Risk Assessment of TBM Construction Based on a Matter-Element Extension Model with Optimized Weight Distribution

Abstract

In order to effectively address the potential hazards associated with the construction of Phase II of the YE Water Supply Project’s KS tunnel in Xinjiang, this study employs the WBS-RBS (Work Breakdown Structure and Risk Breakdown Structure) method for risk identification. This approach aims to identify various risks that may arise during TBM (Tunnel Boring Machine) construction. To prevent incomplete risk factor identification resulting from subjective judgment, a risk index system is established based on the identification results. Subsequently, a matter-element extension model is utilized to quantify the risk factors within this index system, and comprehensive weights are determined using variable weight theory to assess construction risk levels. Importance analysis of each index is then conducted to identify those with significant impact on risk evaluation outcomes. Finally, by comparing actual engineering cases with other risk evaluation models, this paper verifies the reliability of its constructed risk assessment model and proposes measures for controlling potential risks based on these evaluations. The paper provides a clear definition of safety risks encountered during TBM construction and conducts comprehensive risk assessments as a valuable reference for research related to the tunnel boring machine construction period in tunnel engineering.

1. Introduction

The growing trend of adopting the TBM tunnel excavation method instead of the traditional drilling and blasting approach has become increasingly apparent in various industries, including water conservation, transportation, and mining. When constructing tunnels and underground engineering projects, risks are influenced by objective factors such as geological conditions and design requirements, as well as subjective factors like construction technology expertise, disaster detection capabilities, and site organization and coordination abilities. These two sets of factors have a mutual impact on each other’s levels. Due to the complex risks associated with TBM construction, there are multiple risk indicators that need identification; however, the evaluation results for each individual indicator often vary. Therefore, it is neither reasonable nor practical to solely rely on a highest-principle approach for grading evaluations. Consequently, this issue falls under the category of a typical comprehensive evaluation problem [1].

To enhance the scientific robustness of risk assessment in tunnel or underground construction projects, researchers have proposed various methodologies, including the application of techniques such as the Monte Carlo method, artificial neural network method, analytic hierarchy process, entropy weight method, and risk assessment matrix method. F. Sun [2] has developed an improved variable weight model for the comprehensive evaluation of shield tunnel structural health. The model employs variable weight theory to replace traditional fixed weights, thereby reflecting the impact of index value fluctuations on index weights; Y. Li [3] utilizes preference ratio and anti-entropy weight methods to analyze the weight of each index factor. Additionally, considering the uncertainty and fuzziness associated with landslide risk factors in diversion tunnel construction, an entropy theory-extension cloud model-based evaluation system is established for assessing diversion tunnel landslide risks; X. Wu [4] achieves more accurate and effective safety risk evaluations of existing tunnels under shield underpasses by establishing a relatively perfect safety risk evaluation system and standard while introducing evidence theory that can effectively integrate uncertain information. Furthermore, fuzzy Bayesian networks are combined to build a safety evaluation model for existing tunnels under shield underpasses; Z. Song [5] uses an analytic hierarchy process to calculate weights for all risk factors in a risk assessment index system and constructs a fuzzy relationship matrix combined with membership vectors obtained through the expert evaluation method. A nonlinear operator is introduced for comprehensive analysis of the risk weights and fuzzy relation matrix, resulting in a new TBM construction risk assessment model based on nonlinear FAHP; L. Zhang [6] proposes a security analysis method based on a fuzzy Bayesian network that takes into account judgment ability level, reliability level auxiliary pipe revealing data reliability when determining basic events’ fuzzy probability occurrence along with expert confidence indexes; Y. Zhao [7] developed a comprehensive model that combines a fuzzy analytic hierarchy process (FAHP) and set pair analysis (SPA) to assess safety risks in long highway operation tunnels. This integration successfully merges subjective weighting with objective evaluation, resulting in improved accuracy of these assessments.

The construction of the tunnel project is not only large-scale, very deep, and long-distance, but in this kind of tunnel project, the site geological conditions, natural climate, and hydrological conditions are more complex, and in the construction process, under the joint action of various risk factors, the risk of accidents is very high. Therefore, the use of a multi-factor risk assessment system can result in a better start for the whole project, do a good job of safety risk analysis for the overall construction, and analyze the internal links of various risk factors, so as to ensure the normal progress of tunnel construction.

The approach utilized in computing the index weight plays a crucial role in influencing the overall assessment mechanism. The three primary techniques for ascertaining index weight are subjective, objective, and comprehensive weighting [8]. There exist diverse methodologies for assessing subjective and objective weights in risk evaluation. Subjective approaches, such as the analytic hierarchy process and Delphi method, rely on expert opinions but may be susceptible to subjectivity bias. Objective approaches, including principal component analysis, the variable coefficient method, and the entropy weight method, enhance objectivity but necessitate an adequate sample size. A comprehensive approach that integrates both subjective and objective factors can yield a more balanced assessment of risk indices without being constrained by a singular methodology.

In light of the limitations associated with the aforementioned methods, a novel endeavor is undertaken to reasonably determine the weightage of indices in TBM construction risk assessment. By employing the work risk decomposition method, a more comprehensive index system for TBM construction risk assessment is formulated. Subsequently, the TBM construction risk index is quantitatively analyzed using matter-element extension theory, and the index weights are enhanced and revised through an improved variable weight analytic hierarchy process to rectify evaluation distortions caused by fluctuations in index values.

This paper aims to analyze and study the TBM construction section of the KS tunnel in the Xinjiang YE water supply project, conduct a comprehensive risk evaluation of the construction projects, obtain safety risk levels for tunnel sections based on the results of the evaluation, summarize corresponding measures to deal with risks, and enrich existing safety evaluation theories for tunnel construction projects. The importance analysis can conduct a more explicit study on the change of index parameters and obtain the impact of the change of index on the weight. According to the results, we can know which aspects of risk have greater impacts on the project. Additionally, this research on TBM construction risks in Xinjiang’s KS tunnel can help design, construction, and management units identify potential risks in similar engineering projects and timely adjust their plans accordingly.

The structure of this paper is as follows: First, we will outline the relevant theoretical basis and research progress of existing TBM risk assessment models, and clarify the positioning and innovation of this study. Then, the proposed model framework is introduced in detail, including model selection, variable selection, and evaluation index system. Then, the empirical calculation process and analysis results of the model are described. Finally, we will summarize the research results, discuss the limitations of the model, and propose future research directions.

2. Research Status of TBM Risk Assessment

Jafar Khademi used the fuzzy analytic hierarchy process to evaluate potential risks such as unstable surrounding rock, water influx, and collapse encountered during TBM excavation [9]. GU identified key risk factors in TBM construction and evaluated tunneling risks using the fuzzy comprehensive risk assessment method with entropy weight. The risks were mainly divided into equipment risk, excavation risk, and auxiliary construction risk based on engineering characteristics, further subdivided into more specific basic risks [10]. SI analyzed major geological issues encountered in deep-buried water diversion tunnel TBM construction and evaluated them based on indicators such as surrounding rock stability, high ground stress, and groundwater conditions [11]. LIU selected excavation parameters and rock mass parameters as evaluation indicators for coal mine tunnel TBM construction to assess the tunability of the tunnel and adaptability of TBM excavation layers [12]. WEN conducted a risk assessment for jamming caused by collapses during TBM excavation; they studied the relationship between torque and resistance moments of excavation parameters, established a probability calculation formula for jamming based on probability theory, and then evaluated the risk of the TBM cutterhead according to probability levels [13]. LIN assessed the occurrence of jams in TBM construction through interpretation structure models and Bayesian networks; they analyzed factors such as the surrounding rock grade, fault zones, and groundwater conditions that contribute to TBMs getting stuck using posterior probability analysis [14]. Leone studied the risks generated when TBMs pass through squeezing formations during construction; they conducted simulation studies using extensive data to analyze the adaptability of TBMs to various geological conditions, and nonlinear regression equations were established based on excavation parameters for evaluation purposes [15]. Leone adopted a linear elastic–viscoplastic constitutive model based on Perzyna overstress theory, which considered the time dependence of plastic deformation through a single viscous parameter [16]. Ji analyzed the maximum shear stress of surrounding rock and finally obtained the variation law of displacement and shear stress of surrounding rock with different deterioration degrees and different dip angles [17]. Based on field evaluation and numerical analysis, Lu proposed risk control countermeasures such as TBM driving parameter control, sand and gravel backfill, backfill grouting, and bottom grouting [18].

According to the aforementioned studies, it is evident that different studies place varying emphasis on indicator selection for different types of risks in TBM construction risk assessment. These disparities primarily stem from the diverse and intricate nature of the geological conditions, engineering environment, equipment performance, and construction technology involved in TBM construction. However, fully identifying these risks throughout the entire construction process often proves challenging. The risks associated with tunneling using a TBM is a dynamic issue wherein different risk factors may arise during various stages of construction or changes in surrounding rock types at the excavation face. For instance, during excavation, particular attention must be given to geological conditions and the safety performance of TBM equipment. Geological conditions can be influenced by numerous factors such as underground rock formation stability and groundwater conditions, which impact both the safety and efficiency of construction operations. Simultaneously, inherent risks are also present within TBM equipment itself; equipment failure or misoperation can lead to severe accidents. Therefore, it becomes imperative to systematically decompose risks layer by layer throughout each phase of the project when dealing with tunneling using a TBM.

In the TBM construction process, there are many uncertain risk factors, which are complicated and changeable. The complexity and uncertainty of these risk factors make the risk assessment of TBM construction extremely difficult. In order to assess the risk of TBM construction more accurately, considering that the risk in TBM construction is dynamic, full of uncertainty and fuzziness, a risk assessment method that can transform the qualitative analysis of uncertainty into quantitative analysis is needed to evaluate the risk of TBM construction of super-long tunnels.

Proper selection of evaluation methods in line with the characteristics of the project and an evaluation system built with multiple indicators can ensure the reliability of the evaluation process to the greatest extent, effectively improve the accuracy and application value of risk assessment, provide a solid decision basis for TBM operations, help risk control, and ensure the safe and efficient progress of the project. In the face of various unpredictable risks in tunnel boring machine construction, establishing a proper risk management system is the core element of successful tunnel construction.

3. Frameworks and Methodologies for Research

3.1. Frameworks for Research

Figure 1 illustrates the research framework for evaluating construction risks in TBM projects, based on an enhanced variable weight matter-element extension model. The framework comprises four main components: (1) Establishing a comprehensive indicator system to identify construction risks; (2) Using the matter-element extension model to quantify the index; (3) Developing an optimized method for weight allocation through an improved variable weight approach; (4) Validating the TBM construction risk assessment model through actual engineering projects to determine the level of construction risks.

3.2. Methodologies for Research

3.2.1. Risk Identification of TBM Construction Based on the WBS-RBS Method

One of the key factors in conducting TBM construction risk analysis is to determine the influential factors and establish a rational and effective risk index system [19]. In project management, the work breakdown structure (WBS) is a crucial concept that involves systematically dividing the construction process into a well-defined hierarchical framework. On the other hand, the risk breakdown structure (RBS) is a technique used to progressively categorize potential risks originating from major sources into more specific risk factors until they become negligible [20]. Hillson et al. [21] were the first to combine the WBS and RBS methods, constructing a WBS-RBS risk identification coupling matrix for projects, identifying project risk factors, and establishing a project’s risk index system.

In tunnel TBM construction project risk management, according to the site environment and risk management design requirements, the target and limit of risk identification are preliminarily determined. For TBM construction of the tunnel, the goal of risk identification mainly refers to whether safety accidents will occur during TBM construction, including but not limited to equipment failure, casualties, environmental pollution, etc. The boundary of risk identification is more extensive, from the preparation work before TBM construction to the work in TBM excavation construction, etc., for example, in the early stage of TBM construction, the equipment needs to be comprehensively inspected and debuggable to ensure its safety and reliability. It is also necessary to conduct systematic safety education and skill training for personnel to improve their safety awareness and operational skills. In the normal driving process, all parameters should be monitored in real time. In the initial support stage, it is necessary to strengthen the tunnel support in time to avoid a collapse caused by groundwater flooding or rock mass loosening. As for the auxiliary construction stage, such as drainage, ventilation, and transportation, it is also necessary to pay attention to problems such as equipment failure and personnel injury.

• Establish the work breakdown structure for TBM construction [22,23,24,25,26,27].

The WBS work breakdown structure method is founded on system engineering theory, enabling the gradual subdivision of a complex and extensive TBM tunnel project. Based on management content, it is divided into a single operational process, further disintegrating the TBM construction project into multiple work units that possess excellent controllability and operability.

According to the Work Breakdown Structure (WBS) principle, the TBM construction process (W) is divided into two levels:

(1)

Based on the TBM construction process, the first level of the WBS is further decomposed into four stages: TBM construction preparation (W₁), TBM tunneling construction (W₂), TBM preliminary support (W₃), and TBM auxiliary equipment construction (W₄). The stage of TBM construction preparation primarily refers to the preparatory phase when the TBM enters the tunnel excavation.

(2)

According to the operation conditions of each process of TBM construction, the first-level WBS is adjusted and optimized according to the characteristics of the process to form a more detailed second-level WBS, which is specifically the operation unit, and intuitively indicates that the first-level construction stage is composed of various second-level operation units. The obtained decomposition structure for TMB construction work using WBS method is illustrated in Figure 2.

2

Establish the decomposition structure of TBM construction risk sources [28,29,30,31]

By using the RBS method, the potential risks in the TBM construction process are analyzed layer by layer, and a complete risk decomposition tree is established. In this process, the various risks that may cause accidents are classified and summarized in detail to ensure that the various safety risk factors faced in the TBM construction process can be clearly defined and presented in a clear and identifiable state.

The main risks in terms of geology include collapse, sudden water influx, rock burst, and leakage of harmful gases during excavation or support processes. Therefore, factors contributing to these risks are considered to be the joint effect of the rock integrity coefficient, elastic deformation performance index, rock mass classification, internal development degree of the rock mass, moisture content of the rock mass, structural planes within the rock mass, tunnel depth, and groundwater conditions. Additionally, considering the stability, bearing capacity, and deformation characteristics from a geological perspective involves examining the presence of joints and bedding planes as well as whether they are located in an earthquake-prone zone. From a rock-properties perspective, physical properties such as abrasion resistance, frost resistance, permeability resistance, creep behavior, thermal properties, and strength are taken into account.

The equipment risk factors include the type of TBM selected according to the geological conditions, the designed cutterhead structure, the cutters for different rock types, the design of different types of surrounding rock support, the selection of related auxiliary equipment, etc. The equipment risks with higher occurrence frequency include non-timely ventilation and dust removal, TBM blockage, discontinuous slagging, wear of the cutterhead or cutter, the setting of tunneling parameters inconsistent with the actual situation, etc.

The influence of human-made risks in TBM construction cannot be ignored. It has a high degree of importance, because the interference and influence of human factors on TBM construction exist all the time in the construction process, and human activities exist in every construction link, so the area of human-made risks is full of uncertainty. If the organizational structure of the construction management team is unreasonable, it may lead to poor information flow and low decision-making efficiency, affect construction safety, and even lead to serious human-made risks in TBM construction.

The environmental risks mainly include damage to underground pipelines, surface subsidence, groundwater pollution, and building damage. Surface subsidence is a common risk in the process of underground excavation, which may lead to different degrees of surface subsidence, and then lead to deformation and cracking of building structures. Damage to underground pipelines will lead to slow construction progress, so it is also a problem that cannot be ignored. Construction wastewater generated in the process of excavation, and the discharge of pumped leaking water, may pollute groundwater.

According to the engineering RBS principle, a two-level risk decomposition is conducted for TBM construction risk sources (R).

(1)

Firstly, the primary Risk Breakdown Structure (RBS) for TBM construction projects and associated environmental risks comprises four categories: geological risk sources (R₁), equipment-related risk sources (R₂), human-induced risk sources (R₃), and surrounding environment risk sources (R₄).

(2)

Secondly, through a comprehensive analysis of TBM construction risks, and considering the decomposition direction of first-level risk sources, various secondary-level risk structures are derived from the initial structure. The resulting decomposed structure for TBM construction risks obtained using the RBS method is depicted in Figure 3.

3

Establishment of TBM construction risk identification coupling matrix

According to the established Work Breakdown Structure (WBS) and Risk Breakdown Structure (RBS), the lower-level units of both structures are interconnected to derive the coupling matrix for identifying construction risks in TBM projects [25]. In this matrix, “0” signifies that there is no risk generated by the interconnection, while “1” indicates that a risk is generated.

In constructing the coupling matrix, we first ensure that each item (W) in the WBS and each risk category (R) in the RBS are clearly identified. Then, by matching one by one, we create a crossing point for each pair of W × R that indicates whether W creates a risk during construction. For example, hazardous gas leakage is generated by the intersection of “technical preparation W₁₁” and “tunnel depth R₁₅, construction management status R₃₁, security education situation R₃₃”, reflecting that the technical preparation caused by the tunnel burial depth is too large, the construction management is confused, and the safety education is insufficient, resulting in the occurrence of harmful gas, but non-timely feedback and solutions to the problem. The likelihood of accidents increases greatly. The outcomes of the TBM construction risk identification coupling matrix are presented in

Table 1. TBM construction risk identification coupling matrix.

		W1				W2				W3					W4
		W11	W12	W13	W14	W21	W22	W23	W24	W31	W32	W33	W34	W35	W41	W42	W43	W44	W45
R1	R11	0	1	0	0	1	0	0	0	1	0	0	0	0	0	0	0	0	1
	R12	0	1	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	1
	R13	0	1	0	0	1	0	0	0	0	1	1	1	1	0	0	0	0	1
	R14	0	1	0	0	1	0	0	0	0	0	1	1	1	0	0	0	0	1
	R15	1	1	0	0	1	0	0	0	0	0	0	0	0	1	1	1	1	0
R2	R21	0	0	1	1	1	1	1	1	0	0	0	0	0	0	0	0	0	0
	R22	0	0	1	0	1	1	1	1	0	0	0	0	0	1	1	1	1	0
	R23	0	0	1	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
	R24	0	0	1	0	0	0	0	0	1	0	0	0	0	1	1	1	1	0
R3	R31	1	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
	R32	0	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
	R33	1	0	0	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1
R4	R41	0	0	0	1	1	1	1	1	0	0	0	0	0	1	1	1	1	1
	R42	0	0	0	1	1	1	0	0	0	0	0	0	0	1	1	1	1	1
	R43	0	0	0	0	0	0	0	0	0	0	0	0	0	1	1	1	1	1

. Finally, the specific risks are as follows: (1) W₁₁R₁₅, W₁₁R₃₁, W₁₁R₃₃: Hazardous gas leakage; (2) W₁₂R₁₁, W₁₂R₁₂, W₁₂R₁₂, W₂₁R₁₄, W₃₅R₁₄: Rock blast; (3) W₁₂R₁₂, W₁₂R₁₃, W₂₁R₁₃, W₃₅R₁₃: Surging water; (4) W₁₂R₁₄, W₁₂R₁₅, W₂₁R₁₁: Collapse; (5) W₁₃R₂₂, W₁₃R₂₃, W₂₂R₂₁, W₂₁R₂₂, W₄₁R₁₅: Discontinuous slagging; (6) W₁₄R₂₁, W₁₄R₃₁, W₁₄R₃₂, W₁₄R₃₃: TBM jamming; (7) W₂₁R₂₁, W₂₁R₂₂, W₂₁R₃₁, W₂₁R₃₂, W₂₁R₃₃: Support destabilization deformation; (8) W₂₁R₄₁, W₄₂R₄₂: Poor ventilation and dust collection; (9) W₂₃R₂₁, W₂₃R₂₂, W₂₄R₂₁, W₂₄R₂₂: Deviation of digging direction; (10) W₃₁R₁₁, W₃₁R₂₃, W₃₁R₂₄, W₃₁R₂₅: Cave collapse; (11) W₃₂R₂₃, W₂₂R₂₁, W₂₁R₂₂: Water accumulated in the hole; (12) W₃₁R₃₁, W₃₁R₃₂, W₃₃R₁₃: Lining leakage; (13) W₄₁R2₄, W₄₁R₃₁, W4₁R₄₁, W₄₁R₄₂, W₄₁R₄₃: Underground pipeline damage; (14) W₃₄R₁₃, W₃₄R₁₄, W₂₁R₁₅, W₄₄R₁₅: Deformation of surrounding buildings; (15) W₂₁R₄₂, W₁₃R₂₁, W₁₃R₂₂, W₄₄R₄₂: Stratigraphic ground settlement.

Initially, a comprehensive evaluation is conducted to identify potential risks associated with TBM projects involving the construction of exceptionally long tunnels. This assessment follows a hierarchical structure model based on the fundamental principles of the analytic hierarchy process (AHP). The model comprises three layers: the target layer, criterion layer, and indicator layer, arranged in descending order of significance. The target layer represents TBM construction risk for ultra-long tunnels (U), while the criterion layer comprises U = [U₁, U₂, U₃, U₄]. The indicator layer includes geological risk U₁ = [U₁₁, U₁₂, U₁₃, U₁₄], equipment risk U₂ = [U₂₁, U₂₂, U₂₃, U₂₄], tunnel risk U₃ = [U₃₁, U₃₂, U₃₃, U₃₄], and surrounding environment risk U₄ = [U₄₁, U₄₂, U₄₃]. The final system for evaluating TBM construction risks is illustrated in Figure 4.

3.2.2. Extended Matter-Element Model with Variable Weight

Based on the current research status both domestically and internationally, it is evident that the TBM has witnessed a growing utilization in the construction of lengthy tunnels and underground projects in recent years. However, traditional drilling and blasting methods have posed challenges in adapting their risk assessment techniques to the evolving trend of constructing ultra-long and deeply buried tunnels. Insufficient attention has been given to researching risk assessment methods specifically tailored for TBM construction [32].

The initial development of the Matter-Element Extension Model was based on a robust mathematical statistical framework. By integrating principles from both Matter-Element Theory and Extension Set Theory, this model systematically establishes classical domains, segment domains, index levels, and matter elements for precise evaluation using empirical data. Furthermore, it effectively determines appropriate weights while calculating the correlation degree between the target matter element and each rating level to derive a comprehensive assessment outcome. Since its inception, scholars have continuously enhanced this model through various research endeavors. For instance, they have addressed issues related to single index values exceeding limits by employing standardization techniques; furthermore, they have improved evaluation accuracy while minimizing information loss by introducing the closeness criterion as an alternative to the maximum membership criterion [33].

• Basic matter-element extension model.

According to the principles of matter-element theory and extension set, the classical domains, segment domains, index levels, and matter elements are established in the extension model for evaluation purposes using collected data. Additionally, their respective weights are determined. Finally, the comprehensive rating is obtained by calculating the correlation degree of each rating level. In order to further enhance the model’s effectiveness, scholars address the issue of single index values exceeding the limit of matter elements through standardization processing and introduce a closeness criterion to improve evaluation accuracy while reducing information loss.

The assessment criteria are classified into j tiers based on national standards or pertinent specifications. The index weights are adjusted in accordance with the variable weight theory, considering the variability of each evaluation index value as opposed to using a traditional fixed-weight approach. Ultimately, the determination of the comprehensive evaluation level involves assessing the grade variable’s closeness and characteristic values for each level of the matter element being evaluated and selecting the highest obtained closeness value. Furthermore, we assess the closeness between consecutive levels by utilizing the distinctive value of the grade variable.

The fundamental unit that defines entities in terms of “thing, characteristic, and quantity” (represented by P, C, and V, respectively) is known as the matter element. It serves as the elementary logical operation unit in the extension model of matter elements. The proposed approach aims to optimize the evaluation model for extending matter elements through adjustments in variable weights.

(1)

Establish classical domain, section domain, and matter element to be evaluated.

Set

$${\mathit{R}}_{\mathit{j}}=\left({\mathit{P}}_{\mathit{j}},{\mathit{C}}_{\mathit{i}},{\mathit{V}}_{\mathit{i}\mathit{j}}\right)=\left[\begin{array}{c}\begin{array}{ccc}{P}_j& c_1& v_{1j}\\ & c_2& v_{2j}\\ & ⋮& ⋮\\ & c_n& v_{nj}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccc}{P}_j& c_1& \langle a_{1j},b_{1j}\rangle \\ & c_2& \langle a_{2j},b_{2j}\rangle \\ & ⋮& ⋮\\ & c_n& \langle a_{nj},b_{nj}\rangle \end{array}\end{array}\right]$$

(1)

The evaluation level denoted as ${\mathit{P}}_{\mathit{j}}$, which is the jth level, consists of n unique features (c₁, c₂, …, c_n) and their respective value ranges (v₁, v₂, …, v_n), representing the classical domain. The defined boundaries for this value range are $a_{nj}$ and $b_{nj}$.

$${\mathit{R}}_{\mathit{j}}=\left(\mathit{P},{\mathit{C}}_{\mathit{i}},{\mathit{V}}_{\mathit{p}\mathit{j}}\right)=\left[\begin{array}{c}\begin{array}{ccc}{P}_j& c_1& v_{p1}\\ & c_2& v_{p2}\\ & ⋮& ⋮\\ & c_n& v_{pn}\end{array}\end{array}\right]=\left[\begin{array}{c}\begin{array}{ccc}{P}_j& c_1& \langle a_{p1},b_{p1}\rangle \\ & c_2& \langle a_{p2},b_{p2}\rangle \\ & ⋮& ⋮\\ & c_n& \langle a_{pn},b_{pn}\rangle \end{array}\end{array}\right]$$

(2)

In the equation,

$\mathit{P}$ represents the overall grade of the evaluated entity;

v_p1, v_p2, …, v_pn denotes the segment of $\mathit{P}$ that corresponds to c₁, c₂, …, c_n, specifically referred to as the nodal domain.

$${\mathit{R}}_0=\left({\mathit{P}}_0,{\mathit{C}}_{\mathit{i}},{\mathit{V}}_{\mathit{j}}\right)=\left[\begin{array}{c}\begin{array}{ccc}{P}_0& c_1& v_1\\ & c_2& v_2\\ & ⋮& ⋮\\ & c_n& v_n\end{array}\end{array}\right]$$

(3)

In the equation, ${\mathit{R}}_0$ represents the matter element under evaluation; v₁, v₂, …, v_n denotes the measured data of ${\mathit{P}}_0$ in relation to c₁, c₂, …, c_n, respectively.

(2)

Normalized processing

The issue of exceeding the limit in the single index value of the matter element to be evaluated can be addressed through normalization processing, thereby normalizing the classical domain matter element ${\mathit{R}}_{\mathit{j}}$.

$${\mathit{R}}_{\mathit{j}}^{\prime }=\left({\mathit{P}}_{\mathit{j}},{\mathit{C}}_{\mathit{i}},{\mathit{V}}_{\mathit{i}\mathit{j}}^{\prime }\right)=\left[\begin{array}{c}\begin{array}{ccc}{P}_j& c_1& \langle \frac{a_{1j}}{b_{p1}},\frac{b_{1j}}{b_{p1}}\rangle \\ & c_2& \langle \frac{a_{2j}}{b_{p2}},\frac{b_{2j}}{b_{p2}}\rangle \\ & ⋮& ⋮\\ & c_n& \langle \frac{a_{nj}}{b_{pn}} ,\frac{b_{nj}}{b_{pn}}\rangle \end{array}\end{array}\right]$$

(4)

Similarly, the evaluation element ${\mathit{R}}_0$ needs to be normalized, and the following results are obtained:

$${\mathit{R}}_0^{\prime }=\left[\begin{array}{c}\begin{array}{ccc}{P}_0& c_1& v_1/b_{p1}\\ & c_2& v_2/b_{p2}\\ & ⋮& ⋮\\ & c_n& v_n/b_{pn}\end{array}\end{array}\right]$$

(5)

2.

Determine variable weights of indicators.

Firstly, according to the established prediction index system, the 1~9 scale method proposed by Saaty (

Table 2. Criteria for constructing the judgment matrix of AHP.

Scale	Comparison Results of Index Importance Difference
1	i is as important as j, or i is compared with i, j is compared with j itself;
2	i is slightly more important than j, but not to the extent of 3;
3	i is marginally more significant compared to j;
4	i is more important than j, but not to the extent of 5;
5	i holds greater significance compared to j;
6	i is much more important than j, but not to the extent of 7;
7	i holds significantly higher importance than j;
8	i is more important than j, but not to the extent of 9;
9	i is of greater importance than j;
Supplement	When i is compared with j, the importance assignment is the reciprocal of the scalar when i is compared with j.

) is adopted to analyze the relative importance of any two indicators at each level [34], and the judgment matrix of prediction indices is obtained.

$$\tilde{Z}={\left[a_{ij}\right]}_{m\times n}=\left[\begin{array}{cccc}\frac{{\tilde{Z}}_1}{{\tilde{Z}}_1}& \frac{{\tilde{Z}}_1}{{\tilde{Z}}_2}& \dots & \frac{{\tilde{Z}}_1}{{\tilde{Z}}_n}\\ \frac{{\tilde{Z}}_2}{{\tilde{Z}}_1}& \frac{{\tilde{Z}}_2}{{\tilde{Z}}_2}& \dots & \frac{{\tilde{Z}}_2}{{\tilde{Z}}_n}\\ ⋮& ⋮& \dots & ⋮\\ \frac{{\tilde{Z}}_n}{{\tilde{Z}}_1}& \frac{{\tilde{Z}}_n}{{\tilde{Z}}_2}& \dots & \frac{{\tilde{Z}}_n}{{\tilde{Z}}_n}\end{array}\right].$$

(6)

where $a_{ij}$ is an element in the judgment matrix $\tilde{Z}$, and $a_{ij}$ satisfies $a_{ij}=1/a_{ij}$.

Secondly, Equations (7) and (8) are used to calculate the weight vector $w_i$ and the maximum eigenvalue ${\lambda }_{max}$ of $\tilde{Z}$ [35]:

$$w_i={\left({\displaystyle \prod }_{j=1}^n{\tilde{Z}}_{ij}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}/{\displaystyle \sum }_{j=1}^n{\left({\displaystyle \prod }_{j=1}^n{\tilde{Z}}_{ij}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}$$

(7)

$${\lambda }_{max}={\displaystyle \sum }_{i=1}^n\frac{{\left(Mw\right)}_i}{n{w}_i}$$

(8)

Finally, in order to further determine the reliability of the calculation results, Equation (9) is used to verify whether the matrix $\tilde{Z}$ meets the consistency requirements:

$$CR=\frac{\left({\lambda }_{max}-n\right)}{\left(n-1\right)RI}$$

(9)

The random consistency index ($RI$) value can be located in

Table 3. The values of the random consistency index.

n	10	11	12	13	14	15	16	17
RI	1.49	1.52	1.54	1.56	1.58	1.59	1.594	1.60

, indicating the location where it is presented.

When the CR value is less than 0.1, it indicates that the matrix $\tilde{Z}$ meets the consistency requirements, and the calculation results are more reliable.

Through the introduction of the variable weight theory, the influence of index value volatility is taken into consideration based on traditional fixed weights, thereby achieving an improved dynamic calculation method for variable weight indices [36]. The variable weight theory is proposed based on factor space theory. The fundamental statement of the variable weight theory states that if $X=(x_1,x_2,\dots ,x_n)$ represents the factor state vector, $w=\left(w_1,w_2,\dots ,w_n\right)$ represents the factor constant weight vector, and $S\left(W\right)=\left(S_1\left(X\right),S_2\left(X\right),\dots ,S_n\left(X\right)\right)$ represents the state variable weight vector, then the variable weight vector $W\left(W\right)=\left(W_1\left(X\right),W_2\left(X\right),\dots ,W_n\left(X\right)\right)$ can be expressed as a normalized Hadamard product of $W$ and $S\left(W\right)$:

$$w_i\left(X\right)=\frac{w_i{S}_i\left(X\right)}{{{\displaystyle \sum }}_{k=1}^n{w}_k{S}_k\left(X\right)}$$

(10)

where i = 1, 2, …, n, $S_i\left(X\right)$ is the equilibrium function, usually an exponential function with the natural constant e as the base.

The analytic hierarchy process is utilized to assess the relative importance of each factor index, considering both subjective and objective evaluation methods. Moreover, the weight vector for state variables is determined by taking into account the equilibrium function and measured index value, thereby incorporating the impact of fluctuations on index weights. As a result, a calculation formula is devised to determine the variable weight of evaluation indices.

$$S_i\left(X\right)=e^{2a\left[\frac{L}{L^{*}}-\frac{b_{ij}-v_{ip}}{L^{*}\left(b_{ij}-a_{ij}\right)}-c\right]}$$

(11)

$$w_i\left(X\right)=\frac{w_i{e}^{2a\left[\frac{L}{L^{*}}-\frac{b_{ij}-v_{ip}}{L^{*}\left(b_{ij}-a_{ij}\right)}-c\right]}}{{{\displaystyle \sum }}_{k=1}^n{w}_k{S}_k\left(X\right)}$$

(12)

where $a$ = 1.0; $v_i=\left[a_{ij},b_{ij}\right]$;

L represents the rating level of index $v_i$;

$L^{*}$ represents the overall count of ratings within the assessment system;

c determines the threshold used to determine the state of incentives or punishments within the equilibrium function.

After the normalization,

$$s=2\alpha [\frac{L}{L^{*}}\frac{b_{ij}-v_{ip}}{L^{*}\left(b_{ij}-a_{ij}\right)}$$

(13)

where $s\in \left[-1,1\right]$;

$s<0$, $S_i\left(X\right)<1$ is the penalty;

$s>0$, $S_i\left(X\right)>1$ is the reward.

Therefore, the constructed variable weight state vector can be used to punish or encourage according to the measured values of the index.

3.

The value of the closeness function needs to be determined.

Theoretical analysis [37] has led to the development of an asymmetric formula (p = 1) for evaluating closeness, which replaces the previous maximum membership criterion.

$$N=1-\frac{1}{n\left(n+1\right)}{\displaystyle \sum }_{i=1}^{n}D{w}_i$$

(14)

where $N$ represents the proximity factor;

$D$ denotes the measure of separation;

$W$ is the weight.

In addition, the proximity of the item under evaluation to every grade is:

$$N_j\left(p_0\right)=1-\frac{1}{n\left(n+1\right)}{\displaystyle \sum }_{i=1}^n{D}_j\left(v_i^{\prime }\right)w_i\left(X\right)$$

(15)

In the formula,

$$D_j\left(v_i^{\prime }\right)=\left|v_i^{\prime }-\frac{a_{ij}^{\prime }+b_{ij}^{\prime }}{2}\right|-\frac{1}{2}\left(b_{ij}^{\prime }-a_{ij}^{\prime }\right)$$

(16)

where $n$ represents the count of assessment indicators.

4.

Rank confirmation.

By

$$N_{j^{\prime }}\left(p_0\right)=max\left\{N_j\left(p_0\right)\right\}$$

The evaluated item is categorized as level $j^{\prime }$.

$${\overline{N}}_j\left(p_0\right)=\frac{N_j\left(p_0\right)-\underset{j}{\min }{N}_j\left(p_0\right)}{\underset{j}{\max }{N}_j\left(p_0\right)-\underset{j}{\min }{N}_j\left(p_0\right)}$$

(17)

4. Summary of the Project and Preprocessing of Data

4.1. Summary of the Project

The KS tunnel spans a total length of 283 km and is constructed using eleven open-type [22] TBM machines. It reaches an average depth of 428 m, with a maximum depth of 774 m. This project is characterized by its immense scale, spanning multiple regions and involving complex construction techniques. The focus of this article lies on the research conducted on the section between KS 253 + 877 and KS 254 + 588 within the KS tunnel. From a rock classification perspective, this particular section comprises consecutive segments featuring different types of surrounding rocks, including II, IIIa, IV, and V. The geological profile of this section is shown in Figure 5.

Section KS 253 + 877~KS 254 + 045: The exposed lithology of this section comprises tuff, which is partially schistified, exhibiting a gray color and thick layered structure. The rock layers in this section are oriented at 280°NE ∠ 75~80°, indicating a medium-to-hard rock classification. The primary joint occurrence is observed at 290°NE ∠ 75°, with slight fissure development. Along the rock layer, there is a well-developed gray carbonaceous interlayer measuring 0.5~0.8 m in thickness and spaced at intervals of 3~10 m; their count amounts to five. These openings are sealed and exhibit smooth undulation. Within the interlayer, the surrounding rock experiences fragmentation and displays low strength along with minor wrinkling phenomena. The rock wall within this section remains dry while maintaining overall integrity of the surrounding rock mass, resulting in good chamber stability overall. Based on these observations, the overall categorization for the surrounding rocks within this section is determined as IIIa.

Section KS 254 + 045~KS 254 + 411: The exposed lithology of this section comprises tuff, characterized by a blue-gray hue and a thick layered structure. The orientation of the rock layers is 280°NE ∠ 75~80°, indicating its classification as hard rock. The primary joint occurrence is observed at 310°SW ∠ 5~15° and 290°NE ∠ 75°, with a total count of 10 joints exhibiting closed openings and smooth undulations. No fissures are present in this section. The rock walls within this segment exhibit dryness, showcasing excellent overall integrity of the surrounding rock mass and stable cavern conditions.

KS 254 + 411~KS 254 + 542 section: the exposed lithology of this section is the schistosity tuff, with gray-black to gray-green color and thick layered structure. The occurrence of the rock layer is 280°NE ∠ 75~80°, thus belonging to medium hard to soft rock. The surrounding rock of this section is affected by tectonic extrusion and hydrothermal alteration, with obvious crumple, strong carbonization, schistosity development, phyllite fossilization, chlorite fossilization, and a small amount of serpentine fossilization phenomenon; the main joint occurrence is 280~300°SW ∠ 30~45°, 290°NE ∠ 75°, the fracture surface is undulating and smooth and slightly rough and filled with phyllite film; the spacing is 1–3 m, running through the chamber, affected by the combination of fracture cutting and layer; the block drops 30~60 cm along the fracture surface, the waist line collapse on the right side of pile No. 254 + 454; the axial length is 3 m, the circumferential width is 1.3 m, and the radial depth is 1.7–2.0 m. The overall integrity of the surrounding rock of this section is poor to broken, the chamber is basically stable, and the local instability is significantly increased. The overall surrounding rock of this section is determined to be class IV. Since the pile No. 254 + 423, the surrounding rock gradually becomes complete, the fracture is less developed, and the strength is significantly increased.

KS 254 + 542~KS 254 + 588 section: the exposed lithology is the schistosity tuff, the color is mostly blue-gray, it has a thick layered structure, and the rock layer occurrence is 280°NE ∠ 75~80°, thus belonging to medium hard to soft rock. The surrounding rock in this section is obviously wrinkled, strongly altered, strongly carbonized, and poorly bonded between layers, with loose rock mass and loose rock fragments, and it is inferred that it has entered the fault influence zone. The surrounding rock fissures in this section are relatively developed, with main joint occurrence of 290~310°SW ∠ 40~55°; the fracture surface is undulating and smooth, slightly rough, filled with film-like or plate-like phyllite, gray-green, microcrystalline scale-like development, with width 0.1–5 cm, affected by the combination of fracture cutting and unfavorable layersl the top arch is often 40~60 cm, among which the pile number 254 + 582 collapse cavity is 2 m long in axial direction, 3 m wide in circumferential direction, and 5 m deep in radial direction. The overall surrounding rock category of this section is determined to be V.

4.2. The Selection of Risk Assessment Indices

There are numerous factors that can impact tunnel construction, and the mechanism of influence for different factors is intricate. Based on an analysis of existing research findings, these factors can generally be categorized as natural and geological factors. Given the complex characteristics of tunnel construction, it is quite challenging to conduct a thorough and all-encompassing examination of every factor that impacts tunnel construction. Additionally, it is essential to consider the accessibility of relevant information during engineering construction. This necessitates a comprehensive analysis of both the degree of influence on tunnel risk and the availability of information [38,39,40,41,42]. For the risks that may occur in tunnel TBM construction, the corresponding indicators are selected to reflect the degree of danger. For example, the elastic deformation energy index is usually used as the main evaluation index when evaluating the risk of rock burst. The elastic deformation energy index is the ratio of the elastic strain energy stored in the rock sample to its ability of plastic deformation dissipation before the peak strength of the rock is reached. To a certain extent, it can be used to directly reflect the degree of danger of rock burst. Similarly, the risk of sudden water inrush can be expressed by the groundwater level. The higher the value is, the greater the probability of risk occurrence is. The risk of landslide can be expressed by the rock integrity coefficient. The smaller the value is, the more fragmented the rock is in the tunneling process, and the more likely a landslide is. When selecting risk evaluation indicators for TBM construction, the first consideration is to select representative indicators of various risks, which can directly or indirectly reflect the actual situation of geological conditions, construction environment, equipment status, and human activities.

In this paper, 15 factors, including elastic deformation energy index (I₁), groundwater level (I₂), rock integrity coefficient (I₃), gas monitoring data (I₄), cutterhead torque (I₅), ventilation system flow (I₆), surrounding rock classification (I₇), cutterhead speed (I₈), entrance support effect (I₉), water seepage (I₁₀), protective layer thickness (I₁₁), guiding system monitoring data (I₁₂), underground space monitoring data (I₁₃), underground pipeline detection data (I₁₄), and surrounding building displacement monitoring number (I₁₅) are selected to establish a tunnel risk evaluation index system. Referring to the classification standards of tunnel risk in literature, the occurrence probability of tunnel risk is divided into four grades: the ideal state (V₁), low-risk state (V₂), medium-risk state (V₃), and high-risk state (V₄). These four grades correspond to different states of indicators. Before the formal construction, the surveying unit conducted specific detection on different sections of the site and summarized the parameter range for rock formation and rock properties in this project. Therefore, this paper will use these parameter ranges as criteria for dividing risk levels. According to the data obtained from the preliminary survey and on-site measurement, relevant data are input into different grades, such as the elastic deformation energy index obtained from the on-site measurement, which is divided into different intervals according to the actual rock and rock properties obtained from the preliminary survey. For example, the interval [0, 2] represents no rockburst risk, the interval [2, 4] represents a weak rockburst risk, the interval [4, 6] represents a medium rockburst risk, and an interval greater than 6 represents a strong rockburst risk. The classification of rock mass integrity coefficient is also based on the coefficient value obtained from the preliminary survey, with the interval [0, 0.25] representing the faulted and broken rock segment, the interval [0.25, 0.5] representing the softer rock segment, the interval [0.5, 0.75] representing the medium hard rock segment, and the interval [0.75, 1] representing the hard rock segment. Similarly, other indicators are also divided in this way.

Table 4. Scoring criteria for various factor indicators.

Category	Risk	Index	No.	V1	V2	V3	V4	Unit
U1	U11	Elastic deformation energy index	I1	0–2	2–4	4–6	6–10
	U12	Groundwater level	I2	<60	60–90	90–120	>120	m
	U13	Rock integrity coefficient	I3	0.75–1	0.5–0.75	0.5–0.25	0.25–0
	U14	Gas monitoring data	I4	0–12.5	12.5–25	25–37.5	37.5–100	mg/m3
U2	U21	Cutterhead torque	I5	900–1500	1500–2100	2100–2700	2700–3300	kN m
	U22	Ventilation system flow	I6	1800–2000	1000–1800	500–1000	0–500	m3/min
	U23	Surrounding rock classification	I7	II	III(A/B)	IV	V
	U24	Cutterhead speed	I8	7–8	6–7	5–6	<5	R/min
U3	U31	Entrance support effect	I9	Very high stability	High stability	Moderate stability	Low stability
	U32	Water seepage	I10	Nil	Humidification	Trickle	inrush of water
	U33	Protective layer thickness	I11	10–15	40–50	50–55	55–60	cm
	U34	Guiding system monitoring data	I12	Zero deviation	Tiny deviation	Small deviation	Large deviation
U4	U41	Underground space monitoring data	I13	0–0.1	0.1–0.3	0.3–1	1–2	mm
	U42	Underground pipeline detection data	I14	No damage	Tiny damage	Small damage	Large damage
	U43	Surrounding building displacement monitoring number	I15	0–0.1	0.1–0.4	0.4–1	1–6	mm

provides the evaluation indices and classification criteria for evaluating the risk of tunnels.

The present study focuses on the tunnel risk assessment by selecting eight representative sections of the tunnel as evaluation targets. Concrete instances are presented to illustrate the utilization of the extended variable weight matter-element model in evaluating construction hazards while conducting TBM tunneling.

According to the actual tunneling situation of the TBM, the rock strata, lithology, and groundwater level of the tunnel section were detected by equipment, and the data were sorted out and summarized in combination with the construction design and the design survey geological report of the KS tunnel, so as to obtain the specific parameter values of risk indicators. The parameter values of the risk factors of the eight selected tunnel sections are shown in

Table 5. Risk factor parameter values from KS 2253 + 935 to KS 2254 + 586.

Tunnel Section	I1	I2	I3	I4	I5	I6	I7	I8	I9	I10	I11	I12	I13	I14	I15
K1#	1	41	0.73	10	1300	1850	IIIa	7	Very high	Nil	15	Tiny	0.1	Tiny	0.1
K2#	1.2	40	0.72	11	1450	1850	IIIa	7.1	Very high	Nil	15	Tiny	0.1	Tiny	0.1
K3#	1.9	50	0.85	10	1600	1900	II	7.9	Very high	Nil	15	Tiny	0.1	Tiny	0.2
K4#	2	53	0.86	9	1750	1900	II	7.8	Very high	Nil	15	Tiny	0.1	Tiny	0.2
K5#	0.8	55	0.30	11	1400	1800	IV	6.6	Very high	Humidification	40	Tiny	0.3	Small	1.5
K6#	0.7	57	0.31	10	1450	1800	IV	6.5	Very high	Humidification	40	Tiny	0.25	Small	1.5
K7#	0.3	53	0.21	11	1200	1750	V	5.5	Very high	Trickle	40	Tiny	0.5	Large	4
K8#	0.4	51	0.20	12	1300	1750	V	5.3	Very high	Trickle	40	Tiny	0.6	Large	4

.

4.3. Establishment of Matter-Element Model

In order to eliminate the problem of dimensionality disunity among different evaluation indices, Formulas (5) and (6) are adopted to normalize the data in Table 4 and Table 5. The outcomes of various evaluation indices pertaining to distinct risk levels are presented in

Table 6. Risk assessment index level evaluation criteria (dimensionless).

No.	V1	V2	V3	V4
I1	0, 0.2	0.2, 0.4	0.4, 0.6	0.6, 1
I2	0, 0.3	0.3, 0.45	0.45, 0.6	0.6, 1
I3	0, 0.25	0.25, 0.5	0.5, 0.75	0.75, 1
I4	0, 0.125	0.125, 0.25	0.25, 0.375	0.375, 1
I5	0, 0.25	0.25, 0.5	0.5, 0.75	0.75, 1
I6	0, 0.1	0.1, 0.5	0.5, 0.75	0.75, 1
I7	0, 0.25	0.25, 0.5	0.5, 0.75	0.75, 1
I8	0, 0.126	0.125, 0.25	0.25, 0.5	0.5, 1
I9	0, 0.25	0.25, 0.5	0.5, 0.75	0.75, 1
I10	0, 0.25	0.25, 0.5	0.5, 0.75	0.75, 1
I11	0, 0.1	0.7, 0.8	0.8, 0.9	0.9, 1
I12	0, 0.25	0.25, 0.5	0.5, 0.75	0.75, 1
I13	0, 0.05	0.05, 0.15	0.15, 0.5	0.5, 1
I14	0, 0.25	0.25, 0.5	0.5, 0.75	0.75, 1
I15	0, 0.067	0.067, 0.167	0.167, 0.333	0.333, 1

and

Table 7. Risk factor parameter values from KS 2253 + 935 to KS 2254 + 586 (dimensionless).

Tunnel Section	I1	I2	I3	I4	I5	I6	I7	I8	I9	I10	I11	I12	I13	I14	I15
K1#	0.1	0.205	0.73	0.1	0.167	0.075	0.3	0.125	0.1	0	0.1	0.3	0.05	0.19	0.0167
K2#	0.12	0.2	0.72	0.11	0.229	0.075	0.3	0.1125	0.1	0	0.1	0.3	0.05	0.2	0.0167
K3#	0.19	0.25	0.85	0.1	0.291	0.05	0.1	0.0125	0.1	0	0.1	0.2	0.05	0.05	0.0333
K4#	0.2	0.265	0.86	0.09	0.354	0.05	0.1	0.025	0.1	0	0.1	0.2	0.05	0.05	0.0333
K5#	0.08	0.275	0.30	0.11	0.208	0.1	0.5	0.175	0.1	0.55	0.6	0.25	0.15	0.71	0.25
K6#	0.07	0.285	0.31	0.1	0.229	0.1	0.5	0.1875	0.1	0.55	0.6	0.25	0.125	0.72	0.25
K7#	0.03	0.265	0.21	0.11	0.125	0.125	0.8	0.3125	0.1	0.81	0.6	0.23	0.25	0.83	0.667
K8#	0.04	0.255	0.20	0.12	0.167	0.125	0.8	0.3375	0.1	0.81	0.6	0.23	0.3	0.84	0.667

for the classical domain ${\mathit{R}}_{\mathit{i}}$ and segment domain ${\mathit{R}}_{\mathit{p}}$, respectively.

The cumulative domain ${\mathit{R}}_{\mathit{p}}$ for each evaluation index is obtained by adding up its respective classical domain.

4.4. Variable Weight Determination

Table 8. Outcomes of the AHP analytical hierarchy process.

	I1	I2	I3	I4	I5	I6	I7	I8	I9	I10	I11	I12	I13	I14	I15
I1	1	3	3	3	3	5	3	5	5	5	6	7	9	7	9
I2	1/3	1	3	3	3	4	2	5	5	5	5	7	7	7	7
I3	1/3	1/3	1	3	3	4	3	5	5	5	5	7	7	7	7
I4	1/3	1/3	1/3	1	3	3	3	5	6	5	5	7	9	7	7
I5	1/3	1/3	1/3	1/3	1	3	3	3	3	5	7	7	9	7	7
I6	1/5	1/4	1/4	1/3	1/3	1	3	3	3	3	5	5	5	5	5
I7	1/3	1/2	1/3	1/3	1/3	1/3	1	3	3	3	5	5	5	5	7
I8	1/5	1/5	1/5	1/5	1/3	1/3	1/3	1	3	3	3	3	5	5	7
I9	1/5	1/5	1/5	1/6	1/3	1/3	1/3	1/3	1	3	3	3	3	5	5
I10	1/5	1/5	1/5	1/5	1/5	1/3	1/3	1/3	1/3	1	3	3	3	3	3
I11	1/6	1/5	1/5	1/5	1/7	1/5	1/5	1/3	1/3	1/3	1	3	3	3	3
I12	1/7	1/7	1/7	1/7	1/7	1/5	1/5	1/3	1/3	1/3	1/3	1	3	3	3
I13	1/9	1/7	1/7	1/9	1/9	1/5	1/5	1/5	1/3	1/3	1/3	1/3	1	3	3
I14	1/7	1/7	1/7	1/7	1/7	1/5	1/5	1/5	1/5	1/3	1/3	1/3	1/3	1	3
I15	1/9	1/7	1/7	1/7	1/7	1/5	1/7	1/7	1/5	1/3	1/3	1/3	1/3	1/3	1

and

Table 9. Summary of the findings from the consistency testing.

Maximal Characteristic Root	CI	RI	CR	Consistency Test Results
17.089	0.149	1.590	0.094	yes

present the outcomes acquired through employing the analytic hierarchy process with a scale method indexed at 9.

It is worth noting that in AHP analysis, the main diagonal element should theoretically be 1, which reflects the logical self-consistency that the relative importance of the same evaluation index is naturally 1. This study ensures the reliability of the judgment matrix through the consistency test, and all the main diagonal elements are 1 and meet the consistency requirements, thus ensuring the validity and reliability of the evaluation results.

The fuzzy analysis method was employed to analyze the results of weight changes, and auxiliary verification was conducted. It was determined that the changes in weights of indicators 7, 5, and 11 have a significant impact on the evaluation. Therefore, it is crucial to introduce an improved theory for adjusting weights in order to optimize them. The results can be observed in Figure 6.

By determining the constant weights of each evaluation indicator, and then using Equation (12) to calculate the variable weights of each indicator, where the variable weight factor α = 1.0, L* = 4, c = 0.2. For example, for indicator I₁ of criterion K₁^#, the variable weight value can be calculated by substituting the constant weights and correlation coefficients into Equations (12) and (13). The specific calculation process is shown below. According to Equation (13), it is evident that the calculation process penalizes indicator I₁ of criterion K₁^#, resulting in a smaller final result compared to its original value. Therefore, when the weight of this indicator decreases, other indicators will undergo changes accordingly. Increasing the weight of other more important indicators contributes to obtaining more accurate evaluation results. The complete calculation results of the weights of each evaluation index are shown in

Table 10. Weight of evaluation indicators.

No.	Fixed Weight	Variable Weight
		K1#	K2#	K3#	K4#	K5#	K6#	K7#	K8#
I1	0.187	0.126	0.126	0.128	0.126	0.116	0.118	0.107	0.108
I2	0.146	0.108	0.106	0.111	0.109	0.122	0.122	0.121	0.116
I3	0.129	0.124	0.125	0.120	0.122	0.108	0.104	0.113	0.113
I4	0.115	0.090	0.093	0.085	0.085	0.077	0.089	0.086	0.087
I5	0.095	0.104	0.117	0.104	0.100	0.093	0.095	0.079	0.085
I6	0.067	0.061	0.060	0.071	0.064	0.053	0.052	0.046	0.045
I7	0.065	0.139	0.137	0.132	0.132	0.119	0.124	0.115	0.112
I8	0.047	0.061	0.057	0.045	0.049	0.061	0.063	0.077	0.079
I9	0.038	0.037	0.036	0.042	0.044	0.030	0.030	0.025	0.024
I10	0.029	0.034	0.023	0.027	0.028	0.057	0.056	0.079	0.077
I11	0.024	0.046	0.046	0.054	0.056	0.038	0.037	0.031	0.031
I12	0.019	0.018	0.016	0.026	0.027	0.020	0.020	0.016	0.016
I13	0.015	0.020	0.020	0.023	0.024	0.027	0.013	0.026	0.027
I14	0.013	0.023	0.028	0.020	0.021	0.053	0.053	0.056	0.056
I15	0.010	0.009	0.009	0.012	0.012	0.023	0.023	0.024	0.024

.

$$w_i\left(X\right)=\frac{w_i{e}^{2a\left[\frac{L}{L^{*}}-\frac{b_{ij}-v_{ip}}{L^{*}\left(b_{ij}-a_{ij}\right)}-c\right]}}{{{\displaystyle \sum }}_{k=1}^n{w}_k{S}_k\left(X\right)},$$

$$\begin{gathered} =\frac{0.187\times e^{2\times 1\times \left[\frac{1}{4}-\frac{0.2-0.1}{4\times \left(0.2-0\right)}-0.2\right]}}{1.274} \\ \approx 0.126 \end{gathered}$$

4.5. Determine Risk Grade

According to Formulas (15) and (16), the closeness degree of the tunnel section to different risk levels is calculated and standardized, so as to establish an evaluation system. To validate the reliability of the enhanced variable weight matter-element extension model, a comparative analysis was conducted with both the standard matter-element extension model and the fuzzy comprehensive evaluation method. The corresponding findings are presented in

Table 11. Risk level assessment of tunnel collapse from KS 253 + 935-KS 254 + 586.

Tunnel Section	Accessible Degree				Model in This Paper	Standard Extension Model	Fuzzy Synthetic Model
	V1	V2	V3	V4
K1#	1.000	0.831	0.407	0.000	V1	V2	V1
K2#	1.000	0.869	0.426	0.000	V1	V2	V1
K3#	1.000	0.785	0.384	0.000	V1	V1	V1
K4#	1.000	0.802	0.393	0.000	V1	V1	V1
K5#	0.691	1.000	0.713	0.000	V2	V2	V3
K6#	0.685	1.000	0.698	0.000	V2	V2	V3
K7#	0.000	0.900	1.000	0.482	V3	V3	V4
K8#	0.000	0.956	1.000	0.298	V3	V3	V4

.

According to Table 11, the risk level of sections K₁^#, K₂^#, K₃^#, and K₄^# is V₁ (ideal state). Although they are in an ideal excavation condition, it is still necessary to prepare for potential risks during construction. Sections K₅^# and K₆^# have a risk level of V₂ (low-risk state), where the surrounding rock has a significant impact on excavation construction. To reduce risks, necessary support measures and drainage work should be implemented. The use of HW150 system arches (0.45 m) with steel reinforcement and embedded grouting pipes at collapse areas can help form a closed structure as soon as possible. Sections K₇^# and K₈^# have a risk level of V₃ (medium-risk state) due to their location in fractured segments. However, with proper support and initial lining, normal construction can still be carried out. Similarly to sections mentioned earlier, HW150 system arches with steel reinforcement should be used for support along with embedded grouting pipes at collapse areas to form a closed structure promptly. During excavation construction, the possibility of sudden water influx or collapse risks should be considered based on changes in weightage and fuzzy evaluation criteria. Early detection work should be conducted in advance to mitigate these risks.

Based on the actual excavation conditions of sections KS 260 + 052 to KS 262 + 835, the joint and fracture development in the surrounding rock of sections, K₁^# and K₂^# is relatively minor. The overall integrity of the surrounding rock is good during TBM excavation, leaning more towards V₁ grade (ideal state). However, the standard expandable model lacks adaptability when facing changes in indicators and is not sufficiently relevant to risk assessment issues. In contrast, sections K₃^# and K₄^# have no joint or fracture development in the surrounding rock, with mostly dry rock walls and high stability of the tunnel cavity. Under certain circumstances without considering other factors, it can be considered an ideal excavation environment.

Sections K₅^#, K₆^#, on the other hand, are affected by structural compression and hydrothermal alteration. They exhibit significant folding, strong carbonization, developed rock cleavage, and slight surface spalling during TBM construction. However, the fuzzy comprehensive models used do not consider coupling effects resulting from changes in multiple risk indicators, which deviates from reality.

Sections K₇^# and K₈^#, influenced by faulted fractured zones, show poor integrity of surrounding rocks with intense weathering and strong carbonization of rocks. The interlayer bonding is weak, with loose rocky material prone to fragmentation. During the TBM excavation process, severe block falling occurs along with local structural face collapse phenomena in some areas.

4.6. Significance Analysis

One indicator is selected for variable determination of its weight, with other indicators at a fixed value. However, when the weight of this indicator changes greatly, it is an important indicator; on the contrary, if the change is small, it is a less important indicator. The value of other indicators is controlled to 0.125, and the variable indicator is recorded on a scale from 0 to 1 by increments of 0.1. The result is shown in Figure 7, below.

In Figure 7, it can be seen that the weight values of each evaluation index are proportional to the actual measured values. This phenomenon occurs because the model takes into account the influence of the objective fluctuation of the index values on the index weight in the process of model establishment. The fluctuation of the index values in the figure can reflect the importance of the index, thus showing the influence of different indices on the tunnel risk. By sorting the changes in the weight values of each index in Figure 7 and ranking them in order of magnitude, the order is I₇ > I₅ > I₁ > I₃ > I₂ > I₄ > I₆ > I₁₁ > I₈ > I₁₀ > I₉ > I₁₄ > I₁₃ > I₁₅ > I₁₂, with the magnitude of the changes in weight values increasing in the order of 0.449 > 0.406 > 0.388 > 0.381 > 0.365 > 0.356 > 0.317 > 0.247 > 0.245 > 0.228 > 0.203 > 0.116 > 0.093 > 0.090 > 0.077. According to the theory of variable weight, the weight values of each evaluation index will change with the change in actual measured values, and the magnitude of the change in the weight values of different indices is also different, because the model takes into account the objective fluctuation of the index values on the index weight.

Specific analysis of the data shows that the weight changes in the surrounding rock category I₇ and cutter head torque I₅ are obviously large, which indicates that the changes of these two indices have a great impact on the tunnel risk assessment results. The monitoring data I₁₂ of the guidance system has the smallest variation, which indicates that the change in I₁₂ has relatively little impact on the evaluation results in this model. The fluctuation range of the protective layer thickness I₁₁ is relatively obvious, although the importance is not as high as the surrounding rock category; it is still obvious that the protective layer plays a role in reducing the risk.

5. Results

This paper provides a comprehensive discussion and summary of the risk categories associated with TBM construction in super-long tunnels. It also references the relevant literature and the actual construction site conditions to establish a risk evaluation index system for TBM construction in super-long tunnels. Furthermore, by utilizing the WBS-RBS method, the paper meticulously decomposes the TBM construction process step by step, analyzes specific risk sources, and forms a complete systematic risk identification matrix. The results obtained from this method successfully establish a reliable and high-quality risk evaluation index system for TBM construction in super-long tunnels that meets all necessary requirements.

The matter-element extension theory is selected as the research tool for quantitative data analysis. The subjective weights obtained through the analytic hierarchy process are utilized to fully incorporate subjective understanding and judgment of risks in actual projects, thereby humanizing risk evaluation and aligning it with real-world situations. Simultaneously, the objective weights obtained through variable weight theory comprehensively consider the influence of various objective factors on risk evaluation, enhancing its comprehensiveness and scientific rigor. After determining the comprehensive weight of risk assessment indices, the construction risk of a super-long tunnel TBM is evaluated using the asymmetric proximity degree. It can be inferred from the importance analysis that the probability of natural factors causing risks in TBM construction is relatively high, including geological conditions, hydrological environment, and climate conditions.

This paper considers the ability of the TBM to deal with risks and the impact of the interaction of risk factors in the establishment of the model, which makes the risk assessment based on the improved variable weight matter-element extension model in the actual tunneling process more objective and reasonable.

The evaluation outcomes of the improved variable weight matter-element extension model for tunnel risk assessment reveal a significant level of agreement with those obtained from both the standard matter-element extension model and fuzzy comprehensive evaluation method. However, it is important to note that the enhanced variable weight matter-element extension model demonstrates a stronger alignment with actual construction conditions and offers a more precise depiction of TBM excavation situations. These findings underscore its effectiveness and feasibility in accurately evaluating tunnel risks.

Although all three methods have achieved good results in tunnel risk assessment, compared with directly using level IV as a judgment criterion for tunnel risk in the matter-element extension theory model, this study has constructed a comprehensive indicator system for evaluating risks in ultra-long tunnels during TBM construction by introducing the WBS-RBS method. It considers various aspects of tunnel risks from a macro perspective and takes into account the complexity of different indicator levels from a micro perspective. The quantification of the indicators is achieved through the utilization of the matter-element extension model, which is then integrated into the enhanced variable weight theory to improve their practical applicability. As a result, the evaluation outcomes become more scientifically valid.

6. Discussion

The research findings can provide essential guidance for risk identification in the ongoing TBM excavation. Due to the indirect acquisition of a multitude of data during the excavation process, real-time adjustment of construction plans to mitigate construction risks becomes challenging. Given the intricate and dynamic environment in which TBM construction takes place, there exist numerous potential risk factors such as groundwater influx, rock stability issues, equipment failures, etc. Hence, it is imperative to comprehensively assess and control risks throughout the construction process.

6.1. The Impact of Choosing Various Risk Indicators on the Outcomes

Previous research has indicated that the choice of various risk indicators greatly influences the results of risk assessment in TBM construction, due to the intricate and fluctuating surroundings. The choice of risk indicators can considerably influence the results of risk evaluation. For instance, if the assessment process focuses solely on construction progress as a risk indicator, it may overlook potential risks such as groundwater influx, leading to inaccurate assessments. Therefore, when selecting risk indicators, multiple factors need to be comprehensively considered, including the nature of risk factors, their scope of influence, and their controllability to ensure accurate and comprehensive assessment results. The utilization of the WBS-RBS method in constructing a comprehensive system for evaluating risks enables stakeholders to gain a more thorough understanding of various project components while accurately identifying potential risks. WBS-RBS ensures systematic and comprehensive identification of risks while avoiding omissions or overlooking important factors.

6.2. The Influence of Different Risk Assessment Weights and Models on the Results

During the risk assessment process, the selection of appropriate models, data handling techniques, optimization of parameter settings, and consideration of risk factor weights all play crucial roles in influencing the evaluation results. In order to obtain more precise and reliable evaluation outcomes, it is imperative to conduct comprehensive research and extensive discussions in these aspects.

6.2.1. Discussion on Weight Optimization

When evaluating multiple risk factors, it is imperative to consider the interplay and allocation of weights among these risks. Different risk assessment models may make varying assumptions and employ diverse methods in assigning weights to risk factors, thereby potentially influencing the evaluation results. Therefore, when evaluating multiple risk factors, it is necessary to fully consider the correlation between risks. If conditions permit, different variable weight methods should be compared for weight optimization results, so as to select a better method to obtain more accurate evaluation results, for example, the gray correlation degree based on combination weight [43], the variable weight combination model based on XGBoost-LSTM [44], the combination weighting method based on game theory [45], etc.

6.2.2. Exploration of the Model for Evaluating Risks

When applying a risk assessment model, the evaluation results can also be influenced by the quality of data and data processing methods. Data quality encompasses factors such as completeness, accuracy, and consistency. Inadequate data quality may introduce bias into the evaluation results. Furthermore, the choice of data processing techniques and methods (e.g., data imputation, filtering, normalization) can also impact the evaluation outcomes [46]. Hence, it is imperative to employ appropriate data processing techniques and methods to enhance the usability of the data.

6.3. Research on the Limitations of the Study

The construction risk assessment of the TBM is conducted using an enhanced variable weight matter-element extension model, which utilizes a risk index system built upon WBS-RBS. Although it comprehensively identifies risks and optimizes weight allocation based on actual conditions, similarly to any other research, there are still certain limitations. For instance, the parameter indicators corresponding to risks are too singular and insufficient in scale. Additionally, the model is specifically designed for open-type TBM production and may not be easily adaptable to other TBM models. Regarding the establishment of the model, three key points are discussed.

(1)

Firstly, by considering the collection of feature data that is more in line with risk indicators, a more comprehensive risk evaluation index system can be established. The data selected for this study are directly obtained during construction and excavation processes, but the utilization of advanced predictive data is not sufficient. Predictive data can also serve as a risk indicator in risk assessment. Incorporating predictions into the risk evaluation model implies that data processing and indicator quantification will become more complex, and the coupling reactions between predictive data and other data need to be analyzed in depth.

(2)

For risk assessment models in TBM construction, such as this one, the data are extensive and intricate, making it challenging to apply a simple weight distribution approach in such a complex construction environment. Therefore, considering this aspect, we have opted for enhancing the variable weight theory method to optimize the allocation of weights among different risk factors. Other alternative methods include weighting based on additive or multiplicative synthesis normalization, weighting based on the sum of squared deviations, weighting based on game theory principles, and weighting based on objective optimization techniques.

(3)

The construction environment involved in this study is simple, which can provide reference for similar projects. Further optimization analysis is needed for different environments. For example, geological conditions can be analyzed from the perspective of remote sensing, and the changes in geological conditions can be observed on a large scale, and then a comprehensive analysis can be carried out by combining this information with the actual geological conditions during tunneling.

In future research, our focus will be on investigating predictive data indicators that can be incorporated into the existing risk data index system model. We aim to examine the coupling relationship between these predictive indicators and the existing models, enhance the integration of case data, explore the model’s applicability in diverse environments for necessary modifications, and employ advanced equipment for verification purposes. Additionally, we intend to develop a real-time identification system for assessing TBM construction risk levels and identifying risk types promptly to serve as an early warning mechanism during TBM construction.

7. Conclusions

The variable weight theory is introduced to enhance and modernize the risk assessment process for tunnel TBM construction. This modification aims to address evaluation deviations caused by fluctuating index values, ultimately improving the accuracy and applicability of the evaluation method. Additionally, fuzzy analysis is utilized to demonstrate that changes in construction risk index values directly impact the weight factor. The degree of influence of different indicators on risk assessment results when values change is analyzed, aiding in identifying the most important indicators. The key findings can be summarized as follows:

(1)

The WBS-RBS method is utilized to establish a comprehensive risk evaluation index system for TBM construction sections, which compensates for the shortcomings of risk identification that may result in omissions and incomplete identification in expert evaluation methods. This results in a more refined risk evaluation index system that can comprehensively reflect the actual risks at all levels of TBM construction. Furthermore, this approach fully considers the randomness and fuzziness of the risk grade boundary values while directly utilizing original engineering data, thereby avoiding data normalization processes and reducing information loss possibilities.

(2)

The method mentioned in the original text applies a variable weight theory based on the extensible model of physical elements, incorporating both subjective and objective evaluation factors, namely, the analytic hierarchy process (AHP) and an improved variable weight theory. This approach takes into consideration the impact of indicator value volatility on indicator weights, thereby accounting for fluctuations in traditional fixed weights. By employing this model to assess the risk of eight tunnel sections in the KS Tunnel, more precise results are obtained compared to utilizing the traditional method with fixed weights.

(3)

It is evident from the importance analysis that the change in rock mass classification during TBM excavation has a significant impact on the risk assessment of tunnel TBM construction, while the influence of the guidance monitoring system is relatively minor. This is not only because a TBM is a large-scale equipment integrating multiple functions, but also because, when evaluating the construction risk of a TBM, its own ability to deal with risks and the effectiveness of on-site construction management should also be taken into account. By considering these factors in the model’s calculations, the model can be made more closely aligned with reality, and the results will be more accurate.

(4)

The modified variable weight matter-element extension model is used to evaluate the risk of eight TBM construction sections of the KS tunnel, and the comparison and analysis with the traditional risk assessment model are carried out to verify the reasonability and feasibility of constructing the new model. The risk evaluation based on the KS tunnel verifies that the new model has good operability in the risk analysis of TBM construction.

(5)

In application, a series of strategies can be adopted to optimize the model: firstly, the model is applied in a small range of engineering sites to improve the application ability of the model; secondly, the data system is optimized to ensure the comprehensiveness and immediacy of the data required by the model. We hope that this model can be promoted in more infrastructure construction projects in the future to further verify its universality and reliability.