Slope stability prediction for circular mode failure using gradient boosting machine approach based on an updated database of case histories
Introduction
Slope stability analysis is one of the most important and critical problems in mining and geotechnical engineering projects such as open-pit mining operations, dams, embankments, earth dams, landfills and highways. Disastrous consequences of slope collapse necessitate better tools for predicting their occurrences. Such hazards are responsible for heavy destructions of public/private property, disruptions of traffic, and loss of human lives every year (Sah et al., 1994, Shi et al., 2010, Hoang and Pham, 2016, Basahel and Mitri, 2018).
Perhaps starting with Terzaghi’s 1950 work entitled “Mechanism of Landslides” (Terzaghi, 1950), more scholars began to pay attention to analyzing the stability of a slope in terms of theoretical, analytical, experimental, numerical (i.e., finite difference, finite element and discrete element) and statistical approaches which have been used worldwide. For example, literature studies on limit equilibrium method (LEM) and finite element method (FEM) slope stability analyses are extensively available (Xu and Low, 2006, Cheng et al., 2007). However, when a slope fails with a complex mechanism such as internal deformation and brittle fracture, progressive creep, liquefaction of weaker soil layers (Chen and Chameau, 1983, Duncan, 1996, Yu et al., 1998, Eberhardt, 2003), LEM simulations may become inadequate. Moreover, FEM is computationally more time consuming as compared to LEM. On the other hand, numerous studies have been undertaken in recent years to develop several computational intelligence approaches for slope stability analysis (i.e. Sah et al., 1994, Sakellariou and Ferentinou, 2005, Samui, 2008, Das et al., 2011, Manouchehrian et al., 2014, Liu et al., 2014, Gao, 2015, Suman et al., 2016, Hoang and Pham, 2016). For example, Lu and Rosenbaum (2003) combined the artificial neural network (ANN) and the gray system method to evaluate slope stability based on geotechnical properties and historical behaviors of the collected slope cases. Accordingly, Wang et al., 2005, Das et al., 2011 applied the ANN to predict the slope stability. Zhao et al. (2012) employed the relevance vector machine to explore the nonlinear relationship between slope stability and its influence factors. Liu et al. (2014) used extreme learning machine technique for the evaluation and prediction of stability of slopes with 97 cases. Hoang and Pham (2016) introduced metaheuristic-optimized least squares support vector classification for slope assessment with 168 cases. However, few research works have been systematically performed to precisely predict and evaluate a level of safety of the structures. For example, empirical or semi-empirical approaches have been employed with local monitoring data and are open to improvement because they are based on limited collected data (Basahel and Mitri, 2017). Furthermore, the estimation of reliable values of model input parameters is found to be an increasingly difficult task before applying sophisticated numerical methods. Artificial intelligence studies provide new alternatives to empirical methods and some other conventional statistical techniques. However, these methods usually require a large amount of data and they are mostly computationally expensive. Determining suitable tuning parameters and architecture of ANN models remains a difficult task; the optimal choice of kernel and regularization parameters of relevance vector machine and support vector machine models often need expert knowledge for different data characteristics. Additionally, these methods seldom provide information about the relative significance of various parameters. Moreover, it can be shown that part of the data set is duplicated in the aforementioned studies after carefully examining their dataset. Hence, predicting slope stability and interpreting the contribution of influencing parameters still pose a considerable challenge for mining and geotechnical engineers.
Contrastingly, Friedman (2001) proposed a simple and highly adaptive method for many kinds of applications, which is called gradient boosting machine (GBM). As a relatively new algorithm, the GBM is a family of powerful supervised machine learning techniques that have shown promising results in terms of prediction performance, robustness and speed in a wide range of practical applications (Friedman, 2001, Friedman, 2002, Kuhn and Johnson, 2013, Lu et al., 2016, Zhou et al., 2016a, Zhou et al., 2016b, Zhou et al., 2019b). This benefits from two main features: (a) It optimizes hyper-parameters in function space which ensures the custom loss functions much easier to implement; and (b) Boosting focuses progressively on complicated cases that gives an optimal technique to handle unbalanced datasets by enhancing the impact of the positive label. It is therefore motivating to investigate the capability of GBM in slope stability prediction. To construct and confirm the GBM model, a dataset including real cases of slope evaluation has been collected from the literature. In addition, the training process of the GBM is enhanced by the fivefold CV used for the model evaluation.
Section snippets
Data set and predictor variables
In this work, the database consists of 221 cases (the numbers of stable and failure slope cases are 115 and 106, respectively), which are taken from information published by Sah et al., 1994, Xu and Shao, 1998, Feng and Hudson, 2004, He et al., 2004, Jin et al., 2004, Wang et al., 2005, Li et al., 2006, Chen et al., 2009, Su, 2009, Wang, 2009, Xu et al., 2009, Chen et al., 2011, Xiao et al., 2011 and Zhu et al. (2011) over sixty sites which can be found in Table 1. Height (H), overall slope
Descriptive analysis
The violin plots of each property which combine density estimates and box plots in displaying data structure are shown in Fig. 1 for all slope cases histories. Fig. 1 provides the relevant input parameters used to develop the slope stability prediction models range with their maximum values, median values and minimum values, also the third and first quartile is represented as the bottom and the top of the thickline in the center of the violin plots, respectively. The main advantage of violin
Conclusions
In this work, the GBM method has been successfully employed to investigate the state of slope stability using 221 historical cases of slope conditions recorded. The state of slope stability is formulated as a classification problem in which prediction outputs are either “stable” or “failed” using the GBM model. Six different predictive variables that characterize the material behavior and the slope geometrical features as well as the influence of external triggering parameters are considered as
Acknowledgments
This work is supported by the National Natural Science Foundation Project of China (Grant No. 41807259), the Natural Science Foundation of Hunan Province (Grant No. 2018JJ3693), the China Postdoctoral Science Foundation funded project (Grant No. 2017M622610) and the Sheng Hua Lie Ying Program of Central South University.
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