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Article

Time-Varying Reliability Analysis of the Majiagou Landslide

by
Chun Lan
1,2,
Hui Zhang
3,
Guangqing Hu
4,5,*,
Xiaojin Song
6,* and
Heng Sun
6
1
Anhui Province Land Space Planning Research Institute, Hefei 230601, China
2
The Key Laboratory of Jianghuai Arable Land Resources Protection and Eco-Restorstion, Hefei 230601, China
3
College of Resources and Environment, Anhui Agricultural University, Hefei 230036, China
4
Exploration Research Institute, Anhui Provincial Bureau of Coal Geology, Hefei 230088, China
5
Anhui Province Green Mine Engineering Research Center, Hefei 230088, China
6
School of Resource and Environmental Engineering, Hefei University of Technology, Hefei 230009, China
*
Authors to whom correspondence should be addressed.
Water 2025, 17(8), 1185; https://doi.org/10.3390/w17081185
Submission received: 25 February 2025 / Revised: 4 April 2025 / Accepted: 9 April 2025 / Published: 15 April 2025
(This article belongs to the Special Issue Landslide on Hydrological Response)
Browse Figures
Versions Notes

Abstract

:
Rainfall and reservoir water level (RWL) fluctuations are the most important factors affecting reservoir landslide stability. Although extensive research has explored landslide stability under the combined effect of rainfall and RWL fluctuation, quantitative investigations on the individual contributions of rainfall and RWL fluctuation to landslide stability are limited. To address this issue, taking the Majiagou landslide in the Three Gorges Region (TGR) as an example, the seepage field of the Majiagou landslide was simulated and analyzed under three different scenarios: the individual effect of rainfall; the individual effect of RWL fluctuation; and the combined effect of rainfall and RWL fluctuation. The corresponding stability condition of the three scenarios was evaluated. The results show that the fluctuation of RWL is the critical factor that governs the stability of the Majiagou landslide. Specifically, when the water level drops rapidly from 165 m to 145 m, with an average rate of 0.859 m/d, the landslide safety factor decreases most significantly. The reason is that rapid water level decline creates outward-directed seepage forces that promote slope deformation. In contrast, rainfall has a limited effect on slope stability, with the safety factor only decreasing when rainfall exceeds 50 mm/d. This is because a seepage force directed outward from the slope develops only when rainfall reaches a certain threshold, leading to a reduction in the slope’s safety factor. In addition, this study reveals that the combined effect of rainfall and RWL fluctuations generates a synergistic amplification mechanism. Specifically, the safety factor variation under combined hydrological conditions significantly exceeds the arithmetic sum of individual rainfall-induced variation and RWL-induced variation. This study helps us understand how rainfall and RWL fluctuation affect slope stability by altering the seepage field, which is crucial for preventing landslides.

1. Introduction

Since the Three Gorges Dam was completed in 2003, rainfall and fluctuations in the reservoir’s water level have caused a large number of landslides [1,2,3,4,5]. Compared with other types of landslides, the instability of reservoir landslides not only poses a direct threat to the lives of residents but also induces secondary surge waves which will cause serious harm to downstream facilities [6,7,8,9]. Therefore, it is of great significance to carry out stability evaluation of reservoir landslides for the migration of potential landslide hazards.
It is well known that rainfall and reservoir water level (RWL) fluctuation are key factors that influence the stability condition of reservoir landslides [10,11,12,13,14]. For rainfall, the rainwater can increase the soil’s water content, which leads to a reduction in the soil’s matric suction [15,16,17,18,19,20,21]. This reduction in suction lowers the soil’s shear strength, thereby contributing to landslide instability. For RWL fluctuation, it can cause changes in soil water content, which in turn affects the soil’s matric suction and alters its shear strength [22,23,24,25]. Additionally, RWL changes can lead to groundwater flow, generating seepage forces within the landslide and impacting its stability [26,27,28]. In fact, rainfall and RWL fluctuation do not act independently but occur simultaneously. Therefore, the stability of landslides is controlled by the combined effect of rainfall and RWL fluctuation.
Many researchers have carried out numerical studies to explore the triggers and evaluate the stability conditions of landslides under the combined effect. In order to explore the triggering factors of the Qingshi landslide, its dynamic seepage and deformation field was simulated and analyzed [29]. By adopting ABAQUS software, the movement mechanism of the Baijiabao landslide was investigated [30]. By adopting FLAC-3D software, the deformation mechanism of a typical reservoir landslide was investigated. The results demonstrated that the seepage force induced by a decline of reservoir water level is the dominating factor accounting for landslide deformation [31]. The influence of rainfall and RWL fluctuation on the behavior of the Quchi landslide was investigated by utilizing a discrete element method (DEM), and subsequently the deformation pattern of the Quchi landslide is revealed [32]. Additionally, some scholars have explored slope deformation through laboratory tests or in situ monitoring. For example, through laboratory model tests, Wang et al. (2021) investigated the changing law of the seepage and deformation within a slope under varying hydrological conditions. Their study revealed the deformation mechanisms and key factors governing the Shuping landslide [33]. By comparing the hydrological data and the surface deformation obtained by interferometric synthetic aperture radar (InSAR), the triggering factors of the Xinpu landslide were explored and the results showed that the triggers of different sections of the Xinpu landslide were different [34]. A common conclusion drawn by the above studies is that rainfall and RWL fluctuations jointly influence slope stability. However, there is no widely accepted consensus on which of the two factors is the primary cause and how each factor individually affects slope stability.
To address the above issues, based on the 3 years of recorded hydrological data at the site of the Majiagou landslide, this study adopts a numerical method to model the transient seepage field and analyze landslide stability under three scenarios: only considering rainfall condition, only considering reservoir water level fluctuation condition, and the combined effect of both factors. This study explores the contribution of individual and combined factors on landslide stability, which not only helps to determine the most critical influencing factors but also reveals how the hydrological factors cause the evolution of the seepage field, thus affecting the stability of the landslide.

2. Geological Setting of Majiagou Landslide

2.1. Geographical Environment Feature

The Majiagou landslide is situated in Pengjiapo Village, Guizhou Town, Zigui County, Hubei Province. It is located 2.1 km from the Yangtze River estuary, within the Three Gorges Reservoir (TGR) area (Figure 1) [35].
The Majiagou landslide is tongue-shaped distribution, featuring a combination of several gentle slope platforms and steeper ridges. Its slip direction is approximately 290°. The total length of the landslide measures about 560 m, with an elevation of around 124 m. The width of the toe area is roughly 150 m, while the trailing edge has an elevation of about 284 m and a width of approximately 210 m. The total area of the landslide covers roughly 9.8 × 105 m2, with a volume of approximately 1.36 × 107 m3. The overall slope gradient is around 15°.
Since the reservoir was impounded in 2003, the Majiagou landslide has undergone deformation. As shown in Figure 2, there are noticeable deformations from the leading edge to the trailing edge of the Majiagou landslide, with visible cracks appearing in buildings and roads on the landslide. Additionally, boundary erosion and surface deformation can be observed in the middle and front edge of the landslide.
The geological profile of the Majiagou landslide can be divided into two main strata, as shown in Figure 3: the overlying deposits and the bedrock. The bedrock of the Majiagou slope belongs to the Upper Jurassic Suining Formation (J3S), primarily composed of quartz sandstone and siltstone. Within this, there are layers of mudstone, which generally have low strength. The mudstones are prone to softening and becoming argillaceous when exposed to water, making them the most slippery strata in the TGR [36,37,38]. The deformation at B1 is obtained based on the optical fiber displacement monitoring technology [39].
Quaternary loose deposits are found above the bedrock, with residual deposits (Qcol-dl) primarily formed from long-term weathering of the parent rocks, such as quartz sandstone, mudstone, silty sandstone, and silty mudstone. The lithology of these deposits mainly consists of clay and quartz sandstone fragments, with a brown-red color, uneven texture, and medium density. The soil-to-stone ratio is generally 4:6. The fragmented stones are angular to sub-angular, with diameters ranging from 5 mm to 60 mm. The thickness of these residual deposits varies, typically ranging from 7 to 16 m.
Alluvial and diluvial deposits (Qal-pl) are mainly found on the surface of the landslide and its surrounding areas. These deposits are predominantly composed of clay, which is brown-red to yellow in color, uneven in texture, and moderately plastic. A small amount of sandstone gravel also exists, with medium weathering. The fragments are mostly sub-angular, with diameters ranging from 1 cm to 5 cm, making up about 5% of the deposit. The thickness of the alluvial and diluvial deposits varies from 5 to 13 m.

2.2. Hydrometeorological Characteristics

The daily rainfall data from September 2013 to August 2016 is shown in Figure 3. Analysis of the rainfall data reveals that rainfall in this region is most concentrated from April to August each year, which accounts for 60–70% of the annual total. During this period, the maximum daily rainfall can reach up to 70 mm. From October to March of the next year, rainfall is much lower and the intensity is typically under 10 mm/d.
Due to the construction of the Three Gorges Dam, the water level in TGR fluctuates periodically. For the Majiagou landslide, the catchment area influenced by RWL fluctuations is around 8.98 × 104 m2. The time–history curve of the water level and groundwater level of the Majiagou landslide reservoir is shown in Figure 4. It is evident that the RWL exhibits periodic fluctuations. The water level reaches its peak value of 175 m every November. From November to July of the following year, the RWL undergoes a drop period, where it gradually decreases from 175 m to 145 m. From July to September, due to concentrated rainfall, the RWL varies obviously. Finally, from September to November, the reservoir enters a water storage period, where the RWL rises rapidly from the lowest to the highest point.

3. Numerical Model Establishment

In order to investigate the seepage flow and slope stability, the SEEP/W and SLOPE/W of the Canadian simulation software GEOSTUDIO 2021.4 were employed. According to the geological characteristics of the Majiagou landslide illustrated in Figure 3, a two-dimensional finite element model (FEM) for saturated–unsaturated seepage is developed, as shown in Figure 5. Consistent with the dimensions of the actual Majiagou landslide, the model has a length of 600 m and a height of 280 m, with 3835 units and 3947 nodes. It can be simplified into three main components, gravel soil, mudstone, and bedrock, which are represented by green, yellow, and gray, respectively. The boundary and initial conditions are defined as follows: (1) The horizontal and vertical displacements are fixed at the bottom of the model, while only the horizontal displacements are fixed on both sides; (2) the landslide surface above 175 m is designated as the rainfall infiltration boundary, the landslide surface below 175 m is set as the variable head boundary influenced by the reservoir water, and the bedrock surface serves as a zero-flow boundary; (3) the initial groundwater level is set as 145 m. The RWL and rainfall data used for this analysis are based on measured results from 1 September 2013 to 26 August 2016 at the Majiagou landslide site. The physical and mechanical properties of the strata, listed in Table 1, were determined based on the study carried out by Luo et al., 2022 [40]. The failure of the rock and soil follows the Mohr–Coulomb criterion. Based on the SEEP/W module and the saturated volumetric water content of gravel soil, the soil–water characteristic curve (SWCC) was estimated to determine the volumetric water content in the unsaturated region (Figure 6a). Using the estimated SWCC, along with the Van Genuchten prediction model, the permeability coefficient of unsaturated soil was derived (Figure 6b).

4. Results

4.1. Seepgage Field

For the sake of exploring the seepage variation in the Majiagou landslide, the study period was set from 27 June 2014 to 27 June 2015. It should be noted that on 27 June 2014, the RWL was at its lowest point of 145 m. As depicted in Figure 7, by comparing the measured and simulated water level values at B1, it is evident that their variation trends are consistent. We further calculated the absolute error and relative error between the monitored and simulated water levels at B1. As shown in Table 2, the absolute error is within 2.5 m and the relative error is within 2%, demonstrating the reliability and accuracy of our numerical model.
The variation in the phreatic line in response to fluctuations in the reservoir water level is shown in Figure 7b,c. As the RWL rises, the phreatic line begins to curve inward toward the slope. This is because the water level rises rapidly, while infiltration from the slope’s exterior to its interior takes time, causing a delay in the response of the phreatic line to the RWL fluctuation. Similarly, when the RWL drops, it takes time for water to seep from the inside of the landslide to the outside, resulting in the phreatic line being higher than the RWL.

4.2. Landslide Stability

4.2.1. Effect of Rainfall on Landslide Stability

The relationship between rainfall and the landslide safety factor is illustrated in Figure 8. The gray bars represent the rainfall data and the orange curve depicts the change in the safety factor solely due to rainfall. It can be found that the landslide safety factor remains consistently bigger than the unit value, indicating that the landslide is stable. The safety factor primarily fluctuates around 1.115, with only slight variations. However, in certain periods, the safety factor undergoes sharp decreases. These areas with the safety factor dropping are highlighted in light yellow. By examining the rainfall data for these regions, it is evident that the reduced safety factors correspond to periods of higher rainfall intensity, exceeding 50 mm/d. This suggests that rainfall exerts negligible influence on the safety factor of the Majiagou landslide. However, when daily precipitation exceeds 50 mm/d, the safety factor experiences a marked decline.
To explore why this happens, we have analyzed the impact of different rainfall intensities on the Majiagou landslide seepage field. As shown in Figure 9a, when the rainfall intensity is relatively low (5 mm/d), it has little effect on the seepage field of the Majiagou landslide. In contrast, when the rainfall intensity reaches 50 mm/d, as shown in Figure 9b, a seepage force directed outward develops within the landslide. This indicates that a higher rainfall intensity reduces the landslide stability. The results show that only when the rainfall intensity reaches a certain degree will a significant seepage force form inside the slope, inducing landslide deformation.

4.2.2. Effect of RWL Fluctuation on Landslide Stability

The impact of RWL fluctuations on landslide stability can be understood as follows: hydrodynamic interactions induced by hydraulic gradient variations. The first component involves the transient hydraulic pressures generated by differential water infiltration/exfiltration rates across the landslide mass during reservoir drawdown/impoundment cycles. Specifically, rapid water level decline creates outward-directed seepage forces that promote slope deformation, while reservoir impoundment generates inward hydrodynamic pressures acting as temporary stabilizing constraints.
The relationship between the landslide safety factor and RWL fluctuation is illustrated in Figure 10. The landslide safety factor fluctuates within the range of [1.11–1.29]. By comparing the trends of the safety factor and RWL fluctuation, it is evident that the landslide safety factor is influenced by the RWL significantly. The values of the safety factor increase during the rising stage of the RWL and decrease during the falling stage. This demonstrates that the RWL change has a significant impact on the safety factor of the landslide. Notably, when the RWL decreases rapidly from 165 m to 145 m, with an average rate of decline of 0.859 m/d, the safety factor drops most significantly. By simulating the seepage field during this period, as shown in Figure 11b, it is known that when the RWL drops rapidly, the change in the water level inside the landslide lags behind the reservoir’s fluctuation. This creates a hydraulic gradient between the interior and exterior of the Majiagou landslide, resulting in the formation of an unstable seepage flow. The seepage forces generated by this flow intensifies the instability of the landslide. When the RWL rises rapidly from 145 m to 175 m with an average rate of 1.58 m/d, as shown in Figure 11a, reservoir water infiltrates from the outside to the inside of the landslide, creating a dynamic water pressure (seepage force) that acts against the landslide’s sliding direction, enhancing its stability.

4.2.3. Combined Effect of Rainfall and RWL Fluctuation on Landslide Stability

As shown in Figure 12, Figure 12a presents the surface deformation time–history curve of the Majiagou landslide, monitored by inclinometer B1. The displacement curve exhibits a stepwise evolution pattern characterized by a rapid increase, a smooth deformation, and a rapid increase. Figure 12b illustrates the variation in the landslide safety factor under the combined influence of rainfall and RWL fluctuations. The safety factor under the combined effect shows slight differences compared to when only rainfall or only RWL fluctuations are considered. Overall, the safety factor tends to follow the pattern of the RWL fluctuations. However, from May to July each year, intense rainfall causes a significant decline in the safety factor. During this period, the safety factor is lower than that observed when considering only rainfall or only RWL fluctuations. This suggests that the combined effect may amplify the landslide’s instability, making it more susceptible to failure than when either factor acts alone.
By comparing the landslide deformation in Figure 12a with the safety factor in Figure 12b, highlighted with yellow rectangular, it is evident that when the safety factor decreases rapidly, the Majiagou landslide deformation increases significantly. Conversely, when the safety factor rises rapidly or remains at a high level, the deformation of the Majiagou landslide remains relatively stable. The in-situ deformation monitoring results have demonstrated the accuracy of the proposed model.

5. Discussion

To explore the contributions of rainfall and RWL fluctuations, and their combined effect on the landslide safety factor, this study introduces the safety factor variation index (SFVI). SFVI is defined as the change in the landslide safety factor resulting from variations in external hydrological factors. The specific equation is provided as follows:
SFVI = F s ( n ) − F s ( n − 1 )
where Fs(n) denotes the safety factor of the landslide at time n and Fs(n−1) denotes the safety factor of the landslide at time n − 1.
The temporal evolution of the SFVI for the Majiagou landslide, calculated via Equation (1), reveals distinct response patterns to individual triggering factors. As illustrated in Figure 13a, a comparative analysis of single-factor scenarios demonstrates marked disparities in SFVI magnitudes between rainfall and RWL fluctuation. The results suggest that the SFVI fluctuation caused by rainfall changes is small, and the SFVI induced by it is less than 0.01 even during extreme precipitation events. In contrast, the SFVI changes caused by RWL fluctuation are more obvious, and its maximum value can reach about 0.035. This aligns with previous conclusions that the safety factor changes more significantly due to RWL fluctuations than to rainfall.
Figure 13b presents a comparison of the SFVI obtained by mathematically adding the SFVI changes from rainfall and RWL fluctuations and the changes resulting from the combined effect of both factors. The results indicate that the safety factor variation under the coupled hydrological conditions greatly exceeds the arithmetic sum of the individual variations caused by rainfall and RWL fluctuations. This result suggests that the interaction between precipitation and reservoir operation forms a nonlinear, mutually reinforcing mechanism that is not simply a superimposed effect but also disproportionately reduces slope stability.
This study reveals that there exists a nonlinear increase mechanism through which the combination of rainfall and RWL fluctuation can trigger a disproportionate reduction in landslide stability. However, the underlying physical mechanism of this phenomenon remains unclear. We speculate that multiple factors may contribute to its occurrence. One possible explanation is that rainfall and fluctuations in RWL induce seepage forces. This, in turn, alters soil water content and subsequently affects its shear strength. Under the combined influence of these factors, the landslide’s safety factor exhibits a nonlinear variation pattern. Additionally, this study employs the 2D numerical simulation software GEOSTUDIO 2021.4 to analyze the seepage field and calculate the slope safety factor. However, the results from a 2D model differ from those of a real 3D scenario. Therefore, 3D numerical analysis methods, such as FLAC-3D, can be considered for a more accurate assessment in the future.

6. Conclusions

To explore the triggering factors of the Majiagou landslide and evaluate its stability state, this study used a numerical simulation method to simulate the seepage field of the slope under three different hydrological conditions and calculated the corresponding safety factor of the Majiagou landslide. The conclusions are drawn as follows:
(1)
The RWL fluctuation is identified as the most critical factor influencing the stability of the Majiagou landslide. Specifically, when the RWL rapidly decreases from 165 m to 145 m, at an average rate of 0.859 m/d, the safety factor experiences the most significant decline.
(2)
Rainfall has a limited impact on the safety factor. Only when rainfall exceeds 50 mm/day does the safety factor of the slope experience a noticeable decline. At lower levels of precipitation, the impact on landslide stability is negligible.
(3)
The interaction between rainfall and RWL fluctuation forms a nonlinear, mutually reinforcing mechanism. This interaction does not merely have an additive effect; rather, it amplifies the reduction in slope stability in a disproportionate manner.

Author Contributions

Conceptualization, validation, and formal analysis, H.Z.; methodology, and writing—original draft preparation, C.L.; project administration, and funding acquisition, G.H.; writing—review and editing, and visualization, X.S.; investigation, and data curation, H.S. All authors have read and agreed to the published version of the manuscript.

Funding

The authors gratefully acknowledge the financial support provided by the Open Fund of Hebei Cangzhou Groundwater and Land Subsidence National Observation and Research Station (CGLOS-2023-06), the Fundamental Research Funds for the Central Universities (2-9-2022-042), the opening fund of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (SKLGP2023K021), Research and demonstration of key technologies for integrated de-formation monitoring of deep and large foundation pits based on multi-source data fusion (2024-YF002), and the Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University (2023002).

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.

Acknowledgments

Thanks to all the authors for their contributions to this article.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. (a,b) The location of Majiagou landslide, (c) The picture of Majiagou landslide.
Figure 1. (a,b) The location of Majiagou landslide, (c) The picture of Majiagou landslide.
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Figure 2. The outline of the landslide and the specific location of the deformation. (a,c,d) Cracks, (b,e) rockfall and surface deformation, and (f) boundary erosion. (Figure 2 is cited from Zhang et al. [26], with the permission of all the authors).
Figure 2. The outline of the landslide and the specific location of the deformation. (a,c,d) Cracks, (b,e) rockfall and surface deformation, and (f) boundary erosion. (Figure 2 is cited from Zhang et al. [26], with the permission of all the authors).
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Figure 3. Geological profile of Majiagou landslide.
Figure 3. Geological profile of Majiagou landslide.
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Figure 4. Time–history curve of rainfall, reservoir water level fluctuation, and groundwater level change.
Figure 4. Time–history curve of rainfall, reservoir water level fluctuation, and groundwater level change.
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Figure 5. Numerical model of Majiagou landslide.
Figure 5. Numerical model of Majiagou landslide.
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Figure 6. (a) SWCC of soil; (b) permeability function curve.
Figure 6. (a) SWCC of soil; (b) permeability function curve.
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Figure 7. Seepage field of Majiagou landslide. (a) Comparison of measured and simulated water level at B1 (27 June 2014–27 June 2015); (b) variation in phreatic lines along the rising of RWL; (c) variation in phreatic lines along the dropping of RWL.
Figure 7. Seepage field of Majiagou landslide. (a) Comparison of measured and simulated water level at B1 (27 June 2014–27 June 2015); (b) variation in phreatic lines along the rising of RWL; (c) variation in phreatic lines along the dropping of RWL.
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Figure 8. The landslide safety factor changing with rainfall.
Figure 8. The landslide safety factor changing with rainfall.
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Figure 9. Vector diagram of seepage field at different rainfall intensity: (a) vector diagram of seepage field at 5 mm/d; (b) vector diagram of seepage field at 50 mm/d.
Figure 9. Vector diagram of seepage field at different rainfall intensity: (a) vector diagram of seepage field at 5 mm/d; (b) vector diagram of seepage field at 50 mm/d.
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Figure 10. The landslide safety factor changing with RWL fluctuation.
Figure 10. The landslide safety factor changing with RWL fluctuation.
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Figure 11. Vector diagram of seepage field at different times: (a) vector diagram of seepage field at 20 days (reservoir water level rising with the rate of 1.58 m/d); (b) vector diagram of seepage field (reservoir water level dropping with the rate of 0.859 m/d).
Figure 11. Vector diagram of seepage field at different times: (a) vector diagram of seepage field at 20 days (reservoir water level rising with the rate of 1.58 m/d); (b) vector diagram of seepage field (reservoir water level dropping with the rate of 0.859 m/d).
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Figure 12. (a) Displacement recorded by inclinometer B1; (b) the landslide safety factor variation under the combined effect.
Figure 12. (a) Displacement recorded by inclinometer B1; (b) the landslide safety factor variation under the combined effect.
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Figure 13. (a) Comparison of SFVI changing under rainfall and RWL; (b) comparison of SFVI obtained by mathematically adding the SFVI changes from rainfall and RWL fluctuations and the changes resulting from the combined effect.
Figure 13. (a) Comparison of SFVI changing under rainfall and RWL; (b) comparison of SFVI obtained by mathematically adding the SFVI changes from rainfall and RWL fluctuations and the changes resulting from the combined effect.
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Table 1. Physical and mechanical parameters of Majiagou landslide.
Table 1. Physical and mechanical parameters of Majiagou landslide.
ElementUnit Weight γ (kN/m3)Friction Angel φ (kN/m3)Cohension c (Kpa)Permeability Coefficient k (cm/s)
NaturalSaturatedNaturalSaturatedNaturalSaturated
Gravel soil 21.1422.0519.3117.6818.3216.218.25 × 10−4
Mudstone21.8422.5217.1815.2627.3025.151.13 × 10−6
Bedrock26-39-3000--
Table 2. Comparison of the simulated water level with the monitored water level at B1.
Table 2. Comparison of the simulated water level with the monitored water level at B1.
Monitoring Time22 July 201411 August 20145 September 201416 November 20147 January 20156 April 201514 May 201521 June 2015
Monitored water level (m)168.3172.1178180.5176.3175.1172.1163.5
Simulated water level (m)167.5171.6176.2179.1177.1175.8169.8166.0
Absolute error (m)0.80.51.81.40.80.72.32.5
Relative error0.47%0.29%1.01%0.77%0.45%0.39%1.34%1.53%
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Lan, C.; Zhang, H.; Hu, G.; Song, X.; Sun, H. Time-Varying Reliability Analysis of the Majiagou Landslide. Water 2025, 17, 1185. https://doi.org/10.3390/w17081185

AMA Style

Lan C, Zhang H, Hu G, Song X, Sun H. Time-Varying Reliability Analysis of the Majiagou Landslide. Water. 2025; 17(8):1185. https://doi.org/10.3390/w17081185

Chicago/Turabian Style

Lan, Chun, Hui Zhang, Guangqing Hu, Xiaojin Song, and Heng Sun. 2025. "Time-Varying Reliability Analysis of the Majiagou Landslide" Water 17, no. 8: 1185. https://doi.org/10.3390/w17081185

APA Style

Lan, C., Zhang, H., Hu, G., Song, X., & Sun, H. (2025). Time-Varying Reliability Analysis of the Majiagou Landslide. Water, 17(8), 1185. https://doi.org/10.3390/w17081185

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