A hybrid method consisting of bow-tie-Bayesian network (BT-BN) analysis and fuzzy theory is proposed in this research, in order to support predictive analysis of settlement risk during shield tunnel excavation. We verified the method by running a probabilistic safety assessment (PSA) for a tunnel section in the Wuhan metro system. Firstly, we defined the “normal excavation phase” based on the fuzzy statistical test theory. We eliminated the noise records in the tunnel construction log and extracted the occurrence probability of facility failures from the denoised database. We then obtained the occurrence probability of environmental failures, operational errors, and multiple failures via aggregation of weighted expert opinions. The expert opinions were collected in the form of fuzzy numbers, including triangular numbers and trapezoidal numbers. Afterwards, we performed the BT-BN analysis. We mapped the bow-tie analysis to the Bayesian network and built a causal network PSA model consisting of 16 nodes. Causes of the excessive surface settlement and the resulting surface collapse were determined by bow-tie analysis. The key nodes of accidents were determined by introducing three key measures into the Bayesian inference. Finally, we described the safety measures for the key nodes based on the PSA results. These safety measures were capable of reducing the failure occurrence probability (in one year) of excessive surface settlement by 66%, thus lowering the accident probability caused by excessive surface settlement.
There are intrinsic risks associated with shield tunnel excavation because of the limited knowledge about the existing subsurface conditions [
Traditionally, surface settlement in shield tunnel excavation has been studied both empirically and analytically. A number of empirical formulae have been proposed based on extensive experiments and construction practices. Peck proposed in his classic formula that the surface settlement trough could be described by a normal distribution [
In contrast, analytical methods make reasonable simplifications of rock and soil to consider them as a medium with certain physical and mechanical properties and then derive the surface settlement via well-established mathematical models and mechanical theories [
This study aims to (1) clearly define the “normal excavation phase” of shield tunneling based on the fuzzy statistical test theory and extract the occurrence probability of facility failures from existing structured data; (2) in the absence of available data, determine the occurrence probability of environmental failure, operational error, and multiple failures by aggregating fuzzy numbers (triangular numbers and trapezoidal numbers) of expert opinion; (3) perform probabilistic safety assessment (PSA) of settlement failure in tunnel construction through bow-tie-Bayesian network (BT-BN) analysis; (4) identify the key nodes for excessive surface settlement-caused surface collapse; and (5) develop appropriate safety measures.
In this research, we examined the tunneling log of the Xiaodongmen-Wuchang section (XWS) during the construction of Metro Line 7 at Wuhan (Figure
Location of XWS in the Wuhan metro system.
This paper is organized as follows. Section
Surface settlement caused by shield tunnel excavation is a three-dimensional spatial process that involves the transformation, displacement response, and changing mechanical properties of different soil. As an approximation, an area of surface settlement can be seen to be developing as the TBM advances. The size of the area and the severity of settlement need to be determined to evaluate the spatial distribution of the surface settlement. Many countries have set out standards and benchmarks to monitor surface settlement during shield tunnel excavation (Table
Standards for monitoring surface settlement in shield tunnel excavation.
Country | U.S. | Japan | France | Germany | China |
---|---|---|---|---|---|
Acceptable surface settlement (mm) | 10–15 | 25–50 | Hard rock: 10–20 |
50 | Hard soil: 10–40 |
Classification of risk levels.
Level | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|
Description | Negligible | Alarming | Serious | Dangerous | Catastrophic |
Surface settlement (mm) | 0–10 | 5–15 | 10–25 | 20–35 | 30–45 |
In recent years, the artificial intelligence methods have been exploited in studying the risk evolution of surface settlement. Suwansawat and Einstein used artificial neural network (ANN) to evaluate the safety risks due to surface settlement in tunnel excavation by using the earth pressure balance TBM [
Overall, surface settlement in shield tunneling arises from various risk factors that involve geology, construction method, environment, and management. In order to thoroughly study the safety risk of surface settlement, it is necessary to analyze in real time the uncertain information in the risk factors from multiple sources. However, such uncertainty, including fuzziness and stochasticity, is ubiquitous and restricts the application of traditional methodologies such as empirical formula, simulation, and analytical modeling. Other methods based on artificial intelligence such as neural networks also suffer from the memory effect because it is difficult to update the risk factors in real time when new information arises.
In recent years, the bow-tie (BT) model has been combined with the Bayesian network (BN) to tackle various problems in which uncertainty is deeply rooted. The BT-BN approach has a solid foundation in mathematical theory and has unique advantages in dealing with complex dynamic uncertainty. It has been considered as an ideal tool for knowledge representation, inference, and forecasting in an uncertain environment.
Bow-tie analysis is a quantitative model that consists of fault tree (FT) analysis and event tree (ET) analysis [
The focus of these BT models is to depict the entire scenario of the accident to identify and evaluate the potential causes and consequences but does not readily reveal the actual causes through logical connections and occurrence probability. This caveat can be remedied by mapping BT to BN. For example, Badreddine and Amor improved the BT model by exploiting the advantages of BN dynamic analysis. They built the BT chart in an automated and dynamic way to implement appropriate barriers to prevention and protection in dynamic systems [
In summary, mapping BT to BN allows dynamic risk analysis, and the key factors of the system can be identified by calculating the posterior probability through the Bayes theorem. Meanwhile, since the conditional probability can be calculated via the Bayes theorem, the importance measure of PSA can also be introduced [
BT analysis is used to display the scenario of the loss event (LE) in the system. In the BT model, the FT analysis can reveal the cause of the LE, and the consequences of LE can be determined by the ET analysis. In the proposed BT-BN method, the FT and ET analyses in the BT model are mapped to the BN such that the nodes that give rise to accidents can be more easily determined. The BT-BN method requires explicit occurrence probability of failure. Data for the failure probability of the TBM were extracted from construction log during the “normal excavation phase” of the XWS. When existing data could not provide the required information, expert opinion in the form of the fuzzy number was used to determine the corresponding failure probability. The consequences were then predicted by the BT-BN analysis, and the critical nodes related to the consequences were obtained. Figure
Flowchart of the proposed methodology.
The concept of “fuzzy set,” introduced by Zadeh, is a crucial extension of the classic set theory of Cantor [
Two-phase fuzzy statistics divides the domain
In fuzzy statistical tests,
It has been experimentally found that
Excavation speed is a macroscopic measure of the working state of the TBM. Therefore, the normal state of the TBM is characterized by the normal excavation speed. In our case, the normal excavation speed during tunneling was obtained by running a fuzzy statistical test with the construction logs of the XWS.
In this work, the excavation speed of the TBM had a domain of
Partial construction log of the “normal excavation speed” in the XWS.
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30.3–50.6 | 25–32 | 27.6–42.4 | 7.8–42.5 | 25–35 | 18–39 | 27–43 | 20–41 | 30–47 | 20–54 |
32.4–38.8 | 26–34 | 23.2–47.6 | 8.3–41.7 | 28–46 | 20–35 | 24–40 | 10–40 | 30–61 | 32–63 |
28.4–39.6 | 27–42 | 23.3–44.5 | 20.2–47.6 | 17–35 | 15–42 | 27–47 | 20–35 | 20–61 | 32–58 |
30.3–38.8 | 23–36 | 20.5–42.7 | 24.2–42.5 | 28–37 | 27–41 | 20–33 | 17–32 | 30–60 | 20–37 |
30.3–36.3 | 12.3–34.8 | 28.2–45.6 | 28.7–52.6 | 17–36 | 21–37 | 22–34 | 8–40 | 14–58 | 24–40 |
32–44 | 17.8–32.5 | 18.2–42.6 | 19–32 | 20–37 | 31–41 | 27–48 | 8–40 | 27–74 | 25–48 |
31–42 | 19.8–37.4 | 13.7–37.5 | 22–45 | 20–35 | 30–40 | 30–42 | 20–50 | 15–55 | 24–51 |
31–39 | 13.5–32.6 | 15.6–32.6 | 21–44 | 21–37 | 30–35 | 25–43 | 20–50 | 25–45 | 32–46 |
30–42 | 13.4–32.6 | 20–37 | 19–42 | 20–35 | 20–40 | 28–36 | 20–46 | 28–52 | 25–40 |
31–38 | 15.6–36.4 | 15–40 | 20–41 | 20–37 | 25–40 | 22.5–37 | 31–42 | 31–47 | 20–35 |
Distribution of the “normal excavation speed.”
Table
Membership frequency of 23 mm/min belonging to the “normal excavation speed.”
Description | Number and membership | ||||||
---|---|---|---|---|---|---|---|
Number of rings | 50 | 100 | 150 | 200 | 250 | 300 | 350 |
Membership counts | 28 | 51 | 60 | 97 | 128 | 153 | 178 |
Membership frequency | 0.56 | 0.51 | 0.4 | 0.49 | 0.51 | 0.51 | 0.51 |
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Number of rings | 400 | 450 | 500 | 550 | 600 | 650 | 715 |
Membership count | 202 | 252 | 302 | 342 | 382 | 427 | 470 |
Membership frequency | 0.51 | 0.56 | 0.61 | 0.62 | 0.64 | 0.66 | 0.66 |
Membership frequency of 23 mm/min belonging to the “normal excavation speed.”
Membership frequency of the “normal excavation speed.”
No. | Group | Count | Frequency |
---|---|---|---|
1 | 1.5–2.5 | 1 | 0.001 |
2 | 2.5–3.5 | 2 | 0.003 |
3 | 3.5–4.5 | 2 | 0.003 |
4 | 4.5–5.5 | 2 | 0.003 |
5 | 5.5–6.5 | 5 | 0.007 |
6 | 6.5–7.5 | 6 | 0.008 |
7 | 7.5–8.5 | 17 | 0.024 |
8 | 8.5–9.5 | 21 | 0.029 |
9 | 9.5–10.5 | 31 | 0.043 |
10 | 10.5–11.5 | 34 | 0.048 |
11 | 11.5–12.5 | 46 | 0.064 |
12 | 12.5–13.5 | 60 | 0.084 |
13 | 13.5–14.5 | 66 | 0.092 |
14 | 14.5–15.5 | 100 | 0.14 |
15 | 15.5–16.5 | 132 | 0.185 |
16 | 16.5–17.5 | 168 | 0.235 |
17 | 17.5–18.5 | 217 | 0.303 |
18 | 18.5–19.5 | 240 | 0.336 |
19 | 19.5–20.5 | 366 | 0.512 |
20 | 20.5–21.5 | 396 | 0.554 |
21 | 21.5–22.5 | 425 | 0.594 |
22 | 22.5–23.5 | 470 | 0.657 |
23 | 23.5–24.5 | 500 | 0.699 |
24 | 24.5–25.5 | 535 | 0.748 |
25 | 25.5–26.5 | 563 | 0.787 |
26 | 26.5–27.5 | 588 | 0.822 |
27 | 27.5–28.5 | 609 | 0.852 |
28 | 28.5–29.5 | 619 | 0.866 |
29 | 29.5–30.5 | 668 | 0.934 |
30 | 30.5–31.5 | 686 | 0.959 |
31 | 31.5–32.5 | 715 | 1 |
32 | 32.5–33.5 | 698 | 0.976 |
33 | 33.5–34.5 | 685 | 0.958 |
34 | 34.5–35.5 | 670 | 0.937 |
35 | 35.5–36.5 | 643 | 0.899 |
36 | 36.5–37.5 | 623 | 0.871 |
37 | 37.5–38.5 | 586 | 0.82 |
38 | 38.5–39.5 | 562 | 0.786 |
39 | 39.5–40.5 | 536 | 0.75 |
40 | 40.5–41.5 | 495 | 0.692 |
41 | 41.5–42.5 | 456 | 0.638 |
42 | 42.5–43.5 | 406 | 0.568 |
43 | 43.5–44.5 | 358 | 0.501 |
44 | 44.5–45.5 | 332 | 0.464 |
45 | 45.5–46.5 | 290 | 0.406 |
46 | 46.5–47.5 | 246 | 0.344 |
47 | 47.5–48.5 | 201 | 0.281 |
48 | 48.5–49.5 | 157 | 0.22 |
49 | 49.5–50.5 | 136 | 0.19 |
50 | 50.5–51.5 | 116 | 0.162 |
51 | 51.5–52.5 | 101 | 0.141 |
52 | 52.5–53.5 | 91 | 0.127 |
53 | 53.5–54.5 | 88 | 0.123 |
54 | 54.5–55.5 | 77 | 0.108 |
55 | 55.5–56.5 | 69 | 0.097 |
56 | 56.5–57.5 | 62 | 0.087 |
57 | 57.5–58.5 | 56 | 0.078 |
58 | 58.5–59.5 | 51 | 0.071 |
59 | 59.5–60.5 | 45 | 0.063 |
60 | 60.5–61.5 | 41 | 0.057 |
61 | 61.5–62.5 | 38 | 0.053 |
62 | 62.5–63.5 | 35 | 0.049 |
63 | 63.5–64.5 | 32 | 0.045 |
64 | 64.5–65.5 | 30 | 0.042 |
65 | 66.5–67.5 | 28 | 0.039 |
66 | 67.5–68.5 | 28 | 0.039 |
67 | 68.5–69.5 | 25 | 0.035 |
68 | 69.5–70.5 | 23 | 0.032 |
69 | 70.5–71.5 | 23 | 0.032 |
70 | 71.5–72.5 | 21 | 0.029 |
71 | 72.5–73.5 | 20 | 0.028 |
72 | 73.5–74.5 | 19 | 0.027 |
73 | 74.5–75.5 | 19 | 0.027 |
74 | 75.5–76.5 | 18 | 0.025 |
75 | 76.5–77.5 | 18 | 0.025 |
76 | 77.5–78.5 | 18 | 0.025 |
77 | 78.5–79.5 | 18 | 0.025 |
78 | 79.5–80.5 | 16 | 0.022 |
79 | 80.5–81.5 | 16 | 0.022 |
80 | 81.5–82.5 | 15 | 0.021 |
81 | 82.5–83.5 | 15 | 0.021 |
82 | 83.5–84.5 | 12 | 0.017 |
83 | 84.5–85.5 | 11 | 0.015 |
84 | 85.5–86.5 | 8 | 0.011 |
85 | 86.5–87.5 | 7 | 0.01 |
86 | 87.5–88.5 | 6 | 0.008 |
87 | 88.5–89.5 | 5 | 0.007 |
88 | 89.5–90.5 | 4 | 0.006 |
89 | 90.5–91.5 | 4 | 0.006 |
90 | 91.5–92.5 | 4 | 0.006 |
91 | 92.5–93.5 | 4 | 0.006 |
92 | 93.5–94.5 | 4 | 0.006 |
93 | 94.5–95.5 | 3 | 0.004 |
94 | 95.5–96.5 | 2 | 0.003 |
95 | 96.5–97.5 | 2 | 0.003 |
Figure
The histogram of membership frequency and the membership function of TBM excavation speed.
The excavation speed of the TBM reflects the influence exerted by the excavation parameters (e.g., total thrust, face pressure, and cutter head torque) on the force and displacement of the surrounding soil. Therefore, it is necessary to determine the realistic and practical excavation parameters based on the excavation speed.
Formation reinforcement during TBM launching and TBM arrival can exert a strong influence on the shield tunnel excavation and lead to highly discrete parameters. Therefore, the data from the TBM launching and TBM arrival stages were discarded in studying the relationship between excavation speed and TBM parameters. Figure
Variations in the TBM parameters at different excavation speeds (data from XW section): (a) total thrust versus excavation speed; (b) cutter head torque versus excavation speed; (c) face pressure versus excavation speed; (d) grouting pressure versus excavation speed.
In Figure
Standard values and ranges of excavation speed and TBMPs.
Factors |
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Parameter range | [20, 44] | [8300, 13100] | [117, 143] | [1294, 2974] | [197, 302] |
Standard value | 32 | 9700 | 132.6 | 2270 | 302 |
Deviation range (%) | [−37.5, 37.5] | [−14.43, 35.05] | [−11.76, 7.84] | [−43.0, 31.01] | [−34.77, 0] |
The bow-tie analysis combines FT and ET analyses. The FT analysis in bow-tie calculates the occurrence probability of the loss event (LE) as well as the top event (TE). The occurrence probability of the TE can also be obtained from the occurrence probability of the basic event (BE). The events could be evaluated by their logical relationship and their occurrence probability in the BN. Mapping the bow-tie analysis to BN involves converting both FT and ET analyses. Figure
Bow-tie-Bayesian network analysis. Calculation of (a) event probability and (b) importance measures.
Three importance measures, described in the following Borst and Schoonakker [
The BT-BN analysis requires knowing the occurrence probability of each basic event (BE). The basic events fall into four categories: environmental failure, operational error, multiple failures, and facility failures. The occurrence rate of facility failures was obtained from the construction log of the XWS for the tunneling project that spanned 179 days (715 segments in total) and was converted into occurrence probability via the following equation:
The occurrence probability of environmental failure, operational error, and multiple failures cannot be readily derived from existing data and was thus estimated via expert opinion. The fuzzy method combines the opinions of different experts in a weighted manner to calculate the fuzzy fault rate (FFR) from the triangular fuzzy numbers or trapezoidal fuzzy numbers proposed by the experts. The occurrence probability of environmental failure, operational error, and multiple failures was then determined from the FFR [ Determine the weight of the opinion of each expert based on the age, education background, work experience, and position of the consulted expert (Table where where The occurrence probability is divided into the following categories: nonoccurrence, absolute low, very low, low, fairly low, medium, fairly high, high, very high, absolute high, or occurrence. The rank value of the categories escalates from 0 for nonoccurrence to 1 for the occurrence (Table Aggregation of the fuzzy numbers. When the fuzzy numbers are all triangular number or trapezoidal number, the aggregated fuzzy numbers of an event is calculated via equation ( where After the aggregated fuzzy numbers are determined, the centroid index method (equation ( where Assume Finally, the FPS is converted to FFR via equation (
Weight scores for experts.
Factor | Category | Score |
---|---|---|
Age (a) | <30 | 1 |
30–39 | 2 | |
40–49 | 3 | |
≥50 | 4 | |
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Education (b) | High school | 1 |
College | 2 | |
Bachelor | 3 | |
Master | 4 | |
Ph.D. | 5 | |
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Work experience (c) | <5 years | 1 |
5–10 years | 2 | |
11–20 years | 3 | |
21–30 years | 4 | |
≥30 years | 5 | |
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Position (d) | Worker | 1 |
Technician | 2 | |
Junior scholar/engineer | 3 | |
Senior scholar/engineer | 4 |
Rank value of each category.
Classified occurrence probability | Rank value |
---|---|
Nonoccurrence | 0 |
Absolute low | 0.1 |
Very low | 0.2 |
Low | 0.3 |
Fairly low | 0.4 |
Medium | 0.5 |
Fairly high | 0.6 |
High | 0.7 |
Very high | 0.8 |
Absolute high | 0.9 |
Occurrence | 1.0 |
Figure
System diagram of the “normal excavation phase.”
Diagram of bow-tie analysis for excessive surface settlement.
As mentioned earlier, the “normal excavation phase” is under the influence of excavation parameters, catastrophic geology, and unforeseeable factors. Surface settlement can occur once the condition deteriorates. Here we set excessive surface settlement as the TE in the FT analysis. Meanwhile, the tunneling system has a built-in emergency management system. Upon excessive surface settlement, the emergency management system will start to shut down the TBM timely. Hence, in the ET analysis, the excessive surface settlement is set as the IE and TBM shutdown is set as the CE. OEs of various degrees are obtained based on the considered CE. Finally, the surface settlement is set as the LE to connect the FT and the ET and furnish the BT model (Figure
Details of bow-tie components in Figure
Event | Symbol | Logic link type | Failure model |
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Ground settlement | Excessive surface settlement | OR gate | — |
Catastrophic geology |
|
OR gate | — |
Unforeseeable factors |
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OR gate | — |
Excavation parameters |
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AND gate | — |
Confined water |
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— | Environmental failure |
Ground cavity or flow sand |
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— | Environmental failure |
Obstacles |
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— | Environmental failure |
Segment damage |
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— | Operational error |
Abnormal TBM shutdown |
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— | Multiple failure |
Seal failure at shield tail |
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— | Multiple failure |
Excessive deviation from axis |
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— | Operational error |
Equipment failure |
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— | Multiple failure |
Untimely grouting |
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— | Facility failure |
Excessive cutter head torque |
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— | Facility failure |
Improper control of face pressure |
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— | Facility failure |
Excessive thrust |
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— | Facility failure |
Improper control of excavation speed |
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— | Facility failure |
TBM shutdown | CE1 | — | Multiple failure |
Grouting in settlement area | CE2 | — | Multiple failure |
Bentonite injection to soil chamber and TBM shield | CE3 | — | Multiple failure |
Analysis of event occurrence.
Symbol | Event |
---|---|
OE1 | Excessive surface settlement |
OE2 | Grouted cutter head and shield, excessive surface settlement, and minor property damage |
OE3 | Minor surface collapse and property damage |
OE4 | Moderate surface collapse, major property damage, and minor casualties |
OE5 | Excessive surface settlement |
OE6 | Grouted cutter head and shield, moderate surface collapse, and minor property damage |
OE7 | Moderate surface collapse and major property damage |
OE8 | Severe surface collapse, major property damage, and major casualties |
The BN-BT model for excessive surface settlement is constructed by mapping the FT and ET analyses in the BT (Figure
Bow-tie chart of excessive surface settlement.
The maximum surface settlement that resulted from the aberration of the
Probability of equipment fault.
Event | Surface settlement |
Permitted surface settlement |
Value of TBM parameter | Occurrence rate (d−1) | Occurrence probability (in 1 year) |
---|---|---|---|---|---|
|
8.9 | 15 | 302 kPa | 1.0675 |
3.82 |
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8.4 | 10 | 2974 kN·M | 1.7792 |
6.29 |
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8.6 | 15 | 143 kPa | 7.1167 |
2.56 |
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9.8 | 15 | 13100 kN | 1.4233 |
5.06 |
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12.0 | 15 | 41 mm/min | 2.8467 |
9.87 |
All data were obtained from the operation log of the XWS.
To address the uncertainty regarding the events of environmental failure, operational error, and multiple failure, six domain experts who participated in the construction of the Wuhan metro system, including two senior engineers, one senior academic professor, one technical consultant, one junior engineer, and one worker, were invited to evaluate the occurrence probability of events that cannot be readily derived from existing data (Table
Characteristics of experts participated in the occurrence probability evaluation.
Expert | Age | Education | Service (years) | Professional position |
---|---|---|---|---|
1 | 56 | High school | 25 | Worker |
2 | 35 | Master | 10 | Technician |
3 | 41 | Master | 15 | Junior engineer |
4 | 47 | Bachelor | 20 | Senior engineer |
5 | 50 | PhD | 18 | Senior academic |
6 | 59 | PhD | 30 | Senior engineer |
Distribution of each expert opinion weight.
In addition, Table
Expert opinion on environmental failure, operational error, and multiple failures.
Event | Fuzzy numbers proposed by each expert | ||
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|
Expert 1 | Expert 2 | Expert 3 |
(0.2, 0.3, 0.4, 0.5) | (0.1, 0.2, 0.3, 0.5) | (0.2, 0.3, 0.4, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.1, 0.2, 0.3, 0.5) | |
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Expert 1 | Expert 2 | Expert 3 |
(0.1, 0.2, 0.3, 0.5) | (0.2, 0.3, 0.4) | (0.1, 0.2, 0.4, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.2, 0.3, 0.5) | (0.1, 0.2, 0.3, 0.5) | |
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Expert 1 | Expert 2 | Expert 3 |
(0.1, 0.2, 0.4, 0.5) | (0.1, 0.2, 0.3, 0.5) | (0.1, 0.3, 0.4) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.1, 0.2, 0.3) | (0.1, 0.2, 0.3) | |
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Expert 1 | Expert 2 | Expert 3 |
(0.2, 0.3, 0.4, 0.5) | (0.1, 0.2, 0.3, 0.5) | (0.2, 0.3, 0.4, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.2, 0.3, 0.4) | (0.2, 0.3, 0.5) | (0.1, 0.2, 0.3, 0.5) | |
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Expert 1 | Expert 2 | Expert 3 |
(0.1, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.2, 0.3, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.2, 0.3, 0.5) | (0.1, 0.2, 0.3) | |
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Expert 1 | Expert 2 | Expert 3 |
(0.2, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.2, 0.3, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.2, 0.3, 0.5) | (0.1, 0.2, 0.4, 0.5) | |
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Expert 1 | Expert 2 | Expert 3 |
(0.1, 0.2, 0.4, 0.5) | (0.1, 0.2, 0.3, 0.5) | (0.2, 0.3, 0.4) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.1, 0.3, 0.5) | |
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Expert 1 | Expert 2 | Expert 3 |
(0.1, 0.3, 0.4, 0.5) | (0.1, 0.2, 0.3, 0.4) | (0.2, 0.3, 0.4) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.2, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.1, 0.2, 0.3) | |
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CE1 | Expert 1 | Expert 2 | Expert 3 |
(0.2, 0.3, 0.4, 0.5) | (0.2, 0.3, 0.5) | (0.2, 0.3, 0.4, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.1, 0.2, 0.4, 0.5) | |
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CE2 | Expert 1 | Expert 2 | Expert 3 |
(0.2, 0.3, 0.4) | (0.1, 0.2, 0.5) | (0.2, 0.3, 0.4, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.1, 0.3, 0.5) | |
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CE3 | Expert 1 | Expert 2 | Expert 3 |
(0.2, 0.3, 0.4) | (0.1, 0.2, 0.3, 0.5) | (0.3, 0.4, 0.5) | |
Expert 4 | Expert 5 | Expert 6 | |
(0.1, 0.2, 0.3, 0.4) | (0.1, 0.2, 0.4, 0.5) | (0.1, 0.2, 0.3, 0.5) |
Calculation of FPS, FFR, and the occurrence probability of environmental failure, operational error, and multiple failures.
Event | Aggregated fuzzy numbers | FPS | FFR (d−1) | Failure probability (in 1 year) |
---|---|---|---|---|
|
(0.1288, 0.2288, 0.3288, 0.4838) | 0.2951 | 8.3969 |
2.6402 |
|
(0.1325, 0.2325, 0.3163, 0.4713) | 0.2909 | 8.0032 |
2.5336 |
|
(0.1000, 0.2163, 0.2700, 0.3825) | 0.2420 | 4.2986 |
1.4518 |
|
(0.0450, 0.0900, 0.1125, 0.1800) | 0.1082 | 2.2492 |
8.1803 |
|
(0.1363, 0.2488, 0.2775, 0.4263) | 0.2747 | 6.6022 |
2.14155 |
|
(0.1488, 0.2488, 0.3225, 0.4713) | 0.3004 | 8.9125 |
2.7770 |
|
(0.1163, 0.2388, 0.3125, 0.4675) | 0.2855 | 7.5157 |
2.4002 |
|
(0.1450, 0.2538, 0.2950, 0.3100) | 0.2463 | 4.5643 |
1.5338 |
CE1 | (0.1413, 0.2413, 0.3513, 0.4838) | 0.3058 | 9.4598 |
2.9202 |
CE2 | (0.1288, 0.2513, 0.3038, 0.4713) | 0.2916 | 8.0679 |
2.5496 |
CE3 | (0.1450, 0.2450, 0.3363, 0.4713) | 0.3010 | 8.9722 |
2.7937 |
The occurrence probability of basic events is calculated as described in Section
Occurrence probability of surface settlement and other outcome events.
The above analysis shows that the occurrence probability of excessive surface settlement within one year is 0.8299 (Figure
In order to find the key nodes leading to excessive surface settlement, the importance measure of each event was calculated via equations (E)–(G) in Figure
Calculation of importance measure of influential factors.
Symbol | Importance measure | ||
---|---|---|---|
BM | RAW | FV | |
|
2.311 |
7.352 |
7.352 |
|
2.279 |
6.958 |
6.958 |
|
1.990 |
3.481 |
3.481 |
|
1.716 |
1.691 |
1.691 |
|
2.165 |
5.587 |
5.587 |
|
2.356 |
7.884 |
7.884 |
|
2.239 |
6.476 |
6.476 |
|
2.010 |
3.715 |
3.715 |
|
1.370 |
6.306 |
6.306 |
|
8.300 |
6.291 |
6.291 |
|
2.040 |
6.293 |
6.293 |
|
1.030 |
6.280 |
6.280 |
|
5.300 |
6.303 |
6.303 |
After the normalized weight
Ranking results of the key events.
Rank | Symbol | Normalization weighting ( |
Total weighting ( |
||
---|---|---|---|---|---|
|
|
| |||
1 |
|
13.805 | 18.942 | 18.942 | 51.689 |
2 |
|
13.541 | 17.664 | 17.664 | 48.869 |
3 |
|
13.354 | 16.717 | 16.717 | 46.788 |
4 |
|
13.120 | 15.559 | 15.559 | 44.238 |
5 |
|
12.686 | 13.423 | 13.423 | 39.532 |
6 |
|
11.778 | 8.926 | 8.9255 | 29.629 |
7 |
|
11.661 | 8.363 | 8.363 | 28.387 |
8 |
|
10.055 | 0.406 | 0.406 | 10.868 |
9 |
|
0.0002 | 1.512 |
1.512 |
1.498 |
10 |
|
8.028 |
1.515 |
1.515 |
1.106 |
11 |
|
6.035 |
1.509 |
1.509 |
9.053 |
12 |
|
4.863 |
1.511 |
1.511 |
7.886 |
13 |
|
3.106 |
1.514 |
1.514 |
6.134 |
Total | 100 | 100 | 100 | 100 |
It can be seen that
Occurrence probability when safety is ensured at key nodes.
In accordance with the predictive and diagnostic analysis results using the established model, some safety measures for key nodes are displayed in time to reduce the excessive surface settlement risk during the tunnel excavation. The nodes The nodes Node
By adopting corresponding safety measures in shield tunnel excavation, the occurrence probability of various degrees of surface collapse (OE3, OE4, OE6, OE7, and OE8) was significantly decreased (Figure
In this work, we first defined the “normal excavation phase” of shield tunneling based on the fuzzy statistical test theory. Data were extracted from the construction log of the XWS in the Wuhan metro line 7 to determine the occurrence probability of facility fault, and expert opinions were solicited to determine the occurrence probability of environmental failure, operational error, and multiple failures. Probabilistic safety assessment (PSA) of the normal shield tunnel excavation system was then performed accordingly.
We employed the bow-tie analysis to evaluate the occurrence of excessive surface settlement during normal tunnel excavation. The presence of emergency measures could reduce the occurrence probability of surface collapse caused by excessive surface settlement (OE3, OE4, OE6, OE7, and OE8) but have limited effect on the prevention of accidents of OE1, OE2, and OE5. It is essential to decrease the probability of excessive surface settlement in order to prevent the resulting outcome events (OEs).
By mapping the bow-tie analysis to Bayesian networks (i.e., BT-BN analysis), we determined the key nodes that could cause excessive surface settlement (LE). The key nodes included the following:
To ensure safety, careful geological exploration should be carried out before the tunneling project. During the tunneling, safety management and supervision should be strengthened at the construction site. Advanced geological prediction technology should be used to detect poor geological and hydrological conditions ahead of the TBM in real time. Advanced laser locator should be used to monitor and alarm excessive axial deviation. The quality of the tail brush should be improved, and tail brush should be replaced timely when it becomes worn. The occurrence probability of excessive surface settlement was decreased by adopting these safety measures, and the occurrence of the resulting surface collapse was subsequently decreased.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
The authors thank the workers, foremen, and safety coordinators of the main contractors for their participation. The authors also wish to thank the engineers Yun Zhang and Peilun Tu for assistance in gathering field data.