Prioritization of Hazardous Zones Using an Advanced Risk Management Model Combining the Analytic Hierarchy Process and Fuzzy Set Theory

Abstract

Risk management plays a vital role in ensuring the safety and efficiency of tunnel construction by considering various factors, including uncertainties associated with concurrent adverse sources. One key aspect of risk management is prioritizing hazardous zones to devise an optimal countermeasure plan within time and cost constraints. This study developed an advanced tunnel risk management model, combining the analytic hierarchy process (AHP) and fuzzy set theory (FST). The model derived the impact using AHP and the probability using FST. By selectively combining causal factors that met the selection criterion, the risk of each hazardous zone was determined, enabling the prioritization of identified hazardous zones. The model application results indicated that causal combinations associated with significant tunnel convergence posed a relatively high risk. Moreover, the hazardous zones where unstable ground formations were excavated by a gripper tunnel boring machine (TBM) were revealed as the most vulnerable locations. Consequently, adopting a shield TBM or implementing ground reinforcement is recommended. Overall, the developed model effectively prioritizes identified hazardous zones and provides an optimal countermeasure plan, contributing to the overall safety and efficiency of the operations.

1. Introduction

The demand for underground infrastructure has increased due to limited surface space [1,2]. Furthermore, with the increase in urban population density, the social cost of traffic congestion has become a pressing concern [3], which has highlighted the importance of tunnel construction. Given the various uncertainties associated with insufficient information in tunnel construction, proactive risk management becomes essential. Unless risk management is performed appropriately, numerous accidents can occur, including face collapse, excessive ground deformation, and water and mud inflow [4,5].

Numerous pieces of research have been conducted to develop tunnel risk management models for ensuring the safety and efficiency of tunnel construction. Eskesen et al. (2004) [6] developed the guidelines for tunnel risk management, employing a risk matrix approach. Subsequently, a variety of tunnel risk management models emerged, incorporating methodologies such as the Event Tree Analysis (ETA), Fault Tree Analysis (FTA), Bayesian Network (BN), or their combinations [1,7,8,9,10]. Although these previously developed models are well-structured and have various advantages, they have their limitations. Generally, the risk is assessed based on impact and probability, which are frequently evaluated through expert surveys [6]. While impact estimation can be relatively accurate, thanks to quantitative criteria such as downtime, the evaluated probability is often uncertain due to the inherent uncertainties involved in tunnel construction [7,11]. Due to these uncertainties, it can be challenging for experts to choose one survey option in probability evaluation certainly. Conventional studies on tunnel risk management may encounter difficulties in effectively addressing these uncertainties [1,6,7,8,9,10,11].

To address these uncertainties, fuzzy set theory (FST) has been extensively employed in risk management studies using various techniques as the certainty can be distributed into multiple options owing to the ambiguous set boundary of the fuzzy set, including the fuzzy fault tree analysis (FFTA) and the fuzzy inference system (FIS). The FFTA implements the fuzzy set theory to the FTA to complement the FTA’s crisp probability value derived from less information and uncertain situations. Mentes and Helvacioglu (2011) [12] conducted a risk analysis for a spread mooring system. Wang et al. (2013) [13] evaluated the crude oil tank fire and explosion probability and the Fussell–Vesely importance. Hosseini et al. (2020) [14] quantitatively assessed the fire risk by incorporating FTA and ETA. Kuzu and Senol (2021) [15] derived the probability of cargo manifold leakage of an ammonia gas tanker. However, FFTA has a limitation: when numerous basic events are connected to the OR gate, the probability of the top event converges to 1 regardless of the individual probabilities of the basic events. The FIS is a systematic formulation process of input and output data consisting of four stages: Fuzzification, Fuzzy rule base, Fuzzy inference system, and Defuzzification. Jamshidi et al. (2013) [16] proposed a pipeline risk assessment method integrating the FIS and relative risk score (RRS). Rafie and Namin (2015) [17] and Gallab et al. (2019) [18] quantified FIS-based subsidence and maintenance activity risk in terms of occurrence, severity, and detection, respectively. Arbabsiar et al. (2020) [19] predicted the advance rate of rock TBM using FIS-based geological risk levels. However, FIS requires numerous fuzzy rules when dealing with many input parameters and their membership functions. These limitations can undermine the reliability and practicality of risk management, emphasizing the need for an advanced FST-based risk management model.

During tunnel construction, hazardous zones (i.e., high-risk vulnerable locations) associated with one or concurrent adverse geology sources such as mixed ground are inevitably encountered [18,20,21]. Prioritizing these zones in terms of risk is crucial to develop an optimal countermeasure plan, considering the time and cost constraints of the tunnel project. However, none of the previously developed models can address this issue. Therefore, an advanced FST-based risk management model that considers the effects of concurrent sources and prioritizes possible hazardous zones is essential to enhance the safety and efficiency of tunnel projects.

This study developed an advanced risk management model integrating the analytic hierarchy process (AHP) and FST to prioritize hazardous zones identified in a tunnel project. Potential hazardous zones were identified based on accidents and sources associated with the specific tunnel project. The impact of each accident and the probability of each causal combination were calculated using the AHP and FST, respectively. Subsequently, the risk of each causal combination and hazardous zone was determined, leading to the prioritization of the identified hazardous zones. The outcomes of this prioritization process can significantly contribute to the success of a tunnel project by enabling efficient responses to be implemented.

2. Materials and Methods

2.1. Analytic Hierarchy Process (AHP)

The analytic hierarchy process (AHP) has proven to be a valuable tool in addressing complex decision-making problems that involve qualitative multi-criteria elements. In this study, the AHP was employed to assess the impact of each accident [22]. Expert surveys utilizing pairwise comparisons were constructed to evaluate these elements, resulting in the formulation of a pairwise comparison matrix, as expressed in Equation (1).

$$\begin{gathered} \mathrm{A}=\left|{\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right| \mathrm{where} \mathrm{i},\mathrm{j}=\mathrm{1,2},\dots ,\mathrm{n} \\ =\left(\begin{array}{ccc}\begin{array}{cc}1& {\mathrm{a}}_{12}\\ \frac{1}{{\mathrm{a}}_{12}}& 1\end{array}& \begin{array}{c}\cdots \\ \cdots \end{array}& \begin{array}{c}{\mathrm{a}}_{1\mathrm{n}}\\ {\mathrm{a}}_{2\mathrm{n}}\end{array}\\ \begin{array}{cc}⋮& ⋮\end{array}& \ddots & ⋮\\ \begin{array}{cc}\frac{1}{{\mathrm{a}}_{1\mathrm{n}}}& \frac{1}{{\mathrm{a}}_{2\mathrm{n}}}\end{array}& \cdots & 1\end{array}\right) \end{gathered}$$

(1)

Here, ${\mathrm{a}}_{\mathrm{i}\mathrm{j}}$ is the importance ratio of the ith to the jth element. The eigenvalue method was employed to calculate the relative weight of each element, which corresponds to the component of the normalized eigenvector associated with the largest eigenvalue of the pairwise comparison matrix [23]. By deriving and comparing the relative importance values, a systematic prioritization of the relevant elements can be achieved [7].

A logical consistency test on the pairwise comparison matrix should be performed, accompanied by the calculation of the consistency ratio (CR). The CR is determined by the consistency index (CI) divided by the random index (RI) and can be calculated using Equations (2) and (3), respectively.

$$\mathrm{C}\mathrm{R}=\frac{\mathrm{C}\mathrm{I}}{\mathrm{R}\mathrm{I}}$$

(2)

$$\mathrm{C}\mathrm{I}=\frac{{\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\mathrm{n}}{\mathrm{n}-1}$$

(3)

Here, ${\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and $\mathrm{n}$ are the largest eigenvalues and the order of the pairwise comparison matrix, respectively. The RI represents the average consistency index for multiple random pairwise comparison matrices, which corresponds to the matrix order [24,25]. The RI values for matrices ranging from orders 1 to 10 are provided in

Table 1. RI values based on matrix order [24].

Matrix Order	1	2	3	4	5	6	7	8	9	10
RI value	0.00	0.00	0.58	0.90	1.12	1.24	1.32	1.41	1.45	1.49

[24].

A smaller CR indicates better logical consistency. Typically, a CR value below 0.2 is considered acceptable, indicating tolerable logical consistency. If the CR exceeds 0.2, it is advisable to reconstruct the pairwise comparison matrix [24].

2.2. Fuzzy Set Theory (FST)

The fuzzy set theory (FST) has been introduced to address the vagueness inherent in human cognition when dealing with uncertain information [26]. With the aid of its capacity to represent vagueness in linguistic variables through mathematical expressions, the FST has found widespread applications in various domains, including business, engineering, and natural sciences [27,28].

In classical set theory, a set possesses a well-defined boundary, as depicted in Figure 1a. This means that an element in a classical set is either a member (with a membership degree of one) or a non-member (with a membership degree of zero). In contrast, a fuzzy set can exhibit an arbitrary membership degree between zero and one due to its ambiguous set boundary, as illustrated in Figure 1b.

Once a fuzzy set A is defined on a universe of discourse with elements denoted by x, its membership function can be expressed as ${\mathsf{\mu }}_{\mathrm{A}}(\mathrm{x})$, which takes values in the interval [0, 1] [13]. In this context, the degree of membership of an element in a set increases as the membership function value approaches one [29]. Among various types of membership functions [13,29,30], the trapezoidal membership function is commonly adopted due to its ability to adjust certain and uncertain ranges, as well as its ease of definition, representation, and computation [31].

The trapezoidal membership function is defined by Equation (4) and illustrated in Figure 2. It can be represented as $(\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d})$, where $\mathrm{a}\le \mathrm{b}\le \mathrm{c}\le \mathrm{d}$. The interval [b, c] provides the maximal degree of ${\mathsf{\mu }}_{\mathrm{A}}(\mathrm{x})$, while the other constants {a, d} serve as the lower and upper bounds, respectively, of the evaluation data area [29].

$${\mathsf{\mu }}_{\mathrm{A}}(\mathrm{x})=\left\{\begin{array}{c}\mathrm{x}-\mathrm{a}/\mathrm{b}-\mathrm{a}, \mathrm{a}\le \mathrm{x}\le \mathrm{b}\\ 1, \mathrm{b}\le \mathrm{x}\le \mathrm{c}\\ \mathrm{d}-\mathrm{x}/\mathrm{d}-\mathrm{c}, \mathrm{c}\le \mathrm{x}\le \mathrm{d}\\ 0, \mathrm{Otherwise}\end{array}\right.$$

(4)

3. Proposed Approach

3.1. Risk Identification

Expected losses (i.e., risk) can vary depending on the type and number of associated sources, such as fault zone when an accident occurs, such as tunnel boring machine (TBM) jamming. Therefore, this study aims to evaluate the risk corresponding to each causal combination, which represents a one-to-one or one-to-many relationship between accidents and sources. In cases where there is a one-to-many relationship between accidents and sources, the causal combination considers the influence of concurrent sources on a single accident. It is important to note that countermeasures for risk treatment should be applied sequentially to the more hazardous zones along the tunnel alignment. These hazardous zones are defined as areas where the identified sources exist. Thus, the goal of this study is to prioritize the hazardous zones to develop an optimal countermeasure plan. To achieve this, accidents, sources, causal combinations, and hazardous zones related to a specific tunnel project were identified as part of the risk identification process.

Various techniques have been proposed for risk identification, including brainstorming, checklists, literature reviews, questionnaire surveys, and expert interviews, which are commonly adopted in practice [32]. Combining these techniques instead of relying solely on one approach enhances the reliability of risk identification [33]. In the established tunnel risk management model, literature reviews and expert interviews were used for the risk identification process. Initially, potential sources of risk in the target tunnel construction site were identified through a comprehensive review and comparison of various relevant materials, including site characterization reports and literature addressing tunnel construction risk. Subsequently, the identified sources were utilized to analyze possible accidents and establish causal relationships between these sources and accidents, based on an extensive review of the pertinent literature. This process resulted in the formulation of preliminary risk identification results. To ensure the validity and reliability of the preliminary results, the opinions of multiple experts were obtained through expert interviews. The feedback and insights made by these interviews were carefully considered during the revision process, leading to the refinement of the results for risk identification.

3.2. Risk Analysis

3.2.1. Impact Analysis

The impact of each accident was assessed using the AHP, and the results were utilized to prioritize the identified hazardous zones. Expert surveys were conducted to obtain pairwise comparisons between the accidents. In these surveys, experts assigned scores to indicate the relative importance of one accident compared to another (i.e., ${\mathrm{a}}_{\mathrm{i}\mathrm{j}}$ in Equation (1)). The scores were given on a scale from 1/5 to 5, taking into account various factors such as the level of damage and the difficulty of implementing countermeasures.

Table 2. Scale used for pairwise comparisons [24].

Intensity of the Relative Importance	Definition
1	Two items are equally influential.
3	One is considered slightly influential over another.
5	One is considered strongly influential over another.
Reciprocals of above numbers	When the ith item compared to the jth item is assigned one of the above numbers, the jth item compared to the ith item is assigned its reciprocal.

provides the scale used for the pairwise comparisons [24].

After aggregating the expert evaluations with acceptable logical consistency, the modal value was assigned to ${\mathrm{a}}_{\mathrm{i}\mathrm{j}}$, resulting in the formation of a pairwise comparison matrix, as depicted in Equation (1). The relative weight of each accident, obtained using the eigenvalue method, was then considered the impact of that particular accident. In this context, the impact of an accident was assumed to be equivalent to that of a causal combination associated with the accident.

3.2.2. Probability Analysis

The probability of each causal combination was determined by conducting an FST-based analysis of expert survey responses, which can rationally reflect the uncertainties associated with tunnel construction. In this study, seven linguistic classes (i.e., Very-low, Low, Medium-low, Medium, Medium-high, High, and Very-high) of probability were considered, as it is recommended to have a suitable number of variables (between five and nine) for accurate estimation using the FST [15]. The adopted linguistic classes were then transformed into fuzzy sets with trapezoidal membership functions. Specifically, the membership functions of fuzzy sets corresponding to high probability classes (Medium-high, High, and Very-high) were assigned wider ranges compared to the others to ensure a conservative risk analysis approach. Figure 3 illustrates the transformed fuzzy sets and their corresponding membership functions.

Table 3. Linguistic classes and trapezoidal fuzzy sets of probability.

Linguistic Class	Fuzzy Set (a, b, c, d)
Very-low	(0, 0, 0.05, 0.1)
Low	(0.05, 0.1, 0.15, 0.2)
Medium-low	(0.15, 0.2, 0.25, 0.3)
Medium	(0.25, 0.3, 0.35, 0.4)
Medium-high	(0.35, 0.4, 0.55, 0.6)
High	(0.55, 0.6, 0.75, 0.8)
Very-high	(0.75, 0.8, 1, 1)

presents the linguistic classes and trapezoidal fuzzy sets of probability.

The probability of each causal combination was evaluated through expert surveys. As causal combinations involve the combinations between one or multiple sources and an associated accident, the probability analysis in this study can consider the impact of concurrent sources on a specific accident. Each expert was asked to assess the probability of the identified causal combinations by choosing one of the seven classes shown in Figure 3: Very-low, Low, Medium-low, Medium, Medium-high, High, and Very-high. Only the responses from experts that exhibited acceptable logical consistency in the impact analysis were considered. Subsequently, the aggregated fuzzy set was derived by Equation (5), where n represents the number of selected experts.

$$({\mathrm{a}}_{\mathrm{a}\mathrm{v}\mathrm{e}},{\mathrm{b}}_{\mathrm{a}\mathrm{v}\mathrm{e}},{\mathrm{c}}_{\mathrm{a}\mathrm{v}\mathrm{e}},{\mathrm{d}}_{\mathrm{a}\mathrm{v}\mathrm{e}})=({\sum }_1^{\mathrm{n}}\frac{{\mathrm{a}}_{\mathrm{i}}}{\mathrm{n}},{\sum }_1^{\mathrm{n}}\frac{{\mathrm{b}}_{\mathrm{i}}}{\mathrm{n}},{\sum }_1^{\mathrm{n}}\frac{{\mathrm{c}}_{\mathrm{i}}}{\mathrm{n}},{\sum }_1^{\mathrm{n}}\frac{{\mathrm{d}}_{\mathrm{i}}}{\mathrm{n}})$$

(5)

Finally, the probability of each causal combination was determined by employing the centroid defuzzification method, where the x-component of the centroid of the area is bounded by the x-axis and the trapezoidal membership function of the aggregated fuzzy set. This process is illustrated in Figure 4.

3.3. Risk Evaluation

The risk of each causal combination was evaluated, and the risk of each hazardous zone was determined. The individual risk of each causal combination was initially calculated as the product of its impact and probability, allowing for the identification of relatively fatal causal combinations. The risk of each hazardous zone was then derived by selectively adding the risk of causal combinations that met the selection criterion. The selection criterion was as follows: only causal combinations with a risk equal to or greater than $\frac{1}{2\mathrm{n}}\left(=\frac{1}{\mathrm{n}}\times 0.5\right)$ (where n represents the number of identified accidents) were included from the relevant causal combinations for each hazardous zone. In the AHP, the sum of the impacts of all accidents should be 1, resulting in an average impact of $\frac{1}{\mathrm{n}}$, considering it as a relative value. Conversely, the average probability was set at 0.5 (i.e., 50%). The rationale behind selecting only the causal combinations with a risk greater than $\frac{1}{2\mathrm{n}}$ was to exclude causal combinations that require little attention, ensuring a rational approach to risk management. Consequently, hazardous zones without fatal causal combinations were assigned a risk value of zero. Finally, all identified hazardous zones were prioritized based on their risk levels, establishing an optimal sequence and level of countermeasure plans while considering the time and cost constraints of the tunnel project. Figure 5 summarizes the overall flow chart of the established tunnel risk management model.

4. Case Study

4.1. Project Overview

The applicability of the developed risk management model was verified on a tunnel project that encompassed various tunnel types and construction methods during the design stage. The tunnel length considered in this study was approximately 10.625 km. The ground types encountered along the tunnel alignment consisted of weathered rock, soft rock, and hard rock. The geological profile of the site for the target tunnel project is illustrated in Figure 6.

The tunnel project consisted of three types of tunnels in sequence: twin tunnels, double-track tunnels, and enlarged tunnels. Each tunnel type required a specific construction method. The twin tunnels were designed to be excavated using a gripper TBM, while the other tunnels were planned to be constructed using the New Austrian Tunneling Method (NATM). During the design stage, an 11 m diameter gripper TBM was chosen for approximately 3 km of the tunnel drive. Furthermore, the tunnel alignment passed beneath several bridges and train stations.

4.2. Identification of Risks

Accidents, sources, and causal relationships between them associated with the tunnel project were identified through a combination of literature reviews and expert interviews. Specifically, site characterization reports, tunnel design references, and various pieces of literature [15,34,35] were consulted and compared. Furthermore, the opinions of three tunnel experts with professional experience and knowledge were gathered and reflected in the risk identification results. The identified accidents and sources are summarized in

Table 4. Accidents identified in the target tunnel project.

Symbol	Accident
A1	Significant tunnel convergence
A2	TBM jamming
A3	Insufficient TBM reaction force
A4	Significant deformation of adjacent infrastructures

and

Table 5. Sources identified in the target tunnel project.

Symbol	Source
S1	Weathered rock ground
S2	Fault zone
S3	High groundwater level (>30 m from tunnel depth)
S4	Excavation of an enlarged tunnel
S5	Connection b/w twin tunnels and an enlarged tunnel
S6	Connection b/w a vertical shaft and tunnel
S7	Connection b/w double-track tunnels and an enlarged tunnel
S8	Tunnel excavation adjacent to infrastructures
S9	Cavity

, respectively.

The causal relationships between accidents and sources were established as follows. Firstly, the low strength of the weathered rock ground and the occurrence of shear failure along the fault zone can lead to tunnel deformation, TBM jamming, and a lack of TBM reaction force. Numerous cases have been reported where tunnel or adjacent infrastructure deformation resulted from lining cracking and water leakage caused by high groundwater levels [34]. Excavation of an enlarged tunnel can also result in excessive deformation. All the connections between different tunnel sections (S5, S6, and S7 in Table 5) can lead to significant tunnel deformation due to stress concentration induced by different constraints at the connection [35]. Tunnel excavation near existing infrastructures can lower the groundwater level, causing deformation in the foundation of the adjacent structures. Finally, the presence of cavities can lead to unexpected settlements, resulting in the deformation of adjacent infrastructures [15].

Table 6. Causal relationships between the identified accidents and sources.

Accident	Source
Significant tunnel convergence	Weathered rock ground
	Fault zone
	High groundwater level
	Excavation of an enlarged tunnel
	Connection b/w twin tunnels and an enlarged tunnel
	Connection b/w a vertical shaft and tunnel
	Connection b/w double-track tunnels and an enlarged tunnel
TBM jamming	Weathered rock ground
	Fault zone
Insufficient TBM reaction force	Weathered rock ground
	Fault zone
Significant deformation of adjacent infrastructures	High groundwater level
	Tunnel excavation adjacent to infrastructures
	Cavity

summarizes these causal relationships.

Based on the identified sources, the locations where each source was presented were investigated along the tunnel alignment concerning site characterization reports and tunnel design reports. Herein, several sources can exist in one location simultaneously. In this study, the identified locations were considered hazardous zones. These hazardous zones are indicated by numerical labels on the geological profile, as shown in Figure 7. The causal combinations associated with each hazardous zone are summarized in

Table 7. Causal combinations involved in each hazardous zone.

Hazardous Zone Number	Causal Combination
	Symbol	Accident	Source
1	A1-S2	Significant tunnel convergence	Fault zone
	A2-S2	TBM jamming	Fault zone
	A3-S2	Insufficient TBM reaction force	Fault zone
2	A1-[S1,S2]	Significant tunnel convergence	Weathered rock ground
			Fault zone
	A2-[S1,S2]	TBM jamming	Weathered rock ground
			Fault zone
	A3-[S1,S2]	Insufficient TBM reaction force	Weathered rock ground
			Fault zone
	A4-S8	Significant deformation of adjacent infrastructures	Tunnel excavation adjacent to infrastructures
3	A1-[S4,S5,S6]	Significant tunnel convergence	Excavation of an enlarged tunnel
			Connection b/w twin tunnels and an enlarged tunnel
			Connection b/w a vertical shaft and tunnel
	A4-S8	Significant deformation of adjacent infrastructures	Tunnel excavation adjacent to infrastructures
4	A1-[S3,S4,S5]	Significant tunnel convergence	High groundwater level
			Excavation of an enlarged tunnel
			Connection b/w twin tunnels and an enlarged tunnel
	A4-[S3,S8]	Significant deformation of adjacent infrastructures	High groundwater level
			Tunnel excavation adjacent to infrastructures
5	A1-[S2,S3]	Significant tunnel convergence	Fault zone
			High groundwater level
	A4-S3	Significant deformation of adjacent infrastructures	High groundwater level
6	A1-[S3,S6]	Significant tunnel convergence	High groundwater level
			Connection b/w a vertical shaft and tunnel
	A4-S3	Significant deformation of adjacent infrastructures	High groundwater level
7	A1-[S2,S3]	Significant tunnel convergence	Fault zone
			High groundwater level
	A4-S3	Significant deformation of adjacent infrastructures	High groundwater level
8	A1-[S3,S6]	Significant tunnel convergence	High groundwater level
			Connection b/w a vertical shaft and tunnel
	A4-S3	Significant deformation of adjacent infrastructures	High groundwater level
9	A1-[S2,S3,S6,S7]	Significant tunnel convergence	Fault zone
			High groundwater level
			Connection b/w a vertical shaft and tunnel
			Connection b/w double-track tunnels and an enlarged tunnel
	A4-[S3,S8,S9]	Significant deformation of adjacent infrastructures	High groundwater level
			Tunnel excavation adjacent to infrastructures
			Cavity
10	A1-[S3,S6]	Significant tunnel convergence	High groundwater level
			Connection b/w a vertical shaft and tunnel
	A4-S3	Significant deformation of adjacent infrastructures	High groundwater level
11	A1-[S2,S3]	Significant tunnel convergence	Fault zone
			High groundwater level
	A4-S3	Significant deformation of adjacent infrastructures	High groundwater level

.

4.3. Results of Risk Analysis

In this study, the impacts of accidents and the probabilities of causal combinations were determined through survey responses from thirty-six experts with relevant professional expertise and experience. The impacts of significant tunnel convergence, TBM jamming, insufficient TBM reaction force, and significant deformation of adjacent infrastructures were evaluated as 0.471, 0.267, 0.137, and 0.125, respectively, as shown in

Table 8. Results of impact analysis.

Symbol	Impact
A1	0.471
A2	0.267
A3	0.137
A4	0.125

. Notably, the tunnel experts considered significant tunnel convergence to be the most critical accident in this project. Excessive tunnel convergence is highly associated with collapse. This finding is consistent with a previous study that identified collapse as the most severe accident during tunnel construction [36].

Subsequently, the probabilities of fifteen causal combinations associated with one or multiple sources with one accident (as shown in Table 7) were determined using the FST. The resulting overall probability values ranged between 0.407 and 0.741, indicating that all causal combinations fell within the range of Medium-high probability or higher. It is worth noting that the causal combination associated with the accident showing the least impact (i.e., A4-[S3,S8,S9]) yielded the highest probability of 0.741. As the impact and probability can present conflicting values, it is crucial to appropriately consider both factors in risk management. In this study, impact and probability were equally weighted in the subsequent risk evaluation process. However, future studies should consider incorporating appropriate weighting schemes to account for their different levels of significance.

Table 9. Results of probability analysis.

Symbol	Probability
A1-[S1,S2]	0.681 (High)
A1-S2	0.536 (Medium-high)
A1-[S2,S3]	0.573 (Medium-high to High)
A1-[S2,S3,S6,S7]	0.699 (High)
A1-[S3,S6]	0.457 (Medium-high)
A1-[S3,S4,S5]	0.544 (Medium-high)
A1-[S4,S5,S6]	0.569 (Medium-high to High)
A2-[S1,S2]	0.558 (Medium-high to High)
A2-S2	0.538 (Medium-high)
A3-[S1,S2]	0.619 (High)
A3-S2	0.521 (Medium-high)
A4-S3	0.407 (Medium-high)
A4-[S3,S8,S9]	0.741 (High)
A4-[S3,S8]	0.629 (High)
A4-S8	0.572 (Medium-high to High)

presents the results of the probability analysis for the causal combinations.

4.4. Results of Risk Evaluation

Table 10. Risk evaluation results.

Hazardous Zone Number	Causal Combination				Risk
	Symbol	Impact	Probability	Risk
1	A1-S2	0.471	0.536	0.253	0.396
	A2-S2	0.267	0.538	0.144
	A3-S2	0.137	0.521	0.071
2	A1-[S1,S2]	0.471	0.681	0.321	0.470
	A2-[S1,S2]	0.267	0.558	0.149
	A3-[S1,S2]	0.137	0.619	0.085
	A4-S8	0.125	0.572	0.072
3	A1-[S4,S5,S6]	0.471	0.569	0.268	0.268
	A4-S8	0.125	0.572	0.072
4	A1-[S3,S4,S5]	0.471	0.544	0.256	0.256
	A4-[S3,S8]	0.125	0.629	0.079
5	A1-[S2,S3]	0.471	0.573	0.270	0.270
	A4-S3	0.125	0.407	0.051
6	A1-[S3,S6]	0.471	0.457	0.215	0.215
	A4-S3	0.125	0.407	0.051
7	A1-[S2,S3]	0.471	0.573	0.270	0.270
	A4-S3	0.125	0.407	0.051
8	A1-[S3,S6]	0.471	0.457	0.215	0.215
	A4-S3	0.125	0.407	0.051
9	A1-[S2,S3,S6,S7]	0.471	0.699	0.329	0.329
	A4-[S3,S8,S9]	0.125	0.741	0.093
10	A1-[S3,S6]	0.471	0.457	0.215	0.215
	A4-S3	0.125	0.407	0.051
11	A1-[S2,S3]	0.471	0.573	0.270	0.270
	A4-S3	0.125	0.407	0.051

provides a summary of the risk evaluation results for the causal combinations and hazardous zones. As a result of analyzing the risk of each causal combination, it was found that all causal combinations associated with the highest-impact accident (A1) resulted in a risk value exceeding $\frac{1}{2\mathrm{n}}$, indicating the need for countermeasures to mitigate their risk. On the other hand, the causal combinations related to relatively low-impact accidents (A3 and A4) indicated minimal risk, ranging from 0.051 to 0.093. These results can be attributed to the imbalanced impact values, as the impact of A1 was significantly greater than that of the other accidents according to the AHP analysis, which determined the relative values. Although five out of the six causal combinations associated with A3 and A4 had a probability of 0.5 or higher, these causal combinations did not meet the selection criterion (i.e., risk of each causal combination $\ge \frac{1}{2\mathrm{n}}$) due to the relatively low impact of A3 and A4.

The objective of this study is to prioritize hazardous zones to develop an optimal countermeasure plan. Based on the risk evaluation results of each hazardous zone, it was found that hazardous zones 1 and 2 had the highest risk levels, indicating that these locations, where the gripper TBM excavated weak ground formations such as weathered rock and fault zone, were the most vulnerable. Therefore, it is recommended to consider changing the TBM type to a shield TBM or implementing ground reinforcement measures as part of the risk treatment strategy. Alternatively, meticulous operation and management should be implemented continuously, as hazardous zones 1 and 2 can be considered a single, wide section due to their proximity.

Table 11. Prioritization results for identified hazardous zones.

Rank	Hazardous Zone Number	Risk
1	2	0.470
2	1	0.396
3	9	0.329
4	5, 7, 11	0.270
5	3	0.268
6	4	0.256
7	6, 8, 10	0.215

summarizes the prioritization results for the identified hazardous zones.

4.5. Implications of the Proposed Approach

This study effectively considers the inherent vagueness in expert survey responses induced by uncertainties in tunnel construction by incorporating the membership degree property within FST. Moreover, the causal combination composition allows for a comprehensive analysis of the effect of concurrent sources on accidents when estimating both probability and risk. The selection criterion adopted in risk evaluation facilitates a rational approach to risk management by excluding causal combinations of minor concerns. These methodological advantages enable the rational prioritization of hazardous zones within the tunnel construction site. Consequently, the obtained prioritization results serve as a valuable foundation for formulating an optimal countermeasure plan that considers the practical constraints of time and cost associated with the tunnel project.

5. Conclusions

This study developed an advanced risk management model for tunnel construction by integrating the analytic hierarchy process (AHP) and fuzzy set theory (FST), enabling the prioritization of hazardous zones identified along the tunnel alignment. The developed model was applied to a tunnel project that incorporated multiple tunnel types and construction methods. The key conclusions and contributions of this study are as follows:

• All causal combinations associated with the highest-impact accident (i.e., significant tunnel convergence) are determined to be relatively fatal, but those associated with the low-impact accidents indicate minimal risk. It can be attributed to the imbalanced impact values between the highest-impact accident and the others.
• The prioritization results reveal that the locations where the gripper TBM excavates under unstable ground formations such as weathered rock and fault zones are the most vulnerable. Hence, the most recommended countermeasure is adopting a shield TBM instead of a gripper TBM or implementing ground reinforcement. Continuous supervision during the excavation of these sections is required owing to their proximity and high risk.
• FST effectively considers the inherent vagueness in expert surveys, facilitating a comprehensive estimation of both probability and risk. In addition, the causal combination composition addresses the impact of concurrent sources on accidents. The selection criterion adopted in risk evaluation supports rational risk management by excluding insignificant causal combinations. The obtained prioritization results of hazardous zones enable the formulation of an optimal countermeasure plan.
• The limitation of the developed model is due to the impact and probability being equally weighted in the risk evaluation, which may be inconsistent with each tunnel project’s objective and financial margin. Furthermore, the results derived from the developed model can depend on the experts involved. Future research can address these limitations by introducing a weight distribution between impact and probability based on appropriate weighting schemes and establishing an expert composition that is sufficient and not biased.