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Exploration and Improvement of Fuzzy Evaluation Model for Rockburst

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Abstract

Rockburst is a highly destructive geological hazard that can cause casualties and equipment damage. To achieve high-accuracy discrimination of rockburst intensity, this article proposes an improved model that addresses the inefficient maximum membership principle used in traditional rockburst fuzzy evaluation models. The stress coefficient σθ/σc, brittleness coefficient σc/σt, and elastic deformation energy index Wet are selected as evaluation indicators for rockburst classification. Subjective and objective weights are obtained using the Delphi method and entropy weight method (EWM). Three types of membership function distribution forms are then used to obtain the membership degrees of each indicator to rockburst grades: trapezoidal membership function (TMF), normal membership function (NMF), and quadratic parabolic membership function (QPMF). Finally, six traditional models and six improved models are established using the maximum membership principle (MMP) and weighted average-maximum membership principle combination evaluation principle (WMP), respectively. Based on the analysis of 100 sets of rockburst field data, the accuracy, precision, recall, and F1-score of the improved evaluation model are increased by 11.3%, 0.097, 0.068, and 0.089, respectively, compared to the traditional model. The Delphi-NMF-WMP model is selected as the best model, with four performance indices reaching 97.0%, 0.979, 0.979, and 0.978. The best model is applied to evaluate the rockburst intensity of the Cangling Tunnel, Dongguashan Copper Mine, and Jiangbian Hydropower Station Diversion Tunnel, with evaluation results consistent with the actual situation, demonstrating the reliability and scientificity of the model.

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Data Availability

The authors confirm that the data supporting the findings of this study are available within the article [and/or its supplementary materials].

Abbreviations

σ θ :

The maximum tangential stress of the surrounding rock

σ c :

The uniaxial compressive strength of rock

σ t :

The tensile strength of rock

σ θ /σ c :

The stress ratio

σ c /σ t :

The rock brittleness ratio

W et :

The elastic energy index

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This research was supported by the Yunnan Fundamental Research Projects (202301AT070462), the National Natural Science Foundation of China (42367024), the Major Science and Technology Special Project of Yunnan Province (202202AG050014), the Yunnan Innovation Team (202105AE160023), and the College Students’ Innovation and Entrepreneurship Training Programs of Yunnan Province (S202210674092).

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Authors and Affiliations

  1. Faculty of Land Resources Engineering, Kunming University of Science and Technology, Kunming, 650093, China

    Qiwei Wang, Chao Wang, Yu Liu, Jianhui Xu, Tuanhui Wang & Quanrui Liu

  2. Key Laboratory of Geohazard Forecast and Geoecological Restoration in Plateau Mountainous Area, Ministry of Natural Resources of the People’s Republic of China, Kunming, 650093, China

    Chao Wang

  3. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu, 610065, China

    Yuefeng Li

Authors
  1. Qiwei Wang
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  2. Chao Wang
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  3. Yu Liu
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  4. Jianhui Xu
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  5. Tuanhui Wang
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  6. Yuefeng Li
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  7. Quanrui Liu
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Contributions

Qiwei Wang: conceptualization, methodology, formal analysis, and writing—original draft; Chao Wang: conceptualization, methodology, formal analysis; Yu Liu and Jianhui Xu: writing—review and editing; Tuanhui Wang, Yuefeng Li, and Quanrui Liu: data curation and validation.

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Correspondence to Chao Wang.

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Appendices

Appendix 1. Delphi method-fuzzy mathematical model evaluation results

No

Evaluating index

Actual grade

Evaluation results of traditional fuzzy models

Evaluation results of improved fuzzy models

σθ/σc

σc/σt

Wet

Trapezoid

Normal

Quadratic parabola

Trapezoid

Normal

Quadratic parabola

1

0.11

31.23

7.40

I

I

I

I

I

I

I

2

0.20

36.04

2.29

I

II*

I

II*

II*

I

II*

3

0.19

47.93

1.87

I

I

I

I

I

I

I

4

0.13

6.67

1.39

I

I

I

I

I

I

I

5

0.19

6.67

1.39

I

I

I

I

I

I

I

6

0.23

6.67

1.39

I

I

I

I

I

I

I

7

0.28

9.68

1.92

I

I

I

I

I

I

I

8

0.11

27.22

7.00

I

I

I

II*

I

I

I

9

0.14

14.05

1.30

I

I

I

I

I

I

II*

10

0.22

36.42

1.75

I

I

I

I

I

I

II*

11

0.31

42.80

1.80

I

I

I

I

I

I

I

12

0.20

11.20

3.60

I

I

I

III*

I

I

II*

13

0.20

14.10

3.60

I

I

I

III

I

I

II*

14

0.28

42.73

2.17

I

I

I

I

I

I

I

15

0.11

29.40

2.04

I

I

I

II*

I

I

II*

16

0.23

7.52

1.50

I

I

I

I

I

I

I

17

0.43

45.90

1.70

I

I

I

I

I

I

I

18

0.22

36.42

1.75

I

I

I

I

I

I

I

19

0.11

31.2

7.40

I

I

I

II*

I

I

I

20

0.40

15.61

3.50

II

II

II

II

II

II

II

21

0.44

13.13

2.12

II

II

II

II

II

II

II

22

0.37

24.00

5.10

II

II

II

III*

II

II

II

23

0.45

11.2

2.03

II

II

II

II

II

II

II

24

0.67

26.80

0.85

II

III*

III*

III*

II

II

III*

25

0.56

20.40

2.00

II

III*

III*

III*

II

II

III*

26

0.46

20.40

2.00

II

II

II

II

II

II

II

27

0.49

19.70

2.30

II

II

II

II

II

II

II

28

0.28

23.60

4.90

II

III*

III*

III*

II

II

II

29

0.44

19.70

2.30

II

II

II

II

II

II

II

30

0.28

23.80

4.80

II

III*

III*

III*

II

II

II

31

0.46

19.70

2.30

II

II

II

II

II

II

II

32

0.42

19.70

2.30

II

II

II

II

II

II

II

33

0.56

34.30

1.90

II

II

II

II

II

II

II

34

0.30

20.40

5.00

II

III*

III*

III*

III*

III*

II

35

0.35

22.70

3.31

II

II

II

II

II

II

II

36

0.45

14.82

3.10

II

II

II

II

II

II

II

37

0.41

30.70

4.30

II

II

II

II

II

II

II

38

0.45

6.84

2.15

II

II

II

II

II

II

II

39

0.35

12.05

2.85

II

II

II

II

II

II

II

40

0.37

29.73

3.52

II

II

II

II

II

II

II

41

0.42

32.77

2.97

II

II

II

II

II

II

II

42

0.38

28.8

3.00

II

II

II

II

II

II

II

43

0.42

29.90

2.40

II

II

II

II

II

II

II

44

0.42

15.50

3.20

II

II

II

II

II

II

II

45

0.57

31.20

3.20

II

II

II

II

II

II

II

46

0.44

8.98

4.86

II

II

II

II

II

II

II

47

0.43

13.98

7.44

III

IV*

IV*

IV*

III

III

III

48

0.55

11.10

3.97

III

II*

III

III

III

III

III

49

0.34

23.97

6.60

III

II*

II*

II*

III

III

III

50

0.42

21.69

5.00

III

III

III

III

III

III

III

51

0.64

24.40

6.31

III

IV*

IV*

IV*

III

III

III

52

0.40

15.00

7.08

III

IV*

IV*

IV*

III

III

III

53

0.48

24.00

5.10

III

III

III

III

III

III

III

54

0.61

24.00

5.10

III

III

III

III

III

III

III

55

0.70

11.70

2.78

III

IV*

IV*

III

III

III

III

56

0.83

28.90

3.20

III

II*

II*

II*

III

III

III

57

0.74

28.90

3.20

III

II*

II*

III

III

III

III

58

0.79

22.00

2.00

III

III

III

III

III

III

III

59

0.84

19.70

2.30

III

IV*

IV*

III

III

III

III

60

0.38

21.70

5.00

III

III

III

III

III

III

III

61

0.56

9.74

7.27

III

III

III

III

III

III

III

62

0.52

21.20

5.50

III

III

III

III

III

III

III

63

0.60

28.30

3.40

III

III

III

III

III

III

III

64

0.53

21.00

3.60

III

III

III

III

III

III

III

65

0.66

21.50

4.10

III

III

III

III

III

III

III

66

0.52

17.80

4.30

III

III

III

III

III

III

III

67

0.57

25.60

3.80

III

III

III

III

III

III

III

68

0.61

25.60

3.70

III

III

III

III

III

III

III

69

0.56

29.20

4.80

III

III

III

III

III

III

III

70

0.49

49.50

4.70

III

III

III

III

III

III

III

71

0.47

55.00

5.00

III

II*

I*

III

II*

II*

III

72

0.61

25.00

3.70

III

III

III

III

III

III

III

73

0.55

31.30

4.60

III

III

III

III

III

III

III

74

0.50

50.90

5.20

III

I*

I*

III

II*

II*

III

75

0.69

16.87

3.41

III

III

III

III

III

III

III

76

0.54

12.20

4.89

III

III

III

III

III

III

III

77

0.47

16.50

5.52

III

IV*

III

III

III

III

III

78

0.52

18.60

4.20

III

III

III

III

III

III

III

79

0.55

11.10

4.00

III

III

III

III

III

III

III

80

0.56

16.30

3.30

III

III

III

III

III

III

III

81

0.32

21.70

5.00

III

III

III

III

III

III

III

82

0.28

9.50

6.10

III

IV*

IV*

IV*

III

III

III

83

0.66

22.30

3.20

III

III

III

III

III

III

III

84

0.72

27.52

4.30

III

III

III

III

III

III

III

85

0.62

19.35

4.50

III

III

III

III

III

III

III

86

0.59

18.75

4.20

III

III

III

III

III

III

III

87

0.73

29.70

3.80

III

III

III

III

III

III

III

88

0.62

20.00

3.10

III

III

III

III

III

III

III

89

0.61

17.90

5.30

III

III

III

III

III

III

III

90

0.47

11.00

3.97

III

III

III

III

III

III

III

91

0.58

13.18

6.27

IV

IV

IV

IV

IV

IV

IV

92

0.77

17.50

5.50

IV

IV

IV

IV

IV

IV

IV

93

0.66

13.20

6.80

IV

IV

IV

IV

IV

IV

III*

94

0.74

24.40

6.31

IV

IV

IV

III*

IV

IV

III*

95

1.00

11.20

2.00

IV

IV

IV

IV

IV

IV

III*

96

0.72

13.90

9.10

IV

IV

IV

IV

IV

IV

IV

97

0.72

13.20

5.20

IV

IV

IV

IV

IV

IV

III*

98

0.69

16.55

5.72

IV

IV

IV

IV

IV

IV

III*

99

0.65

12.36

5.41

IV

IV

IV

IV

IV

IV

III*

100

0.71

32.20

5.50

IV

IV

IV

IV

IV

IV

III*

  1. “*” indicates samples that are incorrectly classified

Appendix 2. Entropy weight method-fuzzy mathematical model evaluation results

No

Evaluating index

Actual grade

Evaluation results of traditional fuzzy models

Evaluation results of improved fuzzy models

σθ/σc

σc/σt

Wet

Trapezoid

Normal

Quadratic parabola

Trapezoid

Normal

Quadratic parabola

1

0.11

31.23

7.40

I

IV*

IV*

IV*

II*

I

I

2

0.20

36.04

2.29

I

II*

IV*

I

II*

II*

II*

3

0.19

47.93

1.87

I

I

I

I

I

I

I

4

0.13

6.67

1.39

I

I

I

I

I

I

I

5

0.19

6.67

1.39

I

I

I

I

I

I

I

6

0.23

6.67

1.39

I

I

I

I

I

I

I

7

0.28

9.68

1.92

I

I

I

I

I

I

II*

8

0.11

27.22

7.00

I

IV*

IV*

IV*

III*

III*

III*

9

0.14

14.05

1.30

I

I

II*

I

I

II*

I

10

0.22

36.42

1.75

I

I

I

I

I

I

II*

11

0.31

42.80

1.80

I

I

I

I

I

I

II*

12

0.20

11.20

3.60

I

I

I

II*– III*

I

II*

II*

13

0.20

14.10

3.60

I

I

I

II*– III*

I

II*

II*

14

0.28

42.73

2.17

I

I

I

I

I

I

II*

15

0.11

29.40

2.04

I

I

I

I

I

I

II*

16

0.23

7.52

1.50

I

I

I

I

I

I

I

17

0.43

45.90

1.70

I

I

I

II*

I

II*

II*

18

0.22

36.42

1.75

I

I

I

I

I

I

I

19

0.11

31.2

7.40

I

IV*

IV*

IV*

II*

II*

III*

20

0.40

15.61

3.50

II

II

II

II

II

II

II

21

0.44

13.13

2.12

II

II

II

II

II

II

II

22

0.37

24.00

5.10

II

II

II

III*

II

III*

III*

23

0.45

11.2

2.03

II

II

II

II

II

II

II

24

0.67

26.80

0.85

II

I*

I*

I*

II

II

II

25

0.56

20.40

2.00

II

III*

III*

III*

III*

II

II

26

0.46

20.40

2.00

II

II

II

II

II

II

II

27

0.49

19.70

2.30

II

II

II

II

II

II

II

28

0.28

23.60

4.90

II

III*

III*

III*

II

III*

III*

29

0.44

19.70

2.30

II

II

II

II

II

II

II

30

0.28

23.80

4.80

II

III*

III*

III*

III*

II

II

31

0.46

19.70

2.30

II

II

II

II

II

II

II

32

0.42

19.70

2.30

II

II

II

II

II

II

II

33

0.56

34.30

1.90

II

III*

II

I*

II

II

II

34

0.30

20.40

5.00

II

III*

III*

IV*

III*

III*

III*

35

0.35

22.70

3.31

II

II

II

II

II

II

II

36

0.45

14.82

3.10

II

II

II

II

II

II

II

37

0.41

30.70

4.30

II

II

II

II

II

II

III*

38

0.45

6.84

2.15

II

II

II

II

II

II

II

39

0.35

12.05

2.85

II

II

II

II

II

II

II

40

0.37

29.73

3.52

II

II

II

II

II

II

II

41

0.42

32.77

2.97

II

II

II

II

II

II

II

42

0.38

28.8

3.00

II

II

II

II

II

II

II

43

0.42

29.90

2.40

II

II

II

II

II

II

II

44

0.42

15.50

3.20

II

II

II

II

II

II

II

45

0.57

31.20

3.20

II

II

II

II

II

II

III*

46

0.44

8.98

4.86

II

II

II

II

II

II

II

47

0.43

13.98

7.44

III

IV*

II*

IV*

III

III

III

48

0.55

11.10

3.97

III

III

III

III

III

III

III

49

0.34

23.97

6.60

III

IV*

IV*

IV*

III

III

III

50

0.42

21.69

5.00

III

II*

III

III

III

III

III

51

0.64

24.40

6.31

III

III

IV*

IV*

III

III

III

52

0.40

15.00

7.08

III

IV*

IV*

IV*

III

III

III

53

0.48

24.00

5.10

III

III

III

III

III

III

III

54

0.61

24.00

5.10

III

III

III

III

III

III

III

55

0.70

11.70

2.78

III

II*

II*

III

III

III

III

56

0.83

28.90

3.20

III

II*

II*

II*

III

III

III

57

0.74

28.90

3.20

III

II*

II*

II–III*

III

III

III

58

0.79

22.00

2.00

III

IV*

IV*

II*

III

III

III

59

0.84

19.70

2.30

III

IV*

IV*

IV*

III

III

III

60

0.38

21.70

5.00

III

II*

III

IV*

III

III

III

61

0.56

9.74

7.27

III

IV*

IV*

IV*

IV*

IV*

III

62

0.52

21.20

5.50

III

IV*

III

III

III

III

III

63

0.60

28.30

3.40

III

III

III

III

III

III

III

64

0.53

21.00

3.60

III

III

III

III

III

III

III

65

0.66

21.50

4.10

III

III

III

III

III

III

III

66

0.52

17.80

4.30

III

III

III

III

III

III

III

67

0.57

25.60

3.80

III

III

III

III

III

III

III

68

0.61

25.60

3.70

III

III

III

III

III

III

III

69

0.56

29.20

4.80

III

III

III

III

III

III

III

70

0.49

49.50

4.70

III

III

III

III

III

III

III

71

0.47

55.00

5.00

III

II*

III

III

III

III

III

72

0.61

25.00

3.70

III

III

III

III

III

III

III

73

0.55

31.30

4.60

III

III

III

III

III

III

III

74

0.50

50.90

5.20

III

IV*

III

III

III

III

III

75

0.69

16.87

3.41

III

III

III

III

III

III

III

76

0.54

12.20

4.89

III

III

III

III

III

III

III

77

0.47

16.50

5.52

III

IV*

IV*

III

III

III

III

78

0.52

18.60

4.20

III

III

III

III

III

III

III

79

0.55

11.10

4.00

III

III

III

III

III

III

III

80

0.56

16.30

3.30

III

III

III

III

III

III

III

81

0.32

21.70

5.00

III

III

III

III

III

III

III

82

0.28

9.50

6.10

III

IV*

IV*

IV*

IV*

III

III

83

0.66

22.30

3.20

III

III

III

III

III

III

III

84

0.72

27.52

4.30

III

III

III

III

III

III

III

85

0.62

19.35

4.50

III

III

III

III

III

III

III

86

0.59

18.75

4.20

III

III

III

III

III

III

III

87

0.73

29.70

3.80

III

III

III

III

III

III

III

88

0.62

20.00

3.10

III

III

III

III

III

III

III

89

0.61

17.90

5.30

III

III

III

III

III

III

III

90

0.47

11.00

3.97

III

III

III

III

III

III

III

91

0.58

13.18

6.27

IV

IV

IV

IV

IV

IV

III*

92

0.77

17.50

5.50

IV

IV

IV

IV

IV

IV

IV

93

0.66

13.20

6.80

IV

IV

IV

IV

IV

IV

IV

94

0.74

24.40

6.31

IV

IV

IV

IV

IV

IV

IV

95

1.00

11.20

2.00

IV

IV

IV

IV

IV

IV

IV

96

0.72

13.90

9.10

IV

IV

IV

IV

IV

IV

IV

97

0.72

13.20

5.20

IV

IV

IV

IV

IV

IV

III*

98

0.69

16.55

5.72

IV

IV

IV

IV

IV

IV

IV

99

0.65

12.36

5.41

IV

IV

IV

IV

IV

IV

III*

100

0.71

32.20

5.50

IV

IV

IV

IV

IV

IV

III*

  1. “*” indicates samples that are incorrectly classified

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Wang, Q., Wang, C., Liu, Y. et al. Exploration and Improvement of Fuzzy Evaluation Model for Rockburst. Mining, Metallurgy & Exploration 41, 559–587 (2024). https://doi.org/10.1007/s42461-024-00933-3

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