# Application of Machine Learning Techniques for the Estimation of the Safety Factor in Slope Stability Analysis

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## Abstract

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_{d}), cohesion (c), and internal friction angle (φ), which were estimated for 70 slopes in the South Pars region (southwest of Iran), were considered to predict the FS properly. To prepare the training and testing data sets from the main database, the primary set was randomly divided and applied to all predictive models. The predicted FS results were obtained for testing (30% of the primary data set) and training (70% of the primary data set) for all MLP, SVM, k-NN, DT, and RF models. The models were verified by using a confusion matrix and errors table to conclude the accuracy evaluation indexes (i.e., accuracy, precision, recall, and f1-score), mean squared error (MSE), mean absolute error (MAE), and root mean square error (RMSE). According to the results of this study, the MLP model had the highest evaluation with a precision of 0.938 and an accuracy of 0.90. In addition, the estimated error rate for the MLP model was MAE = 0.103367, MSE = 0.102566, and RMSE = 0.098470.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geotechnical Database

_{d}), cohesion (c), and internal friction angle (φ). These five features that were used to prepare the primary database reflect the basic geometrical and mechanical aspects of the slope condition. The samples were taken in summer in dry conditions, and the ratio of the pore water pressure was not applied in the assessments. It should be noted that the pore water pressure is one of the most important factors in stability assessments and has to be considered in the FS calculations. Although this factor was not included in the present study due to the lack of pore water pressure, machine learning models can consider this factor as an input parameter if it is available and use it during prediction processes. In general, changes in the input parameters can affect the final results of predictive models, but it does not have much impact on the forecasting process. Nevertheless, the pore water pressure ratio (if it is applicable) has to be considered in evaluations.

#### 2.2. Data Acquisition

_{min}, which represents the probable sliding surface by LEMs. This classification was used in the predictive models to describe the slope conditions. The FS was estimated based on the relationship between the slope stability factor (which represents the slope durability condition) and the geo-engineering characteristics, which were established through the training process by different machine learning classifiers. Regarding the slope stability analysis methods, the FS can be calculated based on the polyhedral force vector closure or incurring moments in an equilibrium state at an assumed slip surface for two-dimensional and three-dimensional spaces, which is responsible for static failure, with the moveable mass weight and geometry as the geotechnical characteristics (Table 1) of the slope, as defined in this equation.

_{d}values is more concentrated for slopes.

_{d}. Using this correlation can help in estimating the certain overlap between the geo-engineering characteristics and the FS specified. The off-diagonal plots that are presented in Figure 2 are related to stable and unstable slopes and indicate that the stable and unstable zones were concentrated in different regions. Thus, each feature has to be considered as having an independent role in evaluating the slope stability.

#### 2.3. Predictive Model Implementations and Adjustment

#### 2.4. Model Performance Evaluations

_{i}and the predicted value is y

_{i}. The application of these indicators shows that the algorithms perform better when there is less computational error. The performance of the predictive model was assessed in this study using a confusion matrix and errors table.

## 3. Results and Discussion

_{min}of the specific factors presented in Table 1 were estimated from the field via labeled data (supervised). The rotation estimation (cross-validation) procedure was used to predict how well a predictive model would perform in practice. The rotation estimation is a resampling method that tests and trains a model on different iterations using different portions of the data [33]. The equal-fold cross-validation method was used in this study to create equal-sized subsets (1:6|1 for reserved and 6 for training). Figure 3 and Figure 4 show the prediction results for the various classifiers in the training and testing sets. According to the results presented in these figures, the predicted values of the FS in the MLP training set were close to the actual (estimated) values. The K-NN and DT correctly predicted the FS, but the SVM and RF differed from the actual values in the other predictive models. Meanwhile, the predictive models’ predicted the FS values from the testing set follow the same pattern as the training set. During the training stage, the predictive models were trained regarding the stability evaluation based on the labeled geotechnical properties and the estimated FS (supervised) and then tested in a testing set that was responsible for the performance and precision of the applied models. The prediction and capability of the forecasting for both the training and testing sets are shown in Figure 4 and Figure 5. In these figures, the prediction target is the FS value.

Classifier | Parameter | Assessment Score | Accuracy | ||
---|---|---|---|---|---|

Precision | Recall | F1-Score | |||

MLP | Stable | 0.90 | 0.88 | 0.90 | 0.938 |

Unstable | 0.90 | 0.90 | 0.89 | ||

SVM | Stable | 0.73 | 0.73 | 0.74 | 0.756 |

Unstable | 0.77 | 0.75 | 0.75 | ||

k-NN | Stable | 0.85 | 0.84 | 0.84 | 0.849 |

Unstable | 0.85 | 0.80 | 0.85 | ||

DT | Stable | 0.83 | 0.85 | 0.83 | 0.808 |

Unstable | 0.80 | 0.80 | 0.80 | ||

RF | Stable | 0.70 | 0.67 | 0.70 | 0.700 |

Unstable | 0.65 | 0.70 | 0.65 |

Classifier | MAE | MSE | RMSE |
---|---|---|---|

MLP | 0.103367 | 0.102566 | 0.098470 |

SVM | 0.145631 | 0.130764 | 0.128836 |

k-NN | 0.125682 | 0.123009 | 0.120957 |

DT | 0.125369 | 0.121942 | 0.120454 |

RF | 0.138980 | 0.135124 | 0.126821 |

Aim | Applied Models | Target Model | Accuracy | Precision | Reference |
---|---|---|---|---|---|

FS calculation | LR, DT, RF, GBM, SVM, MLP | MLP | 0.84 | - | [17] |

RF, DT, SVM, k-NN, GBDT, AdaBoost, Bagging, MLP | MLP | 0.88 | - | [18] | |

AdaBoost, GBM, Bagging, ET, RF, MLP | MLP | 0.84 | - | [34] | |

MLP, GPR, MLR, SVM, SLR | SVM | - | - | [35] | |

MLP, RBFR, MLR, SVM, k-NN, RF, RT | MLP | 0.50 | - | [22] | |

BR, LR, ENR, ABR, SVM, GBR, ETR, DTR, KNR, Bagging | SVM | 0.86 | - | [36] | |

MLP, SVM, k-NN, DT, RF | MLP | 0.938 | 0.90 | This study |

## 4. Conclusions

_{d}) were picked as input data. The implementation of the models was carried out in the Python high-level programming language. The results were reported for each stage and utilized to calculate the predictive models’ performances. A confusion matrix and errors table were used for the model performance evaluations. According to the results of the modeling, they indicated that the MLP model reached the highest values of accuracy (0.938) and precision (0.90). The k-NN and DT, with 0.849 and 0.808 accuracy, respectively, were followed by the MLP. The RF obtained the lowest rate of prediction for the FS in the database, with 0.700. On the other hand, according to the results of the errors table, the MLP model, with MAE = 0.103367, MSE = 0.102566, and RMSE = 0.098470, reached the lowest errors among all of the classifiers. Regarding the mentioned results, the MLP showed a difference with other classifiers, but it had a slight discrepancy with the k-NN. Therefore, it can be stated that after MLP, k-NN can provide reliably predicted FS values.

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

FS | Factor of safety | MLP | Multilayer perceptron |

H | Slope height | SVM | Support vector machines |

β | Slope angle | k-NN | k-nearest neighbors |

γ_{d} | Dry density | DT | Decision tree |

c | Cohesion | RF | Random forest |

ϕ | Internal friction angle | TP | True positive |

S_{u} | Total cohesion | TN | True negative |

C_{u} | Undrained cohesion | FP | False positive |

Gs | Specific gravity | FN | False negative |

R | Forces resultant vector | MSE | Mean squared error |

W | Movable mass weight | MAE | Mean absolute error |

c′ | Effective cohesion | RMSE | Root mean square error |

ϕ′ | Effective friction angle |

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**Figure 2.**Results of the correlation analysis of the index parameters (green: stable; blue: unstable).

Parameter | Unit | Maximum | Minimum | Mean | SD |
---|---|---|---|---|---|

Water content | % | 6.22 | 1.73 | 3.97 | 2.24 |

Specific gravity (G_{s}) | - | 2.85 | 2.49 | 2.67 | 0.16 |

γ_{d} | kN/m^{3} | 18.99 | 18.69 | 18.84 | 0.18 |

Slope height | m | 135 | 12 | 73.5 | 50.21 |

Slope angle | Degree | 77 | 43 | 60 | 13.88 |

Cohesion (c) | kPa | 97 | 39 | 68 | 23.9 |

Friction (φ) | Degree | 35 | 20 | 27.5 | 7.51 |

Classifier | Hyperparameters | Elements |
---|---|---|

Multilayer perceptron (MLP) | Hidden layers’ size Learning rate Optimization | Activation = ‘relu’; Optimization = ‘rmsprop’; Loss_function = ‘mse’; Metrics = ‘mae’ |

Support vector machines (SVM) | Kernels C value | Kernel = ‘poly’; Degree = 2 C = 100; Epsilon = 0.1 |

K-nearest neighbors (k-NN) | Number of neighbors | n_Neighbors = 3 |

Decision tree (DT) | Max depth Random state | Criterion = ‘Gini’; Max_depth = 5 Ccp_alpha = 0.0; Min_samples_leaf = 1 Random_state = 100 |

Random forest (RF) | Number of estimators Max depth | Criterion = ‘entropy’; N_estimators = 10; Max_depth = 5; Min_samples_leaf = 1; Min_sanmples_split = 2 |

Parameter | Unit | Value |
---|---|---|

Specific gravity (G_{s}) | - | 2.63 |

γ_{d} | kN/m^{3} | 20.00 |

Slope height (H) | m | 14.5 |

Slope angle (β) | Degree | 65 |

Cohesion (c) | kPa | 125 |

Friction (φ) | Degree | 35 |

No. | Analysis Method | Estimated FS |
---|---|---|

1 | MLP | 1.18 |

2 | SVM | 1.1 |

3 | DT | 1.1 |

4 | RF | 1.4 |

5 | SLIDE | 1.21 |

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## Share and Cite

**MDPI and ACS Style**

Ahangari Nanehkaran, Y.; Pusatli, T.; Chengyong, J.; Chen, J.; Cemiloglu, A.; Azarafza, M.; Derakhshani, R.
Application of Machine Learning Techniques for the Estimation of the Safety Factor in Slope Stability Analysis. *Water* **2022**, *14*, 3743.
https://doi.org/10.3390/w14223743

**AMA Style**

Ahangari Nanehkaran Y, Pusatli T, Chengyong J, Chen J, Cemiloglu A, Azarafza M, Derakhshani R.
Application of Machine Learning Techniques for the Estimation of the Safety Factor in Slope Stability Analysis. *Water*. 2022; 14(22):3743.
https://doi.org/10.3390/w14223743

**Chicago/Turabian Style**

Ahangari Nanehkaran, Yaser, Tolga Pusatli, Jin Chengyong, Junde Chen, Ahmed Cemiloglu, Mohammad Azarafza, and Reza Derakhshani.
2022. "Application of Machine Learning Techniques for the Estimation of the Safety Factor in Slope Stability Analysis" *Water* 14, no. 22: 3743.
https://doi.org/10.3390/w14223743