Analysis of Construction Safety Risk Management for Cold Region Concrete Gravity Dams Based on Fuzzy VIKOR-LEC

Abstract

To address potential risks during the construction process, improve construction quality and engineering safety, this paper constructs a construction safety risk analysis model for concrete gravity dams in cold regions based on fuzzy VIKOR-LEC. Firstly, an expert team employs linguistic variables to evaluate the likelihood of accidents (L), the frequency of personnel exposure to hazardous environments (E), and the consequences of accidents (C) for various risk factors in the LEC model. Secondly, the fuzzy analytic hierarchy process (FAHP) and maximum deviation method were used to construct a risk factor weight analysis matrix and find subjective and objective weights, respectively, to obtain the comprehensive weights of risk factors. Thirdly, VlseKriterijumska Optimizacija Kompromisno Resenje (VIKOR) is introduced to improve the traditional LEC model and is used to calculate the risk priority number. Finally, in order to further verify the validity of the model, this paper selects the example of Linhai Reservoir dam in Heilongjiang Province to analyze the management of the construction safety risk. The research results may provide a scientific basis for the safety management of gravity dam construction projects in cold areas, and help to improve the level of project management and reduce construction risks.

1. Introduction

Global climate change has led to an increased frequency of extreme weather events, particularly in cold regions where dramatic temperature fluctuations pose significant challenges to the construction and maintenance of infrastructure [1]. As a critical facility in water conservancy projects, concrete gravity dams shoulder important functions such as water resource management, flood control, and power generation. Their construction safety is directly linked to local ecological security, and economic development [2,3]. However, the construction of concrete gravity dams in cold regions faces substantial risks, such as concrete material embrittlement caused by freeze–thaw cycles, stress concentration within the structure, and limitations in the durability of construction materials [4]. Therefore, it is imperative to establish a scientific safety risk management mechanism for the construction of concrete gravity dams in cold regions., so as to cope with the potential risks in the construction process and improve the construction quality and project safety.

Scholars have made significant progress in studying the safety of concrete gravity dam construction. Both domestic and international researchers have extensively explored construction safety through risk analysis models and multi-criteria decision-making (MCDM) methods. For instance, approaches such as the analytic hierarchy process (AHP) and fuzzy comprehensive evaluation have been used to identify and assess potential risk factors during the construction process [5]. However, most of these studies focus on risk analysis in the non-cold regions, with relatively few studies addressing the unique environmental challenges of cold regions, such as the low temperature, and freeze–thaw cycles. As a result, the distinctive impacts of these environmental factors remain insufficiently considered. Furthermore, existing research tends to emphasize the analysis of individual risk factors rather than developing a systematic, multi-factor comprehensive early warning model. This limitation hinders the ability to address the complexities of construction environments holistically. With the advancement of MCDM methods, the VlseKriterijumska Optimizacija Kompromisno Resenje (VIKOR) method has gradually been applied in engineering risk assessment, gaining recognition for its strengths in optimizing comprehensive decision-making. Compared with other MCDM methods, the VIKOR method is more suitable for complex scenarios with obvious goal conflicts and unclear decision makers’ preferences, which also offers advantages in terms of flexibility, computational efficiency, and practical applicability. However, its application in early warning systems for the risks associated with cold-region concrete gravity dams remains limited [6]. Given these gaps, there is an urgent need to develop a multi-factor early warning model for the construction safety of concrete gravity dams in cold regions.

To address this gap, this study integrates the VIKOR multi-criteria decision-making method with the maximum deviation method to establish a comprehensive risk early warning model suitable for cold-region construction environments. In this study, the term construction safety risk specifically refers to potential accidents, hazards, and unsafe conditions that may occur during the construction phase of concrete gravity dams in cold regions. These risks include worker injuries, material and equipment failures, unsafe management practices, and adverse environmental conditions on site. The focus is not on long-term performance failures or post-construction issues, but rather on assessing safety risks that may impact the progress and safety of dam construction activities.

The hazard evaluation method for operating conditions, proposed by American scholars Graham and Kinney [7], is a semi-qualitative and semi-quantitative safety assessment method for identifying potential hazards in operational environments. The method evaluates the risk of injury to operators using the product of three factor indicators: likelihood (L), exposure (E), and consequence (C), which are associated with system risk. Specifically, L represents the likelihood of an accident occurring due to various risk factors, E denotes the frequency with which personnel are exposed to hazardous environments, and C indicates the severity of the consequences if an accident occurs. Each of the three factors is assigned a score based on defined grading criteria. The product of the three scores gives a composite value D (danger), which is used to evaluate the overall level of risk associated with the working condition. However, the values of L, E, and C often vary depending on the specific context, and their relative influence on risk assessment differs accordingly. Therefore, assigning appropriate weights to these factors is crucial for accurate risk assessment [8]. Traditional LEC methods over-rely on the subjective experience of experts and lack detailed weights, which cannot fully reflect the complex and changeable safety risk scenarios in engineering projects. To address this limitation, this paper employs FAHP and the maximum deviation method to assign both subjective and objective weights to the L, E, and C risk factors in the model. This approach enhances the comprehensiveness and scientific rigor of risk assessment. Furthermore, this paper integrates the weights obtained from FAHP and the maximum deviation method with the VIKOR method to enable a more objective evaluation of risk factors. By combining the established subjective and objective weights with the VIKOR method, we can comprehensively assess the relative importance of risk factors within a multi-factor and multi-objective framework, so as to provide scientific decision support for the early warning of safety risks in construction. This approach expands the application of the VIKOR method and the maximum deviation method in early warning models for construction safety risks in cold-region concrete gravity dams, thereby filling a theoretical gap in the early warning models for risk in construction projects in cold regions.

The structure of this paper is as follows. Section 2 provides a comprehensive literature review on the safety and assessment methods for cold-region concrete gravity dams. Section 3 presents a detailed description of the safety risk model proposed in this study. Section 4 conducts a construction safety risk assessment using the Linhai Reservoir Dam project in Heilongjiang Province as a case study and proposes specific risk control measures. Section 5 discusses the theoretical and practical implications of this study, as well as its limitations.

2. Literature Review

2.1. Research on Construction Safety of Cold-Region Concrete Gravity Dams

Due to the low temperatures, frequent cold waves, and repeated freeze–thaw cycles in cold regions, the performance of concrete dams in such areas tends to deteriorate [9]. Among these factors, ambient temperature is a critical factor affecting the cracking of mass concrete structures during the overwintering period in severely cold regions. Low temperatures increase the internal temperature gradient of concrete, thereby raising the risk of cracking [10,11,12]. Compared with traditional temperature control measures such as surface spraying and water cooling, cold-region concrete dams typically adopt measures like optimizing the concrete mix design and insulating the dam surface to reduce cracking risks [13]. Zhou and Qiao [14] investigated the rapid freeze–thaw performance of ultra-high-performance concrete (UHPC) in cold regions. Meraz et al. [15] explored the effects of various self-healing materials, such as mineral admixtures, fibers, and innovative materials like shape memory alloys, microcapsules, and microorganisms, on crack repair. Chen et al. [16] developed an intelligent prediction and optimization model for concrete durability based on a random forest model and NSGA-II, identifying the optimal mixing ratio of concrete materials. The model was validated using a case study in Northeast China, demonstrating its effectiveness and applicability in cold regions. Selecting appropriate insulation materials is a key task in the crack prevention engineering of cold region concrete dams [17]. Zhang, Li, Li, Ge and Li [13] examined the insulation performance of 5 cm and 8 cm polystyrene boards without thermal isolation and found that when an 8 cm polystyrene board was used, the maximum principal stress was below the allowable stress, that is, the insulation material effectively controlled internal temperature variations within the structure. Zhang et al. [18] conducted dynamic response analysis of gravity dams through freeze–thaw cycle tests and numerical simulations of concrete materials, investigating the impact of concrete performance deterioration on the seismic performance of gravity dams in cold regions. Additionally, Zhang et al. [19] developed a temperature field calculation program for the construction and operation phases of concrete dams using FORTRAN. The accuracy of the program was verified through a case study in Tibet, China.

Additionally, the application prospects of technologies such as intelligent sensors, RFID, and the Internet of Things (IoT) have garnered significant attention. Edirisinghe [20] explored the future applications of intelligent sensor technology, RFID, and IoT in various areas, including procurement management, worker safety, and on-site safety management in construction sites. Moon et al. [21] designed a sensor network prototype, which integrates sensors, wireless networks, safety monitoring applications, and independent power sources, to monitor safety during the concrete pouring process. As an example of the “Iron Gate 1” project, Martac et al. [22] detailed how to automatically identify measurement points through RFID technology, Bluetooth technology for data transmission, and sensors for collecting environmental data, thereby enhancing the safety and efficiency of the construction process. Pujari and Sahasrabuddhe [23] employed a variety of sensors, including temperature, pressure, fire, vibration, and proximity sensors, for real-time safety control on construction sites. Zhu et al. [24] integrated digital twins with IoT and AI, utilizing 3D visualization and real-time data feedback to improve the feasibility and predictability of dam health monitoring.

In addition to technical and environmental challenges, worker safety remains a critical concern during the construction of concrete gravity dams in cold regions. The harsh climate can lead to increased risk of frostbite, slips, and equipment handling incidents, especially under snow, ice, and freezing temperatures. Moreover, the frequent freeze–thaw cycles can affect not only structural materials but also the safety and health of on-site personnel. Research by Orysiak et al. [25] emphasized that cold-induced fatigue and reduced manual dexterity significantly increase accident rates among construction workers. Obioha-Val et al. [26] further noted the value of intelligent sensors and real-time monitoring technologies in reducing human error and improving on-site safety management. These studies underline the need to systematically integrate worker safety indicators into construction risk assessments, particularly under extreme environmental conditions.

Table 1. Impact of cold-region climate on different categories of construction safety risk.

Risk Category	Specific Impacts of Cold Climate
Worker Safety Risk	Low temperatures reduce workers’ physical endurance and mental alertness, increasing accident likelihood [27].
	Ice and snow increase slip/fall risk; inadequate PPE use due to discomfort or lack of enforcement.
Material and Equipment Safety Risk	Machinery prone to hydraulic freezing and lubrication failures, leading to operational errors and downtime.
	Cold weather impairs material performance (e.g., delayed concrete curing, frost damage).
Construction Management Safety Risk	Environmental stress reduces worker efficiency and attention span, leading to managerial difficulties.
	Harsh conditions may cause schedule overruns and reduced equipment uptime.
Construction Environment Safety Risk	Frequent freeze–thaw cycles degrade concrete and cause terrain instability [28].
	Sudden snowstorms or temperature drops create unpredictable hazards.
Construction Technology Safety Risk	Structural design must account for frost resistance and thermal stress; poor design may lead to cracking or failure [29].
	Inadequate technological adaptation results in performance decline under extreme conditions.

summarizes how cold-region climatic conditions affect various categories of construction safety risks in concrete gravity dam projects, based on both literature review and field case observations.

2.2. Research on Construction Safety Risk Assessment Methods

Hazard identification is a critical component of construction safety management [30]. To prevent major injuries and property damage caused by safety violations, risk-based safety management practices have increasingly become a focal point of research.

Risk assessment methods can be categorized into qualitative and quantitative approaches [31]. Qualitative methods typically involve expert evaluation and surveys, while quantitative methods include fuzzy comprehensive evaluation, AHP, and Monte Carlo simulation, etc. Wang et al. [32] identified 16 lifting safety risk factors, applied the entropy weighting method to calculate indicator weights, and determined safety risk levels for prefabricated building lifting operations using reliability theory. Celik and Gul [33] utilized the best-worst method (BWM) based on interval type-2 fuzzy sets to weigh severity and probability, and used the MARCOS method to prioritize risks, offering new approaches for dam construction safety management. Due to the complexity of construction risk factors, some variables lack quantifiable data and rely on expert judgment and literature. Therefore, methods combining both qualitative and quantitative approaches, such as fault tree analysis, probabilistic risk assessments, risk evaluation matrices, and the LEC method, are often used.

In recent years, researchers have introduced various improved models to address the uncertainties inherent in traditional assessment methods. Fu, Zhao, Wang, Wang, Xu and Gu [9] developed an evaluation system for concrete dam performance in cold regions, considering factors such as winter layers, cold waves, and freeze–thaw cycles. Based on the typical small probability methods and AHP, they employed an improved interval intuitionistic fuzzy set method for a comprehensive evaluation of dam structural performance. Based on game theory and extended cloud theory, Ju et al. [34] proposed a BWM–entropy weighting combination model to generate cloud maps for safety indicators, determining the risk levels of construction activities. Liu et al. [35] used cloud models and TOPSIS to refine the traditional FMEA risk assessment method. Zhang et al. [36] applied fuzzy Bayesian networks to explore the relationship between tunnel damage and influencing variables, comparing it with the fuzzy fault tree method to guide tunnel construction safety management.

The LEC method, known for its simplicity and ease of application, is widely used in construction [37], mining [38], and fire risk management [39]. Traditionally, the LEC method calculates risk by multiplying the L, E, and C values, with higher scores indicating greater risks. However, its reliance on expert subjective assessments [40] has led to limitations. To improve the method’s effectiveness, Zhu et al. [41] proposed an enhanced version of the LEC method for identifying risk sources in hydraulic and hydropower construction projects. Zeng, Yin and Li [8] incorporated safety risk control factors into the LEC model, improving its application in the main beam pouring phase of elevated bridges.

To mitigate parameter uncertainty, this study introduces fuzzy set theory, constructs a fuzzy AHP judgment matrix to calculate subjective weights for risk factors, and employs the maximum deviation method to compute objective weights. The VIKOR method is integrated into the traditional LEC model to improve risk ranking, thus enhancing the effectiveness of construction safety assessments for concrete gravity dams in cold regions.

3. Research Methodology

This study employs the LEC method, combined with triangular fuzzy theory, the maximum deviation method, and the VIKOR method, for risk assessment of dam construction safety. The specific process is illustrated in Figure 1. First, based on the construction scenario of gravity dams in cold regions, and informed by expert opinions and literature review, the study selects risk evaluation indicators in the areas of construction worker safety risk (S₁), material and equipment safety risk (S₂), construction management safety risk (S₃), construction environment safety risk (S₄), and construction technology safety risk (S₅). Secondly, k experts are selected to form a set E, $E=\left\{E_1,E_2,\cdots E_k\right\}$. Based on their differing levels of experience, scores are assigned with varying weights. The actual performance of risk factors and their relative importance are evaluated using linguistic variables, and the evaluation results are then converted into a triangular fuzzy matrix. Subsequently, the study employs FAHP and the maximum deviation method to perform a comprehensive weighting of risk factors. Finally, the VIKOR method is used to rank the risk factors and their impacts, followed by evaluation and analysis of the ranking results.

3.1. Risk Expression Based on Triangular Fuzzy Numbers

Definition 1.

Let $U$ be the domain of discourse, called mapping:

$${\mu }_{\underset{˜}{A}}:U\to [0,1], x|\to {\mu }_{\underset{˜}{A}}(x)\in [0,1]$$

(1)

A fuzzy subset $\underset{˜}{A}$ on $U$ is determined. The mapping ${\mu }_{\underset{˜}{A}}$  is called the membership function of  $\underset{˜}{A}$, and ${\mu }_{\underset{˜}{A}}(x)$ is called the membership degree of $x$ to $\underset{˜}{A}$. The greater the ${\mu }_{\underset{˜}{A}}(x)$, the greater the membership degree of $x$ to $\underset{˜}{A}$.

Definition 2.

A triangular fuzzy number can be expressed as $M=(l,m,u)$, and its membership function  ${\mu }_M(x)$ can be expressed as follows:

$${\mu }_M(x)=\left\{\begin{array}{cc}0& x<l\\ {\displaystyle \frac{x-l}{m-l}}& l\le x\le m\\ {\displaystyle \frac{u-l}{u-m}}& m\le x\le u\\ 0& x>u\end{array}\right.$$

(2)

where $l$  and   $u$  represent the upper and lower bounds of the triangular fuzzy number, and   $m$  is the modal value of the fuzzy number   $M$.

Definition 3.

Let   $M_1=(l_1,m_1,u_1)$ and   $M_2=(l_2,m_2,u_2)$  be two triangular fuzzy numbers, given any real number  $\lambda$, $\lambda >0$, $\lambda \in R$ . The algebraic operation of triangular fuzzy numbers can be expressed as follows:

$$M_1\oplus M_2=(l_1+l_2,m_1+m_2,u_1+u_2)$$

(3)

$$M_1\otimes M_2=(l_1\cdot l_2,m_1\cdot m_2,u_1\cdot u_2)$$

(4)

$$\lambda M_1=(\lambda l_1,\lambda m_1,\lambda u_1)$$

(5)

$${(M_1)}^{-1}=({\displaystyle \frac{1}{u_1}},{\displaystyle \frac{1}{m_1}},{\displaystyle \frac{1}{l_1}})$$

(6)

Definition 4.

The distance between any two triangular fuzzy numbers   $M_1=(l_1,m_1,u_1)$  and   $M_2=(l_2,m_2,u_2)$  can be expressed as follows:

$$d(M_1,M_2)=\sqrt{{\displaystyle \frac{1}{3}}[{(l_1-l_2)}^2+{(m_1-m_2)}^2+{(u_1-u_2)}^2]}$$

(7)

3.2. Determining Risk Factor Weights Based on Fuzzy AHP and Maximum Deviation Method

In the traditional LEC method, it is assumed that the risk factors L, E, and C have equal importance, without considering the weights of the risk factors. However, this assumption may oversimplify the actual situation. Directly determining the weights based on subjective judgment alone is also scientifically insufficient. Therefore, this study adopts a combined weighting method that incorporates both subjective and objective perspectives to improve the credibility and accuracy of the evaluation results. First, the subjective weights of the three risk factors ${\alpha }_i$ are calculated using the FAHP, reflecting expert knowledge and preferences. Then, the objective weights ${\beta }_i$ are derived using the maximum deviation method, which captures the dispersion characteristics of data. The final comprehensive weights $w_i=\phi {\alpha }_i+(1-\phi ){\beta }_i$ are obtained through a linear combination of the two, where $\phi$ and $1-\phi$ represent the influence coefficients of subjective and objective weights, respectively. This integrated approach leverages the complementary strengths of FAHP and the maximum deviation method—ensuring both expert insight and data-driven robustness.

3.2.1. Subjective Weight Calculation Based on Fuzzy AHP

FAHP combines AHP with fuzzy theory, converting experts’ linguistic evaluations into fuzzy numbers, constructing fuzzy matrices for processing, and then obtaining the subjective weights of risk factors. In this paper, the evaluation language is converted into triangular fuzzy numbers. Experts provide linguistic evaluations based on their real opinions during the review decision-making process. The relationship between triangular fuzzy numbers and the linguistic terms used by team members to assess the subjective weights of risk factors is shown in

Table 2. Linguistic variables for rating the weights of risk factors.

Linguistic Variable	Fuzzy Number
Absolute strong (AS)	(2,5/2,3)
Very strong (VS)	(3/2,2,5/2)
Strong (FS)	(1,3/2,2)
Slightly strong (SS)	(1,1,3/2)
Equal importance (EI)	(1,1,1)
Slightly weak (SW)	(2/3,1,1)
Weak (FW)	(1/2,2/3,1)
Very weak (VW)	(2/5,1/2,2/3)
Absolute weak (AW)	(1/3,2/5,1/2)

.

Let the object set be $X=\left\{x_1,x_i,\cdots x_n\right\}$ and the target set be $G=\left\{g_1,g_i,\cdots g_n\right\}$. For each object $x_i$, the degree analysis for each target can obtain the degree analysis value under $m$ targets, the symbol is as follows:

$$M_{gi}^i,M_{gi}^j,\cdots ,M_{gi}^m, i=1,2,\cdots n$$

(8)

where $M_{gi}^j(j=1,2,\cdots ,m)$ is a triangular fuzzy number, the steps for calculating the subjective weights of risk factors L, E, and C are as follows:

• Step 1: Calculate the value of the degree of fuzzy synthesis relative to the $i$th object according to the following formula:

  $$S_i={\displaystyle \sum _{j=1}^m{M}_{gi}^j}\otimes {\left[{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^m{M}_{gi}^j}}\right]}^{-1}$$

  (9)

  where ${\displaystyle \sum _{j=1}^m{M}_{gi}^j}$ and ${\left[{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^m{M}_{gi}^j}}\right]}^{-1}$ are calculated as shown in the following formula

  $${\displaystyle \sum _{j=1}^m{M}_{gi}^j}=\left({\displaystyle \sum _{j=1}^m{l}_j,{\displaystyle \sum _{j=1}^m{m}_j,{\displaystyle \sum _{j=1}^m{u}_j}}}\right)$$

  (10)

  $${\left[{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{j=1}^m{M}_{gi}^j}}\right]}^{-1}=\left({\displaystyle \frac{1}{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{u}_j}}}},{\displaystyle \frac{1}{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{m}_j}}}},{\displaystyle \frac{1}{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{l}_j}}}}\right)$$

  (11)

• Step 2: Compare the two triangular fuzzy numbers $S_1=(l_1,m_1,u_1)$ and $S_2=(l_2,m_2,u_2)$

  $$V(S_2\ge S_1)=\underset{y\ge x}{\sup }\left[\min \left(\mu s_2(y),\mu s_1(x)\right)\right]$$

  (12)

The above formula can also be described as follows:

$$\begin{array}{ll}V(S_2\ge S_1)& =hgt(S_1\cap S_2)=\mu s_1(d)\\ & =\left\{\begin{array}{cc}1& m_2\ge m_1\\ 0& l_1\ge u_2\\ (l_1-u_2)/((m_2-u_2)-(m_1-l_1))& else\end{array}\right.\end{array}$$

(13)

where $D$ is located between $\mu s_1$ and $\mu s_2$, and is the coordinate of the highest point of the intersecting part.

• Step 3: The possibility degree that the convex fuzzy number is greater than $k$ convex fuzzy number $S_i(i=1,\cdots ,k)$ can be calculated by Equation (13) as follows:

  $$\begin{array}{ll}V(S\ge S_1,S_2,\cdots ,S_k)& =V[(S\ge S_1) and (S\ge S_2) and\cdots and (S\ge S_k)]\\ & =\min V(S\ge S_i), i=1,2,\cdots ,k\end{array}$$

  (14)
• Step 4: Set $d^{\prime }(A_i)=\min V(S_i\ge S_j),i=1,2,\cdots ,k j=1,2,\cdots k,k\ne j$, the subjective weight of risk factors can be calculated by the following formula:

  $$w_j^{s\ast }={\left(d^{\prime }(A_1),d^{\prime }(A_2),\cdots ,d^{\prime }(A_k),\right)}^T$$

  (15)
• Step 5: The normalized subjective weight vector of each risk factor is expressed as Equation (15):

  $$w_j^s={\left(d(A_1),d(A_2),\cdots ,d(A_k),\right)}^T$$

  (16)

3.2.2. Objective Weight Calculation Based on Maximum Deviation Method

In order to determine the objective weights of risk factors L, E, and C, an objective weight calculation model of risk factors based on the maximum deviation method is established in this section. The safety risk factor of Linhai Reservoir dam construction is set as $A_i(i=1,2,\cdots ,m)$, the evaluation index of risk factors as $C_j(j=1,2,\cdots ,n)$, and the expert as $E_k(k=1,2,\cdots ,s)$. The expert team conducted a linguistic evaluation of the evaluation indicators of each risk factor, and used triangular fuzzy numbers to quantify the evaluation results, as shown in

Table 3. Semantic evaluation table of risk factors.

Linguistic Variables	Triangular Fuzzy Number
Very low (1)	(0,0,0.1)
Low (2)	(0,0.1,0.3)
Medium low (3)	(0.1,0.3,0.5)
Medium (4)	(0.3,0.5,0.7)
Medium high (5)	(0.5,0.7,0.9)
High (6)	(0.7,0.9,1)
Very high (7)	(0.9,1,1)

. ${\tilde{p}}_{ij}^k=(p_{ijl}^k,p_{ijh}^k,p_{iju}^k)$, which represents the evaluation value from expert $E_k$ of evaluation index $C_j$ in risk factor $A_i$, we can use an arithmetic average algorithm to calculate group decision value ${\tilde{p}}_{ij}=(p_{ijl},p_{ijh},p_{iju})$ from evaluation value ${\tilde{p}}_{ij}^{ k}$ given by different experts, and form fuzzy evaluation matrix $\tilde{R}={[{\tilde{p}}_{ij}]}^{m\times n}$ from ${\tilde{p}}_{ij}$.

• Step 1: Defuzzification of evaluation ${\tilde{p}}_{ij}$:

  $${\tilde{p}}_{ij}={\displaystyle \frac{1}{s}}({\tilde{p}}_{ij}^1\oplus {\tilde{p}}_{ij}^2\oplus \cdots \oplus {\tilde{p}}_{ij}^s)$$

  (17)

  $$p_{ij}=L+\mathsf{\Delta }\times {\displaystyle \frac{(p_{ijh}-L){(\mathsf{\Delta }+p_{iju}-p_{ijh})}^2(U-p_{ijl})+{(p_{iju}-L)}^2{(\mathsf{\Delta }+p_{ijh}-p_{ijl})}^2}{(\mathsf{\Delta }+p_{ijh}-p_{ijl}){(\mathsf{\Delta }+p_{iju}-p_{ijh})}^2(U-p_{ijl})+(p_{iju}-L){(\mathsf{\Delta }+p_{ijh}-p_{ijl})}^2(\mathsf{\Delta }+p_{iju}-p_{ijh})}}$$

  (18)
• Step 2: Normalization of matrix. The evaluation matrix $R={[p_{ij}]}^{m\times n}$ is composed of $r_{ij}$. For evaluation index $C_j$, the highest evaluation value among $m$ risk factors is $p_j^{\max }$ and the lowest evaluation value is $p_j^{\min }$. The normalized matrix $NR=[n{p}_{ij}]m\times n$ is obtained by normalizing the matrix $R$.

  $$n{p}_{ij}=(p_{ij}-p_j^{\min })/(p_j^{\max }-p_j^{\min })$$

  (19)
• Step 3: According to the maximum deviation method, establish the calculation model of the evaluation index $C_j$ importance $I{R}_j$ as follows:

  $$\max D(IR)={\displaystyle \sum _{j=1}^n{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{s=1}^m|n{p}_{ij}-n{p}_{sj}|\times I{R}_j}}}$$

  (20)

  where ${\displaystyle \sum _{j=1}^n{(I{R}_j)}^2=1, I{R}_j>0 1\le j\le n}$. The solution results of this model are as follows:

  $$I{R}_j={\displaystyle \frac{{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{s=1}^m|n{p}_{ij}-n{p}_{\mathrm{s}j}|}}}{\sqrt{{\displaystyle \sum _{j=1}^n{\left({\displaystyle \sum _{i=1}^m{\displaystyle \sum _{s=1}^m|n{p}_{ij}-n{p}_{sj}|}}\right)}^2}}}}$$

  (21)
• Step 4: According to the above solution results, the objective weight $w_j^o$ of evaluation index $C_j$ can be obtained as follows:

  $$w_j^o=I{R}_j/{\displaystyle \sum _{j=1}^{n}I{R}_j}$$

  (22)

3.2.3. Comprehensive Weight Calculation

This paper adopts the comprehensive weighting method, introduces the adjustment coefficient of risk factor weight $\phi$ (usually $\phi$ = 0.5), and uses $\phi$ and $1-\phi$ to express the importance of subjective weight and objective weight, and calculates the comprehensive weight as follows:

$$w^c=\phi w_j^c+(1-\phi )w_j^o$$

(23)

3.3. LEC Risk Ranking Based on Fuzzy VIKOR

In this section, an improved VIKOR method based on fuzzy theory is proposed to solve the multi-criteria decision problems with uncertainty and fuzziness. By calculating the fuzzy distance between the risk factor and the ideal solution, this method provides a more reasonable, reliable and stable decision-support tool for finding the compromise solution.

• Step 1: Summarize expert opinions and construct a comprehensive fuzzy evaluation matrix as follows:

  $${\tilde{x}}_{ij}=\left(x_{ij1},x_{ij2},x_{ij3}\right)$$

  (24)

  where $x_{ij2}={\displaystyle \sum _{k=1}^K{\lambda }_k}{x}_{ij1}^k, x_{ij2}={\displaystyle \sum _{k=1}^K{\lambda }_k}{x}_{ij2}^k, x_{ij3}={\displaystyle \sum _{k=1}^K{\lambda }_k}{x}_{ij3}^k$

  $$\tilde{D}=\left[\begin{array}{cccc}{\tilde{x}}_{11}& {\tilde{x}}_{12}& \cdots & {\tilde{x}}_{1n}\\ {\tilde{x}}_{21}& {\tilde{x}}_{22}& \cdots & {\tilde{x}}_{2n}\\ ⋮& ⋮& \cdots & ⋮\\ {\tilde{x}}_{m1}& {\tilde{x}}_{m2}& \cdots & {\tilde{x}}_{mn}\end{array}\right]$$

  where ${\tilde{x}}_{ij}$ is the score of risk factor $A_i$ relative to criterion $C_j$, ${\tilde{x}}_{ij}=\left(x_{ij1},x_{ij2},x_{ij3}\right)$, $i=1,2,\cdots m$, $j=1,2,\cdots n$.
• Step 2: Determine the fuzzy optimal ${\tilde{f}}_j^{\ast }$ and fuzzy worst ${\tilde{f}}_j^{-}$ of all evaluation indexes, $j=1,2,\cdots n$.

  $${\tilde{f}}_j^{\ast }=\left\{\begin{array}{cc}\underset{i}{\max }{\tilde{x}}_{ij},& benefit type\\ \underset{i}{\min }{\tilde{x}}_{ij},& cost type\end{array}\right\}, i=1,2,\cdots ,m,$$

  (25)

  $${\tilde{f}}_j^{-}=\left\{\begin{array}{cc}\underset{i}{\min }{\tilde{x}}_{ij},& benefit type\\ \underset{i}{\max }{\tilde{x}}_{ij},& cost type\end{array}\right\}, i=1,2,\cdots ,m,$$

  (26)
• Step 3: Calculate the normalized fuzzy distance $d_{ij}(i=1,2,\cdots ,m,j=1,2,\cdots ,n)$:

  $$d_{ij}={\displaystyle \frac{d({\tilde{f}}_j^{\ast },{\tilde{x}}_{ij})}{d({\tilde{f}}_j^{\ast },{\tilde{f}}_j^{-})}}$$

  (27)
• Step 4: Calculate the maximum group utility $S_i$ and the minimum individual regret $R_i$, $i=1,2,\cdots m$

  $$S_i=\phi {\displaystyle \sum _{j=1}^n{w}_j^s}{d}_{ij}+(1-\phi ){\displaystyle \sum _{j=1}^n{w}_j^o}{d}_{ij}={\displaystyle \sum _{j=1}^n[\phi w_j^s}+(1-\phi )w_j^o]d_{ij}={\displaystyle \sum _{j=1}^n{w}_j^c}{d}_{ij}$$

  (28)

  $$R_i=\underset{j}{\max }[\phi w_j^s{d}_{ij}+(1-\phi )w_j^o{d}_{ij}]=\underset{j}{\max }(w_j^c{d}_{ij})$$

  (29)

  where $\phi w_j^s+(1-\phi )w_j^o$ is the comprehensive weight of risk factors. $\phi >0.5$ means making decisions based on maximizing group utility, and $\phi <0.5$ means making decisions based on minimizing individual regret mechanisms.
• Step 5: Calculate $Q_i$

  $$Q_i=v{\displaystyle \frac{S_i-S^{\ast }}{S^{-}-S^{\ast }}}+(1-v){\displaystyle \frac{R_i-R^{\ast }}{R^{-}-R^{\ast }}}$$

  (30)

  where $S^{\ast }=\underset{i}{\min }{S}_i, S^{-}=\underset{i}{\max }{S}_i, R^{\ast }=\underset{i}{\min }{R}_i, R^{-}=\underset{i}{\max }{R}_i$, $v$ is the weight of the maximum group utility strategy, and $1-v$ is the weight of individual regret.
• Step 6: Sort the risk factors according to the descending order of $S, R, Q$ values, and the smaller the value, the smaller the risk.
• Step 7: Determine the compromise risk-factor risk ranking, that is, if the following two conditions are met, then the risk ranking measured by $Q$(maximum) is the best.

Condition 1.

$Q_{A^{(1)}}-Q_{A^{(2)}}\ge 1/(n-1)$ , where  $n$  is the total number of risk factors.

Condition 2.

Risk factors’ risk ranking  $A^{(1)}$  is also the optimal risk ranking according to  $S_i$  and  $R_i$ , then  $A^{(1)}$  is determined to be the stable maximum risk ranking.

If the above two conditions cannot be met at the same time, then two compromise solution risk ranking results are obtained, including two situations:

(1)

If Condition 1 is met but Condition 2 is not met, then there are two compromise solution risk rankings: $A^{(1)}$, $A^{(2)}$;

(2)

If Condition 1 is not met but Condition 2 is met, then the compromise solution risk ranking has M: $A^{(1)}$, $A^{(2)}$, …, $M$, where $M$ is the maximum $M$ value determined according to $Q(A^{(1)})-Q(A^{(M)})<1/(m-1)$.

4. Case Study

4.1. Case Description

This study takes the Linhai Reservoir Project, located in Heilongjiang Province, China, as a case to analyze the safety risks during the construction process. The Linhai Reservoir is situated in Hailin City, Mudanjiang City, within the administrative jurisdiction of the Dahailin Forestry Bureau. The catchment area upstream of the dam site is 1562 km², accounting for 29.7% of the Hailang River Basin and 4.15% of the Mudanjiang River Basin. The dam site is located at a straight section of the meandering Hailang River. The river near the dam site exhibits typical characteristics of a mountainous river, with steep slopes, rapid flows, a narrow and deep main channel, and a “U”-shaped single-channel structure. The regional precipitation is significantly influenced by topographic uplift, with an increasing trend from downstream to upstream. The average annual precipitation varies considerably across the basin, reaching up to 1110 mm in the upstream area and 530 mm in the downstream area. The Linhai Reservoir dam is designed as a conventional concrete gravity dam. The dam axis has a total length of 521 m, with a crest elevation of 497.5 m and a maximum dam height of 57.5 m, making it the tallest conventional concrete gravity dam currently under construction in Heilongjiang Province. Considering the engineering characteristics of gravity dams, this study identifies 20 risk factors affecting construction safety from five perspectives: personnel, materials and equipment, management, environment, and design. The results are shown in Figure 2.

4.2. Determination of Risk Factor Weights

4.2.1. Subjective Weight

To ensure the accuracy of the evaluation results, this study invited five experts with extensive experience in hydraulic engineering to score the risk factors. The subjective weight scoring table is shown in

Table A1. L, E, and C subjective weight scoring table.

		The Likelihood of Accidents (L)	The Frequency of Personnel Exposure to Hazardous Environments (E)	The Consequences of Accidents (C)
The likelihood of accidents (L)
The frequency of personnel exposure to hazardous environments (E)		-
The consequences of accidents (C)		-	-

of Appendix A.1. The expert panel includes a research specialist, a hydraulic engineer, an engineering design expert, engineering operation and management personnel, and on-site inspection personnel. The experts use linguistic variables to evaluate the relative importance of the risk factors L, E, and C. Although the experts had varying areas of specialization, their collective expertise ensured comprehensive coverage of the L, E, and C dimensions of risk. To reflect the complementary nature of their knowledge and ensure fairness, each expert was assigned an equal weight in the evaluation process. The evaluation results are presented in

Table 4. Subjective weight scoring of risk factors.

Risk Factor	L	E	C
L	EI, EI, EI, EI, EI	AS, VS, VS, VS, SS	VS, AS, AS, SW, FS
E	-	EI, EI, EI, EI, EI	FS, FS, FS, AS, FW
C	-	-	EI, EI, EI, EI, EI

.

Using the method described in Table 2, the linguistic evaluation information from experts is converted into corresponding triangular fuzzy numbers, forming the fuzzy pairwise comparison matrix for the subjective weights of the risk factors, as shown in

Table 5. Fuzzy pairwise comparison matrix of subjective weights for risk factors.

Risk Factor	L	E	C
L	(1,1,1)	(2,5/2,3) (3/2,2,5/2) (3/2,2,5/2) (3/2,2,5/2) (1,1,3/2)	(3/2,2,5/2) (2,5/2,3) (2,5/2,3) (2/3,1,1) (1,3/2,2)
E	(1/3,2/5,1/2) (2/5,1/2,2/3) (2/5,1/2,2/3) (2/5,1/2,2/3) (2/3,1,1)	(1,1,1)	(1,3/2,2) (1,3/2,2) (1,3/2,2) (2,5/2,3) (1/2,2/3,1)
C	(2/5,1/2,2/3) (1/3,2/5,1/2) (1/3,2/5,1/2) (1,1,3/2) (1/2,2/3,1)	(1/2,2/3,1) (1/2,2/3,1) (1/2,2/3,1) (1/3,2/5,1/2) (1,3/2,2)	(1,1,1)

. After performing a weighted average calculation, the weighted average values of the fuzzy pairwise comparison matrix for the subjective risk factor weights are obtained, as presented in

Table 6. Weighted average of subjective weight matrix for risk factors.

Risk Factor	L	E	C
L	(1,1,1)	(1.63,2.25,2.4)	(1.08,2.13,2.5)
E	(0.44,0.48,0.63)	(1,1,1)	(0.5,1.53,2)
C	(0.39,0.49,0.79)	(0.46,0.78,0.75)	(1,1,1)

.

Through Formulas (8)–(10), the fuzzy comprehensive degree of each risk factor is calculated as follows:

$$\begin{array}{l}{S}_1=(1.844,1.967,2.417)\otimes ({\displaystyle \frac{1}{7.469}},{\displaystyle \frac{1}{10.655}},{\displaystyle \frac{1}{12.067}})=(0.153,0.185,0.324)\\ S_2=(3.125,4.03,4.15)\otimes ({\displaystyle \frac{1}{7.469}},{\displaystyle \frac{1}{10.655}},{\displaystyle \frac{1}{12.067}})=(0.259,0.378,0.556)\\ S_3=(2.5,4.658,5.5)\otimes ({\displaystyle \frac{1}{7.469}},{\displaystyle \frac{1}{10.655}},{\displaystyle \frac{1}{12.067}})=(0.207,0.437,0.736)\end{array}$$

The subjective weight vector is obtained using Formulas (12)–(14).

$$w^s=(0.119,0.406,0.475)$$

4.2.2. Objective Weights

Based on the seven-part Likert scale, experts quantitatively scored the specific performance of 20 potential risk factors for the concrete gravity dam in Linhai Reservoir under three risk factors, L, E, and C, and the results are shown in

Table 7. Expert linguistic variable evaluation information.

Risk Factor	L					E					C
	E1	E2	E3	E4	E5	E1	E2	E3	E4	E5	E1	E2	E3	E4	E5
S11	7	7	6	6	6	4	5	2	4	4	7	6	7	6	5
S12	5	7	6	3	5	5	4	3	4	5	6	5	5	5	4
S13	3	6	7	6	6	4	5	5	5	6	6	6	4	6	5
S14	4	2	3	3	7	3	2	2	2	6	5	2	2	5	6
S21	7	7	5	4	6	6	3	4	5	5	7	5	5	4	6
S22	6	6	3	5	6	5	3	4	5	5	7	6	6	5	7
S23	5	6	4	2	6	3	4	3	3	4	6	6	5	5	7
S24	4	5	2	4	5	3	3	3	4	4	5	4	4	4	5
S31	5	5	3	5	7	2	2	2	3	6	6	4	5	5	6
S32	4	4	3	3	5	3	2	2	3	4	5	3	4	3	5
S33	6	6	3	3	6	4	3	3	3	5	6	4	4	3	6
S34	6	7	4	4	5	6	3	5	5	4	7	6	6	6	4
S41	4	6	5	2	6	3	2	4	4	7	5	6	3	7	6
S42	3	5	4	3	6	2	3	3	3	5	5	4	4	3	6
S43	6	5	6	2	6	4	1	4	2	5	5	5	5	2	5
S44	4	4	4	3	6	2	3	3	4	5	5	5	5	4	6
S51	5	7	5	3	7	3	2	6	3	5	6	5	5	3	6
S52	7	6	6	2	5	5	4	5	2	4	7	6	7	6	7
S53	6	6	4	3	6	3	4	3	4	5	7	4	5	6	6
S54	5	6	5	3	6	4	4	4	3	5	6	6	6	4	5

. The objective weight scoring table is shown in

Table A3. The actual performance of risk factors is scored.

Risk Factor		Very Low–Medium–Very High
S11	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S12	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S13	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S14	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S21	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S22	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S23	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S24	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S31	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S32	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S33	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S34	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S41	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S42	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S43	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S44	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S51	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S52	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S53	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7
S54	L	1	2	3	4	5	6	7
	E	1	2	3	4	5	6	7
	C	1	2	3	4	5	6	7

of Appendix A.2.

Based on the table, the expert’s linguistic evaluation information is converted and the fuzzy levels of the risk factors are calculated. A fuzzy decision matrix is constructed, resulting in the fuzzy comprehensive evaluation matrix of the risk factors, as shown in

Table 8. Fuzzy comprehensive evaluation matrix of risk factors.

Risk Factor	L	E	C
S11	(0.78,0.94,1)	(0.28,0.46,0.66)	(0.74,0.9,0.98)
S12	(0.54,0.72,0.86)	(0.34,0.54,0.74)	(0.5,0.7,0.88)
S13	(0.62,0.8,0.9)	(0.5,0.7,0.88)	(0.58,0.78,0.92)
S14	(0.26,0.44,0.6)	(0.16,0.3,0.48)	(0.34,0.5,0.68)
S21	(0.66,0.82,0.92)	(0.42,0.62,0.8)	(0.58,0.76,0.9)
S22	(0.54,0.74,0.88)	(0.38,0.58,0.78)	(0.74,0.9,0.98)
S23	(0.44,0.62,0.78)	(0.18,0.38,0.58)	(0.66,0.84,0.96)
S24	(0.32,0.5,0.7)	(0.18,0.38,0.58)	(0.38,0.58,0.78)
S31	(0.5,0.68,0.84)	(0.16,0.3,0.48)	(0.54,0.74,0.9)
S32	(0.26,0.46,0.66)	(0.1,0.26,0.46)	(0.3,0.5,0.68)
S33	(0.46,0.66,0.8)	(0.22,0.42,0.62)	(0.42,0.62,0.78)
S34	(0.54,0.72,0.86)	(0.42,0.62,0.8)	(0.66,0.84,0.94)
S41	(0.44,0.62,0.78)	(0.32,0.48,0.64)	(0.58,0.76,0.88)
S42	(0.34,0.54,0.72)	(0.16,0.34,0.54)	(0.38,0.58,0.76)
S43	(0.52,0.7,0.84)	(0.22,0.36,0.54)	(0.4,0.58,0.78)
S44	(0.34,0.54,0.72)	(0.2,0.38,0.58)	(0.5,0.7,0.88)
S51	(0.58,0.74,0.86)	(0.28,0.46,0.64)	(0.5,0.7,0.86)
S52	(0.56,0.72,0.84)	(0.32,0.5,0.7)	(0.82,0.96,1)
S53	(0.5,0.7,0.84)	(0.32,0.5,0.7)	(0.82,0.96,1)
S54	(0.5,0.7,0.86)	(0.3,0.5,0.7)	(0.58,0.78,0.92)

.

Using Formula (17), the defuzzification of the evaluation values in the evaluation matrix is performed. The maximum evaluation value $P_j^{\max }$ and the minimum evaluation value $P_j^{\min }$ are calculated, and the matrix is normalized to obtain the standardized matrix NP as follows:

$$NR=\left[\begin{array}{ccc}\begin{array}{l}1\\ 0.553\\ 0.704\\ 0\\ 0.754\\ 0.584\\ 0.359\\ 0.137\\ 0.479\\ 0.05\\ 0.423\\ 0.553\\ 0.359\\ 0.2\\ 0.512\\ 0.2\\ 0.596\\ 0.555\\ 0.503\\ 0.51\end{array}& \begin{array}{l}0.461\\ 0.638\\ 1\\ 0.09\\ 0.814\\ 0.73\\ 0.268\\ 0.268\\ 0.09\\ 0\\ 0.36\\ 0.814\\ 0.496\\ 0.182\\ 0.318\\ 0.275\\ 0.451\\ 0.554\\ 0.453\\ 0.545\end{array}& \begin{array}{l}0.858\\ 0.427\\ 0.586\\ 0.017\\ 0.552\\ 0.858\\ 0.722\\ 0.179\\ 0.506\\ 0\\ 0.247\\ 0.718\\ 0.546\\ 0.17\\ 0.188\\ 0.427\\ 0.42\\ 1\\ 0.634\\ 0.586\end{array}\end{array}\right]$$

The importance $I{R}_j$ of the evaluation index $C_j$ is calculated based on the maximum deviation method, using Formula (21) to obtain the objective weights of the three risk factors: $w^o=(0.303,0.339,0.358)$.

4.2.3. Combined Weight

Assuming that the importance of subjective and objective weights is the same, the combined weight of the risk factors is calculated as $w^c=(0.211,0.373,0.417)$.

4.3. Risk Factor Ranking Based on Fuzzy VIKOR

This section primarily uses the VIKOR method to calculate the ranking of risk factors. L, E, and C are cost-type risk factors, and the fuzzy best $f_j^{\ast }$ and fuzzy worst $f_j^{-}$ are calculated using Formulae (24) through (25). The normalized fuzzy distance is calculated using Formula (26), as shown in

Table 9. Normalized fuzzy distance of risk factors.

Risk Factor	L	E	C
S11	1	0.461	0.871
S12	0.574	0.636	0.453
S13	0.716	1	0.606
S14	0	0.103	0.052
S21	0.773	0.81	0.577
S22	0.602	0.731	0.871
S23	0.378	0.258	0.744
S24	0.159	0.258	0.198
S31	0.504	0.103	0.529
S32	0.077	0	0
S33	0.434	0.352	0.258
S34	0.574	0.81	0.732
S41	0.378	0.494	0.564
S42	0.213	0.176	0.181
S43	0.532	0.241	0.213
S44	0.213	0.271	0.453
S51	0.618	0.445	0.439
S52	0.735	0.556	1
S53	0.518	0.446	0.654
S54	0.532	0.541	0.606

.

Using Formulas (27)–(29), the S, R, and Q values of all risk factors are calculated, and the results are shown in

Table 10. S, Q, and R values of risk factors.

Risk Factor	S	R	Q
S11	0.745	0.363	0.911
S12	0.547	0.237	0.624
S13	0.776	0.373	0.943
S14	0.06	0.038	0.056
S21	0.705	0.302	0.808
S22	0.762	0.363	0.922
S23	0.486	0.31	0.675
S24	0.212	0.096	0.228
S31	0.365	0.22	0.484
S32	0.016	0.016	0
S33	0.33	0.131	0.349
S34	0.728	0.305	0.827
S41	0.499	0.235	0.59
S42	0.186	0.076	0.185
S43	0.291	0.112	0.3
S44	0.334	0.189	0.424
S51	0.479	0.183	0.511
S52	0.779	0.417	1
S53	0.548	0.272	0.669
S54	0.566	0.252	0.656

. In this study, $\phi =0.5$, $v=0.5$ are chosen.

The risk factors are ranked in descending order based on the S, R, and Q values in Table 10, with smaller values indicating lower risks. The results are shown in

Table 11. Risk factors ranked in descending order based on S, Q, and R values.

Risk Factor	S	R	Q
S11	4	3	4
S12	9	10	10
S13	2	2	2
S14	19	19	19
S21	6	7	6
S22	3	3	3
S23	11	5	7
S24	17	17	17
S31	13	12	13
S32	20	20	20
S33	15	15	15
S34	5	6	5
S41	10	11	11
S42	18	18	18
S43	16	16	16
S44	14	13	14
S51	12	14	12
S52	1	1	1
S53	8	8	8
S54	7	9	9

.

From Table 11, it can be seen that when the risk factors are ranked in descending order based on Q values, the two conditions for the compromise risk factor ranking are satisfied. Therefore, the optimal risk ranking scheme is obtained by ranking the factors in descending order of their values. Figure 3 shows the comparison chart of Q values for the 20 risk factors. From the chart, the comprehensive risk ranking of the risk factors is as follows: S₅₂ > S₁₃ > S₂₂ > S₁₁ > S₃₄ > S₂₁ > S₂₃ > S₅₃ > S₅₄ > S₁₂ > S₄₁ > S₅₁ > S₃₁ > S₄₄ > S₃₃ > S₄₃ > S₂₄ > S₄₂> S₁₄ > S₃₂.

This study ranks 20 construction safety risk factors and analyzes the results using a radar chart. It is found that structural design defects (S₅₂), adherence to safety regulations by construction personnel (S₁₃), and equipment operation errors or malfunctions (S₂₂) have a significant impact on construction safety risks. This indicates that personnel and technical aspects of cold-region construction require special attention. The results, in conjunction with the engineering characteristics of the cold-region concrete gravity dam in Mudanjiang, Heilongjiang Province, highlight the complexity and specificity of the construction environment in cold regions. To effectively reduce these risks, efforts should focus on optimizing structural design, enhancing safety education and supervision for construction personnel, and improving equipment management and maintenance to achieve construction safety goals.

4.4. Sensitivity Analysis

To evaluate the robustness of the hybrid weighting approach, a sensitivity analysis was conducted by varying the influence coefficients of the subjective and objective weights in the combined weighting scheme. Specifically, the subjective weight coefficient $\phi$ was varied from 0 to 1 in increments of 0.1, while the objective weight coefficient $1-\phi$ was adjusted. Among them, φ takes the values of 0, 0.5, and 1, which represent the comprehensive weights obtained by the objective weighting method, the comprehensive weighting method, and the subjective weighting method, respectively.

For each weighting scenario, the final risk rankings of the evaluated work conditions were recalculated using the VIKOR method, as shown in Figure 4. The results show that although slight changes in the composite scores occurred, the overall ranking order of the top- and bottom-risk items remained stable across all scenarios. This indicates that the combined weighting method is relatively insensitive to moderate variations in $\phi$, and thus the proposed risk assessment framework is robust and reliable.

4.5. Results and Discussion

The identification of risk factors may not only help managers to fully understand the potential problems in the operation of the project, but also to develop targeted control measures according to the evaluation results, thus significantly improving the safety of the project. Furthermore, the identification and evaluation process helps take quick response measures after risks occur, keeping the risks within acceptable or tolerable limits and minimizing potential losses. Analyzing the causes of high-risk factors based on the project’s geographical, climatic, and construction environment characteristics is key to formulating effective risk control measures.

From the aspect of safety risk to construction personnel, the implementation of safety regulations by construction personnel directly affects construction safety. In cold-region environments, low temperatures and snow coverage complicate construction conditions. Personnel may neglect safety operations due to harsh environmental conditions or inadequate protective measures [42]. For example, the prolonged low temperatures in Mudanjiang during winter may cause a decline in personnel attention or cause them to neglect protection in high-risk areas, increasing the difficulty of safety management.

In terms of material and equipment safety risks, equipment operation error or failure is the main risk factor. In cold-region concrete gravity dam construction, equipment performance is affected by low temperatures, leading to mechanical failures [43]. For example, the extremely cold environment in Mudanjiang could cause hydraulic equipment systems to freeze or suffer lubrication failure, leading to construction delays or equipment accidents. Additionally, equipment operators may experience a decrease in attention in cold environments, further increasing the risk of operational errors.

In terms of construction management safety risks, overload construction should be avoided. Overloading not only causes excessive wear and frequent malfunctions of machinery but also increases the likelihood of human errors due to prolonged working hours, leading to fatigue [44]. In cold environments, the durability and reliability of mechanical equipment decrease, and the work efficiency and safety awareness of construction personnel may also be affected by environmental pressure [45]. Therefore, reasonable scheduling, scientific construction plans, and strict on-site safety supervision are key measures to reduce the risk of overloading. Optimizing resource allocation, standardizing operating procedures, and implementing reasonable shift schedules can effectively reduce safety hazards in construction management.

In terms of the construction environment safety risk, extreme weather conditions have a great impact on construction safety. Cold regions are prone to frequent freeze–thaw cycles, low temperatures, and sudden snowstorms, making the construction environment highly uncertain [46]. Freeze–thaw cycles not only accelerate the deterioration of concrete surfaces but may also reduce the performance of construction machinery and cause component damage, increasing the risk of equipment malfunctions [46]. Under low temperatures, the growth strength of construction materials slows down, and the setting and hardening process of concrete is significantly affected, potentially causing the project to fail to meet design requirements [47]. These factors require construction managers to consider climate factors during project planning and organization, select appropriate construction windows, implement efficient on-site management, and use freeze-resistant materials to effectively mitigate the safety risks posed by the construction environment.

In terms of the safety risk from construction technology, the problem of structural design defects should be emphasized. In cold-region environments, low temperatures and freeze–thaw cycles significantly affect the performance of concrete structures. If temperature stress and frost resistance are not fully considered in the design, cracks or other structural damage may occur during construction, increasing safety hazards [48,49]. The severe climate in Mudanjiang requires the design to optimize concrete mix ratios and structural parameters to adapt to the extreme environment.

The safety of concrete gravity dam construction is a core issue for ensuring the functionality and long-term operation of hydraulic projects. Risk control needs to be advanced from multiple dimensions, comprehensively implementing risk management. First, in terms of personnel safety, special safety training for cold-region construction environments should be strengthened, the management and use of personal protective equipment should be improved, and health monitoring and safety assessment mechanisms should be established to reduce the risk of accidents caused by personnel conditions. Second, for material and equipment safety, freeze-resistant concrete materials should be selected, the durability of materials should be improved through scientific mixing, and construction equipment should be regularly maintained, with modifications made to adapt to low-temperature environments. Real-time monitoring of materials and equipment conditions using sensor technology should also be employed. Third, for construction management safety, a dynamic risk assessment system should be implemented, with flexibility and real-time adjustment capabilities for construction plans. Information management tools should be used to optimize collaboration among parties, ensuring that construction quality and risk control advance in tandem. Fourth, for construction environment safety, an environmental monitoring system should be established to dynamically assess the impact of climatic conditions (such as temperature differences and freeze–thaw cycles) on construction, while improving on-site protective measures and emergency plans for extreme weather. Finally, for construction design safety, precise pre-risk assessments and simulation technologies should be used to optimize design plans, enhance the structure’s ability to withstand extreme cold-weather conditions, and proactively address potential safety risks from design deviations. By systematically implementing targeted measures in these five areas, the construction safety of concrete gravity dams in complex cold-region environments can be comprehensively improved, providing strong support for the long-term stable operation of the project.

5. Conclusions

This study focuses on the construction safety risks of the concrete gravity dam. Based on the LEC method and incorporating triangular fuzzy theory, FAHP, the maximum deviation method, and the VIKOR multi-criteria decision model, a comprehensive risk assessment model is constructed for dam construction safety, which provides a multi-dimensional and systematic theoretical framework for evaluating dam construction safety risks. Additionally, a case analysis was conducted using the Linhai Reservoir Project in Songhuajiang City, Heilongjiang Province, to assess the construction safety risks of cold-region concrete gravity dams and propose management and control measures.

The main contributions of this study are as follows: first, a multi-factor risk assessment model suitable for cold-region environment was developed, validating the effectiveness of triangular fuzzy theory, FAHP, the maximum deviation method, and VIKOR in integrated decision-making. This model provides a systematic theoretical framework and practical tools for safety assessment in the construction of cold-region concrete gravity dams, and expands the application of multi-criteria decision methods in cold-region engineering safety management. Second, the introduction of the maximum deviation method effectively balances the weight distribution between subjective judgment and quantitative analysis, improving the scientific rigor and accuracy of the risk assessment model. Finally, this study systematically incorporates cold-region factors into the early warning model for the construction risks of concrete gravity dams, clarifying the role of different environmental factors in risk assessment, and offering new perspectives and practical guidance for construction risk early warning in cold regions and other special environments.

In terms of practical applications, this study provides effective support for safety management in cold-region engineering projects and emphasizes the importance of multi-dimensional risk identification and assessment strategies. First, project managers should recognize the dynamic nature of construction safety risks and continuously adjust risk warning strategies based on different construction stages and environmental conditions to improve the timeliness and accuracy of risk prevention. Second, managers need to establish a collaborative mechanism that includes multiple stakeholders to ensure that on-site data and expert judgments are integrated into the risk management process, thereby more comprehensively assessing potential construction risks. Lastly, future engineering management should explore technology-driven dynamic monitoring and intelligent warning systems to enhance the real-time performance and responsiveness of risk management systems, ultimately improving the safety and adaptability of engineering projects.

As with any study, this research has limitations. First, the study focuses on a specific cold-region concrete gravity dam project. While the case study is representative, future research could expand to different types of cold-region engineering projects to enhance the model’s applicability in various contexts. Second, the risk assessment model relies on expert-based weighting, and future studies could integrate data-driven methods such as machine learning algorithms to further improve the objectivity and scientific nature of the model. Additionally, as the risk factors for cold-region construction safety change dynamically with the environment, future research could introduce real-time monitoring systems to build more flexible and dynamic risk assessment models, providing faster response times and greater applicability for risk warning systems.