The mechanical balance of slopes is often destroyed due to natural or man-made factors, which induces landslides and other geological disasters and further causes casualties and economic losses (Palenzuela Baena et al. 2019; Chang et al. 2022). Accurately predicting landslides allows for promptly transferring personnel and property and minimizing losses (Huang et al. 2016; Li et al. 2021). Therefore, it is very important to predict slope stability quickly and accurately.

The occurrence of landslides is a long-term process, which is nonlinear and complex from a gradual evolution to sudden macroscopic slope slippage (Kumar and Basudhar 2018; Criss et al. 2020; Jiang et al. 2022). Due to the complexity of the structure and discontinuity of the physical and mechanical properties of slope mass, as well as the variability and effectiveness of control factors acting on the slope, slope engineering can be regarded as an uncertain, nonlinear, dynamic and open complex system in which the stability is comprehensively affected by geological and engineering factors (Bui et al. 2019; Dai et al. 2021; He et al. 2021; Wu et al. 2022). Most of these control factors have the characteristics of randomness, ambiguity, variability and other uncertainties. Their influence weights on slope stability vary, and there are complex nonlinear relationships between these control factors (Kang et al. 2017).

Many methods were proposed for a slope stability calculation, among which the limit equilibrium method and numerical simulation method were the two most widely used method (Yang et al. 2020). Both methods have their advantages and disadvantages. For the limit equilibrium method, it is very difficult to find the critical slip surface because there are many potential slip surfaces (Yang et al. 2019b). For the numerical simulation method, the selection of constitutive models, mechanical parameters and boundary conditions significantly affect its accuracy, and it often requires rich engineering experience and on-site back analysis to make a rational selection and acquire reasonable results (Qi and Tang 2018; Ray et al. 2020). Moreover, it generally takes a long time to establish a computer model and perform analysis for numerical simulation methods (Abdalla et al. 2014). Therefore, there are still considerable challenges in predicting slope stability.

In recent years, machine learning models have attracted an attention in solving these highly complex, nonlinear, and multi-variable geotechnical issues. Researchers attempt to use the artificial neural networks (ANNs), support vector machine (SVM) algorithms and other methods to solve such issues (Rukhaiyar et al. 2017; Huang et al. 2020a). The ANNs have shown a high degree of success in function approximation in different fields including geotechnical engineering. An ANN is a computer model with a structure that naturally imitates the information processing and optimization strategy of human brain (Zhang and Goh 2016). Through weighted connections, the input variables stored in the input layer neurons are redistributed to hidden neurons and then transformed into the neural network response in the output layer neurons (Selvaraju et al. 2020). Researchers have proposed various ANN models for calculating slope stability. For example, Qian et al. (2019) proposed a slope stability evaluation tool based on the ANN model. Gao et al. (2019) proposed to use the ANN model optimized by the imperialist competition algorithm to solve the slope stability problem.

Deep learning model is a new branch of machine learning developed in recent years and is considered an extension of neural networks. Structurally, it is different from previous machine learning models in that it has more and deeper network layers. Algorithmically, it can automatically extract features instead of manually designing features as in traditional machine learning (Schmidhuber 2015; Huang et al. 2022b). Artificial design features have some shortcomings. First, the design is difficult and requires constant trial because of error. Second, different features need to be designed for different problems (Yao et al. 2017). On facial recognition detection datasets, the deep learning accuracy can be as high as 99.47%, which is much higher than 60% of the traditional face recognition algorithm eigenface because automatically selected features are more accurate than manually designed features (Wu et al. 2019). The “deep” network structure of deep learning can express information hierarchically. The idea is to stack multiple layers; the output of the upper layer is used as an input of the next layer, and different features are extracted from different layers to achieve the layered expression of features (Zhou 2018). Moreover, deep learning extracts global features instead of local features. Therefore, it is more fault tolerant. Even if some local areas are missing, correct results can still be obtained based on other global features, avoiding the classification errors caused by local areas (Liang et al. 2017; Huang et al. 2020b). Shallow machine learning is less fault tolerant because it is difficult to extract global features and cannot make a full use of the contextual information. Thus, the deep learning is more capable of expressing object characteristics than the traditional machine learning. Based on the advantages of deep learning, some scholars have applied deep learning to slope engineering. For example, Wang et al. (2020b) applied deep learning to rock classification to facilitate further study of slope stability. Tan et al. (2021) made a rapid assessment of landslide risk grade based on deep learning, which accelerated the landslide risk grade determination process.

The Long short-term memory (LSTM) neural network is a new deep learning algorithm developed in recent years, which has great advantages in processing dynamically changing data (Zhao et al. 2020). The LSTM is essentially a recurrent neural network having a long-term dependence problem. That is, when learning a long sequence, the recurrent neural network shows gradient disappearance and gradient explosion and cannot determine the nonlinear relationship of a long time span (Wang et al. 2018). The LSTM model is proposed to solve this problem. In the LSTM, the “gate” structure protects and controls the unit state and selectively allows information to pass through, which can effectively solve the recurrent neural network gradient disappearance and gradient explosion problem. Recently, researchers have applied the LSTM to other fields. For example, Chen et al. (2021) predicted China's particulate pollution based on the LSTM, and the results showed that the model has a high prediction accuracy. Liu et al. (2018) proposed a wind speed prediction model based on the LSTM, which achieved a good prediction performance. However, the LSTM model has not been used in slope stability prediction.

In this study, LSTM is applied to landslide stability prediction. Five control factors representing most slope properties including the slope height, slope angle, internal friction angle, cohesion and soil weight, are selected as input variables from landslide influencing factors. Within the value range of each variable, its value is selected according to the idea of interpolation, and the values of each variable are combined to obtain different slope data. Typical soil slopes are established through the Geo-Studio software, and the “true value” of the slope stability factor of each slope is calculated. The obtained training dataset and prediction dataset are input into the LSTM model to predict slope stability. The SVM, random forest (RF) and convolutional neural network (CNN) are used as the comparison models. The prediction data obtained by the four models are compared and analyzed to explore the feasibility of LSTM in slope stability prediction.

2.1 Modelling processes and ideas

First, the landslides inventory of Ganzhou City, Jiangxi province, from 1998 to 2010 was collected and analyzed to obtain the geometric properties of the slope soil material in this area (Fig. 1). By referring to the relevant literature, five control factors, including the slope height, slope angle, internal friction angle, cohesion and volumetric weight, were selected as input variables of the machine learning model, and the value range of each variable was determined (Zhang and Goh 2016; Gao et al. 2019; Qian et al. 2019; Selvaraju et al. 2020). Based on the interpolation method, the variable values were evaluated within their ranges, and the variable values were arranged and combined to obtain several groups of slope data. The obtained slope data were input into the Geo-Studio software, and the slope stability factor of the corresponding slope was calculated by the limit equilibrium method.

Location of the study area and landslide inventory

Each slope stability factor and its five corresponding control factors form a slope sample. A total of 2160 training samples and 450 testing samples were constructed in this study. Then, the slope stability prediction model based on machine learning was established. The fitting ability and prediction performance of these models were trained with training samples and the parameters in each prediction model were determined. Finally, the remaining slope sample was input to the trained model for a slope stability prediction. The slope stability factor of the predicted sample slope is output. The modelling process was shown in Fig. 2.

Modeling flow chart

2.2 Introduction of machine learning models

In this study, four machine learning models, the LSTM, CNN, SVM and RF, were selected to predict slope stability (Sun et al. 2020; Huang et al. 2021). Among them, the LSTM model is the research object of this study with the other three models for comparisons to explore the feasibility of LSTM in slope stability prediction.

2.2.1 Long short-term memory model

The LSTM is a special recurrent neural network, which has great advantages in dealing with dynamically changing data (Fig. 3). The LSTM can effectively prevent the long-term dependence problems in the recurrent neural network, that is, the gradient explosion and gradient disappearance. Due to its memory block mechanism, it can be used to describe continuous output on the time state. The LSTM is applied to the regional dynamic landslide disaster prediction model. The information in this model can directly flow from one sample node to the next sample node (Xie et al. 2019).

Structure diagram of the LSTM model

All recurrent neural networks have the form of a chain of repeated neural network modules. In a standard recurrent neural network, these repeating modules have a very simple structure, such as a single \(\tanh\) layer. Similarly, the LSTM also has this chain structure. However, the repeating LSTM module has a different structure. There is not only one neural network layer but four layers that interact in a very special way (Wang et al. 2020a).

The cell state is the key to the LSTM, and it extends along the horizontal line that runs through the top of the structure diagram. There are only some small linear interactions in the process and information can flow through this chain without changes. The LSTM can delete or add information to the cell state. These functions are carefully adjusted by a structure called “gate”. The gate consists of a sigmoid neural network layer (σ) and a point-by-point multiplication operation, which can selectively allow information to pass through. The sigmoid layer outputs a number between 0 and 1, describing whether each component is allowed to pass. When the value is 0, it means “do not let any content pass”, When the value is 1, it means "let all content pass". The expression of the sigmoid function is as:

There are three such gates in the LSTM: the “forget gate”, the “input gate” and the “output gate”. These three gates are used to protect and control the unit state (Amin et al. 2019). Therefore, as a filter, each door has its job to achieve different purposes:

1. (1)

   The forget gate (\(f_{t}\)) filters the input information to determine which information to keep or forget. The forget gate looks at the input \(h_{t - 1}\) and \(x_{t}\) through the sigmoid neural network layer and outputs a number between 0 and 1 for the information of \(c_{t - 1}\) in a unit state, thereby determining whether the input information is retained or forgotten:

   $$f_{t} = \sigma W_{f} \cdot [h_{t - 1} ,x_{t} ] + b_{f}$$

   (2)

where \(x_{t}\) is the input data at the current moment, \(h_{t - 1}\) is the output of the hidden unit at the previous moment, \(W_{f}\) represents the weight matrix of the forget gate and \(b_{f}\) represents the offset.

1. (2)

   The input gate (\(i_{t}\)) continuously updates the transmitted information, filters out the information that needs to be retained, and updates the unit status at the moment. First, the sigmoid network layer of the input gate filters the input information. Next, the \(\tanh\) layer creates a new vector \(\tilde{c}_{t}\) and combines both \(i_{t}\) and \(\tilde{c}_{t}\) to obtain a new candidate value \(c_{t}\) (Tian et al. 2018):

   $$i_{t} = \sigma (W_{i} \cdot [h_{t - 1} ,x_{t} ] + b_{i} )$$

   (3)
   $$\tilde{c}_{t} = \tanh (W_{c} \cdot [h_{t - 1} ,x_{t} ] + b_{c} )$$

   (4)
   $$c_{t} = f_{t} \cdot c_{t - 1} + i_{t} \cdot \tilde{c}_{t}$$

   (5)

   where \(c_{t}\) represents the cell state at time t, \(c_{t - 1}\) represents the cell state at time t-1, \(W_{i}\) and \(W_{c}\) represent the weight matrix, \(b_{i}\) and \(b_{c}\) represent the offset.

1. (3)

   The output gate (\(o_{t}\)) is a result of combining the forget gate and the input gate to determine the output of the current neural unit. The output data is used as an input to the next unit. The output gate determines which part of the unit state to output through the sigmoid neural network layer. Then, the value of the new cell state \(c_{t}\) is changed to between − 1 and 1 by the activation function \(\tanh\) and then multiplied by the output of the sigmoid neural network layer to obtain an output (Wang et al. 2020a):

   $$o_{t} = \sigma (W_{o} [h_{t - 1} ,x_{t} ] + b_{o} )$$

   (6)
   $$h_{t} = o_{t} \cdot \tanh (c_{t} )$$

   (7)

   where \(W_{o}\) represents the weight matrix and \(b_{o}\) represents the offset.

2.2.2 Convolutional neural network model

CNN is a kind of artificial neural network and its largest feature is weight sharing. Weight sharing can greatly reduce the number of weights, further reducing the complexity of the entire CNN. The CNN can directly accept images as an input and use filters to extract data features directly and automatically. Features do not require tedious and complicated manual design and the entire feature representation process is more automated (Yang et al. 2019a).

The CNN is composed of multiple network layers and each network layer has many independent neurons. The feature extraction filter performs a convolution operation on the input image and generate a feature map in the C1 layer after convolution. Next, neural network operation is carried out on feature map S1, including finding the weight between the two layers of neurons and adding the corresponding bias. Finally, a new feature mapping result S2 is obtained through the sigmoid function, which is a further abstraction of the C1 layer. This process is repeated until finally the result is input to a classifier to obtain an output (Akram et al. 2019).

2.2.3 Support vector machine model

The SVM is built based on statistical learning theory and has a solid theoretical foundation (Cortes and Vapnik 1995). The SVM has a good adaptability to practical problems such as high dimensionality, small samples, nonlinearity and local minima. This model is currently widely used in many fields, such as computers, ecology, medicine and engineering (Kwag et al. 2020). Based on the statistical learning theory, the SVM improves the generalization ability of the learning machine by seeking to minimize the structured risk, experience risk, and confidence range, so that the model can obtain higher accuracy even with a small number of samples (Moayedi et al. 2019).

The basic idea of SVM is as follows: when dealing with the linear indivisibility problem, the nonlinear problem in the original sample space is transformed into a linear problem in the high-dimensional feature space through a nonlinear transformation. Then, a constrained convex quadratic programming problem is solved in this new high-dimensional space, and the unique global optimal solution is obtained (Tinoco et al. 2018).

2.2.4 Random forest model

The random forest algorithm is a combination classification intelligent algorithm based on the statistical theory proposed by Breiman in 2001. It has a strong data mining capability and high prediction accuracy (Lin et al. 2018; Huang et al. 2022a). The RF uses multiple classification trees to follow the ensemble learning rules. During its implementation, the prediction relationship is randomly changed to increase the diversity of the used forest tree species. The RF needs to manually specify the number of trees and that of variables for splitting nodes. The reliability of the model can only be guaranteed when parameter t is high enough. Since each tree is regarded as a completely independent random situation, the abundance of random trees can reduce the possibility of overfitting (Wongvibulsin et al. 2019).

2.3 Evaluation method of model accuracy

In addition to directly comparing the errors between the machine learning model predictions and the numerical simulation results, this study also introduces two quantitative statistics to evaluate the fitting effect of the model—root mean square error (RMSE) (Eq. (8)) and modelling efficiency (EF) (Eq. (9)) (Koopialipoor et al. 2018)—to compare the prediction accuracy of the four machine learning models.

where \(y_{i}\) represents the slope stability factor of each sample, \(\hat{y}_{i}\) represents the predicted value of the machine learning modeling for each sample, and \(\overline{y }\) represents an average value of the slope stability factor.

The RMSE value represents the percentage of a difference between the observed value y and the predicted value \(\hat{y}\) relative to \(\overline{y}{ }.\) Its magnitude reflects the relative error of the model used in fitting.

The EF value is a standard statistical value for evaluating simulation accuracy. When \(\sum\limits_{i = 1}^{n} {(y_{i} - \hat{y}_{i} } )^{2}\) = 0, EF reaches its maximum value of 1. The predicted \(\hat{y}_{i}\) is in complete agreement with the observed y.

3.1 Overview of Ganzhou City

Ganzhou City is located in Jiangxi Province, China, with an area of 39,379.6 km². The natural environment of Ganzhou City is complex and it is one of the areas with more serious geological disasters. The terrain in Ganzhou City is different from east to west, with a trend of low altitude in the southwest and high altitude in the northeast. Most of the landforms are middle-low mountains and hilly areas, accounting for 75.62% of this city’s total area. According to preliminary statistics, a total of 19,555 geological disasters occurred in Ganzhou City from 1998 to 2010, in which collapse and landslides were mainly distributed in the low mountain and hilly areas. The stratum lithology in this area is composed of metamorphic rock, granite, red clastic rock and general clastic rock, and is dominated by soil landslides. Debris flows are mostly developed in the middle and low mountain areas and areas prone to heavy rain, while karst collapses are distributed throughout Ganzhou City. Besides, the ground subsidence in the goaf is mainly distributed in the northern part of Ganzhou City. In general, the occurrence density of geological disasters in Ganzhou City is relatively high, with an average of 20 locations per 100 km².

3.2 Selection of control factors

The main factors affecting the slope stability are stratum lithology, geological structure, in situ stress, rock mass structure, water action, slope geometry and surface morphology. Among these influencing factors, the geometric influencing factors are mainly slope height and slope angles; the influencing factors of rock and the soil mechanics index refer to the volumetric weight, cohesion, internal friction angle and pore pressure ratio of rock and soil (Lu et al. 2020). Machine learning models are based on data mining and need to provide effective parameters for determination. Too many input parameters cause the stability analysis of the final expression irregular, and it is difficult to collect data. Too few parameters do not correctly reflect the slope stability content. After consulting the data (Kumar et al. 2014; Gordan et al. 2016; Zhou et al. 2019), the five control factors, the slope height, slope angle, cohesion, internal friction angle and volumetric weight are selected as the input variables of the machine learning models. The slope height (H) reflects the volume and weight of the slope, and the slope angle (α) is a key factor that generally governs the slope stability. Moreover, the cohesion (c) and internal friction angle (φ) are important mechanical indicators affecting soil strength. Finally, the volumetric weight (γ) reflects the grav–ity that promotes the occurrence of landslides.

3.3 Determination of control factors

In this study, the reasonable value range of each parameter is determined by analyzing the landslide data and geological data of Ganzhou City. The value range of H is 1–260 m, and the value range of α is 0°–44.5°. The value ranges of c and φ are 23.3–56.8 kPa and 12.6°–51.7°, respectively. Besides, the value range of γ is 18.2–23.3 kN/m³. Within the value range of each control factor, the value is selected based on interpolation. Considering that if the slope height and slope angle are set with too many kinds of values, it will be too complex to construct soil slope models. Hence, its most common situation is considered to select its values. The slope height is set to 65 m, 100 m, 135 m and 170 m. The slope angles are 20°, 25°, 30°, 35° and 40°. Because the value range of volumetric weight is small, three values are set to 18.2 kN/m³, 19.7 kN/m³ and 21.2 kN/m³. For cohesion c and the internal friction angle φ, values are taken within the range of values with an interval of 5. The values of all control factors are shown in Table 1.

3.4 Construction of typical soil slope

Furthermore, the evolution characteristics of Ganzhou landslides are summarized, including the rock and soil mechanical indicators, thickness, slope length, slope height and slope angle (Yin et al. 2020). Most of the landslides in Ganzhou City are shallow landslides with a thickness ranging from 2 to 10 m, and the length of the slope is mostly within 40–200 m. Besides, the slope angle is generally between 15° and 40°. According to the evolution characteristics of these landslides, a series of typical accumulation layer slopes are constructed.

Based on these typical slopes, 20 types of slopes are established in the Geo-Studio software by setting different slope heights and slope angles (Table 1). Next, the three control factors of C, φ and γ are transformed and combined and then input to the established 20 types of slopes. This step adds rock and soil material properties to the slopes. As a result, a total of 2160 different soil slopes are obtained. Among them, the soil slope with a slope height of 100 m and a slope angle of 25° is selected as the sample, as shown in Fig. 4.

A typical soil slope with slope height of 100 m and slope angle of 25°

4.1 Data acquisition

According to the values of the slope height, slope angle, cohesion, internal friction angle and volumetric weight determined in Sect. 3.3, a total of 2160 different slope models are constructed by perturbation and their combination. The slope stability factor is calculated by the limit equilibrium method in the Geo-Studio software. Each slope stability factor and its corresponding control factor is a slope sample, and the 2160 obtained groups of slope sample data are used as the training sample data of the machine learning model. Similarly, according to the determined value range of slope stability control factors, the Excel 2016 software is used to randomly set three factor values for slope height and slope angle. Then nine different typical soil slopes are obtained by permutation and combination. After that, 50 groups of cohesion, internal friction angle and volumetric weight are randomly determined for each soil slope within the corresponding value range. A total of 450 soil slopes with different geotechnical mechanicals parameters are obtained. In the machine learning modelling, the 450 soil slopes and their control factors are the testing sample data.

The Geo-Studio software is used to calculate the slope stability factor of each soil slope through the limit equilibrium method (Jiang et al. 2017). The obtained slope stability factor is used as the actual slope stability factor of the slope, and is used for a comparison with the slope stability factors predicted by the machine learning models. Since there are 2160 sets of training sample data and 450 sets of prediction sample data, there are too many data to list them all. The seventy-two samples randomly selected from the training data are shown in Table 2, and 15 from the predicted data are shown in Table 3.

4.2 Machine learning model training

To obtain a more accurate prediction, the machine learning model needs to be trained before slope stability prediction to determine the optimal value of parameters in each machine learning model. For the SVM and RF (two traditional machine learning models), the training dataset is imported into SPSS modeler 18.0 software, and the optimal values of the required parameters in the SVM model and RF model are obtained by cross validation. In this study, the RBF is taken as the kernel function of the SVM model. After training the SVM model, the regularization parameter is set to 10, and the kernel function parameter ϒ is set to 0.1. Additionally, by training the RF model, the number of decision trees constructed in the RF model is set to 10, the maximum number of nodes is set to 500, the maximum tree depth is set to 10 and the minimum child node size is set to 5.

For the LSTM and CNN (two deep learning models), there is no need to manually debug parameter values. When writing the deep learning algorithm, the training dataset and the testing dataset are marked with corresponding labels in the algorithm statement, and they are linked to the corresponding deep learning model. When the deep learning model starts to run, it conducts training through the linked training dataset and automatically searches for the optimal value of the parameters in the deep learning model.

4.3 Slope stability predictions from machine learning models

For the traditional machine learning models, the SVM model and the RF model, there is no need to adjust their parameters because they have been trained previously. The testing dataset is imported into the SPSS modeler 18.0 software and linked to the trained SVM model and RF model. After running, the corresponding dataset of slope stability factors is output. For the deep learning models, the CNN model and LSTM model, the corresponding labels are marked for the training dataset and testing dataset in the algorithm statement. The CNN and LSTM models search for the optimal values of the required parameters through the training data. After training the deep learning models, the slope stability is predicted directly with the testing dataset and the slope stability factor dataset is output.

After the slope stability prediction of 450 testing sample slopes, the prediction accuracy of the four machine learning models is evaluated by comparing the errors between the predicted values and the numerical simulation results and calculating the RMSE values and EF values of the four machine learning models. Because of the large quantity of data, 15 prediction samples are randomly selected from the all 450 samples and are shown in Table 4; the RMSE and EF values of each machine learning model are calculated using the all 450 samples. Table 4 shows that the slope stability factors predicted by the LSTM are close to the results of numerical simulation, and the absolute error of the randomly selected sample data is less than 0.05. Compared with that of other three machine learning models, the error of the slope stability prediction results of the LSTM model is smaller. Namely, the prediction accuracy of the LSTM model is higher.

According to Sect. 2.3, the smaller the RMSE value of the model or the closer the EF value of the model is to 1, the higher the prediction accuracy of the model is. Further information can be seen in Table 4. Figure 5 shows the RMSE value of the LSTM model is only 4.45%, which is the smallest among these of the four machine learning models. The EF value of the LSTM model is 0.9827, which is the closest to 1 among these for the four machine learning models. Therefore, the RMSE and EF values of the four machine learning models both suggest that the LSTM model has the highest slope stability prediction accuracy among all these models.

Comparison of various model predictions

5.1 Innovations of this study

1. (1)

   Deep learning has been widely used in other fields. However, it has rarely been used for slope stability prediction. In other words, the current relevant studies rely on the traditional machine learning models. In particular, the LSTM model of deep learning was innovatively proposed in this study for slope stability prediction. Through comparative studies with the CNN, SVM and RF models, the feasibility and high precision of the LSTM model were revealed.

2. (2)

   The slope used in this study is a generalized soil slope based on a large number of actual slope statistics. Considering the five control factors having great influence on the slope stability, a large number of practical slope models were constructed. Furthermore, by changing the value of each control factor, 2160 slopes were constructed to form the slope knowledge base. The machine learning models were trained through the slope knowledge base to realize a rapid and accurate prediction of the slope stability of any slope within the value ranges of the five control factors.

3. (3)

   Existing studies often only build machine learning models for dozens of slopes. However, machine learning is more suitable for predicting samples with a large quantity of data, and an excessively small quantity of data will lead to a great uncertainty in machine learning modelling. In this study, there are 2160 training data samples and 450 prediction samples. The quantity of data is far greater than that in previous studies, which can effectively reduce the modelling uncertainty.

4. (4)

   In this study, the testing sample data were obtained randomly within the value ranges of the five control factors, and the number was large enough to be sufficiently representative of the possible slopes within the value ranges. If subsequent work or other scholars need to predict the stability of a single slope in the area, the values of the five control factors of a single slope can be input into the LSTM model, and the slope stability factor will be output.

5.2 Existing deficiencies and the future improvement

1. (1)

   In this study, five control factors affecting slope stability were considered as the input variables of machine learning models. These five control factors all belong to the nature of the slope. However, the occurrence of landslides is usually activated by external inducing factors in addition to the slope’s controlling factors. In subsequent studies, external inducers such as rainfall and slope cutting can be added to the input variables of the machine learning model to realize real-time and accurate prediction of the slope stability under external inducer conditions.

2. (2)

   The soil slope in this study is a two-dimensional slope model established by the Geo-Studio software, while the slope in real life is a three-dimensional entity. The two-dimensional soil slope is a simplified treatment of the slope and does not consider the influence of slope width on its stability. In the next study, a three-dimensional soil slope can be considered for slope stability prediction. In the current research, the efficiency of 3D slope stability based on numerical simulation is low. Using machine learning instead of numerical simulation to calculate slope stability can greatly improve the efficiency of slope stability prediction when ensuring accuracy.

3. (3)

   In this study, slope stability factors obtained by the limit equilibrium method were compared with the predictions of the four machine learning models to analyze the prediction accuracy of the four machine learning models. However, the slope stability factor calculated by the limit equilibrium method is only a predicted value, which is not equal to the real value of the slope stability factor. In future study, it will be worth considering whether the data that are closer to the real value of the slope stability factor can be found for comparison with the predicted results of the machine learning models.

In this paper, there were 2160 training sample slopes and 450 prediction sample slopes. The data volume of the sample slopes was much larger than that of the previous studies, and it was representative enough for all the slopes in the study area. The machine learning models were trained through the training sample data. Then the prediction sample data were input into the trained machine learning to predict slope stability. Four machine learning models were adopted, of which the LSTM and CNN were deep learning models and the SVM and RF were traditional machine learning models. The four machine learning models used the same data for a slope stability prediction and evaluated the model prediction accuracy by calculating the RMSE and EF values of their predictions.

According to the evaluation of the predictions of the four machine learning models in Sect. 4.3, the slope stability factor of each sample slope predicted by the LSTM model was closer to that calculated by the limit equilibrium method. The RMSE and EF values of the four machine learning models were calculated, showing the same trend. That is, the prediction accuracy of the LSTM model was the highest, followed by the SVM, RF and CNN models from high to low. It can be concluded that the LSTM model has a great feasibility in slope stability prediction, and a higher prediction accuracy can be obtained through LSTM than the above traditional machine learning models.