameters, as shown in Table 1; (4) defining the boundary conditions, and (5) solve. The definition of boundary condition includes: (1) determination of the basic equation of water movement in the cut slope; (2) determination of infiltration conditions for rainwater to surface of cut slope.

    (1) Determination of the basic equation of water movement in the cut slope

    The groundwater level of the cut slope is generally the boundary between saturated area and unsaturated area. With the increase of rainfall, the range of saturated area and unsaturated area of anchorage slope also changes. Based on the law of conservation of mass and Darcyʼs Law (e.g., Atangana and Vermeulen, 2014; Yeh, 2000), the basic equations of water motion in unsaturated region with multi-dimensional anisotropy are described as follows.

    The subsurface water level of the cut slope is generally the dividing line between saturated and unsaturated regions. With the rainfall, the range of saturated and unsaturated regions in the cut slope body changes accordingly. Based on the law of conservation of mass and Darcy Law (e.g., Atangana and Vermeulen, 2014; Yeh, 2000), the basic equation of water movement in the unsaturated region with multi-dimensional anisotropy is described as follows

    where h is the height of water head, kx, ky, kz is the permeability coefficient in x, y and z directions, θ is the moisture content, C(θ) is the specific water bulk density, and its physical meaning is the change of water content in the soil caused by pressure change

    where n=1/(1–m), n > 1, α, m, n are fitting parameters. θs is the saturated volumetric moisture content, θr is the residual volumetric moisture content (generally considered to be 10% of the saturated volumetric moisture content); Se is relative saturation, whose equation is shown in Eq. (6). The water and soil characteristic curve equation was fitted by van Genuchten (1980), which is the most commonly used method to describe the soil water characteristic curve. And Eq. (7) describes the relationship between the matrix suction of cut slope and the volume moisture content of slope soil, and Eq. (8) is the relationship between the matrix suction of cut slope and the permeability coefficient of soil in cut slope.

    where ψ is the matrix suction of cut slope, α is dimensionless fitting parameter, e=2.718 28, k is permeability coefficient, ks is saturation permeability coefficient, θ is volume water content.

    (2) Determination of infiltration conditions for rainwater to the surface of cut slope

    The surface of the cut slope is the infiltration boundary, which is taken as the flow boundary. Considering that the rainfall infiltration changes with the infiltration capacity of rock and soil, when the rainfall intensity is less than the infiltration capacity of the surface layer of rock and soil, the infiltration speed is the rainfall intensity. At this time, the boundary condition is the flow boundary

    where q' is the water flow in the cut slope, t' is any time of rainfall.

    On the contrary, when the rainfall intensity is greater than the infiltration capacity of the surface layer of the waste slag soil, the water is lost along the cut slope surface, and the infiltration rate is the infiltration capacity of the rock and soil itself, and the boundary condition is the constant head boundary

    The following three curves shown in Fig. 6 are required for numerical simulation, which have been solved by the above seven equations and model test data, which are applied to the numerical simulation. The boundary conditions and initial conditions during rainfall infiltration calculation of anchored slope are shown in Fig. 6a. According to the anchoring slope body, the rain face of natural rainfall is determined. The sections 1-2, 2-3, 4-5 and 5-6 are selected as the natural rainfall infiltration boundary. At the same time, the sections 3-4 and 7-10 are always below the natural water level and in saturated state, so sections 3-4 and 7-10 are selected as known water head boundary. Similarly, sections 7-8, 9-10 are not affected, which are too far away from the rainfall infiltration slope, so they are selected as the known water head boundary. Sections 8-9 is the bottom end of the anchored slope model, which can be regarded as the impermeable boundary. The relationship between matrix suction and volume moisture content of cut slope is shown in Fig. 6b. The relationship between matrix suction and permeability coefficient is shown in Fig. 6c.

    Figure 6.  Diagrams showing (a) the boundary conditions and initial conditions of anchorage slope and (b)–(c) curves required for numerical simulation. (b) Relationship between the matrix suction of cut slope and the volume moisture content of slope soil; (c) relationship between the matrix suction of cut slope and the permeability coefficient of soil in cut slope.

  • The north bank anchorage in Baiyang Town is gravity type, the anchor foundation pit has been directly excavated on the ground for construction. The excavation scheme of foundation pit is as follows: the first floor is from the surface to the -3.25 m below the surface; the second floor is -3.25 m below the surface to 13.25 m below the surface, the third floor is -13.25 m from underground to 22.25 m below the surface; the fourth floor is -22.25 m below the surface to 32.25 m below the surface; the fifth floor is -32.25 m below the surface to 41.5 m below the surface. During the excavation of foundation pit, different excavation methods were adopted for the rock with different depth and weathering degree, and mechanical excavation and blasting were used for construction. Meanwhile, in order to strengthen the stability of the cut slope, the Shotcreting method with bolt and net was adopted in the slope protection. In the early stage of foundation pit excavation, settlement monitoring points were arranged to monitor the safety of the slope, in which the displacement of the cut slope was monitored by the full-automatic total station on the site of the anchorage slope. The high-precision total station named Leica TS02 was used as the monitoring instrument, and the polar coordinate method was used for the monitoring of cut slope. The schematic diagram of the monitoring point for displacement is shown in Fig. 1; the measuring point D1 is located in the selected research area, which is the displacement monitoring point of the left bank of the anchorage slope. The numerical simulation calculation results were compared with the field monitoring results and the model test monitoring results converted according to the similarity ratio. In the three cases, the displacement comparison curve of D1 monitoring point is shown in Fig. 7.

    Figure 7.  Displacement comparison curve of D1 monitoring point.

    It can be seen from the curve in Fig. 7 that the measured value of the field test, the calculated value of numerical simulation and the monitored value of model test fluctuate within a certain range under the condition of rainfall. At the same time, the difference between the measured value of the model test and the field monitoring value is about 13.2%, and the minimum error between the monitoring value of numerical simulation and the field monitoring value is 8.5%. The comparison shows that the numerical model is reasonable, and it can be used to analyze the stability of the anchorage slope.

  • Combined with GeoStudio software and limit equilibrium theory, the change of cut slope safety factor with rainfall duration was obtained. The change of stability coefficient for the cut slope with rainfall time under different rainfall conditions is shown in Fig. 8.

    Figure 8.  Change of stability coefficient for the cut slope with rainfall time.

    (1) It can be seen from Fig. 8 that with the increase of rainfall time, the stability of cut slope decreases rapidly. In a period of time after the rainfall stops, the stability coefficient of cut slope continues to decline to the minimum value, then slowly rises, and finally tends to be stable. When the rainfall intensity is small, the minimum stability coefficient of cut slope does not appear in the process of rainfall, but appears between 10–60 min after rainfall. The stability coefficient of cut slope appears after the rainfall stops, due to the change of combined seepage field. In a period of time after the rainfall ends, the surface area of the cut slope changed from saturated to unsaturated, resulting in the seepage force to the slope surface, thus increasing the sliding force of the cut slope and reducing the stability coefficient of the cut slope. However, when the minimum value of the cut slope stability coefficient appeared, the stability coefficient of cut slope increased again. The reason is that after a period of heavy rain, a relatively thick saturated area was formed on the surface of the cut slope body, and the pore water pressure of cut slope was greater than the unsaturated area of the cut slope body, resulting in the increase of the seepage and anti sliding resistance of the cut slope body, which also led to the increase of the cut slope stability coefficient.

    (2) With the increase of rainfall intensity, the lowest stability coefficient of anchorage slope decreased. Under the condition of heavy rainfall, when the rainfall intensity was 40 or 50 mm/h, the stability coefficient of cut slope under the two rainfall intensities was basically the same, and the trend with rainfall time was basically the same, during the period from rainfall to the end of rainfall, the stability coefficient increased slightly. When the rainstorm reached certain intensity, the main factor that restricted the rainfall infiltration rate changed into the slope rock soil permeability coefficient, which was no longer the rainfall intensity.

  • Factor analysis originated in the early 20th century. Pearson, Spearman and other scholars made efforts to define and measure intelligence. Factor analysis results in many fewer factor variables than the original ones, so it can reduce the dimension and reduce the difficulty of data processing for us (e.g., Kyngdon, 2004; Anderson and Laake, 1998), For example, Kawamura et al. (2003) analyzed the cut slope damage caused by heavy rainfall in the East China Sea in 2000. In this paper, GeoStudio was used to calculate the pore water pressure, volume water content and cut slope stability coefficient of monitoring points in the cut slope under different rainfall conditions. The statistical data is presented in Table 2, and the method of factor analysis was used to analyze the cut slope stability, so as to realize the prediction of cut slope stability under different rainfall conditions.

    Number of tests Rainfall intensity (mm/h) Time of rainfall (min) Earth pressure (kPa) Pore water pressure (kPa) Settlement displacement of slope (mm) Coefficient of slope stability
    1 10 10 100 10 0.1 3.53
    2 10 30 92 35 0.3 3.35
    3 10 60 78 75 0.5 2.80
    4 10 120 26 118 0.9 1.30
    5 10 180 24 110 0.92 1.05
    6 20 10 98 15 0.3 3.37
    7 20 30 88 39 0.6 3.15
    8 20 60 68 89 1.3 2.37
    9 20 120 21 210 1.6 0.80
    10 20 180 20 220 1.7 0.68
    11 30 10 95 25 0.5 2.80
    12 30 30 77 39 1.3 2.20
    13 30 60 44 95 1.9 1.20
    14 30 120 18 258 5.8 0.65
    15 30 180 18 235 6 0.40
    16 40 10 92 38 1 2.50
    17 40 30 72 78 2.6 1.30
    18 40 60 35 180 6.8 0.70
    19 40 120 15 331 19 0.40
    20 40 180 14 330 22 0.25
    21 50 10 90 45 2 2.20
    22 50 30 58 88 5 1.16
    23 50 60 15 150 22 0.30
    24 50 120 12 420 46 0.24
    25 50 180 12 390 44 0.24

    Table 2.  Statistics of influencing factors of cut slope stability coefficient

  • The core principle of the factor analysis method is to conduct a factor analysis on a number of comprehensive indicators and extract common factors, and then establish a score function with sum of the weight of variance contribution rate of each factor and the score multiplier of the factor. The mathematical expression of the factor analysis method is expressed as a matrix, which is X=AF+B, which is

    In the model, vector X(x1, x2, x3, …, xp) is the observable random vector, which is the original observation variable. F(f1, f2, f3, …, fk) is the common factor of X(x1, x2, x3, …, xp), which is the co-occurrence factor in the expression of each original observation variable, and it is an independent and unobservable theoretical variable. A is factor loading matrix, αij (i=1, 2, …, p; j=1, 2, …, k) is factor load, B=(β1, β2, …, βp) is a special factor, which indicates that the original variable cannot be explained by the factor, whose mean value is 0.

    The variable commonality and variance contribution of common factors in a matrix A are very important for the economic interpretation of the results of factor analysis.

    (1) Statistical significance of variable commonality

    The variable commonality is the sum of the squares of the row i of the factor loading matrix A, and is denoted as: $h_i^2 = \sum\limits_{j = 1}^k {\alpha _{ij}^2} \left({i = 1, {\rm{ }}2, {\rm{ }} \ldots, p} \right) $. It measures the contribution of all common factors to the variance of xi and reflects the influence of all common factors on the variable xi. The greater the $h_i^2, $ the greater the dependence of X on each component of F.

    Take the variance of both sides of Eq. (11)

    If $h_i^2 = \sum\limits_{j = 1}^k {\alpha _{ij}^2} $ is close to $Var({x_i}) $ and $\beta _i^2 $ is very small, then the effect of factor analysis is good, and the transformation property from the original variable space to the common factor space is good.

    (2) Statistical significance of variance contribution of common factors

    The sum of squares of the elements in the factor loading matrix is denoted as: $ g_j^2 = \sum\limits_{j = 1}^p {\alpha _{ij}^2}, \left({j = 1, {\rm{ }}2, {\rm{ }}..., k} \right)$, A is the variance contribution of common factor F(f1, f2, f3, …, fk) to X(x1, x2, x3, …, xp), which represents the sum of variance provided by the common factor fi for each component of xi (i=1, 2, ..., p). It is an indicator to measure the relative importance of common factors.

    Transform Eq. (12)

    The larger $ g_j^2$ is, the greater the contribution of the common factor F(f1, f2, f3, …, fk) to X(x1, x2, x3, …, xp), or the greater the effect on X(x1, x2, x3, …, xp). If all the $g_j^2 $ (j=1, 2... k) of the factor loading matrix A are calculated and sorted by size, the most influential common factors can be extracted accordingly.

  • Table 3 showed the total variance analysis of factor analysis, and the first column was the component of factor analysis for cut slope stability. The second column to the third column was the commonality of factor analysis, and the second column was the commonality of variables under the initial solution of factor analysis. It shows that if the principal component analysis was used to extract all the five characteristic roots of the original five variables, then all the variance of the original variables can be explained, and the commonality of the variables was 1. The third column lists the commonality when extracting feature roots according to specified extraction conditions. As can be seen from Table 2, most of the information of all variables can be explained by factors, and the information of these variables was less lost. It shows that the rainfall duration and rainfall intensity have significant influence on slope stability coefficient, which has significant correlation. The fourth to sixth columns in Table 3 were total variance of interpretation, including eigenvalues, percentage of variance and cumulative variance contribution rate of correlation coefficient matrix. As can be seen from the fourth column, the eigenvalues of the first factor was 3.38, which explained 67.76% of the total variance of the original five variables, and the eigenvalue of the second factor was 1.18, which explained 23.49% of the total variance of the original five variables, therefore, only the first factor and the second factor were selected as the main factors.

    Commonality of factor analysis Total variance of interpretation
    Component Initial Extraction Eigenvalues Percentage of variance Cumulative
    Rainfall intensity 1.0 0.959 3.38 67.76% 67.76%
    Rainfall duration 1.0 0.953 1.18 23.49% 91.254%
    Earth pressure 1.0 0.903 0.29 5.8% 97.06%
    Pore water pressure 1.0 0.948 0.09 1.71% 98.77%
    Settlement displacement of slope 1.0 0.849 0.6 1.23% 100%

    Table 3.  Total variance analysis of factor analysis

  • Equation (14) gives the test statistics and parameter estimates in the corresponding equation for nonlinear regression based on the data in Table 2. The overall goodness of fit value of the model was 0.966, which shows that the model has statistical significance. The estimated equation is as follows

    where X1 represents stability coefficient comprehensive influence factor 1, X2 represents stability coefficient comprehensive influence factor 2, Y represents coefficient of slope stability.

    The relationship between the variable of slope stability coefficient and the first main factor and the second main factor is fitted. The estimation formula is as follows

    where q represents rainfall intensity and t represents rainfall duration.

    Therefore, Eq. (17) can be obtained by combining Eqs. (14)–(16).

    where Y represents coefficient of slope stability.

    For a more intuitive analysis of the relationship between rainfall intensity and rainfall time, as well as earth pressure and other variables and slope stability, and the monitoring data in Table 2 were plotted as scatter plots and regressed with exponential and polynomial functions, and the prediction results of slope stability obtained by comparing the three functions, including exponential function, polynomial and factor analysis, are shown in Fig. 8. Where the formula was obtained by exponential function as shown in Eq. (18), and the formula was obtained by polynomial as shown in Eq. (19).

    where α represents earth pressure and β represents pore water pressure, γ represents settlement displacement of slope.

    Figure 9 shows the comparison of cut slope stability coefficient among numerical simulation, theoretical prediction, exponential function and polynomial function. From Fig. 9, it can be found that the correlation between the numerical calculation value and the theoretical prediction value is good, and the theoretical prediction formula can be used to predict the stability coefficient of cut slope under different rainfall intensity. At the same time, the curve of the mathematical prediction model is in good agreement with the curve of numerical calculation, while the data predicted by non-linear prediction formula is far different from the original data, and the mathematical prediction model can reflect the attenuation characteristics of slope stability coefficient under different rainfall intensity well; Moreover, the model does not contain unconventional rock mechanics parameters, which is convenient for engineering application; the research results can provide reference for the treatment and prevention of rainfall induced landslide.

    Figure 9.  Comparison of cut slope stability coefficient among numerical simulation, theoretical prediction, exponential function and polynomial function.

  • (1) Rainfall time and rainfall intensity were important influencing factors of soil pressure attenuation, but rainfall intensity played a more important role in slope stability evaluation. The change of soil pressure of cut slope with rainfall time mainly included three stages: slow attenuation stage, accelerated attenuation stage and stable stage. However, with the increase of rainfall intensity, the slow attenuation stage did not exist in the three stages of soil pressure change, and the change of soil pressure directly entered into the fast attenuation stage, which shows that the influence of heavy rainfall on the stability of cut slope is more and more difficult to be ignored.

    (2) The rainfall intensity had a significant impact on the earth pressure monitoring points near the surface of the cut slope, while the change of the earth pressure monitoring points far away from the surface of the cut slope was absolutely different, which shows that the change of earth pressure increased first and then stabilized.

    (3) The pore water pressure on the slope surface can more directly reflect the stability of the cut slope, as the distance from the surface of the slope determined the change form of the pore water pressure. Meanwhile, the closer the monitoring point of the pore water pressure was to the surface of the cut slope, the faster the increase of the pore water pressure value of the cut slope, and rainfall intensity had a great influence on the stability coefficient of the cut slope; when the rainstorm reached certain intensity, the main factor that restricted the rainfall infiltration rate changed into the slope rock soil permeability coefficient, which was no longer the rainfall intensity.

    (4) The safety factors of cutting slope were compared by numerical calculation, exponential function, polynomial function and factor analysis. The results show that the correlation between numerical value and factor analysis was better than other nonlinear fitting functions. At the same time, factor analysis can highlight the importance of rainfall intensity and rainfall time to slope stability, and factor analysis also reflected the contribution of other factors related to slope stability, which indicates that factor analysis had better results when it was used to predict the problem under the influence of various factors.

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