Evaluation of Tunnel Collapse Susceptibility Based on T-S Fuzzy Fault Tree and Bayesian Network

doi:10.16183/j.cnki.jsjtu.2020.99.011

Abstract

Abstract:

Collapse is one of the common disasters in the process of drilling and blasting tunnel construction. In order to effectively prevent the collapse accident and provide decision-making basis for safety risk analysis and management of tunnel construction, the T-S fuzzy fault tree and Bayesian network were combined, and an evaluation method based on both of them was proposed to calculate tunnel collapse possibility. According to the transformation of T-S fuzzy fault tree to Bayesian network, the Bayesian network model and conditional probability table were determined. In addition, fuzzy number and fuzzy subset were used to describe the fault state and probability of nodes respectively, and the bidirectional reasoning algorithm of Bayesian network was used to calculate. This method can use two different forward inferences to calculate the possibility of tunnel collapse, including the fuzzy subset of root node fault probability and the actual fault state in construction. At the same time, it can check the fault according to the result of importance analysis of root nodes, and can calculate the posterior probability of fault diagnosis of root nodes by back inference. Finally, the application of two engineering examples shows that the method can scientifically evaluate the possibility of tunnel collapse and determine key risk factors. This method can be used as a decision-making tool for tunnel construction safety assurance and management.

Key words: construction tunnel by drilling and blasting, collapse possibility, T-S fuzzy fault tree, Bayesian network, fuzzy number, fuzzy subset, importance

CLC Number:

U458

CHEN Wu, WANG Hao, ZHANG Guohua, WANG Chengtang, ZHONG Guoqiang. Evaluation of Tunnel Collapse Susceptibility Based on T-S Fuzzy Fault Tree and Bayesian Network[J]. Journal of Shanghai Jiaotong University, 2020, 54(8): 820-830.

Figures/Tables 17

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Tab.1

Tab.2

Tab.3

Tab.4

Tab.5

Fuzzy importance of root nodes

根节点	模糊重要度		根节点	模糊重要度
根节点	$I 0.5 F u$ (x_i)	$I 1 F u$ (x_i)	根节点	$I 0.5 F u$ (x_i)	$I 1 F u$ (x_i)
x₁	—	0.12994	x₁₄	—	0.10102
x₂	—	0.14835	x₁₅	—	0.13685
x₃	—	0.13271	x₁₆	—	0.13995
x₄	—	0.13061	x₁₇	—	0.06813
x₅	—	0.13125	x₁₈	—	0.13049
x₆	—	0.13639	x₁₉	—	0.12948
x₇	—	0.13728	x₂₀	0.00192	0.09198
x₈	—	0.13015	x₂₁	0.00309	0.11141
x₉	—	0.12881	x₂₂	0.00183	0.07501
x₁₀	—	0.12881	x₂₃	0.00149	0.06457
x₁₁	—	0.12276	x₂₄	—	0.34127
x₁₂	—	0.13837	x₂₅	0.00886	0.07658
x₁₃	—	0.13401	x₂₆	—	0.08089

Tab.5

Fig.10

Tab.6

Membership degree of current fault state of root node

根节点	当前故障状态	隶属度
根节点	当前故障状态	$μ x ~ i a i$ (x'_i)=0	$μ x ~ i a i$ (x'_i)=0.5	$μ x ~ i a i$ (x'_i)=1
x₁₁	x₁₁=0.15	5/6	1/6	0
x₁₂	x₁₂=0.13	9/10	1/10	0
x₁₅	x₁₅=0.20	2/3	1/3	0
x₁₉	x₁₉=0.20	2/3	1/3	0
x₂₀	x₂₀=0.20	2/3	1/3	0
x₂₂	x₂₂=0.50	0	1	0
x₂₃	x₂₃=0.50	0	1	0
x₂₄	x₂₄=0.32	4/15	11/15	0
其他	0	1	0	0

Tab.6

Tab.7

State importance of root nodes

根节点	状态重要度
根节点	$I 0.5 D e$ (x'_i)	$I 1 D e$ (x'_i)
x₁₁	0	0.00767
x₁₂	0	0.00644
x₁₅	0	0.02559
x₁₉	0	0.02113
x₂₀	0	0.02465
x₂₂	0	0.27841
x₂₃	0	0.27841
x₂₄	0	0.25554
其他	0	0

Tab.7

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中间节点	中间事件名称	中间节点	中间事件名称
y₁	支护措施不当	y₁₀	不良地形地貌
y₂	施工人员操作不当	y₁₁	工程设计不合理
y₃	初支背后空洞	y₁₂	施工组织管理不当
y₄	开挖方法选择不合理	y₁₃	施工质量不满足要求
y₅	衬砌支护参数和方式不合理	y₁₄	不利水文地质
y₆	施工作业不合理	y₁₅	不良工程地质
y₇	支护作用减弱	y₁₆	人为因素不利影响
y₈	辅助措施不到位	y₁₇	自然条件差
y₉	不良地质构造	—	—

等级	可能性	概率
I	频繁的	[0.1,1]
II	可能的	[0.01,0.1)
III	偶尔的	[0.001,0.01)
IV	罕见的	[0.0001,0.001)
V	不可能的	[0,0.0001)