A Study on the Cascade Evolution Mechanism of Construction Workers’ Unsafe Behavior Risk Factors

Abstract

There are numerous risk factors across various dimensions that lead to unsafe behaviors among construction workers, and the interactions between these factors are complex and intertwined. Therefore, it is crucial to comprehensively explore the mechanisms of these risk factors across all dimensions to reduce the accident rate. This paper combines cascading failure and entropy flow models to construct a cascading trigger model for identifying key nodes and paths in a risk network. First, this paper identifies the risk factors in the individual, organizational, managerial, and environmental dimensions, dividing them into deep and surface factors. Based on this, a risk network is constructed, and cascading failure is introduced to simulate the dynamic evolution of risks. Then, the entropy flow model is introduced to quantify the risk flow in risk propagation. Finally, to address the uncertainty of risk occurrence, Visual Studio Code is used for coding, and a simulation platform is built using JavaScript. After conducting simulation experiments, the results are statistically analyzed. The results show that the key nodes of deep factors are mainly concentrated in the individual dimension (herd mentality, negative emotions, physical fatigue, fluke mindset), organizational dimension (poor cohesion, poor internal communication), and managerial dimension (abusive leadership style and insufficient/low-quality safety education and training); the surface factors are mainly the poor safety climate in the organizational dimension. The findings provide theoretical support for reducing the accident rate caused by unsafe worker behaviors, aiming to reduce accident risk losses by cutting off risk propagation paths.

1. Introduction

Due to the characteristics of construction workers, such as highly dispersed work locations, high mobility, and generally lower educational levels, unsafe behaviors can rapidly spread within the worker community once they form [1,2,3]. To prevent and reduce the incidence of accidents caused by unsafe worker behaviors, it is crucial to identify the key nodes in the evolution process of risks. This enables the interruption of risk transmission pathways, thereby reducing the occurrence of unsafe behaviors among construction workers.

Most research on unsafe worker behaviors focuses on verifying causal relationships between risk factors, and such studies are often based on single dimensions such as individuals or organizations. For example, Yao F. [4] and Jiang H. [5] used Structural Equation Modeling (SEM) to explore the impact of individual and organizational factors on unsafe behaviors. However, the causes of unsafe worker behaviors encompass multiple dimensions [6,7,8,9,10,11], which interact with each other. Merely verifying causal relationships between risk factors is of limited significance; understanding the risk mechanisms of unsafe worker behaviors is the key to effectively preventing and reducing accidents. Thus, research should primarily focus on the critical paths and key nodes within the risk network of unsafe behaviors. Regarding research methods for key paths and key nodes in risk networks, Wu K. [12] et al., based on complex network models, identified the critical safety risks and important transmission paths for subway construction safety accidents. Similarly, Wang W. [13] used complex network theory to construct and analyze risk networks, identifying key causative factors in urban rail transit systems. Yuxin W. [14], through the calculation of the topological structure of the constructed mine accident unsafe acts network (MAUAN), determined the critical unsafe behaviors and key behavior paths in gas explosion accidents. These scholars quantified the key nodes and critical paths in unsafe behavior risk networks by analyzing network density, network centrality, cohesion, and centrality indicators of the network models. In summary of previous research, it is evident that risk factors, once they occur, not only propagate within their respective dimensions but also transmit across multiple dimensions, causing a chain reaction that triggers multiple risk factors and leads to unsafe behaviors. However, current studies rarely explore the formation mechanisms of unsafe behaviors from a multi-dimensional perspective, nor do they clearly illustrate the dynamic process of risk transmission post-occurrence. Therefore, this paper introduces cascading failures into the risk propagation network of unsafe behaviors. This concept has been applied in risk network research within crisis management [15], information network security management [16], and supply chain management fields [17], and it can clearly demonstrate the transmission and evolution process of risks across various dimensions. Furthermore, merely using indicators such as network centrality to determine key paths and key nodes overlooks the transmissibility of risks during the propagation process, i.e., whether the amount of risk transmission can meet the trigger conditions of subsequent nodes to continue spreading within the network. Thus, this paper introduces the entropy flow model to quantify risk transmission. Finally, considering the randomness of risk occurrence, in actual construction processes, risks are often highly uncertain. Risks may occur individually or several risks may occur simultaneously. In such cases, the triggering of unsafe behaviors is complex and variable.

In summary, this paper aims to identify the key nodes and effective paths in the risk network of unsafe behaviors among construction workers, addressing three key issues in the study of the mechanisms of these behaviors: (1) the issue of multidimensional identification and transmission of risk factors for unsafe worker behaviors; (2) the issue of risk transmissibility during the transmission process; (3) the issue of risk uncertainty when it occurs. The structure of this paper is arranged as follows: (1) Section 2 mainly identifies risk factors for unsafe worker behaviors from four dimensions, individual, organizational, managerial, and environmental, and evaluates the relationships between risk factors using the expert scoring method to construct the risk network of unsafe worker behaviors. (2) Section 3 focuses on constructing the cascading trigger model. Based on the constructed risk network, cascading failure is introduced, and the entropy flow model is used to precisely quantify risks. The cascading failure process based on load–load capacity limit-load redistribution is used to construct the cascading trigger model for unsafe worker behaviors. (3) Section 4 mainly determines the key nodes and paths in the risk network through simulation. First, Visual Studio Code is used for coding, and a simulation platform is built using JavaScript to simulate the uncertainty of risk occurrence, i.e., simulating the evolution paths of randomly combined risk nodes in the triggered state. Based on the simulation results, statistical analysis is conducted on network failure rates, the distribution of network nodes, and effective paths to identify key nodes and paths. This study aims to provide project managers with ideas and recommendations for reducing unsafe worker behaviors.

2. Risk Factor Analysis and Theoretical Basis of Workers’ Unsafe Behavior

2.1. Risk Factors of Workers’ Unsafe Behavior and Their Uncertainty Analysis

Research on the risk factors of unsafe worker behaviors, both domestically and internationally, primarily focuses on four dimensions: individual, organizational, managerial, and environmental [18,19]. The individual dimension emphasizes the analysis of workers’ physiological and psychological conditions [20,21]. The organizational dimension focuses on organizational cohesion and internal communication and interaction within the organization [22,23,24]. The managerial dimension primarily targets management styles and reward and punishment mechanisms of the managers [25,26,27]. The environmental dimension analyzes factors such as job requirements and the working environment [28,29,30,31,32]. Based on the initial variables in these four dimensions, scholars have introduced mediating variables, mainly including workers’ risk perception abilities, safety awareness, safety motivation, and the safety climate within the organization [33,34]. We will consider the mediating variables as surface factors and the initial variables (i.e., risk factors in the four dimensions) as deep factors to analyze the risk transmission paths.

In actual construction processes, the environment is often complex and variable, leading to highly uncertain risk occurrences [35]. This uncertainty is evident not only in the random occurrence of individual risk factors but also in the simultaneous occurrence of multiple risk factors. The latter can manifest as multiple factors occurring simultaneously within the same dimension or across different dimensions. For example, physical fatigue at the individual dimension may occur independently, but when negative emotions arise simultaneously, the interaction between these two risk factors can lead to more serious consequences. Similarly, physical fatigue at the individual dimension may coincide with poor communication and interaction within the organization at the organizational dimension. The occurrence of different combinations of risk factors will lead to various risk propagation paths. In this paper, the role relationship between the dimensions of the deep layer factors and their role mechanism on the surface layer factors are represented in Figure 1.

2.2. Cascading Failure and Entropy Flow Model

Cascading failure [36,37,38] refers to the phenomenon in networks or other complex systems where the failure of one component or node triggers a series of chain reactions, leading to the successive failure of other components or nodes. This failure mode can rapidly propagate through the connection paths between nodes, potentially resulting in the paralysis of the entire system, much like an avalanche. The impact can be physical, such as a piece of equipment malfunctioning and causing the entire system to shut down, or informational, such as the failure of data transmission at one node leading to data loss at other nodes [39]. In either case, cascading failure spreads and gradually expands its scope of influence. Cascading failure is a pattern that can trigger domino-like fault propagation, posing a serious threat to the stability and reliability of the system. One of the main causes of cascading failure is the instability of weak links within the system. When a fragile component or node fails, that is, when the additional load or pressure it bears exceeds its threshold, it causes surrounding components or nodes to malfunction [40]. This paper introduces cascading failure into the risk propagation network of unsafe worker behaviors to describe the triggering states of various nodes within the network and to explore the cascading evolution mechanism of risks within the network.

Subsequently, this paper introduces the entropy flow model to quantify the flow of risk transmitted between nodes within the network [41]. The entropy flow model is used to describe the process of information transfer and flow within a system. It is based on the concept of entropy, analyzing the flow and transformation of information in a system through changes in entropy. Entropy is a measure of the average amount of information produced by a system or information source. Entropy flow refers to the movement of entropy within a system. In the entropy flow model, a system can be viewed as being composed of multiple subsystems, each interconnected through the exchange of information. Each subsystem has its own entropy value, representing the amount of information it generates. Through information exchange between subsystems, entropy values change, leading to the flow of information. For example, in fields such as transportation management [42] and coal mine safety management [43], the entropy flow model can be used to analyze the transmission and propagation of information within a network, thereby optimizing the network’s performance and reliability. Therefore, this paper employs the entropy flow model to measure and analyze the uncertainty and fluidity of risk factors as they propagate through the network.

3. The Effective Path Identification Method for the Risk of Unsafe Worker Behaviors

3.1. Construction of a Risk Network Model for Workers’ Unsafe Behavior

3.1.1. Risk Factor Identification

This study first utilized the literature review method as the foundation for theoretical construction. By extensively reviewing relevant academic literature both domestically and internationally, it systematically organized previous research findings on unsafe worker behaviors and their causes, providing a solid theoretical basis for the subsequent identification of risk factors. Subsequently, to enhance the support of research data, this study also conducted an in-depth reading and analysis of safety accident reports from construction sites. By meticulously analyzing typical safety accident cases in recent years and focusing on the direct and indirect causes of unsafe worker behaviors mentioned in the accident reports, this study extracted numerous risk factors. Subsequently, this study adopted a multidimensional analytical perspective to scientifically categorize the identified risk factors into four dimensions: individual, organizational, managerial, and environmental. To further validate and refine these risk factors, this study also used expert interviews and on-site safety officer surveys. Experienced experts and scholars in the field of construction safety and front-line safety officers were invited for in-depth discussions. The interview content focused on the strength of the associations between risk factors in each dimension, as well as the occurrence probability and impact degree of each risk factor, aiming to gather professional insights and practical experience. After organizing and analyzing the interview records, 22 risk factors were finally identified. The constructed list of risk factors is shown in

Table 1. List of risk factors for workers’ unsafe behaviors.

Dimension	Risk Factor
Individual Dimension	Physical Fatigue R1
	Negative Emotions R2
	Paranoia and Hostility R3
	Fluke Mindset R4
	Herd Mentality R5
	Young Age R6
	Low Educational Level R7
	Short Work Experience R8
	Low-Risk Perception Ability of Workers R9
	Weak Safety Awareness of Workers R10
	Unsafe Motivation of Workers R11
Organizational Dimension	Poor Safety Climate of the Organization R12
	Poor Organizational Support for Workers R13
	Poor Organizational Cohesion R14
	Poor Internal Communication and Interaction within the Organization R15
Management Dimension	Abusive Leadership Style R16
	Laissez-Faire Leadership Style R17
	Inconsistent Reward and Punishment Mechanisms R18
	Insufficient/Low-Quality Safety Education and Training R19
Environmental Dimension	High Job Demands R20
	Complex Work Environment R21
	Work–Family Conflict R22

.

3.1.2. Risk Network Modeling

This paper uses the expert interview method to organize the interaction relationships between various risk factors. The interviewees include 2 on-site safety officers and 4 researchers in the professional field. Specific information is given in

Table 2. Expert information.

Number	Expert	Working Years	Educational Background	The Title of a Professional Post
1	Li **	21	Master	Associate Professor
2	Tang **	23	Master	Professor
3	Guo **	19	Doctor	Professor
4	Xia **	21	Master	Associate Professor
5	Chu **	6	Bachelor	Safety Officer
6	Chen *	6	Bachelor	Safety Officer

Note: * and ** indicates that the names of the scoring experts have been anonymized.

. According to the experts’ experience, the influence intensity between each risk factor is represented on a scale of 0–5. This paper considers that on-site safety officers often need to face various safety issues directly in their actual work, and their experience in responding to safety risks is more abundant and closely aligned with the actual environment. Therefore, when using Equation (1) to balance expert opinions, the scoring weights for on-site safety officers and professional researchers are assigned as 0.2 and 0.15, respectively.

The expert scoring table is statistically analyzed, and based on the calculation weights of Equation (1), the weighted average value of the association strength of each expert’s score, υ_i,j, is calculated, as shown in

Table 3. Weighted average of strength of association of risk factors.

i→j	${\overline{\mathit{v}}}_{\mathit{i},\mathit{j}}$	i→j	${\overline{\mathit{v}}}_{\mathit{i},\mathit{j}}$	i→j	${\overline{\mathit{v}}}_{\mathit{i},\mathit{j}}$
R1→R2	4.5	R6→R4	3	R17→R4	3.15
R1→R4	2.8	R6→R10	2.6	R17→R5	3.15
R1→R5	2.9	R7→R4	2.7	R17→R10	3.25
R1→R9	4	R7→R9	2.55	R17→R12	3.1
R1→R10	4	R7→R10	3.35	R17→R14	3.2
R1→R12	4.3	R8→R9	3.6	R18→R4	2.85
R1→R22	2.65	R8→R10	3.2	R18→R5	3.05
R2→R9	3.55	R13→R14	2.75	R18→R10	3.55
R2→R11	3.85	R13→R15	3.5	R18→R12	3
R2→R15	2.65	R14→R11	2.55	R19→R4	4
R3→R11	2.9	R14→R15	2.85	R19→R5	3
R3→R12	4.15	R15→R11	3	R19→R10	3.75
R3→R14	2.55	R15→R12	2.85	R19→R12	2.9
R3→R15	2.8	R15→R14	3.6	R20→R1	2.8
R4→R10	3.75	R16→R1	3.75	R20→R2	3.05
R4→R11	3.55	R16→R2	4	R21→R1	3.9
R5→R10	3.15	R16→R3	3.05	R21→R2	3.9
R5→R11	3	R16→R11	2.85	R22→R2	4.1
R5→R12	2.85	R16→R14	2.75	R22→R11	2.7

. Based on this, the correlation and direction between each pair of factors in the risk list are determined. Using Gephi 0.10.1 graphing software, a risk network model of unsafe worker behaviors is drawn based on the attributes of the 22 nodes and the relationships and directions between the nodes, as shown in Figure 2. Four different colors represent the four dimensions of the nodes: individual dimension (purple), organizational dimension (green), managerial dimension (orange), and environmental dimension (blue). Two shapes distinguish the two levels of the nodes: circular nodes represent deep factors (18 nodes in total), and square nodes represent surface factors (4 nodes in total). For example, the purple circular node R1 in the figure represents a factor in the individual dimension at the deep factor level, while the purple square node R9 represents a factor in the individual dimension at the surface factor level. Blue lines represent the interactions between deep factors, and purple lines indicate the transmission of risk from the deep factor level to the surface factor level.

$${\omega }_m=v_m/{\displaystyle \sum _{m=1}^2{v}_{m}k}$$

(1)

In the equation, ω_m represents the calculated weight of each type of expert, where m = 1, 2; v_m represents the assigned weight of each type of expert; k represents the proportion of the number of each type of expert.

3.2. Construction of a Cascading Trigger Model for Workers’ Unsafe Behavior

Based on the constructed risk network of unsafe worker behaviors, cascading failure is introduced to demonstrate the dynamic transmission process following risk occurrence. The entropy flow model is introduced to quantify the transferable risk between nodes, constructing a cascading trigger model for unsafe worker behaviors to identify effective paths within the unsafe behavior propagation network.

3.2.1. The Calculation Method for Risk Occurrence Probability and Impact Range

(1)

Expert scoring method based on confidence index

To eliminate cognitive differences among experts when scoring, this paper introduces a confidence index in the data collection process of using the expert scoring method to assess the probability of risk occurrence and its impact range. Experts, when evaluating risk factors, also assess their confidence in their judgments. This index can be viewed as the reliability of the data source and can reduce the subjectivity of expert scoring. Based on the above method, the scoring table format for the probability of occurrence and impact range of unsafe worker behavior risk factors, as well as the scoring standard table, are designed, as shown in

Table 4. Scoring table for the probability of occurrence and impact range of risk factors in workers’ unsafe behaviors.

Risk Factor	Probability of Occurrence of Risk Factors		Range of Influence of Risk Factors
	Range of Probability of Occurrence	Confidence Index	Scope of Influence	Confidence Index
R1	Yiu, Kiu	hiu	Yiu, Kiu	hiu
R2	Yiu, Kiu	hiu	Yiu, Kiu	hiu
……	Yiu, Kiu	hiu	Yiu, Kiu	hiu
Rn	Yiu, Kiu	hiu	Yiu, Kiu	hiu

and

Table 5. Scoring standard table for the probability of occurrence and impact range of risk factors in workers’ unsafe behaviors.

Grading Criteria (W)	Range of Probability of Occurrence of Risk Factors	Scope of Influence of Risk Factors on Workers’ Unsafe Behaviors
1	0%	0%
2	0%~0.1%	0%~0.5%
3	0.1%~0.5%	0.5%~1%
4	0.5%~1%	1%~2%
5	1%~5%	2%~3%
6	5%~10%	3%~5%
7	10%~20%	5%~10%
8	20%~30%	10%~15%
9	30%~40%	15%~20%
10	40%~50%	20%~25%
11	50%~60%	25%~30%
12	60%~70%	30%~40%
13	70%~80%	40%~50%
14	80%~90%	50%~60%
15	90%~100%	60%~70%
16		70%~80%
17		80%~90%
18		90%~100%

. The confidence index is filled in the corresponding position on a scale of 1 to 10.

(2)

The collection and data processing of expert scoring results

After obtaining the basic data by combining the confidence index with the expert scoring method, the data are processed according to the needs of model construction. This paper will use the weighted average method to evaluate the probability of occurrence and the impact degree of each risk factor.

In the survey, assuming the total number of scoring experts is τ and the number of risk factors is n, the calculation weight of the u-th expert, ω_m, is obtained through Equation (1). The judgment interval of the u-th expert on the occurrence probability of risk factor R_i is [Y_iu, K_iu], and the confidence index when scoring R_i is h_iu.

The specific steps for data processing are as follows:

Step 1: The interval for the u-th expert’s judgment on risk factor R_i is calculated based on Equation (2):

$${\Delta }_{iu}=K_{iu}-Y_{iu}$$

(2)

Step 2: Using triangular fuzzy numbers to adjust the confidence index.

To incorporate the confidence index [44] into the calculation of risk occurrence probability, this paper uses the interval Δ_iu as a reference to adjust the confidence index hiu with triangular fuzzy numbers, resulting in the adjusted confidence index, as shown in

Table 6. Values of triangular fuzzy numbers taken for the confidence index.

Inter Vrange Δiu /%	Confidence Index hiu
	10	9	8	7	6	5	4	3	2	1
0.1	0	0.025	0.05	0.075	0.1	0.15	0.2	0.25	0.3	0.35
0.4	0	0.1	0.2	0.3	0.4	0.6	0.8	1	1.2	1.4
0.5	0	0.125	0.25	0.375	0.5	0.75	1	1.25	1.5	1.75
1	0	0.25	0.5	0.75	1	1.5	2	2.5	3	3.5
2	0	0.5	1	1.5	2	3	4	5	6	7
4	0	1	2	3	4	6	8	10	12	14
5	0	1.25	2.5	3.75	5	7.5	10	12.5	15	17.5
10	0	2.5	5	7.5	10	15	20	25	30	35

.

Step 3: The risk contribution of the u-th expert to the risk factor R_i is calculated based on Equation (3):

$${\gamma }_{iu}={\omega }_{iu}({\lambda }_{iu}-{\sigma }_{iu},{\lambda }_{iu},{\lambda }_{iu}+{\sigma }_{iu})$$

(3)

In the equation, γ_iu represents the contribution of the u-th expert to the occurrence probability of risk factor R_i; σ_iu represents the adjusted confidence index of the u-th expert when scoring the risk occurrence probability, with values taken from Table 5; λ_iu represents the median judgment of the u-th expert on the occurrence probability of risk factor R_i; where u = 1, 2, 3 … τ, i = 1, 2, 3 … n.

Step 4: After calculating the results of each expert and summing them up, the occurrence probability of risk factor R_i can be obtained based on Equation (4):

$$\begin{array}{l}{\gamma }_i={\displaystyle \sum _{u=1}^{\tau }{\omega }_{iu}(}{\lambda }_{iu}-{\sigma }_{iu},{\lambda }_{iu},{\lambda }_{iu}+{\sigma }_{iu})\\ =({\gamma }_{i\tau }-{\sigma }_i,{\gamma }_{i\tau },{\gamma }_{i\tau }+{\sigma }_i)\end{array}$$

(4)

In the equation, γ_iτ represents the sum of the contributions of τ experts to R_i; γ_i represents the accumulated contribution value of R_i, which is the occurrence probability of the risk factor. Since γ_i is an isosceles triangular fuzzy number, it needs to be converted into an exact value using the median method for calculation. The median is the abscissa where the membership degree is 1, i.e., γ_i = γ_iτ.

Step 5: The impact degree of the risk factor is calculated based on Equation (5).

According to the above calculation steps, assuming the impact degree of the risk factor R_i is ρ_i, the interval for the u-th expert’s judgment on the impact degree of the risk factor is [E_iu, D_iu], the confidence index when scoring is ε_iu, and the adjusted confidence index is ξ_iu, the impact degree value of R_i can be obtained. Therefore, the impact degree of the risk factor is as follows:

$$\{\begin{array}{l}{\lambda }_{iu}=(E_{iu}+D_{iu})/2\\ {\rho }_{iu}={\omega }_{iu}({\lambda }_{iu}-{\xi }_{iu},{\lambda }_{iu},{\lambda }_{iu}+{\xi }_{iu})\\ {\rho }_i={\displaystyle \sum _{u=1}^{\tau }{\omega }_{iu}({\lambda }_{iu}-{\xi }_{iu},{\lambda }_{iu},{\lambda }_{iu}+{\xi }_{iu})}\\ =({\rho }_{i\tau }-{\xi }_{iu},{\rho }_{i\tau },{\rho }_{i\tau }+{\xi }_{iu})\end{array}$$

(5)

In the equation, ρ_iu represents the contribution value of the u-th expert’s judgment on the impact degree of R_i; ξ_iu represents the adjusted confidence index of the u-th expert when scoring the impact degree of the risk factor; λ_iu represents the median judgment of the u-th expert on R_i, where u = 1, 2, … τ, i = 1, 2, … n; ρ_i represents the accumulated contribution value of R_i, which is the impact degree of the risk factor. The method for obtaining the exact value of ρ_i in the calculation process is the same as for γ_i, i.e., ρ_i = ρ_iτ.

3.2.2. Calculation of Conditional Probability of Risk Factors Based on Association Strength

After obtaining the association strength between risk factors of unsafe worker behaviors through the expert scoring method, the acquired data are processed using the weighted average method. Assuming the probability interval of the conditional probability is [0, 100%] and the calculation coefficient is η, the conditional probability P(R_j|R_i) for each risk factor is calculated based on the processed association strength υ_i,j, as shown in Equation (6):

$$P(R_j|R_i)=\eta {\overline{\upsilon }}_{i,j}\times 100\%$$

(6)

In the equation, P(R_j|R_i) represents the probability of risk factor R_j occurring given that risk factor R_i has occurred; R_j is the succeeding node of R_i; η represents the calculation coefficient, which is set to 0.2; υ_i,j represents the processed association strength between risk factors R_i and R_j.

3.2.3. Constructing a Cascading Trigger Model for Risk Factors of Unsafe Worker Behaviors

Three conditions must be met for a cascading failure phenomenon to occur in a system: First, the system under study must be a network with existing traffic; second, there must be local failure rules within the network; third, there must be a traffic redistribution mechanism when nodes in the network are activated. Clearly, the risk network of unsafe worker behaviors meets these three conditions. For example, when the risk factor of abusive leadership fails, the risk network has a traffic redistribution mechanism, and the risk volume (traffic) will be allocated to its next nodes, namely, physical fatigue, paranoia and hostility, and poor internal organizational cohesion. When the state of a risk node changes, the local risk node in the network becomes activated. If the load on a network node exceeds its upper limit for normal operation, meaning the risk volume acting on this node is greater than its threshold, the node is triggered. The risk flow passes through the triggered node and flows to its succeeding nodes, leading to risk flow redistribution and causing cascading failure. If the load on the risk node does not exceed its threshold, the node is not triggered, and the risk factor remains in an inactive state. This paper defines the upper limit of load capacity, the triggering conditions for initial and non-initial nodes, and the load redistribution rules for failed nodes. The process of node load redistribution is shown in Figure 3.

(1)

Upper Limit of Load Capacity

The upper limit of load capacity refers to the maximum load that a risk node can withstand without being triggered, i.e., the threshold. In this paper, the occurrence probability of the risk node is used as the threshold.

(2)

Trigger conditions for initial nodes

Initial nodes refer to the source nodes of the risk flow. When an initial node is triggered, it means that the initial load acting on this node exceeds its upper load capacity limit, i.e., greater than the occurrence probability of this node. Only then will the risk flow emanate from this node. In this paper, the occurrence probability data of the nodes are obtained through the expert scoring method and processed using the confidence index method, as shown in Section 3.2.1. In the subsequent simulation of attack nodes, the initial load of the initial node is directly set to its upper load capacity limit, i.e., the occurrence probability of the initial node.

$$L_0(i)\ge {\gamma }_i$$

(7)

In the equation, L₀ represents the initial load of node i.

(3)

The rule for redistributing loads of failed nodes

Since the risk factor transmission process studied in this paper is unidirectional, load redistribution for failed nodes refers to the flow of load to its succeeding nodes according to the flow distribution rules after a node fails. Therefore, this paper uses the entropy flow model to quantify the transmission of risk flow between risk nodes. The calculation formula for risk flow (Entropy) is as follows:

$$E(R_i,R_j)=-P(R_j|R_i)\mathrm{lnP}(R_j|R_i)\rho (R_j)$$

(8)

In the equation, E(R_i,R_j) represents the risk flow from node R_i to its succeeding node R_j; ρ(R_j) represents the impact strength of R_j. This paper simulates the load redistribution process for nodes. Assuming node a reaches its failure condition, the set of succeeding nodes for node a is Q(a) = {b,d,e}. The redistributed loads E_ab⁺, E_ad⁺, and E_ae⁺ are calculated, and it is found that nodes d and e are not triggered, while node b is in an overloaded state, as shown in Figure 3a. At this point, the failed node redistribution needs to be performed. The set of succeeding nodes for node b is Q(b) = {h,c}. The redistributed loads E_bh⁺ and E_bc⁺ are calculated, as shown in Figure 3b. It is found that node h is not triggered, while node c is in an overloaded state, as shown in Figure 3c. At this point, node c needs to perform failed node redistribution. The set of succeeding nodes for node c is Q(c) = {f,g}. The redistributed loads E_cf⁺ and E_cg⁺ are calculated, and it is found that nodes f and g are not triggered.

(4)

Trigger conditions for non-initial nodes

The initial load of a non-initial node refers to the total risk-bearing capacity of a non-source risk node in the path. When a non-initial node is triggered, it means that the total load acting on this node exceeds its upper load capacity limit, i.e., greater than the occurrence probability of this node. Subsequently, the risk flow moves to the next node. The calculation formula for the total risk flow to a non-initial node is as follows:

$$S(R_j)=E(R_{i1})+E(R_{i2})+\cdots +E(R_{in})$$

(9)

In the equation, S(R_j) represents the total risk flow from all preceding nodes of risk node R_j to R_j; E(R_in) represents the risk flow from the n-th preceding node R_in to node R_j. Therefore, the trigger condition for non-initial nodes is as follows:

$$S(R_i)\ge {\gamma }_i$$

(10)

(5)

Effective Pathways

The path through which risk is transmitted from the deep factors layer to the surface factors layer.

4. Simulation Operation and Result Analysis of Risk of Unsafe Worker Behaviors

4.1. Simulation Strategy for Risk of Unsafe Worker Behaviors

The simulation strategy for the transmission paths of the risk of unsafe worker behaviors in this paper is divided into the following situations:

(1)

Attack on a single deep factor (assuming only one factor is triggered)

• Attack every single deep factor separately, totaling 18 situations (The reason is that this paper identified 22 risk factors, 18 of which are deep factors and 4 are surface factors. Risks are transmitted from deep factors to surface factors, leading to unsafe behaviors. Surface factors do not appear without cause; they are induced by deep factors. Therefore, only the scenarios in which the 18 deep factors occur independently are simulated);
• Output the effective path after attacking each node (In the risk network, we assume that certain risk nodes have already occurred, and this assumed state is referred to as attacking the nodes).

(2)

Attack on randomly combined and simultaneously occurring deep factors

• Use the simulation results obtained in 4.1.(1) as the control group;
• Perform permutations and combinations of all deep factors, resulting in a total of 4029 combinations (153 combinations of two factors, 816 combinations of three factors, and 3060 combinations of four factors):

  $${{\displaystyle C}}_{18}^2=153,{{\displaystyle C}}_{18}^3=816,{{\displaystyle C}}_{18}^4=3060$$
• Attack these combination nodes separately and output the effective paths.
• Compare the simulation results of the combination nodes with the control group results.

4.2. Analysis of Simulation Results

This paper studies the risk network constructed in Figure 2 and 22 network nodes. Based on simulation strategy 4.1, 4047 simulation calculations were conducted for random attack experiments (18 for single-factor attacks and 4029 for multi-factor attacks). The analysis was conducted from three aspects: network failure rate, changes in effective paths, and the distribution of individual nodes. The analysis results are as follows:

(1)

Network failure rate

Simulation experiments show that under random attacks on different combinations of deep factors, 4047 simulations were conducted, and 789 combination nodes had effective path outputs after being attacked. Among them, in the category of two-node combinations, the total number was 153, with 0 effective outputs, resulting in a failure rate of 0%. In the category of three-node combinations, the total number was 816, with 54 effective outputs, resulting in a failure rate of 6.62%. In the category of four-node combinations, the total number was 3060, with 735 effective outputs, resulting in a failure rate of 24.02%. As the number of nodes increases, the failure rate of the risk network increases.

(2)

Changes in effective action paths

This paper first simulates the single node condition (control group) and finds no effective path output. Considering only the control condition of attacking a single node, we conducted simulation experiments for the other three conditions. The results show that among the 4047 simulations, there were a total of 1083 effective path outputs. There were no effective paths in the two-node combination category because the cumulative risk flow failed to exceed the threshold of its succeeding node at a certain point during transmission, thus blocking its propagation and resulting in no effective path output. However, when the number of randomly combined nodes increased to three, we observed the generation of effective paths for the first time, totaling 68. Furthermore, when the number of node combinations increased to 4, the number of effective paths significantly increased to 1015. After statistical classification, there are 34 types of paths in total. This paper selects the top 13 effective paths for analysis, as shown in

Table 7. Summary of effective action pathway.

Number	Effective Action Pathways	Frequency of Occurrence	Ranking
A	x→R12	394	1
B	x→R14→R12	85	2
C	x→R5→R12	76	3
D	x→R11	58	4
E	x→R2→R9	57	5
F	x→R9	48	6
G	x→R15→R14→R11	38	7
H	x→R15→R14→R12	38	7
I	x→R1→R9	28	8
J	x→R1→R2→R15→R14→R11	28	8
K	x→R1→R2→R15→R14→R12	28	8
L	x→R14→R11	25	9
M	x→R2→R15→R11	21	10

Note: ① The letters A–M in the table indicate the top 13 effective paths; ② the “x” in the column of effective paths in the table represents the initial nodes of random combinations.

.

The distribution of the top 13 paths from Table 6 under different node combination categories is shown in Figure 4. It can be seen that the number of effective path outputs increases with the number of node combinations. The change in the top-ranked path A is particularly notable, increasing from 30 to 364, accounting for 36.38% of the total number of effective paths. In contrast, the changes in paths ranked 2–10 are relatively small, with little difference in numbers between the paths. An effective path is one where the risk is transmitted from the deep factor level to the surface factor level, leading to the occurrence of unsafe worker behaviors. Therefore, the higher the number of node combinations, the higher the output rate of effective paths, and consequently, the higher the rate of unsafe worker behaviors.

(3)

Node distribution

1. Distribution of deep factors in effective combined nodes

By statistically analyzing the combination nodes with effective path outputs, the frequency of occurrence of each deep factor in these effective combination nodes can be determined. The top five factors are herd mentality (R5), poor organizational cohesion (R14), poor internal organizational communication (R15), abusive leadership style (R16), and insufficient/low-quality safety education and training (R19).

2. Distribution of risk factors at various levels in effective paths:

(a) Deep Factors

By statistically analyzing the frequency of occurrence of the 18 deep factors in the total effective paths, the simulation results determined the frequency of each deep factor. The top five are poor internal communication (R15), poor organizational cohesion (R14), negative emotions (R2), physical fatigue (R1), herd mentality (R5), and fluke mindset (R4).

(b) Surface Factors

Statistical analysis and ranking of the four surface factors in the effective paths show that they are poor organizational safety climate (R12), unsafe motivation of workers (R11), weak risk perception ability of workers (R9), and weak safety awareness of workers (R10).

The distribution of deep and surface factors within effective combination nodes and effective paths was comprehensively analyzed, with a summary provided for each of these two levels. For deep factors, key elements across three dimensions were identified: at the individual level, factors such as conformity, negative emotions, physical fatigue, and risk-taking mentality were most prevalent; at the organizational level, poor group cohesion and ineffective internal communication were significant; and at the management level, abusive leadership style and insufficient/low-quality safety education and training were prominent. Subsequently, the proportions of the four surface factors within the total effective paths were calculated. Poor organizational safety climate accounted for 62.43% of the surface factors in effective paths, making it the most influential single factor. At the individual level, unsafe worker motivation (21.31%), weak risk perception ability (13.93%), and poor safety awareness (2.34%) were also identified as key factors.

4.3. Analysis of the Causes Behind the Simulation Results

Based on the three simulation results in Section 4.2, this paper discusses the underlying causes.

(1)

As the number of nodes in the combinations increases, the failure rate of the risk network also increases. This phenomenon occurs because more node combinations introduce more potential paths for risk propagation. Each additional node combination increases the likelihood of risk spreading. Consequently, when multiple risk nodes coexist, the probability of triggering certain nodes in the network increases, leading to an increased failure rate.

(2)

The number of effective paths increases with the number of node combinations. This is because combining more nodes amplifies the cumulative risk effect. A single node’s risk may not be sufficient to surpass the threshold of a critical node. However, when multiple nodes are combined, their cumulative risk may exceed the threshold, triggering the critical node and activating more potential paths, thereby increasing the number of effective paths.

(3)

Regarding the statistical results on node distribution in Section 4.2 (3), the reasons behind these findings are further discussed. Deep factors serve as the root causes, influencing surface factors through complex transmission paths. Understanding and identifying these deep factors are crucial for preventing and reducing unsafe behaviors triggered by surface factors. By deeply studying the relationship between deep and surface factors, more effective strategies can be developed to reduce the occurrence of unsafe behaviors among workers. Given that surface factors are directly triggered by deep factors, this study focuses on the causes of the prominent deep factors identified in the results.

• Individual factors are the most prevalent, including physical fatigue, negative emotions, conformity, and risk-taking mentality. In Chinese construction workers, physical fatigue and negative emotions are common. The Chinese construction industry is known for its high efficiency, with frequent overtime work. Long hours of intense labor and insufficient rest, coupled with the pressure of the work environment, often lead to fatigue and negative emotions among workers. Additionally, conformity and a risk-taking mentality are also common. Due to generally low levels of education and weak safety awareness, workers are easily influenced by the unsafe behaviors of their peers, imitating non-compliance with safety regulations. Furthermore, a risk-taking mentality causes workers to underestimate risks, become overconfident, and believe that accidents will not happen to them, further increasing the risk of unsafe behavior.
• At the organizational level, poor group cohesion and ineffective internal communication are significant factors. These issues are prevalent in large construction projects, where the workforce is diverse and highly mobile, often leading to inadequate teamwork and coordination. This directly results in poor internal communication and a lack of cohesion within the group, making workers more reliant on individual judgment rather than collective rules, thereby increasing the likelihood of unsafe behaviors.
• At the management level, abusive leadership style and insufficient/low-quality safety education and training are key factors. In the Chinese construction industry, an authoritarian management style is relatively common, especially in more traditional enterprises. This style can lead to low employee morale, frustration, and even resistance, neglecting the psychological well-being and work motivation of employees, thereby increasing safety risks. Additionally, in many small and medium-sized enterprises and temporary construction sites, safety training often becomes a formality or is difficult to implement effectively due to limited resources. Many workers come from rural areas with low educational levels, making it difficult for them to understand complex safety regulations and technical requirements, resulting in the poor application of training content in actual work. Thus, although safety training has become a necessary measure in the Chinese construction industry, its effectiveness is greatly reduced due to poor implementation and insufficient resources, making it difficult to effectively prevent unsafe behaviors.

Overall, the study of deep and surface factors in the context of unsafe behavior among Chinese construction workers reflects the realities of China’s construction industry. These prominent factors are deeply influenced by China’s management practices, cultural background, and current state of development. A comparison between China and Southeast Asian countries reveals that these nations share some overlapping risk conditions, such as Malaysia [45,46] and the Philippines [47]. These countries are also experiencing rapid economic growth and urbanization, with similar cultural backgrounds, leading to comparable safety challenges in the construction industry, including work environment, management practices, and high safety requirements. Each country’s research has focused on identifying the impact of these factors to develop more effective management measures aimed at improving worker safety performance. Despite these similarities, each country also exhibits unique characteristics in the study of unsafe behavior. In China, there is a significant emphasis on organizational factors due to the large scale, complex organizational structure, and lengthy management chains in its construction industry. As a result, improving safety through optimized organizational management has become a key research focus. Malaysia, with its multicultural background and hot, humid climate, places more emphasis on the impact of individual factors and working conditions on unsafe behavior. In contrast, the Philippines focuses more on management-related research, prioritizing worker safety training due to limited domestic capital accumulation and resource constraints.

Although the research focus varies across different countries, the similarities between the construction industry in China and those of some other developing countries suggest that the findings of this study hold significant reference value. The research methodology presented in this paper is also broadly applicable. By adjusting the approach to suit the specific conditions of each country, other developing nations can effectively identify key risk nodes and develop safety management measures tailored to their own circumstances, thereby reducing safety risks on construction sites. Consequently, the risk identification and management methods proposed in this study are equally valuable and have potential applications in the engineering practices of these countries.

5. Conclusions

• Through the literature research method and expert scoring method, this paper identifies the risk factors of workers’ unsafe behavior from the four dimensions of individual, organization, management, and environment and solves the problem of multidimensional identification of workers’ unsafe behavior risk factors.
• In this paper, the relationship between risk factors is evaluated by the expert scoring method, the risk network of workers’ unsafe behavior is built, the cascade failure phenomenon is introduced, the entropy flow model is adopted to accurately quantify the risk, the risk quantification formula is formulated to accurately measure the risk propagation, and the trigger conditions of each risk node are set up, and the cascade trigger model is built. The problem of risk transmission and transferability is solved.
• The study also utilizes Visual Studio Code for coding and combines it with JavaScript to build a simulation platform that models the uncertainty of risk occurrences. This involves simulating the evolution paths of various risk nodes in random combinations when triggered, thereby closely replicating the uncertainty of risk occurrences.
• According to the simulation results, as the number of nodes in the combination category increases, the network failure rate also increases. By statistically analyzing the 1083 identified effective paths, this paper determines the key paths and nodes of unsafe worker behaviors. The deep factors include individual dimensions (herd mentality, negative emotions, physical fatigue, fluke mindset), organizational dimensions (poor cohesion, poor internal communication), and managerial dimensions (abusive leadership style, insufficient/low-quality safety education and training). Surface factors mainly exist in organizational dimensions (poor safety climate) and individual dimensions (unsafe motivation, weak risk perception ability, weak safety awareness). These findings can help managers effectively control key risk factors and block risk propagation paths.
• The theoretical significance of this paper lies in the introduction of a risk identification method based on cascading failure and entropy flow models, offering a new perspective for analyzing the evolution of unsafe behaviors. This theoretical framework not only helps deepen the understanding of the root causes of unsafe behaviors but also provides a new foundation for future research, particularly in multidimensional and multilayered risk management studies, addressing some gaps in the field of construction site safety management. The practical significance of this paper is that its findings provide practical guidance for safety management in the construction industry. By identifying and analyzing the key risk factors and pathways of unsafe behaviors among construction workers, this research can help managers more effectively prevent and reduce the occurrence of unsafe behaviors in actual construction processes.

However, despite the rigorous design of this model and its close alignment with real-world environments, there are still some limitations. Although this study accurately quantified the effective paths and key nodes of risk factors for unsafe behaviors among construction workers, this quantification method also has certain limitations. During the quantification process, there were some deficiencies in setting the impact degree of certain risk factors. The severity level of risk factors each time they occur determines the size of their impact. Future research could classify the impact degree of risk factors into levels for more detailed settings.