Risk Assessment of Small-Diameter Shield Construction in a Deep Drainage Tunnel Based on an ISM–CRITIC–Cloud Model

Abstract

The deep drainage tunnel project is an important measure to alleviate urban waterlogging. The construction of a deep drainage tunnel is a complicated process, involving many influencing factors, and there are correlations among these influencing factors, so the risk assessment is difficult. In this study, the ISM method, CRITIC method and cloud model are combined to build a risk assessment model for the small-diameter shield construction of a deep drainage tunnel. Firstly, the risk index system of small-diameter shield construction in a deep drainage tunnel is put forward. Secondly, the ISM method is used to divide the risk indicators and extract the key risk factors. Then, these key risk factors are weighted with the CRITIC method, and the cloud model is used to evaluate the construction risk of a small-diameter shield of a deep drainage tunnel. Finally, the feasibility and accuracy of the proposed method are verified by a practical case. It was found that the risk assessment method proposed in this study can not only effectively assess the level of security risk, but also identify the key risk factors and rank the importance of these factors. The results of this study can reduce the interference items and workload of risk assessment to a certain extent, and help provide managers with an accurate decision-making basis.

1. Introduction

Urban waterlogging not only affects people’s transportation, but also influences personal safety and causes economic losses [1]. According to the 2024 flood statistics, 154 cities in China experienced urban waterlogging due to heavy rains, affecting 2.55 million people. In order to prevent urban waterlogging, optimize urban space utilization and promote sustainable development, many large cities have planned the construction of deep tunnel drainage projects [2]. The shield construction method has been widely used in the construction of subway, traffic tunnel and large-scale infrastructure because of its advantages of safety and speed, a high degree of automation, not being affected by the environment and climate, and a highly technical economy [3,4]. The section size of a deep drainage tunnel is small, and the construction of a small-diameter shield is generally adopted [5]. Compared with large and medium-sized shield tunnel construction, the diameter of small-diameter shield tunnel is less than 6 m. The initial inlet is small, the space is narrow, and the transportation of material is difficult [6]. Meanwhile, the deep drainage tunnel is generally at the lowest level of the underground space, and the tunnel construction personnel, construction materials and construction machinery that are needed enter the tunnel shield construction surface through the shaft. Shaft construction directly affects the safety of tunnel shield construction. In addition, the shield construction of deep drainage tunnels also has the characteristics of complex groundwater and a geological environment, which further increases the difficulty and uncertainty [7]. There are many factors affecting the construction of small-diameter shield construction in deep drainage tunnels. How to analyze and evaluate the safety risk of small-diameter shield construction in deep drainage tunnels and provide an accurate decision-making basis for managers is the key problem that needs to be solved.

At present, the threshold early warning method directly using monitoring data is usually used in the construction monitoring of tunnel structures [6]. This method can reflect the real state of a tunnel structure, but it is difficult to deal with the fluctuation of monitoring data caused by random factors in the tunnel construction process, which often leads to a high false-positive rate [8]. Therefore, it is necessary to use reasonable risk assessment methods to improve the accuracy and effectiveness of safety assessments for small-diameter shield construction. Traditional risk assessment methods, such as AHP, the fuzzy analytic hierarchy process, the entropy weight method, a risk matrix, a fault tree, the fuzzy comprehensive evaluation method and the matter-element method, have been widely used and verified in engineering practice [7,9,10,11,12]. They play a vital role in engineering risk assessment. However, the working face of small-diameter shield construction with deep tunnel drainage is narrow [7], and its safety risk is affected by many factors, such as geological conditions, construction equipment and construction methods. In the actual construction process, these influencing factors do not exist in isolation, and there is mutual influence between them. Meanwhile, in different regions and different environments, the relationship between risk factors is also different, and these factors are uncertain.

Interpretive structure modeling is a method to analyze the structural relationship of complex systems, and it is often used to analyze the interaction between factors [13]. CRITIC is an objective evaluation method of indicator weight, which can comprehensively consider the importance, complexity, operability and other factors of evaluation indicators, and assign reasonable weights to each indicator [14]. The cloud model is a mathematical model that comprehensively describes randomness, fuzziness and certainty, which can more accurately describe the randomness and uncertainty of risk factors [10,15]. Therefore, by combining these three safety risk assessment methods, this study proposes a safety risk assessment method for the construction of a small-diameter shield with deep tunnel drainage, and applies it to practical engineering projects to provide suggestions and a decision-making basis for project managers.

2. Literature Review

Security risk assessment is a complex engineering system, which mainly includes evaluation index identification, index weight assignment and risk grade evaluation [16]. Many experts and scholars have studied the safety risk of shield construction from different perspectives. In terms of risk factor identification, some studies have listed the safety risk factors of shield construction via literature reviews and experience summaries [17,18,19]. Tang et al. [20] used the text mining method to identify the safety risk factors of subway shield construction. Choosing a reasonable risk evaluation index is an important basis for risk evaluation [21]. Huang and Wu [9] indicated that personnel and management factors were the main influencing factors. Guo et al. [10] and Hu et al. [7] suggested that the selection and parameter setting of shafts and shield mechanical equipment directly affected the construction quality of the shaft and tunnel. Chung et al. [3] and Wu and Zou [12] suggested that the quality of grouting materials, tunnel construction precision control and soil reinforcement were important factors affecting construction safety. Guo et al. indicated that the surrounding geological condition, engineering depth and surrounding rock grade would affect the construction safety of the small-diameter shield construction. Previous studies have listed the risk list of shield construction based on five aspects: human, mechanical, material, method and environment; as shown in

Table 1. The small-diameter shield construction risk list in the deep drainage tunnel.

Number	Risk Factor	Risk Index	Literature Resources
1	Personnel and management factors	Safety awareness	Yu and Ma [21] and Huang and Wu [9]
2		Safety skill
3		Safety protection
4		Safety behavior
5		Safety system implementation
6		Safety hazard investigation
7	Mechanical factor	Shaft drilling rig selection	Hu et al. [7], Guo et al. [10] and Huang et al. [22]
8		Shield equipment selection
9		Rig parameter setting
10		Parameter setting of shield tunneling machinery
11		Vertical degree of shaft
12	Material factor	Grouting material quality	Chung et al. [3] and Hu et al. [7]
13		Shield machine tool quality
14		Damage degree of shield segment
15		Muck improvement and transportation
16	Technical factor	Grouting effect	Hu et al. [7], Wu and Zou [12] and Lin et al. [23]
17		End reinforcement effect
18		Tunnel sealing effect
19		Tunnel secondary lining construction level
20		Starting base and rail installation accuracy
21		Tunnel axis control level
22		Tunnel ventilation effect
23		Soil reinforcement effect
24		Negative ring pipe construction effect
25	Environmental factor	Surrounding rock grade	Guo et al. [24] and Wang et al. [25]
26		Minimum cover thickness
27		Minimum radius of curvature
28		Geological complexity
29		Groundwater condition
30		Settlement monitoring of underground pipelines and surrounding buildings

.

The 30 safety risk factors of small-diameter shield construction for deep tunnel drainage are shown in Table 1. According to Lin et al. [11], most of the influencing factors of shield construction safety risk do not exist in isolation, and there are mutual influences among them. Hu et al. [7] suggest that the quality of shaft construction in small-diameter shield construction affects material transportation and storage. Some studies have analyzed the correlation between safety risk factors in shield construction. Chung et al. [3] used causal network method to analyze the causal relationship between risk factors and risk events in shield tunnel construction, and built the relationship network between risk factors. Pan et al. [26] used social network analysis to analyze the relationship between safety risk factors in subway shield tunnel construction. These research results provided an approach to solve the problem for this study.

In terms of risk assessment, Huang et al. [22] proposed a risk assessment method for shield tunnel engineering based on a two-dimensional cloud model. Huang and Wu [9] proposed a safety risk assessment method for shield tunnel construction in coastal areas by combining the matter-element method and entropy weight method. Xu et al. [4] adopted a dynamic Bayesian network and a three-stage dynamic safety risk assessment model of shield launching, shield tunneling and shield tunneling. Meng et al. [17] proposed a safety risk assessment model of subway shield construction, which combines confirmatory factor analysis and fuzzy evidence reasoning. Guo et al. [10] combined contingency theory and the cloud model to evaluate the risk of shield tunneling through buildings.

Previous studies used literature reviews, experience summaries, text mining and other methods to identify the safety risk factors of tunnel shield construction [17,18,19,20], social network analysis, causal network and other methods to analyze the correlation between safety risk factors [3,26], and AHP, the entropy weight method, the fuzzy comprehensive evaluation method, the matter element method, cloud model and other methods to assess the safety risk level of tunnel shield construction [5,10,22,23]. Most of the existing studies analyze the safety risk of shield construction from unilateral aspects, and rarely integrate the risk identification, risk factor correlation and risk grade evaluation. There are many risk factors in the construction of shafts and tunnels in deep drainage tunnels, and these risk factors have a strong correlation. In order to improve the accuracy and efficiency of risk assessment, in this study, the ISM method, CRITIC method and cloud model were combined to build a safety evaluation model for small-diameter shield construction in a deep drainage tunnel. Through the hierarchy of security risk factors, the key risk factors are extracted. Then, the objective index empowerment and comprehensive evaluation method are used to evaluate the engineering safety risk level, so as to provide a scientific and accurate decision basis for managers.

3. Methodology

3.1. ISM

Interpretive structure modeling (ISM) is a method for analyzing the complex relationships between the various elements of a system, revealing the hierarchy of interrelated elements and explaining their interactions [27]. There are many risk factors in the small-diameter shield construction of deep drainage tunnels, including shaft and tunnel shield construction risk factors, which increase the difficulty of risk assessment [7]. At the same time, these risk factors interact with each other [11]. Therefore, it is necessary to analyze the causal relationship between risk factors and identify the key factors affecting the risk level prior to carrying out risk level evaluation, so as to improve the accuracy of the evaluation results. ISM can classify the risk factors of small-diameter shield construction in deep drainage tunnels and find out the key risk factors. ISM is divided into four steps [13], including establishing an adjacency matrix, establishing a reachable matrix, decomposing a reachable matrix, and an output element hierarchy model.

3.2. CRITIC Method

The CRITIC method is an objective weighting method, and it is used to solve multi-criteria decision problems containing a lot of information [14]. The weight assignment of the evaluation index directly affects the accuracy of risk assessment [16]. It is difficult to directly observe and measure some quantifiable risk indicators in the small-diameter shield construction of a deep drainage tunnel, such as the displacement of the soil layer around the tunnel [6,7]. In this case, risk assessment is generally carried out by expert scoring, which is subjective to some extent. The CRITIC method is an enhancement of the entropy weight method [28]. This method determines the weight of each indicator by capturing the differences and conflicts among indicators and calculating the information contained in the indicator data, which could effectively reduce the subjectivity of expert decision making [29]. The evaluation of indicator weight by the CRITIC method is mainly divided into five steps [15], including evaluation indicator data standardization, calculation of the indicator standardization deviation, calculation of the indicator correlation coefficient, determination of the indicator information and calculation of the weight of each indicator.

3.3. Cloud Model

The cloud model is a method of analyzing uncertainty problems [25]. This method could connect the qualitative concept with the quantitative uncertainty, and embody the fuzziness and randomness of objective things, and it is widely used in decision analysis, data mining, intelligent control and other fields [10,23]. The normal cloud model is a new model based on normal probability distribution and Gaussian membership function, which has strong universality [30]. Some studies have applied this method to tunnel shield risk assessment [10,14,17].

The cloud model represents the qualitative concept through expectation ($Ex$), entropy ($En$) and hyper-entropy ($He$), reflecting the overall characteristics of the qualitative concept [10]. $Ex$ represents the expectation of the spatial distribution of cloud droplets in a domain, representing the point of a qualitative concept or the most typical sample quantified by that concept. $En$ can comprehensively measure the ambiguity range and probability density of qualitative concepts and reflect the uncertainty of qualitative concepts. $He$ is used to measure the uncertainty of entropy, which reflects how dispersed the cloud droplets are in the number domain. There is fuzziness and uncertainty in the construction risk of deep drainage tunnels, and most of these risk factors are qualitative indicators [7]. Applying the cloud model to the risk assessment of small-diameter shield construction in a deep drainage tunnel could quantify these qualitative indicators and display them visually by graphical means, which is conducive to improving the effect of risk assessment.

4. Risk Assessment Model for Small-Diameter Shield Construction in a Deep Drainage Tunnel

The risk assessment process of small-diameter shield construction in a deep drainage tunnel is a complex system, which involves the selection of an evaluation index, the establishment of a risk grade standard, the determination of the index weight and the uncertain reasoning system. Based on the ISM, CRITIC and cloud model, this study proposes a risk assessment model for small-diameter shield construction of a deep drainage tunnel. The risk assessment process is shown in Figure 1.

4.1. Key Risk Factor Identification Model

The construction safety of a small-diameter shield in a deep drainage tunnel is affected by many risk factors, and there is a certain causal relationship between these risk factors. In order to improve the efficiency of risk assessment, this study proposes a risk factor identification model for small-diameter shield construction in a deep drainage tunnel based on the ISM method.

According to the risk list of small-diameter shield construction in the deep drainage tunnel, a set of risk factors is established, expressed by S. s_i represents a risk indicator in Table 1, namely, $s_i\in S(i=1,2,\cdots 30)$.

n represents experts with experience in the industry who were invited to evaluate the direct influence between risk factors in the construction of the small-diameter shield in the deep drainage tunnel. $e_{ij}^k$ represents the influence value of s_i on s_j by an expert’s evaluation. The value of $e_{ij}^k$ is established as Equation (1).

$$e_{\mathit{ij}}^k=\left\{\begin{array}{l}1,\hspace{1em}{s}_i{ \mathit{has} \mathit{effect} \mathit{on} s}_j\hfill \\ 0,\hspace{1em}{s}_i{ \mathit{has} \mathit{no} \mathit{effect} \mathit{on} s}_j\hfill \end{array}\right.$$

(1)

where $i,j=1,2,\cdots 30$, $k=1,2,\cdots ,n$.

Based on the opinions of experts, the risk factor adjacency matrix of small-diameter shield construction in the deep drainage tunnel is established. $E={\left(e_{ij}\right)}_{30\times 30}$ represents the risk factor adjacency matrix.

The accessibility matrix of risk factors for small-diameter shield construction in the deep drainage tunnel is established by Equation (2). M represents the reachable matrix. I represents the identity matrix.

$$M={\left(E+I\right)}^{m+1}={\left(E+I\right)}^m\ne \cdots \ne {\left(E+I\right)}^2\ne \left(E+I\right),m=1,2,\cdots 30$$

(2)

The reachability set, antecedent set and intersection of two sets are calculated according to the risk reachability matrix M of the small-diameter shield in the deep drainage tunnel. The reachability set is the set of all risk factors reachable from a certain risk factor. The antecedent set is the set of all risk factors that can reach that risk factor. $R\left(s_i\right)$ represents the reachable set, $A\left(s_i\right)$ represents antecedent set and $C\left(s_i\right)$ represents the intersection of two sets. Equation (3) shows the relationship between them.

$$C\left(s_i\right)=R\left(s_i\right)\cap A\left(s_i\right)$$

(3)

When a certain risk index $s_i$ meets $R\left(s_i\right)=C\left(s_i\right)$, it indicates that $s_i$ is the highest-level indicator. Then, the rows and columns of the risk factor $s_i$ are removed from the reachable matrix M, and the next layer of the risk factor is found in the same way. Equation (4) shows the process of stratification of the risk factors.

$$\begin{array}{l}{L}_0=\varnothing \\ L_1=\left\{s_i\in Y-L_0\left|C\left(s_i\right)=R\left(s_i\right),i=1,2,\cdots ,30\right.\right\}\\ L_2=\left\{s_i\in Y-L_0-L_1\left|C_1\left(s_i\right)=R_1\left(s_i\right),i < 30\right.\right\}\\ ⋮\\ L_x=\left\{s_i\in Y-L_0-L_1-\cdots -L_{x-1}\left|C_{x-1}\left(s_i\right)=R_{x-1}\left(s_i\right),i < 30\right.\right\}\end{array}$$

(4)

where $L_x$ represents the level of risk factors of small-diameter shield construction in the deep drainage tunnel, ${\displaystyle \prod Y}=L_1,L_2,\cdots L_x$ represents the level division.

According to the calculation results, the risk factor hierarchy of the small-diameter shield construction of the deep drainage tunnel is output. The risk indicator at the lowest level of each risk path is the key risk factor for the construction of the small-diameter shield of the deep drainage tunnel.

4.2. Indicator Weight Calculation Model

The key risk indicators of small-diameter shield construction in the deep drainage tunnel are weighted by the CRITIC method. There are n key risk indicators and m experts were invited to evaluate the key risk indicators of the small-diameter shield construction of the deep drainage tunnel. Based on the evaluation data, the key risk indicator score matrix is constructed and represents $X={\left(x_{pq}\right)}_{m\times n}$. $x_{pq}$ represents an expert’s rating of a key risk indicator.

Equation (5) is used to standardize the data in the matrix X. A standardized matrix is obtained and represents $X*=\left(x_{pq}^{*}\right)$.

$$x_{pq}^{*}={\displaystyle \frac{x_{pq}-\min \left(x_q\right)}{\max \left(x_q\right)-\min \left(x_q\right)}}$$

(5)

Equation (6) is used to calculate the standard deviation of the key risk index score of the small-diameter shield construction in the deep drainage tunnel. $\overline{x_q^{*}}$ represents the mean of a risk indicator score in the standardized matrix $X*$.

$${\sigma }_q=\sqrt{{\displaystyle \frac{1}{m-1}}{\displaystyle \sum _{p=1}^m{\left(x_{pq}^{*}-\overline{x_q^{*}}\right)}^2}}$$

(6)

Equation (7) is used to calculate the Pearson correlation coefficient between the key risk indicators of small-diameter shield construction in the deep drainage tunnel. The correlation matrix is established and represents $R=\left(r_{pq}\right)$

$$r_{pq}={\displaystyle \frac{{\displaystyle {\sum }_{k=1}^m\left(x_{kp}^{*}-\overline{x_p^{*}}\right)\left(x_{kq}^{*}-\overline{x_q^{*}}\right)}}{\sqrt{{\displaystyle {\sum }_{k=1}^m{\left(x_{kp}^{*}-\overline{x_p^{*}}\right)}^2{\displaystyle {\sum }_{k=1}^m{\left(x_{kq}^{*}-\overline{x_q^{*}}\right)}^2}}}}}$$

(7)

Equation (8) is used to calculate the information contained in the key risk indicator of the small-diameter shield construction in the deep drainage tunnel. $w_q$ represents the information contained in a key risk indicator.

$$w_q={\sigma }_q\times {\displaystyle \sum _{q=1}^n\left(1-r_{pq}\right)}$$

(8)

Equation (9) is used to calculate the weight value of the key risk indicator of small-diameter shield construction in the deep drainage tunnel. $w_q^{*}$ represents the weight value of a key risk indicator.

$$w_q^{*}={\displaystyle \frac{w_q}{{\displaystyle {\sum }_{q=1}^n{w}_q}}}$$

(9)

4.3. Risk Grade Evaluation Model

By referring to the relevant literature and norms, the evaluation criteria for the risk factors of the small-diameter shield construction of the deep drainage tunnel are divided into five grades: very dangerous, dangerous, qualified, secure and very secure [7,10]. Very dangerous means that the construction risk of the small-diameter shield in the deep drainage tunnel is very high, and the construction should be stopped immediately. The very dangerous scale is [0, 20). Dangerous means that the construction safety risk is high, and corresponding measures must be taken to reduce the construction safety risk. The dangerous scale is [20, 40). Qualified means that the construction risk can be accepted, and corresponding measures should be taken to reduce the safety risk. The qualified scale is [40, 60). Secure means that the construction risk is acceptable, it only needs to be monitored and the implementation of safety management measures need to be checked. The secure scale is [60, 80). Very secure means that the construction safety risk can be accepted without any additional measures being taken. The very secure scale is [80, 100].

According to the above risk assessment grade interval, Equation (10) is used to calculate the standard cloud digital characteristic value $\left(E{x}_i,E{n}_i,He\right)$. The standard cloud map for the risk assessment of the small-diameter shield construction of the deep drainage tunnel was generated by MATLAB2023a software programming, as shown in Figure 2.

$$\left\{\begin{array}{l}E{x}_i={\displaystyle \frac{\left(x_i^{\max }+x_i^{\min }\right)}{2}}\hfill \\ E{n}_i={\displaystyle \frac{\left(x_i^{\max }-x_i^{\min }\right)}{6}}\hfill \\ He=k\hfill \end{array}\right.$$

(10)

where $x_i^{\max }$ and $x_i^{\min }$, respectively, indicate the upper and lower limits of different risk rating ranges for the small-diameter shield construction of the deep drainage tunnel. k reflects the fuzzy threshold of the assessment model, and its value can be adjusted according to the specific situation of the risk assessment object. In this study, the value of k is 0.5.

There are n key risk indicators by identifying the risk factors of small-diameter shield construction in the deep drainage tunnel. m experts are invited to evaluate each risk indicator according to the risk grading criteria. The evaluation matrix is established after collecting and sorting the data, and is represented by $Z={\left(z_{ij}\right)}_{m\times n}$. $z_{ij}$ represents an expert’s rating of a risk indicator.

The digital characteristic value of each risk indicator in the construction of the small-diameter shield of the deep drainage tunnel is calculated by Equation (11). $C_j\left(E{x}_j,E{n}_j,H{e}_j\right)$ represents the digital characteristic value of risk indicators.

$$\left\{\begin{array}{l}E{x}_j={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{z}_{ij}}\hfill \\ E{n}_j=\sqrt{{\displaystyle \frac{\pi }{2}}}\times {\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N\left|z_{ij}-E{x}_j\right|}\hfill \\ S_j^2={\displaystyle \frac{1}{N-1}}{\displaystyle \sum _{i=1}^N{\left(z_{ij}-E{x}_j\right)}^2}\hfill \\ H{e}_j=\sqrt{\left|S_j^2-E{n}_j^2\right|}\hfill \end{array}\right.$$

(11)

Introducing the calculation results of Equations (9) and (11) into Equation (12), the digital characteristic value of the comprehensive risk evaluation cloud of small-diameter shield construction in the deep drainage tunnel can be obtained.

$$\left\{\begin{array}{l}Ex={\displaystyle \sum _{j=1}^n\left(E{x}_j·w_j\right)}\hfill \\ En=\sqrt{{\displaystyle \sum _{j=1}^{n}E{n}_j^2·w_j}}\hfill \\ He={\displaystyle \sum _{j=1}^n\left(H{e}_j·w_j\right)}\hfill \end{array}\right.$$

(12)

The membership grade of each risk index of small-diameter shield construction in the deep drainage tunnel is calculated by Equation (13).

$${\mu }_j=\exp \left(-{\displaystyle \frac{{\left(Ex-E{x}_j\right)}^2}{2{\left(E{n}_j\right)}^2}}\right)$$

(13)

The integrated membership grade of small-diameter shield construction of the deep drainage tunnel is calculated by Formula (14).

$$\mu ={\displaystyle \sum _{j=1}^n{w}_j·{\mu }_j}$$

(14)

5. Engineering Applications

5.1. Project Overview

The total length of the Donghu deep drainage tunnel project is about 17.5 km. The tunnel diameter is D3000 mm~D3400 mm, which belongs to the small-diameter tunnel project. The project is constructed by the shield method. There are 11 ultra-deep wells with small sections along the main tunnel project, and the well depth is 32.8 m~51.5 m. The maximum cross-section is a rectangle with a diameter of 15 m × 11 m, and the minimum cross-section is a circle with a diameter of 12 m. Due to the small diameter and long distance of the tunnel in this project, there is a large construction safety risk. In order to provide an accurate basis for managers to make decisions, the method proposed in this paper is used to evaluate the construction risk of the project.

5.2. Application of Risk Assessment Model

5.2.1. Identification of Key Risk Factors

According to the risk list of small-diameter shield construction in Table 1, the risk factor correlation questionnaire is designed. Invite experts in the industry to identify the relationship between risk factors based on the actual situation of the project, and the adjacency matrix $E$ of risk factors for small-diameter shield construction in the Donghu deep drainage tunnel is established.

$$E=\left[\begin{array}{cccccccccccccccccccccccccccccc}0& 1& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 1& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0& 0\end{array}\right]$$

Then, through the calculation and analysis of Equations (2)–(4), the hierarchical classification results of risk factors for small-diameter shield construction of the Donghu deep drainage tunnel are obtained. It is shown in Figure 3.

In Figure 3, some risk factors are pre-causes of other risk factors. These risk factors include safety awareness (K1), safety hazard investigation (K2), shaft drilling rig selection (K3), shield equipment selection (K4), grouting material quality (K5), muck improvement and transportation (K6), tunnel secondary lining construction level (K7), starting base and rail installation accuracy (K8), tunnel axis control level (K9), tunnel ventilation effect (K10), surrounding rock grade (K11), geological complexity (K12) and groundwater condition (K13). Thus, these risk factors are the key risk factors for the safety of small-diameter shield construction in the Donghu deep drainage tunnel.

5.2.2. Calculation of Risk Indicator Weight Value

Ten experts in the industry were invited to score the key risk factors in small-diameter shield construction of the Donghu deep drainage tunnel according to the risk rating interval and the actual situation. The results of the expert ratings are shown in

Table 2. Expert scoring results of key risk indicators for small-diameter shield construction of the lake deep drainage tunnel.

Number	K1	K2	K3	K4	K5	K6	K7	K8	K9	K10	K11	K12	K13
Expert 1	64	70	66	70	70	70	68	66	62	71	64	66	67
Expert 2	70	66	63	71	67	68	73	67	68	65	60	55	61
Expert 3	68	70	66	63	72	56	63	55	64	81	63	61	53
Expert 4	65	71	58	67	52	66	66	57	68	72	64	68	62
Expert 5	63	69	62	58	66	71	71	69	54	70	64	76	59
Expert 6	65	65	71	63	75	63	69	66	58	64	66	69	64
Expert 7	70	66	68	68	71	57	61	51	53	55	65	63	60
Expert 8	64	65	56	71	55	62	60	72	73	67	62	73	64
Expert 9	56	55	66	57	54	55	62	64	63	58	56	64	63
Expert 10	68	71	68	68	66	65	51	67	71	57	63	70	65

.

Introducing the scores of each risk index in Table 2 into Equations (5) and (6), the variability value of key risk index for the small-diameter shield construction of the Donghu deep drainage tunnel is obtained. The index conflict values of key risk factors are obtained by Equation (7). Then, the value of index variability and the value of index conflict are introduced into Equation (8), and the information quantity values of key risk factors are obtained. The weight value of the key risk indicators of small-diameter shield construction in the Donghu deep drainage tunnel is obtained by introducing the information quantity value into Equation (9). The calculation results of all indicator weights are shown in

Table 3. Calculation results of key risk index weights for small-diameter shield construction of the Donghu deep drainage tunnel.

Risk Index	Index Variability	Index Conflict	Information Amount	Weighted Value	Rank
K1	0.843	12.272	10.349	0.076	7
K2	0.949	12.334	11.701	0.086	5
K3	0.823	12.433	10.236	0.075	9
K4	1.179	11.723	13.816	0.102	1
K5	1.033	13.184	13.616	0.100	2
K6	0.738	12.822	9.461	0.070	11
K7	0.527	10.486	5.527	0.041	12
K8	0.516	11.01	5.686	0.042	13
K9	0.789	13.107	10.339	0.076	7
K10	1.059	12.201	12.925	0.095	3
K11	0.949	12.414	11.777	0.087	4
K12	0.919	11.469	10.539	0.077	6
K13	0.919	11.013	10.12	0.074	10

.

5.2.3. Assessment of Risk Grade

By introducing the scoring values of risk indicators in Table 2 into Equation (11), the digital characteristic values $C_j({Ex}_j,{En}_j,{He}_j)$ of the key risk indicators for small-diameter shield construction in the Donghu deep drainage tunnel are obtained. Then, by introducing the characteristic value and weight value of these risk index evaluation clouds into Equation (12), the digital characteristic value of the comprehensive evaluation cloud is obtained. The calculation results are shown in

Table 4. Calculation results of digital characteristic values of key risk indicators for small-diameter shield construction in the Donghu deep drainage tunnel.

Risk Index	Ex	En	He
K1	65.3	3.71	1.833
K2	66.8	4.261	2.215
K3	64.4	4.662	0.291
K4	65.6	5.364	1.584
K5	64.8	8.372	1.674
K6	63.3	5.891	1.164
K7	64.4	6.267	1.452
K8	63.4	6.818	0.941
K9	63.4	6.768	0.952
K10	66.0	7.771	1.843
K11	62.7	2.532	1.351
K12	66.5	5.891	1.571
K13	61.8	3.559	1.618
Comprehensive evaluation cloud	64.662	6.02	1.406

.

According to the characteristic values of the comprehensive evaluation cloud and standard cloud in Table 4, MATLAB2023a software is used to program and generate a key risk evaluation cloud map of small-diameter shield construction in the Donghu deep drainage tunnel, as shown in Figure 4.

In Figure 4, the position of the integrated evaluation cloud is between the qualified risk and the safe cloud image, which indicates that the small-diameter shield construction risk in the Donghu deep drainage tunnel is low. At the same time, by introducing the characteristic values of evaluation clouds and standard clouds of each risk index in Table 4 into Equations (13) and (14), the comprehensive membership degree of key risk levels of small-diameter shield construction in the Donghu deep drainage tunnel is obtained. The integrated membership grade is (0, 0, 0.062, 0.329, 0). Based on the principle of maximum membership degree, the risk level of small-diameter shield construction in the Donghu deep drainage tunnel is secure.

5.3. Analysis of Risk Assessment Results

By applying the risk assessment model proposed in this study to the small-diameter shield construction of the Donghu deep tunnel drainage project, it is found that the overall risk of the project is between qualified and secure. This shows that the construction risk of the project is basically acceptable, but it is still necessary to take corresponding measures to reduce the construction safety risk.

Identifying key risk factors helps managers optimize resource allocation and make decisions [13]. According to the actual situation of the project, the key risk factor identification model is used to divide 30 major risk factors into 5 levels and reveal their mutual influence relationship. The identification results show 13 key risk factors, including safety awareness, safety hazard investigation, shaft drilling rig selection, shield equipment selection, grouting material quality, muck improvement and transportation, tunnel secondary lining construction level, starting base and rail installation accuracy, tunnel axis control level, tunnel ventilation effect, surrounding rock grade, geological complexity and groundwater condition. Therefore, in the construction process, managers can formulate corresponding control measures for these key risk factors.

Project risk management needs to invest a lot of capital, personal, materials and other resources. The weight value reflects the importance of the evaluation index [10]. According to the calculation results of the weight assignment of these key risk indicators, the importance of these risk factors can be ranked, and the ranking results are shown in Table 3. The results show that shield equipment selection, grouting material quality, tunnel ventilation effect, surrounding rock grade, and safety hazard investigation are more important than other factors. Under resource constraints, managers can give priority to developing risk response measures for risk factors with high importance.

6. Discussion

6.1. Verification of Model Accuracy

In order to verify the validity of the small-diameter shield construction risk assessment model of a deep drainage tunnel based on the ISM–CRITIC–cloud model, the calculation results of traditional risk assessment methods are compared in this study. The fuzzy comprehensive evaluation method is used to evaluate the membership degree of the risk index of small-diameter shield construction in the deep drainage tunnel. Evaluation set V = very dangerous, dangerous, qualified, secure and very secure. The result of obtaining the integrated membership grade is (0, 0, 0.216, 0.773, 0.011). Based on the principle of maximum membership grade, the risk level of small-diameter shield construction in the Donghu deep drainage tunnel is secure. This is the same as the calculated result in this study.

In order to further demonstrate the scientificity of the risk assessment model, it is compared with the evaluation results of the small-diameter shield construction in the Donghu deep drainage tunnel by using hierarchical holographic modeling [7]. The calculated results of this method show that the risk level is four. It is consistent with the calculated results in this study. This shows that the risk assessment model of small-diameter shield construction in the deep drainage tunnel based on an ISM–CRITIC–cloud model is feasible and accurate.

6.2. Implication

Compared with the traditional risk assessment model, the risk assessment model of small-diameter shield construction of a deep drainage tunnel proposed in this study based on the ISM–critical–cloud model has certain advantages. Many traditional risk assessment methods directly apply the existing risk index system [9,11,25]. If there are many risk factors, a lot of time and resources need to be invested to obtain the raw data for evaluation. This study fully considers the numerous and interrelated characteristics of risk factors in the construction of a small-diameter shield of a deep drainage tunnel. The ISM method is adopted to analyze the influential relationship between these factors, divide the levels of risk factors, so as to find the pre-cause of risk occurrence and extract the key risk factors. This reduces the interference and calculation of risk assessment to some extent.

Meanwhile, the risk assessment of small-diameter shield construction in the deep drainage tunnel is fuzzy and random. Some existing evaluation models can only calculate the level of risk, and cannot be presented in a quantitative way [7,12,20]. Based on identifying key risk factors, this study combined the CRITIC and cloud model, and through objective weight assignment and the transformation from qualitative concept to quantitative representation, quantitatively analyzed and demonstrated the specific position of risk level for small-diameter shield construction in the deep drainage tunnel in the evaluation set, which is conducive to improving the objectivity and accuracy of risk assessment.

In addition, the risk assessment model for small-diameter shield construction in a deep drainage tunnel proposed in this study can not only evaluate the overall risk level of the project, but also extract the key risk factors from the numerous risk factors and rank their importance, which is helpful for managers to understand potential risk sources and influencing factors, optimize resource allocation and make reasonable decisions.

6.3. Limitations and Future Research

The risk assessment method proposed in this study has some limitations. Firstly, in the evaluation index system construction, 30 risk assessment indicators were selected from 5 aspects. Most of these indicators are qualitative indicators, and more quantifiable risk indicators, such as groundwater depth and grouting amount, can be introduced in future studies to further improve the accuracy of risk assessment. Secondly, in terms of data collection, this study uses the risk assessment data of 10 industry experts through questionnaires. In future studies, the sampling range of data can be expanded to obtain more cases to improve the validity of the original data. Thirdly, the evaluation method adopted in this study is mainly based on experience and statistical data. Engineering project construction is a dynamic process, and other methods can be introduced into the risk assessment of small-diameter shield construction in deep tunnel drainage in the future, such as machine learning, dynamic Bayesian networks and neural networks.

7. Conclusions

In this study, the ISM, CRITIC and cloud models are comprehensively applied to the risk assessment of small-diameter shield construction in a deep drainage tunnel, and a new risk assessment model is proposed. The effectiveness and feasibility of this method are verified by applying it to the Donghu deep drainage tunnel project. The main conclusions are as follows:

(1)

The risk assessment model constructed by combining the ISM, CRITIC and cloud model can solve the ambiguity and uncertainty of the risk assessment of small-diameter shield construction in a deep drainage tunnel, and effectively evaluate the risk level of small-diameter shield construction in a deep drainage tunnel.

(2)

The risk assessment model proposed in this study can identify the key risk factors from the numerous risk factors in small-diameter shield construction of deep tunnel drainage, which can not only reduce the interference project and workload of risk assessment, but also provide support for managers’ decision making.

(3)

The risk assessment model proposed in this study can rank the importance of the risk factors in small-diameter shield construction of deep tunnel drainage, and provide a theoretical basis for the optimization of resource allocation under the resource constraints of project risk management.