Keywords

1 Introduction

With the rapid development of China’s economy and the accelerating process of urbanization, the contradiction between the shortage of urban land resources is becoming increasingly prominent. More and more people turn their attention to the direction of underground space utilization. The rapid development of underground space construction has also brought many engineering problems. Among them, the prediction of rockburst has always been a difficult problem in the field of rock engineering.

Rockburst is a kind of elastic deformation energy accumulated in rock mass, which is suddenly and violently released under certain conditions, resulting in rockburst and ejection phenomenon [1]. As one of the main disasters of deep tunnel, rockburst will threaten the safety of construction workers and machine facilities and affect the construction progress. Therefore, the prediction of rockburst is particularly important. The disaster-causing factors of rockburst are complex, domestic and many scholars have made in-depth research. There is no uniform standard for rockburst prediction methods, but the traditional rockburst prediction methods usually only consider a single index, and have strong subjectivity and low efficiency [2]. According to the characteristics that the damage, deformation and failure of rock is a nonlinear process, this paper attempts to establish a rockburst prediction model based on support vector machine. Compared with the traditional learning methods, its advantage is that it can use the kernel function to high-dimensional space mapping, which can better deal with nonlinear, small sample problems [3]. Feng et al. [4, 5] first applied the classification method of support vector machine to rockburst prediction. The results show that the prediction accuracy based on this machine learning method is considerable and practical.

Based on a large number of data samples collected, this paper attempts to establish a rockburst prediction model by means of support vector machine, which is used for rockburst prediction and engineering verification.

2 Establishment of Rockburst Database

2.1 Selection of Rockburst Prediction Factors

There are many factors that lead to the rockburst, and reasonable rockburst prediction factors should be chosen to establis the rockburst database [6]. The selection principles include: strong correlation with rockburst cases, high accuracy, and simple acquisition method. The factors that lead to rockburst can be divided into two aspects of internal and external factors. The internal factor refers to the rock mass itself, only the hard rock will store sufficient elastic deformation energy, so that the broken rock obtains the power of ejection, forming rockburst phenomenon. The evaluation indexes include energy storage and consumption index, elastic strain energy index, rock brittleness index, tangential stress size, rock brittleness coefficient and so on. The external factor refers to the engineering characteristics, the evaluation indexes include the buried depth of cavern, the size of ground stress, the excavation method and the excavation speed, etc.

The occurrence of rockburst must first satisfy the conditions of strength, energy, brittleness and so on, so this paper does not consider the influence of external factors on rockburst. In summary, combined with the selection principle, this paper selects the stress concentration factor SCF (σθ/σc), the strain energy storage index (Wet) and the rock brittleness index (σc/σt) as the prediction factors of rockburst. The stress concentration factor reflects the strength of the surrounding rock, and the index of Wet reflects the energy characteristics of the surrounding rock and the index of σc/σt reflects the brittle failure mechanism [7].

2.2 Collection of the Rockburst Cases

This paper refer to the collection including Erlang Mountain tunnel [8], Xuefeng Mountain tunnel [9], Gaoligongshan mountain tunnel [10], jinping II Hydropower Station [11], Qinling tunnel [12] 246 rock data, case, contains dozens of different types of rocks, rockburst grade is divided into no rockburst, minor rockburst, medium rockburst, strong rockburst level, and record each case of three predictors. These data were first recorded in Excel and then analyzed and processed with spss software. Some of the rockburst data are shown in Table 1.

Table 1 Data summarye domestic and foreign rockburst cases
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The relationship between the strain energy storage coefficient (Wet) and the rockburst intensity is shown in Fig. 1. From the above scatter diagram we can intuitively see that the group of data has a good aggregation, different levels of rockburst index numerical boundaries more obvious. The strain energy storage index Wet decreases with the decrease of rockburst intensity, indicating that the lower the rockburst intensity, the smaller the energy stored in the rock mass, which is also consistent with our understanding of rockburst. However, there are still a few data that are far away from the data group. In order to ensure the accuracy of the rockburst prediction model, it is necessary to eliminate such outliers by mathematical methods.

Fig. 1
A scatterplot of W E T versus the number of rockburst cases has 4 types of values. The plots for minor rockburst are maximum between (148,30 and (200,5), medium between (50,5) and (150,5), strong between (0,2) and (50,10), and no rockburst between (200,2) and (250,2). Values are approximated.

Scatter plot of rockburst index WET

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2.3 Cluster Analysis and Data Processing

This paper uses the idea of cluster analysis to analyze data. Cluster analysis is an important research content in the field of data mining and artificial intelligence. It is limited by the problems of dimension disaster and data scale [13]. By using the SPSS software to realize the system clustering analysis, the pedigree diagram between the samples under each rockburst intensity is drawn. The pedigree diagram corresponding to the strong rockburst is shown in Fig. 2.

Fig. 2
A pedigree chart for the case number and rescaled distance clustering combination has 29 cases, with a few combined cases. It has a few merged data groups, and case number 17 merges with the topmost group.

Pedigree diagram corresponding to case of intense rockburst

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It can be seen from the above pedigree diagram that in the case of strong rockburst, the No. 17 rockburst case was merged with the data group at the end, indicating that the case belongs to the outlier data and should be eliminated. After eliminating the discrete values and abnormal values of all the cases of intensity grade rockburst cases, the most representative 185 data are finally obtained, including 35 data of strong rockburst, 57 data of medium rockburst, 57 data of minor rockburst and 36 data of no rockburst.

3 Rockburst Prediction Model Based on Support Vector Machine

3.1 The Basic Idea of Support Vector Machine

The basic idea of support vector machines is to focus on the points close to the hyperplane and divide the training number correctly in the set case, the interval from the nearest point to the hyperplane is the largest, that is, the ultimate goal is to find an optimal classification surface based on the training data. The problem of solving the optimal classification surface of support vector machine can be transformed into the solution of the quadratic function of maximizing the classification interval of data samples [14]. The key is to obtain the target solution of the maximum classification interval. Taking two types of linear separable data as an example, one type of data is represented by circle, and the other type of data is represented by square. The optimal classification line is shown in Fig. 3.

Fig. 3
A graph of x 2 versus x 1 has 1 solid decreasing line for optimal hyperplane and 2 dotted decreasing lines. The dotted line at the top has a filled dot on it and a few hollow dots above it. The dotted line at the bottom has 2 filled squares on it and a few hollow squares below it.

Sample diagram of optimal classification line

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3.2 Support Vector Machine Prediction Model

In this paper, the Libsvm software package is used to construct the rockburst prediction model of support vector machine, and the corresponding program is compiled in MATLAB. The detailed steps are as follows:

  1. (1)

    Generate test set and training set of samples

After setting up the test environment, we import the Excel files of the rockburst case database into Matlab, randomly generate the training set and the test set, a total of 185 data, of which 80% (148) is used for learning and training, and the remaining 20% (37) data is used for model prediction.

  1. (2)

    Normalize the input sample data

When using the constructed support vector machine model to predict, the sample data should be normalized to eliminate the interference of dimension on the comparability of the original data. The data are normalized by [−1,1] interval here.

  1. (3)

    Select the kernel function

Support vector machine kernel function has RBF kernel function, package linear kernel function, polynomial kernel function, etc. The RBF kernel function requires fewer parameters and the parameter constraints are simple. Based on the above advantages, this paper selects the RBF kernel function to apply.

  1. (4)

    Parameter optimization

In the regression modeling of support vector machine, there are many important parameters, which have a great influence on the prediction level of the model. Nowadays, the commonly used parameter optimization methods at home and abroad include gradient descent method, bootstrap method, Bayesian method and intelligent algorithm. The cross-validation method can obtain the optimal parameters under certain specific premises, and can better solve the ‘over-learning’ and ‘under-learning’ problems well, so that the accuracy of the prediction results can meet the requirements. Therefore, the cross validation method is selected for parameter optimization. In this paper, the parameter ‘t’ of the support vector machine is selected as 2, and the cross validation method is used. The output of the selected parameters is: bestc = 64, bestg = 0.0625. That is, the model we constructed, the final choice of fitting parameters: ‘−t’ is equal to 2, ‘−c’ is equal to 64, ‘−g’ is equal to 0.0625. Parameter selection results in matlab printed contour map is shown in Fig. 4, 3D view is shown in Fig. 5.

Fig. 4
A contour map has a log of 2 g on the vertical axis and a log of 2 c on the horizontal axis. It has a few numbered colored curves that start from the right and bulge outwards towards the left. It has the maximum concentration of lines at the bulged part.

Contour map of rockburst cases

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Fig. 5
A 3-dimensional graph of M S E, log of 2 g, and log of 2 c have a dark-colored base and a multi-color shaded outward bulge.

3D picture of rockburst cases

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  1. (5)

    Training SVM model

After the process of model training and simulation test, the prediction accuracy of the final rockburst sample data is 89.2%, as shown in Fig. 6.

Fig. 6
A graphical representation of the test set sample category and number has a zig-zag pattern with 2 categories. It has the peak value for the real category at (17,30, and (27,3) and the peak value for the predicted label at (12,3), (15,3), (22,3), and (37,3). Values are approximated.

Comparison of test set and prediction results of rockburst cases

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In the case of 185 samples, the learning accuracy of support vector machine can reach 84.5%, the prediction accuracy can reach 89.2%, and the prediction results have high reliability. This shows that the machine learning level of SVM is very high, and it is completely reasonable and feasible to use this model to predict rockburst.

4 Application

In order to verify the accuracy and applicability of the rockburst prediction model, Daxiangling Tunnel project [15] is selected as the verification object to predict the rockburst grade. The Daxiangling extra-long highway tunnel of Yalu Expressway in Sichuan Province is located in Daxiangling at the junction of Yingjing County and Hanyuan County, Ya’an City, Sichuan Province. It is a key and difficult control project of Yalu Expressway. In the large deformation section of Daxiangling tunnel, the surrounding rock is broken and the stability is extremely poor. It is easy to collapse after excavation. There is not only the interference in construction, but also the mutual influence and superposition on the formation disturbance. The poor geological conditions have promoted the rockburst in this area.

The surrounding rock grade of the tunnel is mainly grade III surrounding rock and grade IV surrounding rock. There are many rockburst phenomena in the construction, mainly minor and medium rockburst, accompanied by strong rockburst in some areas, which is harmful, as shown in Fig. 7. Therefore, reasonable prediction of rockburst intensity level is more important. We selected the data of 14 typical measuring points in the data sample of Daxiangling Tunnel, and listed the three indicators of the previous chapter, as shown in Table 2.

Fig. 7
Two photographs of the interior of a tunnel. Both photos have cracks and degradation of the rocks.

Partial rockburst occurred in Daxiangling tunnel

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Table 2 Prediction of rockburst Intensity of Daxiangling tunnel
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These 14 sets of data are used as test sets. For a set of data, the three independent variables are stress concentration factor SCF, strain energy storage index Wet, rock brittleness index σc/σt, and the dependent variable is rockburst intensity level. The fitting results are shown in Fig. 8 with an accuracy of 85.7%. The accuracy rate shows that the rockburst prediction model based on support vector machine has high applicability in Daxiangling Tunnel, which shows that this machine learning method is more reasonable in dealing with nonlinear problems such as rockburst.

Fig. 8
A graphical representation of the test set sample category and number has 2 categories of data. The prediction test set category lies along the horizontal line from 2, while the actual category lies along the baseline and the horizontal line from 3. Values are approximated.

Daxiangling tunnel rockburst monitoring point prediction results schematic diagram

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5 Conclusion

Through research, the conclusions of this paper are as follows:

  1. (1)

    Rockburst is a multi-factor and multi-mechanism geological phenomenon, so its prediction is a nonlinear problem. For a long time, experts and scholars at home and abroad have proposed many criteria to predict the intensity level of rockburst, but these methods have contingency and randomness. The method of machine learning is simple to operate and the model has strong generalization ability, which can further improve the reliability of the prediction model.

  2. (2)

    In this paper, a representative case is collected to establish a sample database of rockburst data, and the main factors affecting the occurrence of rockburst are discussed. According to the engineering characteristics and the mechanism of rockburst, the stress concentration factor SCF, the strain energy storage index Wet, and the rock brittleness index σc/σt are used as predictors. Through data processing methods such as cluster analysis, the most representative 185 samples are obtained to construct a rockburst case database.

  3. (3)

    This paper introduces the basic working idea of support vector machine, and combines the cross validation method to optimize the parameters, and clarifies the advantages of support vector machine in solving nonlinear problems. The prediction results are analyzed, and the prediction accuracy is 89.2%, which is more accurate.

  4. (4)

    The support vector machine rockburst prediction model is used to predict the rockburst of Daxiangling Tunnel, and the accuracy rate is 85.7%, which shows that the model has strong feasibility and applicability in practical engineering.

The rockburst prediction model is a meaningful attempt to use machine learning methods for disaster prediction. Although there are still many immature places in the application, it is believed that there will be broader development in this field in the future.