Landslide displacement prediction using kinematics-based random forests method: A case study in Jinping Reservoir Area, China
Introduction
Landslide occurrence causes huge human loss and economic cost (Petley, 2012). The early warning system is a powerful tool to reduce the risk caused by catastrophic landslides, including failure in spatial and temporal terms. On the temporal aspect, the displacement prediction and time-of-failure forecast for landslides at the slope scale are regarded as the main components of early warning systems. Systematic monitoring and the recorded displacement and its rate are the most reliable and commonly used approach to obtain kinematic parameters for temporal prediction. Temporal prediction at the slope scale based on these kinematics parameters is often calculated with empirical and numerical methods as classified in a recent literature review (Intrieri et al., 2019).
The most classical rationale of empirical methods for slope movement prediction is that slopes deform in a way similar to a creep curve before rupture (Tavenas and Leroueil, 1981). Creep is material deformation that varies with time under constant stress. Creep deformation contains three stages that are also typically found in slope movement. The first stage is a primary creep, with a decreasing creep rate, followed by a secondary (or steady-state) creep with a constant strain rate, and then a tertiary creep with an increasing strain rate leading to failures (Fig. 1). Saito, 1965, Saito, 1969 firstly proposed a forecasting method for slope failure based on three-stage creep. Fukuzono (1985) developed Saito's concept and proposed a simpler graphical method by calculating the inverse velocity. Voight, 1988, Voight, 1989 mathematically generalized Fukuzono's solution and applied it to a volcanic eruption. Petley (2004) improved the inverse velocity approach by associating the influence of crack propagation to the presence of linearity to rupture. Xu et al., 2009, Xu et al., 2011 further subdivided the accelerated deformation stage into three substages and proposed an early warning index using tangential angle. This index and its derivatives have been successfully applied in landslide forecasts in China (Fan et al., 2019). Although these above-mentioned methods can predict the time of failure of landslides and slopes, the predictions only apply to the tertiary creep stage. This discrepancy makes the empirical methods not suitable for forecasting over a long deformation period (Rose and Hungr, 2007), especially predictions under primary or secondary creep stages.
Numerical methods describe the behavior of a landslide by mathematical and statistical parameters. A wide range of algorithms and models for landslide movement prediction have been developed recently. Predictions consider the influences of various external factors, like rainfall, reservoir water level, porewater pressure, and subsurface water tables. Bernardie et al. (2015) introduced a combined statistical-mechanical model to predict the variation in displacement rates using the monitoring data of precipitation and pore water pressure at Super-Sauze mudslide in France. Liu et al. (2014) applied the support vector machine (SVM), the relevance vector machine (RVM), and the Gaussian process (GP) for predicting ground movement at the Super-Sauze mudslide and the Baishuihe landslide (China). Liu et al. (2020) developed the trend sequence and sensitivity states to quantify landslide displacement related to external factors and internal landslide states. However, Intrieri et al. (2019) discovered that these numerical models do not provide more accurate predictions than the monitored data. To fill this gap, Carlà et al. (2016) linked the probability of rupture occurrence of a volcano's flank with slope deformation measurement. The displacement was predicted by an auto-regressive integrated moving average model. Guo et al. (2019) developed the formula for prediction movement using variational mode decomposition, wavelet analysis, back-propagation neural network model, and gray wolf optimizer. Nevertheless, the literature on machine learning models that can predict time-dependent displacement or forecast the timing of slope failure is still limited. Besides, Miao et al. (2018) suggested that the influence of triggers on landslide displacement is closely related to the deformation state of landslides. Both triggers and deformation states should be considered for landslide displacement prediction. Tang et al. (2019) also indicated that the interior geological characteristics and external dynamic factors shall be considered in landslide prediction.
Empirical models are advantageous in describing a landslide deformation trend in terms of landslide kinematics. Numerical methods can accurately link the influences of external factors to landslide movement. The present study aims to establishing a prediction model that can both consider the landslide kinematics and the influence of external factors. The Verhulst function was firstly developed in the 1840s by Pierre François Verhulst for studying population growth. The functional curve is a common “S” shape (sigmoid curve). Based on this function, Li et al. (1996) derived a Verhulst inverse function (VIF) to forecast the timing of landslide failure. The VIF is further extended in the current study to fit the three-stage creep deformation and predict the displacement of landslides. The random forests (RF) algorithm is an ensemble learning method for classification and regression, which corrects the overfitting of decision trees. The RF algorithm is distinguished by low overfitting and low computational cost, and accurate predicting ability (Breiman, 2001; Krkač et al., 2017). Applications of the RF algorithm are mostly related to landslide susceptibility mapping (Hong et al., 2016; Youssef et al., 2016), but few authors used it at the slope scale, Krkač et al., 2017, Krkač et al., 2020 adopted the RF algorithm for modeling underground water levels using precipitation data and thereafter predicting slope movements in the Kostanjek landslide in Croatia. Li et al. (2018) used the RF algorithm as one of benchmark data-driven models to develop ensemble-based extreme learning machines for predicting landslide displacement. In this paper, the advantageous RF algorithm is incorporated into the VIF model to account for the external factors on landslide movement prediction.
In terms of applications, reservoir-induced landslides have been studied for over half a century (Jones et al., 1961; Schuster, 1979; Huang, 2009; Yin et al., 2016). These landslides are associated with external factors and some of them are catastrophic and difficult to predict (Paronuzzi et al., 2013; Zangerl et al., 2010; Wang et al., 2004; Zhou et al., 2016; Zou et al., 2020a). Hence, in the current study, the VIF-RF method is applied to predict the displacement of reservoir-induced landslides. The Gapa landslide, a typical reservoir landslide, was reactivated by the impoundment of a high head dam reservoir in Southwest China. The Gapa landslide has shown large deformation and responds sensitively to cyclic high water level fluctuations and rainfall. This landslide has typical features of reservoir landslides and thus will be used as an example to apply and validate the novel prediction method. The information on displacement, reservoir level, and rainfall is continuously monitored for analysis. Over the monitoring period, two representative displacement monitoring sites and eight indexes of external factors are selected to establish and train the VIF-RF model. The prediction results of the hybrid VIF-RF approach are compared with the pure empirical/numerical methods. The accuracy of the model in predicting the displacement of a reservoir landslide in the Three Gorges Area is also tested. The VIF-RF model is used to predict the displacement of the Gapa landslide over the next years, overcoming the shortcomings of previous numerical models in predicting future displacement.
Section snippets
Verhulst inverse function
The curves of the Verhulst function and its inverse function are illustrated in Fig. 2. The curve of the Verhulst inverse function (VIF) has the intact characteristics of three-stage creep deformation (Fig. 2b). Besides, the recorded cumulative displacement curve of landslides can show different characteristics (Fig. 2c, d, and e) depending on the influence of external factors as well as the timing of starting to collect monitoring data. The features of these displacement curves can all be
Study area and monitoring system
The Gapa landslide is located on the right bank of the Yalong River, Southwestern China. The location is approximately 11.5 km upstream of the Jinping first-stage hydropower station, which is one of the world's highest dams. The reservoir behind the dam was initially impounded from an elevation of 1650 m in November 2012. The reservoir has a regulated water level fluctuation of 80 m ranging from 1800 to 1880 m during the operation. Due to the impoundment of the reservoir and the water table
Fitting and training results
The VIF model was fitted to the measured displacement rate at the G1 and G2 monitoring points to obtain its kinematic parameters and identify the deformation stage. Fig. 11 shows four fitting displacement curves at the G1 monitoring location for four monitoring periods with different time lengths. It can be seen that the accuracy of the VIF model increases with the length of the fitting period. Two longer monitoring periods, January 2016–January 2019 (marked phase #1) and January 2016–July 2019
Discussion
The accuracy of the VIF model increased with the length of the monitoring period, as shown in Fig. 11. In this regard, new monitoring data can be input to the VIF model to obtain new model parameters. Likewise, new reservoir level and rainfall information can be used to update the VIF-RF model, thus increases its prediction accuracy. Hence, it is practical to constantly update the model with new monitoring information, which renders the prediction of the VIF-RF model from static to dynamic.
The
Conclusion
This study presents a robust model to satisfactorily predict the displacement of reservoir landslides by integrating empirical and numerical methods to capture both the landslide kinematics and the influence of external factors. The kinematic characteristics of reservoir landslides can be well described with the Verhulst inverse function (VIF) that is based on the rationale of three-stage creep deformation. The relationship between external factors and landslide displacement can be quantified
Author statement
The all authors’ individual contributions are as follows:
Xinli Hu: Project administration and Funding acquisition.
Shuangshuang Wu: Conceptualization, Methodology, Formal analysis, Data Curation, Investigation, and Writing- Original draft.
Guangcheng Zhang: Writing - Review & Editing.
Wenbo Zheng: Software, supervision, and validation.
Chang Liu: Investigation.
Chuncan He: Investigation.
Zhongxu Liu: Investigation.
Xuyuan Guo: Resources.
Han Zhang: Data curation.
Declaration of Competing Interest
None.
Acknowledgment
This study is funded by the National Key Research and Development Program of China (No. 2016YFC0401908), the Key Program of National Natural Science Foundation of China (No. 41630643), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (CUGCJ1701), the General Program of National Natural Science Foundation of China (No. 41877263).
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