A Study of Rockburst Prediction Method Based on D-S Evidence Theory

doi:10.12068/j.issn.1005-3026.2024.02.012

Abstract

Abstract:

To effectively predict rockburst， a rockburst prediction method based on D-S evidence theory is proposed. Firstly， six indicator factors related to rockburst occurrence are selected as evidence， and the basic probability assignment of evidence is constructed through fuzzy matter-element framework and normal type degree of membership function. Then， the evidence is classified using K-means and a combined fusion rule of fusing evidence within clusters in classical Dempster’s rule while fusing evidence between clusters in the weighted way is proposed to reduce the adverse effects of high conflict evidence fusion. Finally， the model is applied to the No.2 shaft project of the Qinling Zhongnanshan highway tunnel and compared with the empirical method. To address the uncertainty in the prediction process and to estimate the probability of rockburst occurrence， Monte Carlo simulation is used to perform sampling simulations and the global sensitivity of the input indicators is measured by Spearman’s rank correlation coefficient. The results show that the influence of the input indicators varies widely and in different directions for different rockburst cases； the probability of occurrence of the five rockburst cases ranges from 40.8% to 70.1%. The model shows outstanding predictive classification performance and can provide reference for rockburst prediction in deeply buried underground projects.

Key words: rock mechanics, rockburst prediction, D-S evidence theory, fuzzy matter-element, K-means

CLC Number:

TD 05

Yong-tao GAO, Qiang ZHU, Shun-chuan WU, Yong-bing WANG. A Study of Rockburst Prediction Method Based on D-S Evidence Theory[J]. Journal of Northeastern University(Natural Science), 2024, 45(2): 244-251.

Figures/Tables 10

Fig. 1 Flow chart for improving the D-S evidence theory model

Table 1 Classification criteria for rockburst evaluation indicators

评价指标	无岩爆（Ⅰ）	轻微岩爆（Ⅱ）	中等岩爆（Ⅲ）	强烈岩爆（Ⅳ）
$σ θ$	0～24	24～60	60～126	126～200
$σ c$	0～80	80～120	120～180	180～320
$σ t$	0～5	5～7	7～9	9～14
$σ θ / σ c$	0～0.3	0.3～0.5	0.5～0.7	0.7～1
$σ c / σ t$	40～55	26.7～40	14.5～26.7	0～14.5
$W e t$	0～2	2～4	4～6	6～10

Table 1 Classification criteria for rockburst evaluation indicators

评价指标	无岩爆（Ⅰ）	轻微岩爆（Ⅱ）	中等岩爆（Ⅲ）	强烈岩爆（Ⅳ）
$σ θ$	0～24	24～60	60～126	126～200
$σ c$	0～80	80～120	120～180	180～320
$σ t$	0～5	5～7	7～9	9～14
$σ θ / σ c$	0～0.3	0.3～0.5	0.5～0.7	0.7～1
$σ c / σ t$	40～55	26.7～40	14.5～26.7	0～14.5
$W e t$	0～2	2～4	4～6	6～10

Table 2 Rockburst actual data with true levels

序号	$σ θ$	$σ c$	$σ t$	$σ θ / σ c$	$σ c / σ t$	$W e t$	岩爆烈度
1	43.1	122	5.38	0.35	22.7	3.31	Ⅱ
2	87.5	121	8.73	0.72	13.9	9.05	Ⅳ
3	79.1	124	8.64	0.64	14.4	7.74	Ⅳ
4	56.2	119	7.21	0.47	16.5	5.52	Ⅲ
5	62.8	120	6.45	0.52	18.6	4.16	Ⅲ

Table 2 Rockburst actual data with true levels

序号	$σ θ$	$σ c$	$σ t$	$σ θ / σ c$	$σ c / σ t$	$W e t$	岩爆烈度
1	43.1	122	5.38	0.35	22.7	3.31	Ⅱ
2	87.5	121	8.73	0.72	13.9	9.05	Ⅳ
3	79.1	124	8.64	0.64	14.4	7.74	Ⅳ
4	56.2	119	7.21	0.47	16.5	5.52	Ⅲ
5	62.8	120	6.45	0.52	18.6	4.16	Ⅲ

Table 3 Basic probability assignment for rockburst cases

序号	指标	BPA
序号	指标	$m A Ⅰ$	$m A Ⅱ$	$m A Ⅲ$	$m A Ⅳ$	$m Θ$
1	$σ θ$	0.007 8	0.821 5	0.170 0	0.000 7	0.000 0
	$σ c$	0.047 9	0.380 8	0.481 6	0.089 7	0.000 0
	$σ t$	0.334 1	0.642 1	0.008 4	0.015 5	0.000 0
	$σ θ / σ c$	0.254 1	0.732 5	0.013 0	0.000 5	0.000 0
	$σ c / σ t$	0.000 4	0.148 6	0.809 7	0.041 2	0.000 0
	$W e t$	0.022 1	0.833 3	0.123 0	0.021 6	0.000 0
2	$σ θ$	0.000 0	0.011 4	0.935 4	0.053 2	0.000 0
	$σ c$	0.050 8	0.406 1	0.456 3	0.086 8	0.000 0
	$σ t$	0.011 9	0.005 0	0.607 7	0.375 4	0.000 0
	$σ θ / σ c$	0.000 0	0.000 8	0.368 6	0.594 2	0.036 3
	$σ c / σ t$	0.000 0	0.002 7	0.433 4	0.558 2	0.005 8
	$W e t$	0.000 0	0.000 0	0.000 0	0.826 1	0.173 9
3	$σ θ$	0.000 0	0.052 6	0.884 3	0.028 3	0.034 7
	$σ c$	0.042 1	0.330 1	0.532 1	0.095 7	0.000 0
	$σ t$	0.013 0	0.006 8	0.638 1	0.342 2	0.000 0
	$σ θ / σ c$	0.000 5	0.015 8	0.764 2	0.219 5	0.000 0
	$σ c / σ t$	0.000 0	0.003 6	0.487 8	0.508 6	0.000 0
	$W e t$	0.000 0	0.000 0	0.005 5	0.988 4	0.006 1
4	$σ θ$	0.000 1	0.604 1	0.392 7	0.003 1	0.000 0
	$σ c$	0.057 0	0.455 6	0.406 3	0.081 1	0.000 0
	$σ t$	0.068 9	0.292 5	0.523 6	0.115 0	0.000 0
	$σ θ / σ c$	0.039 6	0.661 0	0.287 8	0.011 6	0.000 0
	$σ c / σ t$	0.000 0	0.011 0	0.685 6	0.303 4	0.000 0
	$W e t$	0.000 0	0.010 3	0.699 2	0.290 5	0.000 0
5	$σ θ$	0.000 0	0.396 4	0.559 7	0.006 2	0.037 8
	$σ c$	0.053 9	0.431 1	0.431 1	0.083 9	0.000 0
	$σ t$	0.134 5	0.659 5	0.150 2	0.055 8	0.000 0
	$σ θ / σ c$	0.013 9	0.347 4	0.604 9	0.033 8	0.000 0
	$σ c / σ t$	0.000 0	0.028 9	0.811 2	0.159 9	0.000 0
	$W e t$	0.000 9	0.362 4	0.564 6	0.072 1	0.000 0

Table 3 Basic probability assignment for rockburst cases

序号	指标	BPA
序号	指标	$m A Ⅰ$	$m A Ⅱ$	$m A Ⅲ$	$m A Ⅳ$	$m Θ$
1	$σ θ$	0.007 8	0.821 5	0.170 0	0.000 7	0.000 0
	$σ c$	0.047 9	0.380 8	0.481 6	0.089 7	0.000 0
	$σ t$	0.334 1	0.642 1	0.008 4	0.015 5	0.000 0
	$σ θ / σ c$	0.254 1	0.732 5	0.013 0	0.000 5	0.000 0
	$σ c / σ t$	0.000 4	0.148 6	0.809 7	0.041 2	0.000 0
	$W e t$	0.022 1	0.833 3	0.123 0	0.021 6	0.000 0
2	$σ θ$	0.000 0	0.011 4	0.935 4	0.053 2	0.000 0
	$σ c$	0.050 8	0.406 1	0.456 3	0.086 8	0.000 0
	$σ t$	0.011 9	0.005 0	0.607 7	0.375 4	0.000 0
	$σ θ / σ c$	0.000 0	0.000 8	0.368 6	0.594 2	0.036 3
	$σ c / σ t$	0.000 0	0.002 7	0.433 4	0.558 2	0.005 8
	$W e t$	0.000 0	0.000 0	0.000 0	0.826 1	0.173 9
3	$σ θ$	0.000 0	0.052 6	0.884 3	0.028 3	0.034 7
	$σ c$	0.042 1	0.330 1	0.532 1	0.095 7	0.000 0
	$σ t$	0.013 0	0.006 8	0.638 1	0.342 2	0.000 0
	$σ θ / σ c$	0.000 5	0.015 8	0.764 2	0.219 5	0.000 0
	$σ c / σ t$	0.000 0	0.003 6	0.487 8	0.508 6	0.000 0
	$W e t$	0.000 0	0.000 0	0.005 5	0.988 4	0.006 1
4	$σ θ$	0.000 1	0.604 1	0.392 7	0.003 1	0.000 0
	$σ c$	0.057 0	0.455 6	0.406 3	0.081 1	0.000 0
	$σ t$	0.068 9	0.292 5	0.523 6	0.115 0	0.000 0
	$σ θ / σ c$	0.039 6	0.661 0	0.287 8	0.011 6	0.000 0
	$σ c / σ t$	0.000 0	0.011 0	0.685 6	0.303 4	0.000 0
	$W e t$	0.000 0	0.010 3	0.699 2	0.290 5	0.000 0
5	$σ θ$	0.000 0	0.396 4	0.559 7	0.006 2	0.037 8
	$σ c$	0.053 9	0.431 1	0.431 1	0.083 9	0.000 0
	$σ t$	0.134 5	0.659 5	0.150 2	0.055 8	0.000 0
	$σ θ / σ c$	0.013 9	0.347 4	0.604 9	0.033 8	0.000 0
	$σ c / σ t$	0.000 0	0.028 9	0.811 2	0.159 9	0.000 0
	$W e t$	0.000 9	0.362 4	0.564 6	0.072 1	0.000 0

Table 4 Classification of evidence in rockburst cases

序号	类1	类2	类3
1	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
2	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
3	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
4	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
5	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$

Table 4 Classification of evidence in rockburst cases

序号	类1	类2	类3
1	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
2	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
3	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
4	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$
5	$σ t$ ， $σ θ / σ c$ ， $σ c / σ t$ ， $W e t$	$σ θ$	$σ c$

Table 5 Results of evidence fusion and rockburst prediction

序号	$m A Ⅰ$	$m A Ⅱ$	$m A Ⅲ$	$m A Ⅳ$
1	0.020 2	0.738 4	0.203 5	0.037 9
2	0.014 7	0.117 0	0.219 3	0.649 0
3	0.011 5	0.090 2	0.194 8	0.703 5
4	0.014 9	0.118 9	0.843 8	0.022 3
5	0.016 5	0.169 6	0.787 9	0.026 0

Table 5 Results of evidence fusion and rockburst prediction

序号	$m A Ⅰ$	$m A Ⅱ$	$m A Ⅲ$	$m A Ⅳ$
1	0.020 2	0.738 4	0.203 5	0.037 9
2	0.014 7	0.117 0	0.219 3	0.649 0
3	0.011 5	0.090 2	0.194 8	0.703 5
4	0.014 9	0.118 9	0.843 8	0.022 3
5	0.016 5	0.169 6	0.787 9	0.026 0

Table 6 Comparison of results with empirical methods

序号	$σ θ$	$σ c$	$σ t$	$σ θ / σ c$	$σ c / σ t$	$W e t$	本文方法
1	Ⅱ	Ⅲ	Ⅱ	Ⅱ	Ⅲ	Ⅱ	Ⅱ
2	Ⅲ	Ⅲ	Ⅲ	Ⅳ	Ⅳ	Ⅳ	Ⅳ
3	Ⅲ	Ⅲ	Ⅲ	Ⅲ	Ⅳ	Ⅳ	Ⅳ
4	Ⅱ	Ⅱ	Ⅲ	Ⅱ	Ⅲ	Ⅲ	Ⅲ
5	Ⅲ	Ⅲ	Ⅱ	Ⅲ	Ⅲ	Ⅲ	Ⅲ

Table 6 Comparison of results with empirical methods

序号	$σ θ$	$σ c$	$σ t$	$σ θ / σ c$	$σ c / σ t$	$W e t$	本文方法
1	Ⅱ	Ⅲ	Ⅱ	Ⅱ	Ⅲ	Ⅱ	Ⅱ
2	Ⅲ	Ⅲ	Ⅲ	Ⅳ	Ⅳ	Ⅳ	Ⅳ
3	Ⅲ	Ⅲ	Ⅲ	Ⅲ	Ⅳ	Ⅳ	Ⅳ
4	Ⅱ	Ⅱ	Ⅲ	Ⅱ	Ⅲ	Ⅲ	Ⅲ
5	Ⅲ	Ⅲ	Ⅱ	Ⅲ	Ⅲ	Ⅲ	Ⅲ

Fig. 2 BPA distribution of 5 cases after 1000 iterations

Fig. 3 Prediction results for 5 rockburst cases after 1 000 iterations

Fig. 4 Global sensitivity of 6 input factors for 5 rockburst cases

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