# Study on Dynamic Stability Prediction Model of Slope in Eastern Tibet Section of Sichuan-Tibet Highway

Authors: Tangjin Ye; Tao Shu; Junjie Li; Penghui Zhao; Ying Wang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

The stability of the slope along the middle section of Tibet controls the safety and smoothness of the Sichuan-Tibet highway, which is affected by multiple and uncertain factors such as rainfall. The slope dynamic stability is evaluated to the benefit of that salvager can prepare in advance and preserve timely and accurately. Therefore, engineering treatment scheme in different batches, stages, and grades can be proposed prospectively. Random Forest algorithm was used to rank 10 primary factors: precipitation, earthquake, human factors, groundwater, slope height, slope gradient, dense degree, weathering depth, vegetation, and slope shape. Considering precipitation and earthquake as dynamic factors, a wavelet and NARX dynamic neural network were used to predict the trend and quantity of precipitation and earthquake, followed by developing a dynamic stability evaluation model by combining a fuzzy neural network model with other indexes. Results show that (1) the superposition error in rainfall and earthquake prediction is 0.21%, proving that the ranking of influencing factors is reasonable, and (2) the back-judgment and test accuracy of the dynamic evaluation model are 93.98% and 91.67%, respectively, indicating that the model is accurate and applicable. The model can evaluate the dynamic stability of slopes and provide more reasonable engineering protection countermeasures so that Highway Public Works Department can deal with emergencies and disasters timely and precisely.


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## Body

## 1. Introduction

The eastern Tibet section of Sichuan-Tibet highway, from Jinsha River to Lhasa, crosses three major mountain systems and four major river systems: the Hengduan Mountains, the Himalayas, and Nyainqentanglha mountains and the Jinsha, Lancang, Nujiang, and Yarlung Zangbo rivers [1]. The road shuttles through mountains and valleys, where various geological disasters occur frequently due to the climate, complex geological conditions, and intense tectonic movements. According to incomplete statistics, 3482 disasters have occurred in the eastern Tibet section of Sichuan-Tibet highway, of which debris flows, collapses, and landslides account for 85.6% of the total [2]. In addition to being controlled by internal factors, slope stability is often induced by rainfall and earthquake dynamic factors, showing dynamic stability process and progressive failure phenomenon. Consequently, a large amount of manpower and material resources have been invested in the maintenance of this section. Although the dangers posed by disasters have been alleviated to some extent, there are still many hidden dangers. Therefore, it is of great significance to determine the dynamic stability of the slope and to rectify it in batches, stages, and grades.Due to the limitations in technology and insufficient collected information, analogy analysis was the most commonly used method in early slope stability prediction; however, analogy analysis is highly subjective and uncertain, making it difficult to formulate a unified evaluation standard [3]. In 1968, based on the three-stage theory of creep failure, Saito [4] presented a basic empirical method and diagram for landslide prediction and successfully applied it to real-life cases, creating a precedent for the quantitative prediction of slope stability. In 1992, Lee and Sterling developed a model recognition system of slope failure pattern based on neural networks [5]. Because the neural network adopts the idea of a “black box,” there is no longer a need to clarify the relationships between factors in the system, and it is thus widely used for slope stability prediction. In 1994, Sah et al. used the artificial neural network method to study slope stability prediction, based on a more efficient use of existing research results [6]. In 2005, Ercanoglu used backpropagation (BP) artificial neural network to evaluate the stability of the Se Bartin (Turkey) landslide in the West Black Sea region. After dividing the geological disasters, it was verified that the prediction accuracy of landslide stability was 82.5% [7]. In 2014, Polykretis et al. [8] used artificial neural network and 8 landslide indexes, including land coverage, slope, and geological conditions, to make a comparative study of the landslide stability of the Creole River Basin in the Peloponnese Peninsula; the evaluation accuracy of landslides in the basin was found to be 84%, demonstrating that the artificial neural network was a feasible method for slope stability evaluation. In 2017, Wang [9] identified the factor influencing slope stability through principal component analysis and took this factor as the eigenvector of the support vector machine (SVM), before treating the support vector parameters using particle swarm optimization to establish the slope stability evaluation model. These results show that the PCA-PSO-SVM model is fast and has high prediction accuracy [10]. In 2018, considering factors such as potential slide height, up and down slide surface dip angles, slope dip angle, and slide area, Dai et al. established the GA-BP prediction model of safety factors for slope stability after optimizing the weight and threshold of the BP neural network using a genetic algorithm [11]. In 2018, Wen and Zhu used statistical analysis of a large number of engineering examples and selected pore water pressure, cohesion, and other parameters as the main discrimination indicators [12]. They used a factor analysis model to perform attribute reduction on the data, extracted common factors, and used a simulated annealing particle swarm optimization to optimize the parameters of the limit learning machine, thereby improving the convergence speed and prediction accuracy. Most recently, in 2019, Liu used the particle swarm optimization algorithm to search and iterate for obtaining the optimal parameters of the SVM model, avoiding the blindness and randomness of parameters selected artificially by SVM [13, 14]. The calculation speed is fast [15], with an average relative error of 3.58% [16]. In recent years, achievements had been made in the application of neural networks in slope engineering [17]. However, much of this work had been focused on the static stability analysis of highway slope, which mainly concentrated in the mine and the embankment slope research. Therefore, the dynamic stability analysis of a large number of highway slopes in eastern Tibet section of Sichuan-Tibet Highway is still in blank.Concerning slope disasters in the eastern Tibet section of the Sichuan-Tibet highway, Zhou et al. investigated the types and characteristics of all geological disasters in this region [18]. Liao et al. systematically analyzed the influence of geological disasters on temporary construction, subgrade, bridge, tunnel, and other engineering constructions and put forward targeted safety control measures [19]. Wang et al. found that areas with a higher frequency of major geological disasters along the Sichuan-Tibet highway (within Tibet) are mainly concentrated in three major sections: the Palong Zangbu riverside section from Dongjiu to Ranwu, the Lengqu riverside section from Baxoi to Nujiang bridge, and the Xiqu riverside section from east Zongla mountain to Jinshajiang bridge [20]. Fan et al. quantitatively analyzed the influence of various factors on large-scale geological disasters along the Ranwu–Lulang section, which, to some extent, solved the problem of the quantitative analysis of the influencing factors [21]. Ding et al. analyzed the main influencing factors of slope stability through information entropy and established an evaluation model for debris slope static stability based on SVM, for which the accuracy was shown to be greater than 86% [22]. Furthermore, based on Random Forest theory, a slope stability evaluation model was established. This model evaluated slope stability according to the importance of the calculated influencing factors and recorded an accuracy of more than 94.44% [23].In this paper, all the parameters of the unstable slope in the eastern Tibet section of Sichuan-Tibet highway were collected, and the factors affecting slope stability were extracted and quantified under Random Forest, after which the main factors were sequenced and analyzed. It is known that slope stability is significantly affected by precipitation and earthquakes, both of which are dynamic. Therefore, wavelet analysis and NARX dynamic neural network were used to predict these parameters, after which they were combined with other major factors. Precipitation and earthquakes were taken as dynamic factors to establish the dynamic stability evaluation model of slope under the use of a fuzzy neural network model. Model construction of dynamic stability of slope is shown in Figure1. It is hoped that the dynamic stability evaluation of the slope stability can be carried out, and the reference can be provided for the management of the highway in different batches, stages, and grades.Figure 1
Model construction of dynamic stability of slope (WA is an abbreviation of wavelet analysis, NARX is the abbreviation of NARX neural network, RF is the abbreviation of Random Forest algorithm, and T-S is the abbreviation of fuzzy neural network).


## 2. Data Source and Characteristics of Slope

### 2.1. Slope Data Source

During the period from June 2015 to July 2019, a comprehensive survey of soil slopes within 1365 km of the Jinsha River, Qushui section, was conducted. 143 sets of slope data were collected along the highway, of which 136 were found to be valid after screening. These parameters were summarized as 5 main influencing factors and 26 indicators. The field data acquisition area can be seen in Figure2.Figure 2
Field data acquisition area.


### 2.2. Slope Characteristics

The main components of the slope are slope wash, eluvium, alluvial deposits, and glacial till, which are evenly distributed along the Sichuan-Tibet highway but predominantly concentrated in mountain valley sections with abundant rainfall, such as the Ranwu to Lulang and Haitonggou sections. The slope is mainly in the range of 30°–40°, which is relatively sensitive to stability. Due to the combined effects of precipitation, earthquakes, and road construction, the slope is prone to instability and damage, resulting in road congestion, which is the main type of geological disaster. Congestion is relatively high risk and is hard to control. Many measures, such as retaining walls, anchoring, and antisliding piles, have been adopted but with limited effect.


## 2.1. Slope Data Source

During the period from June 2015 to July 2019, a comprehensive survey of soil slopes within 1365 km of the Jinsha River, Qushui section, was conducted. 143 sets of slope data were collected along the highway, of which 136 were found to be valid after screening. These parameters were summarized as 5 main influencing factors and 26 indicators. The field data acquisition area can be seen in Figure2.Figure 2
Field data acquisition area.


## 2.2. Slope Characteristics

The main components of the slope are slope wash, eluvium, alluvial deposits, and glacial till, which are evenly distributed along the Sichuan-Tibet highway but predominantly concentrated in mountain valley sections with abundant rainfall, such as the Ranwu to Lulang and Haitonggou sections. The slope is mainly in the range of 30°–40°, which is relatively sensitive to stability. Due to the combined effects of precipitation, earthquakes, and road construction, the slope is prone to instability and damage, resulting in road congestion, which is the main type of geological disaster. Congestion is relatively high risk and is hard to control. Many measures, such as retaining walls, anchoring, and antisliding piles, have been adopted but with limited effect.


## 3. Analysis of Influencing Factors

### 3.1. Data Preprocessing

According to field survey and qualitative analysis of slope, 10 indexes were selected from 26 indicators as follows: human factors (X1), earthquake (X2), groundwater (X3), precipitation (X4), slope height (X5), slope gradient (X6), slope shape (X7), dense degree (X8), vegetation coverage (X9), and weathering depth (X10). The data are shown in Table1.Table 1
Partial sample original data.
SampleX1X2X3X4X5X6X7X8X9X101LittleEffectWater seepage511.92441ConvexMedium compact31%Unweathered2MediumEffectNone414.112537IrregularIncompact74%Slightly weathered3TinyNo effectWetted451.43237LinearCompact67%Slightly weathered……………………………134MediumNo effectWetted414.16130IrregularMedium compact79%Slightly weathered135LittleEffectWater seepage4442138IrregularIncompact95%Medium weathered136LargeEffectNone5294042ConcaveSlightly compact88%UnweatheredTo quantitatively calculate the order of main influencing factors, 5 qualitative evaluation indexes were divided into 5 categories, which could be assign values and quantize. Through expert scoring, the values of evaluation indexes were between 0 and 1. 0 represents minimum effect, and 1 represents maximum effect. The classification and standardization of evaluation factors of debris slope stability are shown in Table2.Table 2
Classification and standardization of evaluation factors of debris slope stability.
Evaluation indexesIndex classification standard (score)[0, 0.2](0.2, 0.4](0.4, 0.6](0.6, 0.8](0.8, 1.0]Human factorsTinyLittleMediumLargeHugeGround waterNoneWettedWater seepageObvious water seepageSprings exposedSlope shapeStep-shapedLinearIrregularConcaveConvexDense degreeCementationCompactMedium compactSlightly compactIncompactWeathering depthUnweatheredSlightly weatheredMedium weatheredStrongly weatheredFully weatheredThe earthquake is represented by Boolean value; 1 represents that there is an earthquake effecting, and 0 represents there is no earthquake effecting. Meanwhile, the vegetation impact is represented by “100%-vegetation coverage.” The evaluation indicators have all become dimensionless value by scoring, as shown in Table3.Table 3
Quantified slope sample data.
SampleX1X2X3X4X5X6X7X8X9X1010.3210.54511.924410.960.7669%0.1120.5610.00414.1125370.490.9126%0.3430.0800.34451.432370.330.2533%0.23……………………………1340.5100.29414.161300.540.7321%0.251350.3710.5644421380.540.885%0.561360.7510.0352940420.680.5512%0.00Combined with the characteristics of data, maximum and minimum methods were used for normalization. The formula is as follows:(1)vs=v−vminvmax−vmin.In the above formula,vs is the normalized value, v is the original value, and vmax and vmin, respectively, represent the maximum and minimum values of the attribute in the dataset.After processing, each slope stability evaluation index is normalized, as shown in Table4.Table 4
Part of slope data after normalization.
SampleX1X2X3X4X5X6X7X8X9X1010.321.000.650.350.130.810.970.790.730.1520.571.000.000.210.830.560.370.960.250.4630.080.000.410.260.190.560.170.180.330.31……………………………1340.520.000.350.210.390.130.440.750.200.341350.381.000.670.250.110.630.440.930.020.771360.771.000.040.370.240.880.620.540.100.00


### 3.2. Analysis of Factors Affecting Slope Stability

Random Forest (RF) is a type of classification and regression model that is both efficient and intuitive method [24, 25]. The Random Forest algorithm was proposed by Leo Breiam and Adele Cutler, which combines Breimans’ “bootstrap aggregating” and Ho’s “random subspace” methods [26].The Random Forest algorithm is, in essence, a classifier containing multiple decision trees that take the form of random methods and are also called random decision trees. There is no correlation between trees in Random Forest. When the test data enters the Random Forest, it is classified by each decision tree, and the tree with the most classification results is taken as the final result.


#### 3.2.1. Resampling Using Bootstrap Method [27]

Supposing that setS contains n different samples {x1, x2, …, xn}, if one sample is extracted from the complete set S at a time, extracting n times independently to form a new set S∗, then the probability that set S∗ does not contain a certain sample xi (i = 1, 2, …, n) is given as follows:(2)p=1−1nn.Whenn ⟶ ∞,(3)limn⟶∞p=limn⟶∞1−1nn=e−1≈0.37.Therefore, although the total number of samples in setS∗ is equal to that in S (all of which are n), the new set S∗ may contain duplicate samples. Set S∗ contains only approximately (1–0.368) × 100% = 63.2% of the samples in set S after removing the duplicate samples.


#### 3.2.2. Overview of Bagging Algorithm

The Bagging algorithm is the earliest integrated learning algorithm, and its basic concept is shown in Figure3 [28].Figure 3
Basic concept of the Bagging algorithm.The specific steps of the algorithm can be described as follows [29]:(1)
The Bootstrap method is used to resample and randomly generateT training sets S1, S2, …, ST.(2)
Each training set is used to generate the corresponding decision treeC1, C2, …, CT.(3)
For the test set samplex, each decision tree is used to test and obtain the corresponding category C1(x), C2(x), …, CT(x).(4)
Using the voting method, the category with the most output inT decision trees is taken as the category to which the test set sample x is deemed to belong.After processing, the data needs to be sampled, which mainly includes random sampling and stratified sampling. Firstly, stratified sampling is used to determine the accuracy of data and improve the recognition ability of model. Before evaluation, the data should be divided into training set and testing set, which were used for model training and in-sample testing. After that, the remaining samples from the above stratified sampling were randomly sampled; 80% of them were selected as training sets, while the remaining 20% were test sets. After the above processing, 136 groups of effective slope data were finally determined for factor analysis.


#### 3.2.3. Variable Importance Measures

In this paper, the variable importance mark (VIM) of random forest was used to evaluate the characteristics of each slope stability evaluation index. The process is as follows: calculate the contribution of each index feature to each decision tree in the random forest and take the average; the contribution degree of each index feature is compared and ranked [30]. The contribution of each feature in random forest can usually be measured by Gini index and out-of-bag (OOB) error rate [31]. In this paper, the importance of feature vectors was measured by out-of-bag data observation. Out-of-bag (OOB) data refers to the samples that were not selected after self-help sample aggregation. Therefore, the OOB error is often used to test the generalization error of random forest.(4)EOOBG=1N∑n=1Nerryn,Gn−xn,where equation (4) is the decision tree that only includes OOB.The method of feature importance calculation using OOB is to reorder the features of each index in OOB samples; by calculating the “permutation importance,” the sorting of index eigenvalues is realized. The “permutation importance” is the importance of random arrangement, andVI(t) (xi) is the importance of characteristic variable xi obtained from decision tree gI; the calculation formula is(5)VIxi=EOOBG−EOOBpG.EOOBpG is the error of OOB samples rearranged randomly.Finally, the importance value of each eigenvalue is the average value of all decision trees as follows:(6)VIxi=∑t=1ntreeVItxintree.Following this, the Random Forest was used for calculating and analyzing the influence factors of each type. The regression effect of the Random Forest model is shown in Figure4. The correlation coefficient R is 0.99993, showing that a model based on Random Forest influence factor analysis has good fitting and convergence data. The training set coincides with the expected value, indicating that the model is highly reliable and meets analysis requirements. It can be seen from the model error diagram in Figure 5 that, in the Random Forest, when the number of decision trees is 50, the error is greatly reduced to the value of 2 × 10−3%. For increased accuracy, more than 200 decision trees must be selected; therefore, this study uses 200 trees for calculation and analysis.Figure 4
Regression effect of model.Figure 5
Error graph of model.Results of the calculation are shown in wavelet, as seen in Figure6, demonstrating that the order of importance of influencing factors of slope is as follows: precipitation, earthquake, slope gradient, human factors, compactness, slope shape, groundwater, slope height, vegetation, and weathering depth. This ordering of influencing factors is considered reasonable by comparative analysis [32].Figure 6
Ordination graph of influencing factors of slope.


## 3.1. Data Preprocessing

According to field survey and qualitative analysis of slope, 10 indexes were selected from 26 indicators as follows: human factors (X1), earthquake (X2), groundwater (X3), precipitation (X4), slope height (X5), slope gradient (X6), slope shape (X7), dense degree (X8), vegetation coverage (X9), and weathering depth (X10). The data are shown in Table1.Table 1
Partial sample original data.
SampleX1X2X3X4X5X6X7X8X9X101LittleEffectWater seepage511.92441ConvexMedium compact31%Unweathered2MediumEffectNone414.112537IrregularIncompact74%Slightly weathered3TinyNo effectWetted451.43237LinearCompact67%Slightly weathered……………………………134MediumNo effectWetted414.16130IrregularMedium compact79%Slightly weathered135LittleEffectWater seepage4442138IrregularIncompact95%Medium weathered136LargeEffectNone5294042ConcaveSlightly compact88%UnweatheredTo quantitatively calculate the order of main influencing factors, 5 qualitative evaluation indexes were divided into 5 categories, which could be assign values and quantize. Through expert scoring, the values of evaluation indexes were between 0 and 1. 0 represents minimum effect, and 1 represents maximum effect. The classification and standardization of evaluation factors of debris slope stability are shown in Table2.Table 2
Classification and standardization of evaluation factors of debris slope stability.
Evaluation indexesIndex classification standard (score)[0, 0.2](0.2, 0.4](0.4, 0.6](0.6, 0.8](0.8, 1.0]Human factorsTinyLittleMediumLargeHugeGround waterNoneWettedWater seepageObvious water seepageSprings exposedSlope shapeStep-shapedLinearIrregularConcaveConvexDense degreeCementationCompactMedium compactSlightly compactIncompactWeathering depthUnweatheredSlightly weatheredMedium weatheredStrongly weatheredFully weatheredThe earthquake is represented by Boolean value; 1 represents that there is an earthquake effecting, and 0 represents there is no earthquake effecting. Meanwhile, the vegetation impact is represented by “100%-vegetation coverage.” The evaluation indicators have all become dimensionless value by scoring, as shown in Table3.Table 3
Quantified slope sample data.
SampleX1X2X3X4X5X6X7X8X9X1010.3210.54511.924410.960.7669%0.1120.5610.00414.1125370.490.9126%0.3430.0800.34451.432370.330.2533%0.23……………………………1340.5100.29414.161300.540.7321%0.251350.3710.5644421380.540.885%0.561360.7510.0352940420.680.5512%0.00Combined with the characteristics of data, maximum and minimum methods were used for normalization. The formula is as follows:(1)vs=v−vminvmax−vmin.In the above formula,vs is the normalized value, v is the original value, and vmax and vmin, respectively, represent the maximum and minimum values of the attribute in the dataset.After processing, each slope stability evaluation index is normalized, as shown in Table4.Table 4
Part of slope data after normalization.
SampleX1X2X3X4X5X6X7X8X9X1010.321.000.650.350.130.810.970.790.730.1520.571.000.000.210.830.560.370.960.250.4630.080.000.410.260.190.560.170.180.330.31……………………………1340.520.000.350.210.390.130.440.750.200.341350.381.000.670.250.110.630.440.930.020.771360.771.000.040.370.240.880.620.540.100.00


## 3.2. Analysis of Factors Affecting Slope Stability

Random Forest (RF) is a type of classification and regression model that is both efficient and intuitive method [24, 25]. The Random Forest algorithm was proposed by Leo Breiam and Adele Cutler, which combines Breimans’ “bootstrap aggregating” and Ho’s “random subspace” methods [26].The Random Forest algorithm is, in essence, a classifier containing multiple decision trees that take the form of random methods and are also called random decision trees. There is no correlation between trees in Random Forest. When the test data enters the Random Forest, it is classified by each decision tree, and the tree with the most classification results is taken as the final result.


### 3.2.1. Resampling Using Bootstrap Method [27]

Supposing that setS contains n different samples {x1, x2, …, xn}, if one sample is extracted from the complete set S at a time, extracting n times independently to form a new set S∗, then the probability that set S∗ does not contain a certain sample xi (i = 1, 2, …, n) is given as follows:(2)p=1−1nn.Whenn ⟶ ∞,(3)limn⟶∞p=limn⟶∞1−1nn=e−1≈0.37.Therefore, although the total number of samples in setS∗ is equal to that in S (all of which are n), the new set S∗ may contain duplicate samples. Set S∗ contains only approximately (1–0.368) × 100% = 63.2% of the samples in set S after removing the duplicate samples.


### 3.2.2. Overview of Bagging Algorithm

The Bagging algorithm is the earliest integrated learning algorithm, and its basic concept is shown in Figure3 [28].Figure 3
Basic concept of the Bagging algorithm.The specific steps of the algorithm can be described as follows [29]:(1)
The Bootstrap method is used to resample and randomly generateT training sets S1, S2, …, ST.(2)
Each training set is used to generate the corresponding decision treeC1, C2, …, CT.(3)
For the test set samplex, each decision tree is used to test and obtain the corresponding category C1(x), C2(x), …, CT(x).(4)
Using the voting method, the category with the most output inT decision trees is taken as the category to which the test set sample x is deemed to belong.After processing, the data needs to be sampled, which mainly includes random sampling and stratified sampling. Firstly, stratified sampling is used to determine the accuracy of data and improve the recognition ability of model. Before evaluation, the data should be divided into training set and testing set, which were used for model training and in-sample testing. After that, the remaining samples from the above stratified sampling were randomly sampled; 80% of them were selected as training sets, while the remaining 20% were test sets. After the above processing, 136 groups of effective slope data were finally determined for factor analysis.


### 3.2.3. Variable Importance Measures

In this paper, the variable importance mark (VIM) of random forest was used to evaluate the characteristics of each slope stability evaluation index. The process is as follows: calculate the contribution of each index feature to each decision tree in the random forest and take the average; the contribution degree of each index feature is compared and ranked [30]. The contribution of each feature in random forest can usually be measured by Gini index and out-of-bag (OOB) error rate [31]. In this paper, the importance of feature vectors was measured by out-of-bag data observation. Out-of-bag (OOB) data refers to the samples that were not selected after self-help sample aggregation. Therefore, the OOB error is often used to test the generalization error of random forest.(4)EOOBG=1N∑n=1Nerryn,Gn−xn,where equation (4) is the decision tree that only includes OOB.The method of feature importance calculation using OOB is to reorder the features of each index in OOB samples; by calculating the “permutation importance,” the sorting of index eigenvalues is realized. The “permutation importance” is the importance of random arrangement, andVI(t) (xi) is the importance of characteristic variable xi obtained from decision tree gI; the calculation formula is(5)VIxi=EOOBG−EOOBpG.EOOBpG is the error of OOB samples rearranged randomly.Finally, the importance value of each eigenvalue is the average value of all decision trees as follows:(6)VIxi=∑t=1ntreeVItxintree.Following this, the Random Forest was used for calculating and analyzing the influence factors of each type. The regression effect of the Random Forest model is shown in Figure4. The correlation coefficient R is 0.99993, showing that a model based on Random Forest influence factor analysis has good fitting and convergence data. The training set coincides with the expected value, indicating that the model is highly reliable and meets analysis requirements. It can be seen from the model error diagram in Figure 5 that, in the Random Forest, when the number of decision trees is 50, the error is greatly reduced to the value of 2 × 10−3%. For increased accuracy, more than 200 decision trees must be selected; therefore, this study uses 200 trees for calculation and analysis.Figure 4
Regression effect of model.Figure 5
Error graph of model.Results of the calculation are shown in wavelet, as seen in Figure6, demonstrating that the order of importance of influencing factors of slope is as follows: precipitation, earthquake, slope gradient, human factors, compactness, slope shape, groundwater, slope height, vegetation, and weathering depth. This ordering of influencing factors is considered reasonable by comparative analysis [32].Figure 6
Ordination graph of influencing factors of slope.


## 3.2.1. Resampling Using Bootstrap Method [27]

Supposing that setS contains n different samples {x1, x2, …, xn}, if one sample is extracted from the complete set S at a time, extracting n times independently to form a new set S∗, then the probability that set S∗ does not contain a certain sample xi (i = 1, 2, …, n) is given as follows:(2)p=1−1nn.Whenn ⟶ ∞,(3)limn⟶∞p=limn⟶∞1−1nn=e−1≈0.37.Therefore, although the total number of samples in setS∗ is equal to that in S (all of which are n), the new set S∗ may contain duplicate samples. Set S∗ contains only approximately (1–0.368) × 100% = 63.2% of the samples in set S after removing the duplicate samples.


## 3.2.2. Overview of Bagging Algorithm

The Bagging algorithm is the earliest integrated learning algorithm, and its basic concept is shown in Figure3 [28].Figure 3
Basic concept of the Bagging algorithm.The specific steps of the algorithm can be described as follows [29]:(1)
The Bootstrap method is used to resample and randomly generateT training sets S1, S2, …, ST.(2)
Each training set is used to generate the corresponding decision treeC1, C2, …, CT.(3)
For the test set samplex, each decision tree is used to test and obtain the corresponding category C1(x), C2(x), …, CT(x).(4)
Using the voting method, the category with the most output inT decision trees is taken as the category to which the test set sample x is deemed to belong.After processing, the data needs to be sampled, which mainly includes random sampling and stratified sampling. Firstly, stratified sampling is used to determine the accuracy of data and improve the recognition ability of model. Before evaluation, the data should be divided into training set and testing set, which were used for model training and in-sample testing. After that, the remaining samples from the above stratified sampling were randomly sampled; 80% of them were selected as training sets, while the remaining 20% were test sets. After the above processing, 136 groups of effective slope data were finally determined for factor analysis.


## 3.2.3. Variable Importance Measures

In this paper, the variable importance mark (VIM) of random forest was used to evaluate the characteristics of each slope stability evaluation index. The process is as follows: calculate the contribution of each index feature to each decision tree in the random forest and take the average; the contribution degree of each index feature is compared and ranked [30]. The contribution of each feature in random forest can usually be measured by Gini index and out-of-bag (OOB) error rate [31]. In this paper, the importance of feature vectors was measured by out-of-bag data observation. Out-of-bag (OOB) data refers to the samples that were not selected after self-help sample aggregation. Therefore, the OOB error is often used to test the generalization error of random forest.(4)EOOBG=1N∑n=1Nerryn,Gn−xn,where equation (4) is the decision tree that only includes OOB.The method of feature importance calculation using OOB is to reorder the features of each index in OOB samples; by calculating the “permutation importance,” the sorting of index eigenvalues is realized. The “permutation importance” is the importance of random arrangement, andVI(t) (xi) is the importance of characteristic variable xi obtained from decision tree gI; the calculation formula is(5)VIxi=EOOBG−EOOBpG.EOOBpG is the error of OOB samples rearranged randomly.Finally, the importance value of each eigenvalue is the average value of all decision trees as follows:(6)VIxi=∑t=1ntreeVItxintree.Following this, the Random Forest was used for calculating and analyzing the influence factors of each type. The regression effect of the Random Forest model is shown in Figure4. The correlation coefficient R is 0.99993, showing that a model based on Random Forest influence factor analysis has good fitting and convergence data. The training set coincides with the expected value, indicating that the model is highly reliable and meets analysis requirements. It can be seen from the model error diagram in Figure 5 that, in the Random Forest, when the number of decision trees is 50, the error is greatly reduced to the value of 2 × 10−3%. For increased accuracy, more than 200 decision trees must be selected; therefore, this study uses 200 trees for calculation and analysis.Figure 4
Regression effect of model.Figure 5
Error graph of model.Results of the calculation are shown in wavelet, as seen in Figure6, demonstrating that the order of importance of influencing factors of slope is as follows: precipitation, earthquake, slope gradient, human factors, compactness, slope shape, groundwater, slope height, vegetation, and weathering depth. This ordering of influencing factors is considered reasonable by comparative analysis [32].Figure 6
Ordination graph of influencing factors of slope.


## 4. Precipitation and Earthquake Prediction

Dynamic slope stability depends considerably on external disturbances, with rainfall and earthquakes being the most sensitive and direct factors [33]. As these factors change frequently with time, it is necessary to predict precipitation and earthquakes in the dynamic evaluations of slope stability. Since there is no rainfall superposition forecast in meteorological department, it is used to forecast rainfall [34]. In this paper, we used Wavelet to analyze their trends. Wavelet transform and wavelet decomposition in Wavelet were used, respectively, to decompose the original precipitation and earthquake data and obtain the corresponding characteristic curve and its degree of fitting. Thereafter, their changing trends were obtained by analyzing the characteristic curve and variogram [35]. Finally, NARX dynamic neural network was used to predict precipitation and earthquake data, which can provide dynamic data for dynamic stability evaluation.


### 4.1. Precipitation and Earthquake Trend Prediction

The isoline diagram of the real part of a wavelet coefficient can reflect the periodic changes in the precipitation series over different time scales and its distribution in the time domain and can then judge the trend of precipitation over different time scales in the future. To clearly illustrate the role of the isoline in the real part of wavelet coefficients when analyzing multiple time scales of precipitation, it can be seen from Figure7 that the precipitation has oscillation periods of quasi-22, -12, -8, and 4-year timescales, which are shown to have influenced precipitation in the period from 1955 to 2018. The quasi-10-year and quasi-15-year oscillation periods are the main periods affecting precipitation. Figure 8 shows the total characteristics of precipitation, allowing the trend of precipitation to be discerned.Figure 7
Wavelet variance diagram.Figure 8
Total characteristic timescale scheme.Precipitation data from seven meteorological stations along the eastern Tibet section of Sichuan-Tibet highway were analyzed using the same method. Data were used from stations including Lhasa, Maizhokunggar County, Nyingchi, Bome County, Baxoi County, Zogang County, and Markam County. The predicted trend curves of Lhasa and Nyingchi meteorological stat are shown in Figures9 and 10.Figure 9
Precipitation tendency at Zogang.Figure 10
Precipitation tendency at Baxoi.Since the spatial location of the earthquake is closely related to the fault zone, the relative location of the active fault and the highway should be fully considered when evaluating the seismic zoning of the Batang-Lhasa section. The division of the precipitation section should also be combined to conveniently evaluate slope stability. With reference to earthquake-prone areas, hot spring locations, and active fault zones, the region is divided as follows: Lhasa-Mira mountain section (A section), Mira mountain-Bahe section (B section), Bahe-Tongmai section (C section), Tongmai-Ranwu section (D section), Ranwu-Yela mountain section (E section), Yela mountain-Dongda mountain section (F section), and Dongda mountain-Jinsha river section (G section). The earthquake occurrence trend prediction obtained for the 7 sections is shown in Figure11.Figure 11
Earthquake occurrence trend curves of the seven studied sections along the Sichuan-Tibet highway.


### 4.2. Precipitation and Earthquake Data Prediction

NARX dynamic neural network has both feedback and memory functions and the ability to learn automatically [36]. Through feedback and memory, the neural network can retain data from the previous period and add it to the next data calculation, making both network dynamic and retained system information more complete. Based on multiresolution functions of wavelet analysis and the nonlinear approximation ability of artificial neural network, the NARX dynamic neural network model has high prediction accuracy, is based on a simple principle, and has fast calculation speed. Therefore, the NARX dynamic neural network was used to predict the precipitation and number of earthquakes.The parameters of the dynamic neural network prediction model include input delay, output delay, the number of hidden neurons, training set proportion, verification set proportion, and test set proportion. The parameters used from the NARX neural network prediction model set in this paper are shown in Table5.Table 5
Parameters in NARX neural network prediction model.
Input delayOutput delayNumber of hidden neuronsTraining set proportionVerification set proportionTest set proportion (%)1 : 51 : 52570%15%15Taking the precipitation data of seven weather stations as the input value in the NARX neural network and using the NARX dynamic neural network to make time series predictions, the error analysis results are as follows.In the training of the NARX neural network model, the validation set error remains essentially unchanged after four trainings, demonstrating that the training can be ended, and the error in the entire data is 0.21% at this time. The lower number of yellow lines (error lines) in Figure12 denotes the better prediction effect inherent to the NARX neural network. The error in Figure 13 should be largest when the lag is 0. In other cases, it is best to not exceed the confidence interval. By analyzing the regression effect diagram of NARX dynamic neural network, the correlation coefficient R is 0.99993, indicating that the training model is excellent and can be used for prediction. Using this model, the prediction of monthly precipitation for the seven sections along the line throughout 2019 is shown in Table 6.Figure 12
Error in prediction effect of neural network.Figure 13
Autocorrelation of error.Table 6
Monthly precipitation prediction of seven weather stations in 2019 (mm).
Weather stationJanFebMarAprMayJunJulAugSeptOctNovDecLhasa0.630.842.526.8124.6169.52120.1128.767.328.451.280.80Mozhu2.913.3720.053.774.75131.3132.1123.4126.736.83.550.91Linzhi0.630.842.526.8124.6169.52120.1128.767.328.451.280.80Bomi5.2125.084.999.9103.3141.610275.97104.283.517.905.54Basu0.201.685.1215.215.5225.3852.4646.8025.936.181.781.08Zuogong0.762.398.7017.728.6972.32158102.247.6314.94.210.45Mangkang1.323.759.3825.633.08102.0182.8141.084.0516.43.661.20For earthquakes, the NARX dynamic neural network was used in a similar way as for precipitation prediction. Based on earthquake data with magnitude ≥3 collected in the Lhasa-Batang section from 1985 to 2018, seven sections were predicted according to the trend. The predicted data of earthquakes with magnitude ≥3 occurring in each section in 2019 are shown in Table7.Table 7
The number of predicted earthquakes from Lhasa to Jinsha river in 2019.
SectionABCDEFGTimes (time/year)0032010


## 4.1. Precipitation and Earthquake Trend Prediction

The isoline diagram of the real part of a wavelet coefficient can reflect the periodic changes in the precipitation series over different time scales and its distribution in the time domain and can then judge the trend of precipitation over different time scales in the future. To clearly illustrate the role of the isoline in the real part of wavelet coefficients when analyzing multiple time scales of precipitation, it can be seen from Figure7 that the precipitation has oscillation periods of quasi-22, -12, -8, and 4-year timescales, which are shown to have influenced precipitation in the period from 1955 to 2018. The quasi-10-year and quasi-15-year oscillation periods are the main periods affecting precipitation. Figure 8 shows the total characteristics of precipitation, allowing the trend of precipitation to be discerned.Figure 7
Wavelet variance diagram.Figure 8
Total characteristic timescale scheme.Precipitation data from seven meteorological stations along the eastern Tibet section of Sichuan-Tibet highway were analyzed using the same method. Data were used from stations including Lhasa, Maizhokunggar County, Nyingchi, Bome County, Baxoi County, Zogang County, and Markam County. The predicted trend curves of Lhasa and Nyingchi meteorological stat are shown in Figures9 and 10.Figure 9
Precipitation tendency at Zogang.Figure 10
Precipitation tendency at Baxoi.Since the spatial location of the earthquake is closely related to the fault zone, the relative location of the active fault and the highway should be fully considered when evaluating the seismic zoning of the Batang-Lhasa section. The division of the precipitation section should also be combined to conveniently evaluate slope stability. With reference to earthquake-prone areas, hot spring locations, and active fault zones, the region is divided as follows: Lhasa-Mira mountain section (A section), Mira mountain-Bahe section (B section), Bahe-Tongmai section (C section), Tongmai-Ranwu section (D section), Ranwu-Yela mountain section (E section), Yela mountain-Dongda mountain section (F section), and Dongda mountain-Jinsha river section (G section). The earthquake occurrence trend prediction obtained for the 7 sections is shown in Figure11.Figure 11
Earthquake occurrence trend curves of the seven studied sections along the Sichuan-Tibet highway.


## 4.2. Precipitation and Earthquake Data Prediction

NARX dynamic neural network has both feedback and memory functions and the ability to learn automatically [36]. Through feedback and memory, the neural network can retain data from the previous period and add it to the next data calculation, making both network dynamic and retained system information more complete. Based on multiresolution functions of wavelet analysis and the nonlinear approximation ability of artificial neural network, the NARX dynamic neural network model has high prediction accuracy, is based on a simple principle, and has fast calculation speed. Therefore, the NARX dynamic neural network was used to predict the precipitation and number of earthquakes.The parameters of the dynamic neural network prediction model include input delay, output delay, the number of hidden neurons, training set proportion, verification set proportion, and test set proportion. The parameters used from the NARX neural network prediction model set in this paper are shown in Table5.Table 5
Parameters in NARX neural network prediction model.
Input delayOutput delayNumber of hidden neuronsTraining set proportionVerification set proportionTest set proportion (%)1 : 51 : 52570%15%15Taking the precipitation data of seven weather stations as the input value in the NARX neural network and using the NARX dynamic neural network to make time series predictions, the error analysis results are as follows.In the training of the NARX neural network model, the validation set error remains essentially unchanged after four trainings, demonstrating that the training can be ended, and the error in the entire data is 0.21% at this time. The lower number of yellow lines (error lines) in Figure12 denotes the better prediction effect inherent to the NARX neural network. The error in Figure 13 should be largest when the lag is 0. In other cases, it is best to not exceed the confidence interval. By analyzing the regression effect diagram of NARX dynamic neural network, the correlation coefficient R is 0.99993, indicating that the training model is excellent and can be used for prediction. Using this model, the prediction of monthly precipitation for the seven sections along the line throughout 2019 is shown in Table 6.Figure 12
Error in prediction effect of neural network.Figure 13
Autocorrelation of error.Table 6
Monthly precipitation prediction of seven weather stations in 2019 (mm).
Weather stationJanFebMarAprMayJunJulAugSeptOctNovDecLhasa0.630.842.526.8124.6169.52120.1128.767.328.451.280.80Mozhu2.913.3720.053.774.75131.3132.1123.4126.736.83.550.91Linzhi0.630.842.526.8124.6169.52120.1128.767.328.451.280.80Bomi5.2125.084.999.9103.3141.610275.97104.283.517.905.54Basu0.201.685.1215.215.5225.3852.4646.8025.936.181.781.08Zuogong0.762.398.7017.728.6972.32158102.247.6314.94.210.45Mangkang1.323.759.3825.633.08102.0182.8141.084.0516.43.661.20For earthquakes, the NARX dynamic neural network was used in a similar way as for precipitation prediction. Based on earthquake data with magnitude ≥3 collected in the Lhasa-Batang section from 1985 to 2018, seven sections were predicted according to the trend. The predicted data of earthquakes with magnitude ≥3 occurring in each section in 2019 are shown in Table7.Table 7
The number of predicted earthquakes from Lhasa to Jinsha river in 2019.
SectionABCDEFGTimes (time/year)0032010


## 5. Dynamic Stability Analysis of Slope

### 5.1. Principle of Dynamic Stability Discrimination

Fuzzy mathematics is used for describing, studying, and evaluating the fuzzy characteristics of algorithms [37, 38]. The core principle of fuzzy mathematics is membership grade μfu, a number between [0, 1], which refers to the membership degree of an element u belonging to fuzzy subset f. The closer this is to 0, the lesser the degree to which u belongs to subset f; accordingly, the closer it is to 1, the greater the degree of belonging is.The membership function formula used in this paper is as follows:(7)μfu=1d2/d12/q−1+1.In the above formula, q is the fuzzy weighted index, whose value is (1, +∞), and d1 and d2 are the Euclidean distances between the cluster center and the sample points.Combined with slope data and research objectives, a multidimensional fuzzy system with strong adaptive ability, the T-S fuzzy model, is selected. This can update automatically and constantly modify the membership functions of its fuzzy subset. Its principle is as follows [39]:(8)Ri:ifxiisA1i,x2isA2i,…xkisAki,thenyi=p0i+p1ix1+⋯+pkixk,where Aji is the fuzzy set of the fuzzy system, pki (j = 1, 2, 3, …, k) is the fuzzy system parameter, and yi is the output obtained according to the fuzzy rules. The input part (if part) is fuzzy, and the output part (then part) is determined. This indicates that the output is a linear combination of the input.For input quantityx=x1,x2,…,xk, the degree of membership of each input variable xj is calculated according to the following fuzzy rule:(9)μAji=exp−xj−cji2bji,j=1,2,…,k;i=1,2…,n.In the above formula, cji and bji are the center and width of the membership function, respectively, k is the input parameter, and n is the number of fuzzy subsets.In the fuzzy calculation of each membership, the multiplication operator is used as the fuzzy operator:(10)ωi=μAj1x1∗μAj2x2∗⋯∗μAjkxk.The output value of the fuzzy modelyi is calculated according to the result of the fuzzy calculation:(11)yi=∑i=1nωip0i+p1ix1+?+pkixk∑i=1nωi.In the above formula, pk is an evaluation index and xk is a dynamic quantitative index level. The total weight of the slope stability can be obtained using formula (11).The T-S fuzzy neural network is divided into input, fuzzy, fuzzy rule calculation, and output layers [40]. In the fuzzy layer, the membership function is used to fuzzy the input layer in order to obtain the fuzzy membership value u, whereas, in the fuzzy rule calculation layer, fuzzy value ω is calculated using the fuzzy multiplication formula (10).When learning of fuzzy neural networks, the error is calculated as follows:(12)e=12yd−yc2,where yd is the expected output of the network, yc is the actual output of the network, and e is the error between the expected and actual outputs. Optimal results for the expected value and error value can be found by using formula (12). To optimize the expected value and error value, constant coefficient correction is required:(13)pjik=pjik−1−α∂e∂cji,∂e∂cji=yd−ycωi∑i=1mωi⋅xj.In addition, parameter correction is also needed:(14)cjik=cjik−1−β∂e∂cji,bjik=bjik−1−β∂e∂bji.In the above formula, cji and bji are, respectively, the center and width of the membership function. When the coefficient correction and parameter correction meet the optimal expectation and error values, the total weight of the slope dynamic stability can be obtained by substituting the evaluation index and dynamic quantitative index into formula (11).


### 5.2. Establishment of Dynamic Stability Discrimination Model

It is challenging to integrate all of these influencing factors into the evaluation of the index system because most factors are multidimensional, discrete, nonlinear, and interactive. Therefore, the extension theory combining qualitative and quantitative analysis was used to quantify the influencing factors, thereby solving the problem of earthquake and precipitation being difficult to quantify as a discrete index. When establishing a dynamic stability prediction model, it is necessary to quantify these two influences and classify them using four grades, (0, 0.25], (0.25, 0.50], (0.50, 0.75], and (0.75, 1], expressed as S1, S2, S3, and S4, respectively (Table8).Table 8
Quantitative grading of precipitation and earthquakes.
S1S2S3S4(0, 0.25](0.25, 0.50](0.50, 0.75](0.75, 1]In slope dynamic stability evaluation, although the entropy weight method can calculate the entropy weight of information entropy in combination with the variation degree of each index, it removes the index with lower contribution to the evaluation result through entropy weight. Therefore, to ensure the high objectivity of index weight, the entropy weight method was used for obtaining the weight of each single index in the slope dynamic stability evaluation.A fuzzy neural network model was used for determining the total weight of the slope stability in the evaluation model [41, 42]. Because earthquakes and precipitation change with time, S1–S4 must be revised on a monthly basis during the dynamic evaluation, such that the stability of the slope was predicted for every month. The total weight of the dynamic stability of the slope is calculated using this model and then divided into five intervals according to the interval of the weight value, with each interval corresponding to a different slope stability. In Table 9, 2 indicates particularly stable, 1 indicates stable, 0 indicates less stable, −1 indicates unstable, and −2 indicates extremely unstable.Table 9
Stability corresponding to weight.
Particularly stableStableCritical stableUnstableExtremely unstable[0, 0.20](0.20, 0.40](0.40, 0.60](0.60, 0.80](0.80, 1.00]210−1−2The calculation of slope stability weight is shown in Table9. In the dynamic stability evaluation model, a comprehensive correlation degree can be determined using the 10 indexes X1–X10 and the quantitative grade matrices S1–S4. The value of the quantitative grade matrix depends on the number of earthquakes and the amount of precipitation. Considering the four values of the comprehensive correlation degree, it is found that this value becomes increasingly small. This reflects the optimization process in the fuzzy neural network, which requires a larger expected value and smaller error value. Using formulas (5) and (6), when the value of the fourth comprehensive correlation degree is taken, the error of the model is the smallest (0.13%) and the expected value is the largest (98.5%). Therefore, the fourth comprehensive correlation degree of 0.064 was taken as the best judgment result. Therefore, as shown in Table 10, the slope is particularly stable.Table 10
Dynamic evaluation results.
Dynamic evaluation factorsQuantitative grade matrixWeightIndexDynamic assignmentS1S2S3S4X10.320.3000.1090.40.1550.060X21.000.6670.5560.3330.3330.063X30.650.2140.0570.2840.1320.115X40.350.8330.7200.6000.4000.178X50.130.4670.2730.250.1110.116X60.81000.3330.5000.187X70.970.4090.2780.0710.0560.145X80.790.5000.5000.6670.7500.045X90.730.4670.2000.4000.2730.091X100.150.1290.1240.2350.4000.120Comprehensive correlation degree0.3810.3120.1310.064Particularly stableIn model training, detection, and back-judgment, 136 sets of slope data were first divided into 100 groups of training data, 18 groups of test data, and 18 groups of back-judgment data. After the prediction model was established, the reserved back-judgment data were substituted into the model to conduct the back-judgment test, and dynamic stability test results were obtained as shown in Figure14, where the blue ball is the prediction error.Figure 14
Test pattern for dynamic evaluation result back-judgment (the orange ball represents actual slope stability grade, the blue ball represents predicted slope stability grade, and the purple ball represents the coupling of predicted and actual values).Figure15 shows that there are 13 predicted values exhibiting deviation (Sept of 1; Mar of 2, 7, and 18; Jul of 4 and 9; Oct of 6, 12, and 16; Aug of 10; May of 11 and 15; and Jan of 17). The large dynamic weight value of precipitation and earthquake, together with the conservative stability dynamic prediction model, causes the deviation. Despite this, the prediction accuracy is 93.98%, which is reasonable for engineering safety considerations.Figure 15
Comparison between actual and predicted results for the dynamic stability model.


### 5.3. Testing of Dynamic Stability Models

To further test the generalization and applicability of the model, slope data recollected in 2018 from Lhasa-Xigaze of G318 were used. The field verification was carried out according to 5 grades: particularly stable, stable, less stable, unstable, and extremely unstable. The detailed verification criteria are shown in Table11.Table 11
Verification standard of slope dynamic stability.
StabilityCriteriaParticularly stableThere is no possibility of any damage.StableThe slope has no deformation, but its stability is more sensitive.Less stableThere are cracks, but they are in critical stable state.UnstableThe rock and soil particles roll down, the slope deforms, and cracks expand.Extremely unstableLocal sliding of slope; the damage will be further aggravated.A total of 84 sets of data for 7 slopes over 1–12 months were selected for testing (the blue ball indicates the prediction error). Figure15 shows a comparison between the predicted and actual results.Errors occurring in Jun of 1, Feb of 2, Nov of 3, Jan of 4, Jul of 5, Mar of 6, and Oct of 7 are not consistent with the real situation. The reason is consistent with the prediction error in the back-judging test. The prediction accuracy is 91.67%, which is reasonable for engineering safety considerations. Therefore, the developed prediction model of slope dynamic stability has good applicability and generalization.


## 5.1. Principle of Dynamic Stability Discrimination

Fuzzy mathematics is used for describing, studying, and evaluating the fuzzy characteristics of algorithms [37, 38]. The core principle of fuzzy mathematics is membership grade μfu, a number between [0, 1], which refers to the membership degree of an element u belonging to fuzzy subset f. The closer this is to 0, the lesser the degree to which u belongs to subset f; accordingly, the closer it is to 1, the greater the degree of belonging is.The membership function formula used in this paper is as follows:(7)μfu=1d2/d12/q−1+1.In the above formula, q is the fuzzy weighted index, whose value is (1, +∞), and d1 and d2 are the Euclidean distances between the cluster center and the sample points.Combined with slope data and research objectives, a multidimensional fuzzy system with strong adaptive ability, the T-S fuzzy model, is selected. This can update automatically and constantly modify the membership functions of its fuzzy subset. Its principle is as follows [39]:(8)Ri:ifxiisA1i,x2isA2i,…xkisAki,thenyi=p0i+p1ix1+⋯+pkixk,where Aji is the fuzzy set of the fuzzy system, pki (j = 1, 2, 3, …, k) is the fuzzy system parameter, and yi is the output obtained according to the fuzzy rules. The input part (if part) is fuzzy, and the output part (then part) is determined. This indicates that the output is a linear combination of the input.For input quantityx=x1,x2,…,xk, the degree of membership of each input variable xj is calculated according to the following fuzzy rule:(9)μAji=exp−xj−cji2bji,j=1,2,…,k;i=1,2…,n.In the above formula, cji and bji are the center and width of the membership function, respectively, k is the input parameter, and n is the number of fuzzy subsets.In the fuzzy calculation of each membership, the multiplication operator is used as the fuzzy operator:(10)ωi=μAj1x1∗μAj2x2∗⋯∗μAjkxk.The output value of the fuzzy modelyi is calculated according to the result of the fuzzy calculation:(11)yi=∑i=1nωip0i+p1ix1+?+pkixk∑i=1nωi.In the above formula, pk is an evaluation index and xk is a dynamic quantitative index level. The total weight of the slope stability can be obtained using formula (11).The T-S fuzzy neural network is divided into input, fuzzy, fuzzy rule calculation, and output layers [40]. In the fuzzy layer, the membership function is used to fuzzy the input layer in order to obtain the fuzzy membership value u, whereas, in the fuzzy rule calculation layer, fuzzy value ω is calculated using the fuzzy multiplication formula (10).When learning of fuzzy neural networks, the error is calculated as follows:(12)e=12yd−yc2,where yd is the expected output of the network, yc is the actual output of the network, and e is the error between the expected and actual outputs. Optimal results for the expected value and error value can be found by using formula (12). To optimize the expected value and error value, constant coefficient correction is required:(13)pjik=pjik−1−α∂e∂cji,∂e∂cji=yd−ycωi∑i=1mωi⋅xj.In addition, parameter correction is also needed:(14)cjik=cjik−1−β∂e∂cji,bjik=bjik−1−β∂e∂bji.In the above formula, cji and bji are, respectively, the center and width of the membership function. When the coefficient correction and parameter correction meet the optimal expectation and error values, the total weight of the slope dynamic stability can be obtained by substituting the evaluation index and dynamic quantitative index into formula (11).


## 5.2. Establishment of Dynamic Stability Discrimination Model

It is challenging to integrate all of these influencing factors into the evaluation of the index system because most factors are multidimensional, discrete, nonlinear, and interactive. Therefore, the extension theory combining qualitative and quantitative analysis was used to quantify the influencing factors, thereby solving the problem of earthquake and precipitation being difficult to quantify as a discrete index. When establishing a dynamic stability prediction model, it is necessary to quantify these two influences and classify them using four grades, (0, 0.25], (0.25, 0.50], (0.50, 0.75], and (0.75, 1], expressed as S1, S2, S3, and S4, respectively (Table8).Table 8
Quantitative grading of precipitation and earthquakes.
S1S2S3S4(0, 0.25](0.25, 0.50](0.50, 0.75](0.75, 1]In slope dynamic stability evaluation, although the entropy weight method can calculate the entropy weight of information entropy in combination with the variation degree of each index, it removes the index with lower contribution to the evaluation result through entropy weight. Therefore, to ensure the high objectivity of index weight, the entropy weight method was used for obtaining the weight of each single index in the slope dynamic stability evaluation.A fuzzy neural network model was used for determining the total weight of the slope stability in the evaluation model [41, 42]. Because earthquakes and precipitation change with time, S1–S4 must be revised on a monthly basis during the dynamic evaluation, such that the stability of the slope was predicted for every month. The total weight of the dynamic stability of the slope is calculated using this model and then divided into five intervals according to the interval of the weight value, with each interval corresponding to a different slope stability. In Table 9, 2 indicates particularly stable, 1 indicates stable, 0 indicates less stable, −1 indicates unstable, and −2 indicates extremely unstable.Table 9
Stability corresponding to weight.
Particularly stableStableCritical stableUnstableExtremely unstable[0, 0.20](0.20, 0.40](0.40, 0.60](0.60, 0.80](0.80, 1.00]210−1−2The calculation of slope stability weight is shown in Table9. In the dynamic stability evaluation model, a comprehensive correlation degree can be determined using the 10 indexes X1–X10 and the quantitative grade matrices S1–S4. The value of the quantitative grade matrix depends on the number of earthquakes and the amount of precipitation. Considering the four values of the comprehensive correlation degree, it is found that this value becomes increasingly small. This reflects the optimization process in the fuzzy neural network, which requires a larger expected value and smaller error value. Using formulas (5) and (6), when the value of the fourth comprehensive correlation degree is taken, the error of the model is the smallest (0.13%) and the expected value is the largest (98.5%). Therefore, the fourth comprehensive correlation degree of 0.064 was taken as the best judgment result. Therefore, as shown in Table 10, the slope is particularly stable.Table 10
Dynamic evaluation results.
Dynamic evaluation factorsQuantitative grade matrixWeightIndexDynamic assignmentS1S2S3S4X10.320.3000.1090.40.1550.060X21.000.6670.5560.3330.3330.063X30.650.2140.0570.2840.1320.115X40.350.8330.7200.6000.4000.178X50.130.4670.2730.250.1110.116X60.81000.3330.5000.187X70.970.4090.2780.0710.0560.145X80.790.5000.5000.6670.7500.045X90.730.4670.2000.4000.2730.091X100.150.1290.1240.2350.4000.120Comprehensive correlation degree0.3810.3120.1310.064Particularly stableIn model training, detection, and back-judgment, 136 sets of slope data were first divided into 100 groups of training data, 18 groups of test data, and 18 groups of back-judgment data. After the prediction model was established, the reserved back-judgment data were substituted into the model to conduct the back-judgment test, and dynamic stability test results were obtained as shown in Figure14, where the blue ball is the prediction error.Figure 14
Test pattern for dynamic evaluation result back-judgment (the orange ball represents actual slope stability grade, the blue ball represents predicted slope stability grade, and the purple ball represents the coupling of predicted and actual values).Figure15 shows that there are 13 predicted values exhibiting deviation (Sept of 1; Mar of 2, 7, and 18; Jul of 4 and 9; Oct of 6, 12, and 16; Aug of 10; May of 11 and 15; and Jan of 17). The large dynamic weight value of precipitation and earthquake, together with the conservative stability dynamic prediction model, causes the deviation. Despite this, the prediction accuracy is 93.98%, which is reasonable for engineering safety considerations.Figure 15
Comparison between actual and predicted results for the dynamic stability model.


## 5.3. Testing of Dynamic Stability Models

To further test the generalization and applicability of the model, slope data recollected in 2018 from Lhasa-Xigaze of G318 were used. The field verification was carried out according to 5 grades: particularly stable, stable, less stable, unstable, and extremely unstable. The detailed verification criteria are shown in Table11.Table 11
Verification standard of slope dynamic stability.
StabilityCriteriaParticularly stableThere is no possibility of any damage.StableThe slope has no deformation, but its stability is more sensitive.Less stableThere are cracks, but they are in critical stable state.UnstableThe rock and soil particles roll down, the slope deforms, and cracks expand.Extremely unstableLocal sliding of slope; the damage will be further aggravated.A total of 84 sets of data for 7 slopes over 1–12 months were selected for testing (the blue ball indicates the prediction error). Figure15 shows a comparison between the predicted and actual results.Errors occurring in Jun of 1, Feb of 2, Nov of 3, Jan of 4, Jul of 5, Mar of 6, and Oct of 7 are not consistent with the real situation. The reason is consistent with the prediction error in the back-judging test. The prediction accuracy is 91.67%, which is reasonable for engineering safety considerations. Therefore, the developed prediction model of slope dynamic stability has good applicability and generalization.


## 6. Conclusions

In this paper, a dynamic stability model of slope is established based on field investigation, extraction, and ranking of influencing factors, as well as the prediction of precipitation and earthquake influences. Through back-judgment and testing, the following conclusions are drawn:(1)
Based on the analysis of the instability mechanism and influencing factors of the slope, the following order of importance is obtained using the Random Forest algorithm: precipitation, earthquake, slope gradient, human factors, dense degree, slope shape, groundwater, slope height, vegetation, and weathering depth.(2)
Using Wavelet and NARX dynamic neural network to predict precipitation and earthquakes, the superposition prediction error is 0.21% and the correlation coefficientR of the regression effect diagram is 0.99993, providing accurate prediction data for evaluating the dynamic stability of the slope.(3)
Extension theory is used to quantify the evaluation index, and the entropy weight method is used to determine the weight of each evaluation index. The matter-element extension method and dynamic neural network are then combined to establish an evaluation model for the dynamic stability of the slope based on a fuzzy neural network. Through back-judgment and tests, the accuracy rates reached 93.98% and 91.67%, respectively, indicating that the developed prediction model of slope dynamic stability has good applicability and generalization.(4)
The model can accurately predict the dynamic stability process of the slope in the next 1‐2 years, for the slope treatment along the main traffic trunk lines of the Qinghai-Tibet Plateau, such as Sichuan-Tibet highway, Yunnan-Tibet highway, and Xinjiang-Tibet highway in different batches, stages, and grades.



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*Source: 4230674-2022-04-21.xml*