Research Article | Open Access
Guangfu Chen, Guodong Zhang, Shuqiang Lu, Xiang Wang, "An Attempt to Quantify the Lag Time of Hydrodynamic Action Based on the Long-Term Monitoring of a Typical Landslide, Three Gorges, China", Mathematical Problems in Engineering, vol. 2018, Article ID 5958436, 13 pages, 2018. https://doi.org/10.1155/2018/5958436
An Attempt to Quantify the Lag Time of Hydrodynamic Action Based on the Long-Term Monitoring of a Typical Landslide, Three Gorges, China
Hydrodynamic action plays an important role in the development of reservoir bank accumulational landslides. Despite recent concern over hydrodynamic action’s hysteresis effects, there is still no unified efficient method for quantifying lag time, which is a critical input to landslide prediction and early warning systems. To address this shortcoming, we selected a typical landslide, located in Three Gorges Reservoir, China, as a case study. On the basis of long-term monitoring data, we suggest that correlation analysis may work and attempt to use linear correlation first to quantify the lag time. We conclude that, from the macroscopic behavior point of view, linear correlation analysis does not work; neither the daily reservoir water level and its variation nor the daily rainfall and its accumulation exhibit a linear relationship with the surface accumulative displacement. Future studies will use nonlinear correlation analysis to analyze data by different time segments as the hydrodynamic factors have different effects in different periods.
The construction of dams for electric power and water storage across the world has led to the reactivation of old landslides and the development of new landslides. Vajont landslide (Italy), which has caused many problems, is a typical example. Much research has been conducted on reservoir bank landslides. Water is a primary triggering and driving factor for reservoir bank landslides. The widely accepted understanding is that water infiltrating into the bank increases the fluid pressure, which, in turn, reduces the effective stress, thus altering the strength of rock and soil mass. This can lead to surface rupture, which in turn promotes sliding [1, 2]. So far, most attention has focused on the interpretations of the hydrodynamic factors’ action mechanism; in contrast, few studies have investigated how to quantify the lag time between changes in hydrodynamic factors and movement on the landslide. Historically, the hysteresis effect has been described from the view of qualitative analysis or as a rough description based on observation—in short, it remains an inexact science. Chaoying Zhao et al.  observed that the response of landslide deformation to rainfall is not instantaneous. Instead, there is a time lag between peak landslide motion and peak rainfall. The authors pointed out that, at the Boulder Creek slide, the lag is about 1-2 months. Similar findings have been reported for the Berkeley Hills slide (up to 3 months of lag time) , Portuguese Bend landslide in southern California (2–6 weeks of lag time) , and Jinlongshan slide in Southwest China (1-2 months of lag time) . Haifeng Huang et al.  reported that the Shuping landslide located in Three Gorges Reservoir exhibits a lag time of approximately 6 days after the reservoir water level is reduced.
Determination of the exact lag time will play an important part in landslide prediction and early warning. In an effort to determine an efficient method for quantifying the lag time from the macroscopic perspective, we first summarize and analyze the hydrodynamic action for the interpretation and better understanding of the hysteresis effect. Then, we select a typical accumulational landslide (Baishuihe, in Three Gorges, China) as a case study. We finally attempt to use correlation analysis to determine the temporal relationship, based on its long-term monitoring data, between surface displacement, reservoir water level, and rainfall.
2. Background of Hydrodynamic Action
Reservoir bank landslides are common; as a result, scholars have studied them extensively, especially focusing on the effect of hydrodynamic action on stability. Hydrodynamic action is mainly caused by reservoir water level changes and rainfall events. Its effects can be divided into physical processes and chemical processes.
2.1. Physical Process
The physical process often plays a dominant role in the hydrodynamic action. The process involves three separate effects: a lubricating effect, a softening and argillization effect, and a force effect.
Underground water can lubricate preexisting discontinuity surfaces within the rock and soil mass. This effect will reduce the frictional resistance at the boundary, resulting in shearing motion along the discontinuity surface. The lubricating effect can be notable if the water table rises over the sliding surface. In short, the lubricating effect leads to a lower frictional angle of the rock and soil mass.
The softening and argillization effect is mainly reflected in the fillings’ physical property changing process contained in the soil and the rock’s structural surfaces. The filling evolves from a solid to liquid state as its water content changes. In the fault zone, the softening and argillization effect can be found frequently. For the rock and soil mass, the softening and argillization effect will result in decreases in its cohesive strength and frictional angle.
The force effect can be divided into changes caused by changes in hydrostatic pressure and those caused by changes in hydrodynamic pressure. Increasing hydrostatic pressure will reduce the effective stress of the rock and soil mass, resulting in reduced strength . For the fractured rock mass, increasing hydrostatic pressure will enlarge the fracture, resulting in deformation. When seepage exists in the rock and soil mass, hydrodynamic pressure acts. If the resulting forces point to the outside of the slope, the stability of the slope is decreased. The higher the hydraulic gradient, the higher the hydrodynamic pressure, and the lower the slope stability.
2.2. Chemical Process
Chemical processes begin to act as soon as the landslide is exposed to water. The main chemical processes are ion-exchange, dissolution, and hydration. During these chemical processes, the rock and soil mass’s properties change, resulting in changes in the sliding mass or the sliding zone’s strength, and finally changes in stability.
The water that moves inside the landslide contains many negative and positive ions. The rock and soil mass also contains many negative and positive ions. The ions’ binding forces are different from each other; therefore, during the contact processing, some ions with strong binding forces may replace the substance’s weak binding force ions, resulting in the formation of new minerals. The ion-exchange that happens between the water and the rock and soil mass changes the rock and soil mass’s structure, as well as its mechanical properties.
The dissolution effect plays an important part in the evolution of groundwater chemistry. It generates most of the ions contained in the groundwater. Before the water infiltrates into the landslide, many gases become dissolved in it, resulting in higher chemical aggressivity. When the aggressive water meets soluble rocks, dissolution occurs. As a result, corrosion fissures form. These magnify the rock unit’s porosity and permeability [9–11].
The hydration between the water and the rock and soil mass is a common natural phenomenon and is the primary mechanism of rock weathering. The water molecules infiltrate into the rock and soil mass’s mineral crystal framework or stick to the soluble rocks’ ions; this process changes the mineral’s structure and, therefore, its physical properties.
2.3. Hysteresis Effect
From the analysis above, we can infer that correlation between the hydrodynamic action and the landslide displacement ought to exist to a certain extent and that the stability of a given reservoir bank landslide is affected by the hydrodynamic action. In our daily life, we observe that landslides occur after the reservoir water level changes or a rainfall event occurs. As from the macro-behavior view, the surface displacement lags behind changes in hydrodynamic conditions (water level, rainfall).
The hysteretic nature of the hydrodynamic action has attracted a lot of attention. It is not hard to understand the phenomenon that the slope body itself has a certain thickness and a hydraulic diffusion coefficient. Hydrodynamic action can be divided into two steps: seepage (infiltration, exudation) and erosion. The chemical process of hydrodynamic action is slower, yet it can take a long time to move from a quantitative change to a qualitative change. The physical process of hydrodynamic action often plays a dominant role in reservoir bank landslide sliding. It directly influences the slip force and the antislip force. Water needs time to infiltrate and exude after the change of hydrodynamic conditions. Therefore, the landslides are often observed after reservoir water level changes or heavy rainfall. Keqiang He et al.  found that landslides could occur as late as 10 days after a heavily raining day in the Three Gorges Reservoir region, China (Table 1).
3. Description of Baishuihe Landslide
3.1. Typicality of the Baishuihe Landslide
Landslides can be categorized as soil landslides and rock landslides. Accumulational landslides are a typical kind of soil landslide. They are formed by all kinds of debris, are easy to trigger, and could result in huge damage. Due to the particularity of its components and structure, its stability is highly sensitive to hydrological factors. Accumulational landslides are widely distributed in the Three Gorges Reservoir region. Zigui county alone has 154 shallow accumulational landslides greater than 5 × 105 m3 in volume.
The Baishuihe landslide is mainly made up of colluvial deposits, slope wash, and landslide debris. It is a typical reservoir-bank accumulational landslide (Figure 1(d)). The overburden displays no unified stratified rule, and it is composed of detritus, rubble, breccia, silty clay, and clay. Due to changes in compositional content with depth, no unified continuous stratified boundaries exist between the rock and soil layers. The sliding zone is mainly composed of silty clay which contains detritus or breccia (Figures 1(a) and 1(c)). A large fracture crushing belt of the slide bed was not found in the exploration (Figure 1(b)).
3.2. Surface Displacement Monitoring Network
Since June 2003, the surface deformation of Baishuihe landslide has been monitored. According to the monitoring data, macroscopic deformation characteristics, and survey results, in July 2004, the landslide was divided into two sections: the early warning zone and the outside early warning zone. For the outside early warning zone, the long-term monitoring data showed no obvious deformation and the survey results showed that there no distinct sliding zone exists. The deformation is well monitored in the early warning zone. The surface displacement monitoring sites ZG93, ZG118, and XD-01 are located here. Surface displacement monitoring sites of ZG92, ZG94, ZG119, and ZG120 are located in the outside early warning zone. Surface displacement is monitored monthly using the Global Positioning System (GPS). The surface displacement monitoring network is shown in Figure 2.
4. Analysis of the Long-Term Monitoring Data
According to the analysis above and the research referenced above, hydrodynamic action (rainfall, reservoir water) plays an important part in the landslide development, especially for accumulational landslides. Past research has mainly focused on the effects of hydrodynamic action on the landslides’ stability and rarely refers to the reaction time that the hydrodynamic action works on the landslide. If the reaction time was found out, it will play an important part in landslide prediction and early warning. According to the reaction time, the prediction simulation could be done more accurately, the human source could be arranged more properly, and the patrol work could be carried out more efficiently following changes in hydrodynamic factors changing.
We now consider how we might quantify this lag time. We attempt to determine this using correlation analysis; if a correlation exists between the surface displacement and the hydrodynamic factor monitored some days before the surface displacement monitoring day, then the time segment between the surface monitoring day and some days before of the hydrodynamic factor monitoring day is the lag time.
Focusing on the typical Baishuihe landslide introduced above, we attempted to find out the lag time through the correlation analysis based on the selected monitoring data. The rainfall and the reservoir water level monitoring sites are shown in Figure 3. The rainfall monitoring site is Shan Xiying (monitored once per 300 s); the Rain gauge can detect as little as 0.2 mm rainfall. The reservoir water level monitoring site is Badong; the reservoir water level is monitored once per 300 s and the Water Level gauge can monitor the fluctuation of water levels by as little as 2 cm.
4.1. Reservoir Water Level Correlation Analysis
According to the presentation above, the monitoring data have been collected since 2003. In this research we focused on data collected between 2014 and 2016 to study the correlation between the reservoir water level and the surface displacement. That choice is based on the consideration that during this period the reservoir water level changed regularly and peacefully and this station had already kept for a time before; therefore effects like sudden changes could be reduced.
Figure 4 shows the reservoir water level and the surface accumulative displacement. To provide for flood control, shipping, and electricity generation, the reservoir water level changes significantly every year. Before the flood season, the reservoir water level declines step by step; after it, the reservoir water level rises gradually. The reservoir water level rises and falls by up to 30 m.
Two sets of series data have been selected for the correlation analysis. One is between the surface accumulative displacement of different monitoring sites and the reservoir water level from the day of surface displacement monitoring to 30 days before; the other is between the surface accumulative displacement of different monitoring sites and the reservoir water level variation from 1 day before the surface monitoring day to 30 days before (RWLV_1DB=RWL_1D−RWL_0DB). If from one day of the time series value a correlation exists between the reservoir water level or its variation and the surface accumulative displacement, it could be inferred that the lag time is the interval between that day and the surface displacement monitoring day. Results of the correlation analysis are shown in Table 2.
According to previous research, many landslides have been observed to reactivate in association with water level fluctuations of reservoirs. Therefore, there should be correlation between the reservoir water level and the surface displacement. Min Xia et al.  pointed out that the stability of the landslide is influenced by the rate of fluctuation in the level of the reservoir. In Figure 4, we can see this phenomenon in July 2015; during that month, the sites in the early warning zone had a large displacement after a rapid decline in the reservoir water level. Despite what has been suggested, we could see from the results of correlation analysis that, for all of the monitoring sites, no linear correlation exists between neither the reservoir water level nor its variation and the displacement.
Such results suggest that (a) in future work, nonlinear correlation analysis should be adopted to figure out the relationship between the reservoir water level and the surface displacement; (b) the correlation analysis should be carried out to different time segments in case the reservoir water level’s rise and fall have different effects on the landslide’s stability.
4.2. Rainfall Correlation Analysis
The rainfall is regular from year to year. 123 days of rainfall occur per year; they are concentrated between May and September. The annual rainfall was 970.4 mm in 2014 and 905.8mm in 2015. The maximum daily rainfall in 2014 was 89.4 mm, compared to 69.2 mm in 2015. Compared with the outside early warning zone, the early warning zone shows more sensitivity to the rainfall. Therefore, at first, the surface displacement monitoring sites in the early warning zone were selected to do the analysis. Figure 5 shows the rainfall and the surface accumulative displacement over time.
From the figure, we can see that the surface displacement monitoring sites show synchronicity in the displacement development process. Site XD-01 was selected as representative for the analysis. For the rainfall, two sets of series data were also selected for correlation analysis. One is between the surface accumulative displacement of monitoring sites XD-01 and the rainfall from the day of surface displacement monitoring to 29 days before; another is between the surface accumulative displacement of monitoring site XD-01 and the accumulative rainfall from 1 day before the surface monitoring day to 30 days before (AR_2DB = R_0DB+R_1DB+R_2DB). If from one day of the time series value correlation exists between the daily rainfall and the surface accumulative displacement or between the accumulative rainfall and the surface accumulative displacement, it could be inferred that the lag time is the interval between that day and the surface displacement monitoring day. Results of correlation analysis are shown in Table 3.
Though these results also show that no linear correlations exist, we can see from Figure 5 that heavy rainfall occurred every time the displacement took a big step forward. On July 13th, 2015, a large displacement of the monitoring sites was recorded. This date was 14 days after the biggest rain event of the year (June 30). So, they should have a certain correlation. Getting such result, we suggest that (a) the correlation analysis should be carried out to different time segment as that the rainfall does not happen every day; (b) combining Figures 4 and 5, we can see that the displacement mutant sites are under different rainfall and reservoir water level changing conditions—the rainfall and the reservoir water level have different effects on the landslide stability. Therefore, the effects of the reservoir water level should be removed when we next perform the rainfall correlation analysis.
5. Discussions and Conclusions
In landslide research, it is known to all that hydrodynamic action plays an important part in the analysis of landslide stability [14–18], especially for reservoir bank accumulational landslides. Many researchers have focused on investigating the hydrodynamic factors’ action mechanism. Shilin Zhang et al.  studied the deformation process for a planar slide in the Mayanpo massive bedding rock slope at Xiangjiaba Hydropower Station and found that rainfall can both (a) enable kinematic feasibility and creep deformation and (b) trigger the ceaseless propagation of the sliding zone. Based on a full-scale experiment on a natural slope failure due to rainfall, Amin Askarinejad et al.  analyzed the rate of the changes in various hydromechanical parameters and studied the precursors of instability. Javed Iqbal et al.  focused on analyzing the role of reservoir filling and fluctuation in the activation/reactivation of the landslide and selected an active landslide in the Xiangjiaba Reservoir area, Southwest China, as a case study. The study confirmed that the water level fluctuations have an adverse effect on slope stability. These studies have deepened our understanding of the reaction of a landslide to changing hydrodynamic factors. Few researchers mentioned and tried to find the lag time of hydrodynamic action, which can be directly used to increase the effectiveness of landslide prediction and the early warning patrol. Lesław Zabuski et al.  observed that there is a significant time lag between a movement and hydrometeorological conditions and pointed out that the influence of hydrologic conditions on slope deformations is complex. In other words, it is hard to formulate a simple relationship between landslide displacement events and the factors triggering these phenomena. In this paper, we tried to quantify the lag time from the macroscopic behavior view of when the landslide will show its reaction to changes in the hydrodynamic factors. We also took the opportunity to call attention to the problem.
Considering the fact that accumulational landslides are the most sensitive kind to hydrodynamic factors and the fact that there are so many such landslides in the Three Gorges region, a typical reservoir bank accumulational landslide, Baishuihe landslide (Three Gorges, China), was selected for this study. We suggested that if correlations exist between the surface displacement and the hydrodynamic events (i.e., rainfall or reservoir level changes) that occurred a given time before, that time period could be defined as the lag time. Based on the long-term monitoring data of Baishuihe landslide, some steadily changing data were selected to figure out the lag time using correlation analysis. Although the attempt failed to achieve the aim, it also allowed us to conclude a few things: First, from the macroscopic behavior view, linear correlation analysis does not work in this scenario; neither the daily reservoir water level and its variation nor the daily rainfall and its accumulation have a linear correlation with the surface accumulative displacement. However, according to the surveys, we inferred that a certain correlation between the surface displacement and the hydrodynamic factors exists. Thus, further study with other methods will be required. Second, nonlinear correlation analysis is needed in further study, and the monitoring data need to be analyzed by different time intervals as the hydrodynamic factors have different effects over different periods of time. Third, the rainfall and the reservoir water are external environments—the direct acting factor is seepage. Qiang Xu et al.  found that the time when the pore-water pressure of a slope began to respond significantly to a heavy rainfall event lagged behind the onset of the event. In future studies, we will first try to find the relationship between the reservoir water level and the seepage and the rainfall and the seepage. Then, we will find the relationship between the seepage and the surface displacement. Next, we must determine the correlation between the hydrodynamic factors and the surface displacement. Finally, we could use these correlations to determine the lag time.
The data used to support the findings of this study are included within the article, and they are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
This work was supported by the Natural Science Foundation of Hubei Province (Grant no. 2012FFA040), the Science and Technology Support Plan of Hubei Province (Grant No. 2013BEC005), and the Open Fund of Key Laboratory of Geological Hazards on Three Gorges Reservoir Area, Ministry of Education (China Three Gorges University) (Grant No. 2017KDZ05). We would like to thank LetPub (www.letpub.com) for providing linguistic assistance during the preparation of this manuscript.
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