Prediction of stability of a slope with weak layers using convolutional neural networks

Abstract

Artificial intelligence (AI)-based methods have been widely applied to slope stability assessment, but due to the scarcity of samples, most AI models are used under certain working conditions, such as the homogeneous or fixed-size slopes. In actual situations, the slope stability is affected by factors such as geometries, weak layers, etc. Therefore, in order to further consider more parameters affecting slope stability in AI models, this study used digital twin (DT) technique to build a database of the slopes with weak layers through practical cases. Meanwhile, in order to improve the prediction performance of the model, a convolutional neural network (CNN) is constructed. In this paper, the process of establishing a database of slopes with weak layers is elaborated in detail. Meanwhile, the performance of the CNN models is investigated thoroughly through several evaluators. Finally, the trained CNN is applied to actual slope cases. The results show that the CNN achieves the highest scores in a range under the receiver operating characteristics (0.99), accuracy (95.4%), and F1 score (95.3%) compared with other machine learning (ML) methods on the testing dataset, and also correctly classifies the actual slope cases, which provides valuable practical and engineering insights for slope stability assessment with weak layers in terms of efficiency and accuracy, especially for practitioners with limited knowledge of slope stability assessment.

Appendices

Appendix 1

As shown in Fig. 

Fig. 14

The comparison of the origin slope and the simplified slope and the corresponding stress distributions

14, the purpose of Experiment 1 is to compare the stress situation of the bottom edge between two slope models (complete and simplified) in order to ensure the correct application of the load. Here, layer 1 and layer 2 are considered to be the same elastic material, E = 100,000 kPa and μ = 0.35. The x-direction displacement of the left boundary and y-direction displacement of the bottom boundary of the slope are constrained. The body forces of layer 1 and layer 2 are − 20.0 kPa and − 19.63 kPa, respectively. The Mises stress results are shown in Fig. 14, and the stress distribution of the two cases is consistent. In addition, the total force in the Y direction of the bottom nodes of the original model and the simplified model is 37,730.8 and 37,730.9, respectively.

The purpose of Experiment 2 is to compare the stability coefficients of the original model and the simplified model. Based on Experiment 1, the slope layers are assigned the Mohr–Coulomb plasticity for layer 1 (c = 33.5 kPa and φ = 11.0°) and layer 2 (c = 11.9 kPa and φ = 20.0°). The bottom boundary condition was changed to displacement constraint in x- and y-directions. The left and right boundary conditions were changed to x-direction displacement constraint only. According to the results, the safety factor of the original model and the simplified model are 1.4 and 1.5, respectively. Other 59 models are analyzed in the same way, and the results of the safety factor are shown in Fig. 

Fig. 15

The analyzed safety factor comparison of the origin slopes and the simplified slopes

15. The safety factor of the simplified model is lower than that of the original model. Compared to the original model, the equivalent load of the simplified model is completely applied to layer 1, resulting in a decrease in the safety factor. However, the R2 remained at 0.84 in both cases, indicating a small deviation. Therefore, this article simplifies the upper slope as an equivalent load in the stability analyses of the slopes.

Appendix 2

The hyperparameters of ELM are the transfer function and the number of hidden neurons, and their relationship with the prediction performance is shown in Fig. 

Fig. 16

Sensitivity analysis of the ELMs on testing dataset

16. It can be seen that the prediction performance of the model is mainly influenced by the transfer function compared to the number of hidden neurons. When Sine and Sigmoidal transfer functions are used, the effect is better than Hardlim.

For SVMs, there are five hyperparameters: standardization, kernel function, polynomial order, kernel scale and box constraint. Among them, polynomial order must be selected when polynomial is selected as the kernel function, and kernel scale must be selected when Gaussian is selected as the kernel function. The relationship between the five hyperparameters and prediction performance is shown in Fig. 

Fig. 17

Sensitivity analysis of the SVMs on testing dataset

17. For parameter sensitivity, model performance is less affected by standardization. For kernel functions, the Gaussian prediction model performs best, followed by the polynomial, and then the linear. Performance is not affected by the box constraint, but is more affected by the polynomial order or kernel scale values for certain kernel functions.

For decision trees, there are three hyperparameters to vary: minimum leaf size, Maximum number of splits and split criterion. The sensitivity of these parameters to the predictive performance is shown in Fig. 

Fig. 18

Sensitivity analysis of the decision trees on testing dataset

18. Compared to the split criterion, minimum leaf size and maximum split number have a strong correlation with the prediction performance. Smaller minimum leaf size and larger maximum split numbers are beneficial for improving the prediction performance of the model. When minimum leaf size = 1, maximum split number = 1024 and split criterion = deviation, the decision tree achieves the best predictive performance.

Overall, the sensitivity analysis of hyperparameters in traditional machine learning is best observed by the control variable method. However, due to the large number of hyperparameters, the sensitivity analysis of hyperparameters in traditional machine learning should be further explored in detail in future research.

Appendix 3

See Table 7.

Table 7 The situations of slope cases