Research Article  Open Access
Predictive Analysis of Settlement Risk in Tunnel Construction: A BowTieBayesian Network Approach
Abstract
A hybrid method consisting of bowtieBayesian network (BTBN) 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 BTBN analysis. We mapped the bowtie 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 bowtie 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.
1. Introduction
There are intrinsic risks associated with shield tunnel excavation because of the limited knowledge about the existing subsurface conditions [1, 2]. Although the majority of shield tunnel construction projects have been completed safely, the surface collapse caused by excessive surface settlement did occur in several tunneling projects which resulted in major damage, injury, and loss of life. The worst accident of metro construction in China took place on November 15, 2008, in Hangzhou [3]. A massive cavein during the construction of Metro Line 1 near the Xianghu station caused 21 injuries and 24 deaths, and the direct economic loss amounted to 49.61 million Yuan. A more recent accident took place on May 14, 2017, in Nanchang [4]. Excessive surface settlement during the construction of Metro Line 2 near the Bayi square station caused a cavein more than 10 m in diameter and led to severe property losses. Therefore, it is imperative to systematically assess and manage the safety risks associated with shield tunnel excavation.
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 [5]. Since then, the Peck formula had been further improved and modified by many scholars, including Attewell et al. [6] and Rankin [7]. Attewell and Woodman proposed the cumulative probability curve [8]. O’Reilly and New suggested a predictive formula to estimate trough width, formation loss, and surface settlement [9]. Mair et al. and coworkers established their formula to calculate subsurface formation displacement [10]. Empirical formulae are widely used in practical engineering because of their simplicity, but their use is limited to crude estimations of the surface settlement because they are not accurate enough.
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 wellestablished mathematical models and mechanical theories [1]. The stochastic medium theory considered rock and soil as a “stochastic medium” and regards the surface settlement caused by tunnel excavation as a stochastic process [11–13]. Numerical analysis integrates the elasticviscoplastic theory into numerical calculations and reduces the dimension of the calculations with discrete interpolation and analytic functions [14–16]. The primary problem with analytical methods is an oversimplification. In most cases, the task is reduced to solving the plane strain that is uniform, isotropic, and axisymmetric, although the practical situation in engineering and the geological formation at the construction site are much more complicated. In order to address those issues, artificial intelligence (AI) methods provide possible solutions, which have been exploited in studying the risk evolution of surface settlement.
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 bowtieBayesian network (BTBN) analysis; (4) identify the key nodes for excessive surface settlementcaused surface collapse; and (5) develop appropriate safety measures.
In this research, we examined the tunneling log of the XiaodongmenWuchang section (XWS) during the construction of Metro Line 7 at Wuhan (Figure 1). Data were collected from XWS, and the key nodes that could cause cavein due to the excessive surface settlement were extracted. We proposed safety measures that targeted the key nodes to reduce the likelihood of accidents. The XWS went from south to north, mainly along the Zhongshan road. The left tunnel was 1115.208 m in length and was excavated with a tunnel boring machine (TBM). The right tunnel was 1107.169 m in length and was excavated with a Komatsu tunnel boring machine. Both tunnels were excavated by using the earth pressure balance TBM. The minimum horizontal curve radius of the section was 400 m, and the line spacing was 12.6–50.5 m. The minimum longitudinal curve radius of the section was 3000 m. The section adopted a concave slope with the overlying soil of 10.5–45.4 m in thickness. Figure 1 shows a picture taken during the excavation of the XWS.
This paper is organized as follows. Section 2 presents the existing knowledge on the definitions of surface settlement incurred by shield tunnel excavation, classifies existing research methods on surface settlement in metro construction, and introduces the dynamic safety analysis of the BTBN methodology. Section 3 defines the “normal excavation phase” of shield tunneling and presents the detailed procedures in carrying out the fuzzy BTBN analysis. Section 4 examines the normal tunnel excavation in detail and applies the proposed fuzzy BTBN method to the PSA analysis of excessive surface settlementcaused surface collapse in the XWS of Wuhan metro system. The conclusions and future works are drawn in Section 5.
2. Literature Review
2.1. Surface Settlement in Tunnel Construction
Surface settlement caused by shield tunnel excavation is a threedimensional 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 1). Based on the Chinese standard GB 509112013 “Code for monitoring measurement of urban rail transit engineering” [17] as well as the standards of other countries, in this work, we classified risk levels of the surface settlement for the soft soil in the XWS as shown in Table 2.


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 [18]. They took various influence factors as the inputs to their ANNs and predicted the surface settlement. Sun et al. introduced the theories and techniques of both artificial intelligence and automatic control into geotechnical engineering [19]. Specifically, an ANN model called “multistep circulation” was adopted for predicting the safety risk of surface settlement in shield tunneling. Fuzzy logic control was also applied to enable active safety control of deformation displacement in real time. However, existing artificial intelligence methods cannot analyze the key nodes with regard to surface settlement in shield tunnel excavation. Besides, long learning time is needed and the requirement on known parameters can be demanding.
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.
2.2. Bayesian Network and BowTie
In recent years, the bowtie (BT) model has been combined with the Bayesian network (BN) to tackle various problems in which uncertainty is deeply rooted. The BTBN 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.
Bowtie analysis is a quantitative model that consists of fault tree (FT) analysis and event tree (ET) analysis [20] and allows investigating the causes and consequences of a given undesirable event. Cherubin et al. applied BT analysis as a simple and effective quantitative risk assessment (QRA) approach for the identification and evaluation of potential hazards and associated risks with the baseline risk assessment tool (BART) [21]. Targoutzidis argued that BT analysis is an effective tool for identifying environmental risk sources because it can clearly show the connections between the cause, the loss events (LEs), the conditional events (CEs), and the outcome events (OEs) [22]. The BT approach has been applied in the risk assessment of hexane distillation, the risk management of harbor and maritime terminals, and the risk assessment of airworthiness in military aviation [23–25].
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 [26]. Khakzad et al. made a dynamic risk analysis of systems whose physical reliability is updated periodically [27]. They made use of the Bayes theorem to periodically update the failure probability of safety barriers in the BT chart and estimated the probability of consequences based on the enhanced BT chart. It was argued that mapping BT to BN [28] could alleviate the limitations of BT caused by static factors. Abimbola et al. used BT and BN to determine the key factors of the integrity model. In their study, the posterior probability was obtained through the Bayes theorem, and the key factors were determined by the ratio of the posterior probability to the prior probability [29].
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 [30], and BN can be fitted with these important measures very well to calculate the importance measures accurately and easily. Therefore, the BTBN analysis can not only analyze surface collapse caused by excessive surface settlement in shield tunneling metro construction but also use PSA to confirm the critical causes of accidents by adding the importance measures.
3. Methodology
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 BTBN 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 BTBN 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 BTBN analysis, and the critical nodes related to the consequences were obtained. Figure 2 shows the flowchart of the proposed methodology.
3.1. “Normal Excavation Phase” of TBM
3.1.1. Fuzzy Statistical Test Theory
The concept of “fuzzy set,” introduced by Zadeh, is a crucial extension of the classic set theory of Cantor [31]. The fuzzy set theory has matured over the past years to a wellestablished research area in mathematics and has found extensive applications in many fields. The fuzzy set A on domain X is, in fact, a function of X ⟶ [0,1]. The primary task of dealing with fuzziness in practical applications is to determine the membership function A(x). Just like probabilistic theory cannot give precise but only approximate probability, due to limited knowledge and information, the fuzzy set theory can only establish the approximate degree of membership and consequently an estimated membership function. Fuzzy statistical tests that demonstrate the stability of frequency can be carried out to characterize the objectivity of degree of membership and to derive an approximate membership function.
Twophase fuzzy statistics divides the domain X (e.g., TBM excavation speed) into two statistical sets, i.e., A (“normal”) and A^{c} (“abnormal”). That is, two opposite fuzzy concepts compete for statistics in domain X. The socalled “twophase” indicates P_{2} = {A, A^{c}} [32], i.e., each fuzzy test will establish a mapping e: X ⟶ P_{2}. This mapping divides the domain X, i.e., ∀x ∈ X, A(x) + A^{c}(x) = 1. The twophase fuzzy statistical test contains four elements: (1) domain X; (2) a fixed element x_{0} in X; (3) a varying classical set in X ( reflects the flexible boundary of the fuzzy set A and allows to determine if the x_{0} in each test conforms to the fuzzy concept described by A); and (4) condition S, which restricts the changes of .
In fuzzy statistical tests, x_{0} remains fixed while is varied. In each test, a decision must be made as for whether x_{0} belongs to . Note that the changing is always a subset of X. After n tests, the membership frequency of x_{0} belonging to the fuzzy set is calculated as l_{n}(A)(x_{0}):
It has been experimentally found that l_{n}(A)(x_{0}) tends to stabilize as n increases. The stabilized value is referred to as the degree of membership that x_{0} belongs to A:
3.1.2. Fuzzy Statistical Test of the Excavation Speed of TBM
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 V = [1, 96] (mm/min). The fuzzy set A represents the fuzzy concept of “normal excavation speed.” For the purpose of illustration, select an arbitrary excavation speed = 23 mm/min. Fuzzy statistical tests were then applied to determine the degree of membership that belonged to A. For the construction project at the XWS, the appropriate project logs over n = 179 days (715 segment rings for left and right tunnels) were selected. The appropriate logs excluded abnormal engineering situations (restrictive condition S) such as TBM launching, TBM arrival, and abnormal downtime, during which the formation was reinforced and the excavation speed could not be considered normal. In this way, the boundaries for the daily “normal excavation speed” could be determined for the left and right tunnels of the XWS (Table 3; Figure 3).

Table 4 shows the membership frequency that = 23 mm/min belonged to the normal excavation speed, as was determined by the statistical tests. Figure 4 shows that the membership frequency f that = 23 mm/min falls within the “normal excavation speed” of the TBM stabilized around 0.66. Hence, = A(23) = 0.66. The membership frequency f of other excavation speeds could also be obtained similarly. The data from the construction logs recorded a minimum and maximum excavation speed of 2 mm/min and 96 mm/min, respectively. Hence, we divided the domain V into 96 intervals each spanning 1 mm/min, starting from 1.5 mm/min and ending at 96.5 mm/min. The mean of each interval was used to calculate the membership frequency, and the results are shown in Table 5. A program was developed in MATLAB to reduce the computational complexity and save time.


Figure 5 plots the histogram of membership frequency based on the data in Table 5. The fitted curve of the membership function was then drawn accordingly. The fitted curve conformed to the Cauchy distribution and could be expressed as follows:
(1) Determination of the Standard Excavation Speed. In the fuzzy set theory [31], the element with the membership frequency = 1 is designated as the kernel of the fuzzy set A and written as “kerA.” Figure 5 shows that kerA = {32}, i.e., = 32 mm/min, was the kernel of the fuzzy set of “normal excavation speed.” Therefore, = 32 mm/min was considered as the standard excavation speed in the ensuing PSA analysis.
(2) Determination of the Range of Excavation Speed. In the fuzzy set theory, all elements whose membership frequency > 0 constitute a support of the fuzzy set A and is written as “supp A,” and all elements whose membership frequency > α is designated as the α cut set of the fuzzy set A and written as A_{α}. Figure 5 shows that the excavation speed fluctuated around the kernel (32 mm/min) during shield tunnel excavation. In order to express the range of normal excavation speed, the confidence level α = 0.5 was selected and the excavation speed whose membership frequency satisfied > 0.5 was considered to constitute the interval of normal excavation speed (i.e., the 0.5 cut set of A). The set of normal excavation speed in Zadeh’s form was ordered, as shown in equations (4) and (5). Thus, = 20–44 mm/min was considered as the range of normal excavation speed in the ensuing PSA analysis:
3.1.3. Fuzzy Statistical Tests of Excavation Parameters
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 6 shows how the TBM parameters varied with the excavation speed during the construction of the 715 segments in the XWS. The curves were fitted via MATLAB, and the slope of the curves was highly indicative of the correlation between the TBM parameters and the excavation speed.
(a)
(b)
(c)
(d)
In Figure 6(a), the total thrust (F) increased with rising excavation speed. This was because bentonite was used as a lubricant and injected around the shield of the TBM during excavation to reduce friction. When the amount of injected bentonite was appropriate, the friction coefficient between the shield and the surrounding soil would decrease, and the excavation speed would then increase when the thrust (F) was higher. In Figure 6(b), the excavation speed decreased when the cutter head torque (M_{T}) increased. This was because when the soil body of the tunneling face was relatively difficult to cut, a larger torque of the cutter head would be needed and the excavation speed would decrease. Figure 6(c) shows that during normal excavation, the pressure of the tunneling face increased slightly with rising excavation speed. Besides, Mair pointed out that during segment assembly, the downtime of TBM would decrease the soil and water pressure on the tunneling face, which could reduce the control pressure of the tunneling face [33]. The same pattern was observed in the current construction logs, and the R^{2} value of the curve in Figure 6(c) was hence relatively low. Figure 6(d) shows that the grouting pressure decreased slightly with rising excavation speed. However, since the pressure of primary grouting was read off from the grouting pressure pump, the actual grouting pressure exerted on the surrounding soil was smaller, and the primary grouting pressure hence had limited impact on excavation speed.
(1) Determination of Standard TBM Parameters. It was determined from the fuzzy statistical tests above that the standard excavation speed was 32 mm/min. The corresponding standard TBM parameters could be determined accordingly from the following equation:where TBMP is the TBM parameter and is the excavation speed (mm/min).
(2) Determination of the Range of TBM Parameters. It was determined from the fuzzy statistical tests above that the range of excavation speed was 20–44 mm/min. The corresponding boundaries of TBM parameters could be determined from the extreme values in the monitoring records (Figure 6) via the following equation:
(3) “Normal Excavation Phase” of TBM. According to the fuzzy set theory, the excavation speed in the “normal excavation phase” fell within 20–44 mm/min. The TBM was considered to be in the “normal excavation phase” when the excavation speed and the TBM parameters all fell within the prescribed ranges specified above and listed again in Table 6. The standard values and ranges were used further in the subsequent PSA analysis. Table 6 shows that among the examined parameters, the face pressure had a deviation interval of merely 19.6% and was controlled the best, whereas the cutter head torque had a deviation interval of 74.01% and was controlled the worst.

(4) Statistical Relationship between TBM Parameters and Excavation Speed. The monitoring results in Figure 6 demonstrated that in the “normal excavation phase” of the XWS, the total thrust and the face pressure were positively correlated with the excavation speed. In particular, the total thrust had a stronger correlation to the excavation speed than the face pressure. In contrast, the cutter head torque and the primary grouting pressure were negatively correlated with the excavation speed.
3.2. BowTieBayesian Network Analysis
The bowtie analysis combines FT and ET analyses. The FT analysis in bowtie 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 bowtie analysis to BN involves converting both FT and ET analyses. Figure 7(a) provides a brief description of calculation steps.
(a)
(b)
Three importance measures, described in the following Borst and Schoonakker [30], were introduced in the new methodology according to the Bayes theorem. Figure 7(b) gives a brief description of their calculation. In the proposed methodology, the critical nodes that could more easily trigger accidents were obtained by calculating these importance measures.
3.3. Confirming Failure Occurrence Probability
The BTBN 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:where F denotes the occurrence probability of the failure and λ denotes the occurrence rate of the failure.
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 [34]. The general procedure of the fuzzy method is as follows:(1)Determine the weight of the opinion of each expert based on the age, education background, work experience, and position of the consulted expert (Table 7). The crude weight score of each expert is calculated via the following equation: where S_{n} represents the total weight score of the expert. The relative weight score of each expert is calculated via the following equation: where m represents the number of experts.(2)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 8). The occurrence probability of the event is then evaluated based on the corresponding triangular number or trapezoidal number given by the experts.(3)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 (11) [35]. The aggregated fuzzy number considering the expert weight is shown in equation (12). where represents the aggregated fuzzified number given by expert m and represents the weight of the expert’s opinion:(4)After the aggregated fuzzy numbers are determined, the centroid index method (equation (13)) is used to handle the fuzzy numbers and obtain the fuzzy probability score (FPS) [36]: where X is the defuzzified output, is the membership function, and x is the output variable. Assume a triangular number and a trapezoidal number. The FPS is calculated via equation (14) when a fuzzy number is a triangular number and via equation (15) when the fuzzy number is a trapezoidal number:(5)Finally, the FPS is converted to FFR via equation (16) [37], and the FFR is further converted to the occurrence probability of environmental failure, operational error, and multiple failures (equation (8)):


4. Results
4.1. Analysis of Excessive Surface Settlement in Normal Tunnel Excavation
Figure 8 shows that the normal excavation phase involves the environment, TBM operation, supervision, management, and emergency handling. Risk analysis of the “normal excavation phase” in soft soil engineering based on the XWS allows the identification of potential risk factors that may trigger surface settlement and consequently lead to accidents. Eskesen et al. have described three principles for risk analysis as follows: (1) eliminate risk factors that are easy to detect and can be controlled timely and effectively, (2) eliminate risk factors with low occurrence probability and no catastrophic consequences, and (3) combine risk factors with similar loss consequences [38]. Accordingly, the risk factors during shield tunneling were organized into three basic categories: improper control of excavation parameters (e.g., poor control of face pressure), catastrophic geology (e.g., ground cavity or flow sand), and unforeseeable factors (e.g., segment damage). Figure 9 shows the bowtie model built from the categorized factors for the risk of surface collapse caused by excessive surface settlement during shield tunneling. OEs of various degrees were successfully predicted based on the CEs (Figure 9). Many risk factors exist in any given surface collapse. In this section, based on the previous calculation results in Section 3.1, we selected the manageable shield excavation parameters (shield total thrust, grouting pressure, cutter head torque, soil pressure, etc.) in the “normal excavation phase” as the base events, assigning their weights according to Section 3.3, and then performed PSA analysis.
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 builtin 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 9; Table 9). Eight OEs of various degrees were predicted based on the CEs, including surface collapse events OE_{3}, OE_{4}, OE_{6}, OE_{7}, and OE_{8} (Figure 9; Table 10). The TBM shuts down if CE_{1} occurs and continues to operate if otherwise.


The BNBT model for excessive surface settlement is constructed by mapping the FT and ET analyses in the BT (Figure 9) model to BN (Figure 10). All the nodes of BN have previously been described in the BT except the node OE, which is the consequence node. OE is added to accommodate the outcomes of BT. By connecting the node of excessive surface settlement to OE, another state also called the safe state is added to the state set. It includes consequences OE_{1} to OE_{8} to account for the nonoccurrence of the top event, i.e., when excessive surface settlement = controlled. To show the dependence among the safety barriers and the top event, causal arcs are also drawn between TBM shutdown and grouting in the settlement area and bentonite injection to soil chamber and TBM shield. It is worth noting that since various combinations of the failure and success of the sequential safety barriers result in different consequences in the BT, all the safety nodes of BN are connected to node OE.
4.2. Determination of Event Occurrence Probability
The maximum surface settlement that resulted from the aberration of the ith TBM parameter is denoted as δ_{max,i}. The probability of safety accident becomes higher when δ_{max,i} approaches the permitted surface settlement δ_{i}. When δ_{max,i} = δ_{i}, the accident will occur as soon as the TBM parameter gives rise to a surface settlement of δ_{max,i}. The probability of equipment fault for the normal excavation system was calculated via equation (8) from the engineering log data of the XWS over 179 days of construction (715 segments rings in total). The construction of all 715 rings fell within the “normal excavation phase” as was defined by the fuzzy statistical test ( = 20–44 mm/min). Table 11 lists the calculation results.
 
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 12). The weights of their opinion were then calculated by using equations (9) and (10), and the distribution of each opinion weight is shown in Figure 11.

In addition, Table 13 lists the expert opinions regarding the events of environmental failure, operational error, and multiple failures in the form of fuzzy numbers based on Table 8. The fuzzy numbers were aggregated via equations (12) and converted to FPS and FFR via equations (13)–(16) (Table 14). The occurrence probabilities were finally derived from FFR (Table 14). Generally, the expert knowledge is considered as a scarce resource which cannot provide universal consultation or realtime guidance. Thus, there is much room to improve the data use efficiency.


4.3. Update in Occurrence Probability of LE and OE
The occurrence probability of basic events is calculated as described in Section 4.2, including the occurrence probability of facility failure from the engineering log data of the XWS as well as that of environmental failure, operational error, and multiple failures derived from expert opinion. The occurrence probability of excessive surface settlement (LE) is determined via equations (A) and (B) by considering the logical relationship between events in Figure 7. Finally, the occurrence probability of OEs including surface collapse can be calculated via equation (C) in the figure by mapping the FT and ET analyses in the BT model to BN. Figure 12 shows the occurrence probabilities of the LE (i.e., excessive surface settlement) and that of the OEs.
The above analysis shows that the occurrence probability of excessive surface settlement within one year is 0.8299 (Figure 12). This occurrence probability of surface collapse (OE_{3}, OE_{4}, OE_{6}, OE_{7}, and OE_{8}) may be decreased when emergency measures are put in place, including grouting in settlement area and bentonite injection to soil chamber and TBM shield. However, these measures cannot help to reduce minor accidents since the occurrence probability remains at high levels for OE_{1}, OE_{2}, and OE_{5}. Admittedly, grouting and bentonite injection are necessary measures and they can decrease the effects of excessive surface settlement during shield tunneling. However, the key point of avoiding outcome events including surface collapse to ensure project safety is to prevent the excessive surface settlement from occurring in the first place. Hence, we sought to determine the key nodes leading to excessive surface settlement via BTBN analysis and propose the corresponding preventive measures.
4.4. Identify Key Nodes and Provide Safety Measures
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 7, as shown in Table 15. Assume the number of events as “n.” The normalized weight could be calculated from the importance measure I_{i} via the following equation:

After the normalized weight is calculated for each importance measure, the total weight could be calculated via equation (18). The total weight of events was finally ranked in descending order to find the key nodes, as shown in Table 16:

It can be seen that X_{6} (seal failure at shield tail), X_{1} (confined water), X_{2} (ground cavity or flow sand), X_{5} (abnormal TBM shutdown), and X_{7} (excessive deviation from axis) have far higher weight than other events and are thus the key nodes to accidents related to excessive surface settlement. Measures can be taken to particularly ensure safety at these nodes. The occurrence probability of excessive surface settlement can be reduced by 66% when X_{6}, X_{1}, X_{2}, X_{5}, and X_{7} are ensured safe (Figure 13).
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.(1)The nodes X_{5} (abnormal TBM shutdown) and X_{7} (excessive deviation from the axis) mostly involve operational error. Safety management and supervision need to be strengthened at the construction site to eliminate such errors and ensure that the TBM is operated properly. Besides, an advanced realtime laser locator may help to alarm in the case of large axial deviation.(2)The nodes X_{1} (confined water) and X_{2} (ground cavity or flow sand) belong to environmental failure. In order to reduce the influence of environmental failure, careful geological exploration should be carried out before tunneling to identify the poor geological and hydrological conditions that may be encountered. During excavation, the advanced geological prediction technology may be employed to detect adverse geological and hydrological conditions ahead of the TBM in real time, including confined water, ground cavity, and flow sand.(3)Node X_{6} (seal failure at shield tail) belongs to multiple failures. The quality of the tail brush needs to be enhanced, and tail brush should promptly be replaced when it is worn.
By adopting corresponding safety measures in shield tunnel excavation, the occurrence probability of various degrees of surface collapse (OE_{3}, OE_{4}, OE_{6}, OE_{7}, and OE_{8}) was significantly decreased (Figure 13). Finally, the TBMs successfully passed through the left track of DCS on March 3, 2017, and the right track on June 11, 2017, without any surface collapse accident, demonstrating the effectiveness of our proposed hybrid method.
5. Conclusions and Future Works
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 bowtie 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 (OE_{3}, OE_{4}, OE_{6}, OE_{7}, and OE_{8}) but have limited effect on the prevention of accidents of OE_{1}, OE_{2}, and OE_{5}. It is essential to decrease the probability of excessive surface settlement in order to prevent the resulting outcome events (OEs).
By mapping the bowtie analysis to Bayesian networks (i.e., BTBN analysis), we determined the key nodes that could cause excessive surface settlement (LE). The key nodes included the following: X_{6} (seal failure at shield tail), X_{1} (confined water), X_{2} (ground cavity or flow sand), X_{5} (abnormal TBM shutdown), and X_{7} (excessive deviation from the axis). Effective safety measures at these nodes could reduce the occurrence probability of excessive surface settlement (LE) by 66%.
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.
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
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.
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