Coupled analysis and simulation of safety risk in subway tunnel construction by shallow-buried excavation method based on system dynamics

Abstract

To address the existing shortcomings in the research on the coupling of safety risk factors in subway tunnel construction using the shallow-buried excavation method, this paper conducts a coupled analysis and dynamic simulation of the safety risks associated with this construction method. Firstly, by analyzing the mechanisms and effects of risk coupling in shallow-buried excavation construction of subway tunnels, this study divides the risk system into four risk subsystems (human, material, management, and environment), establishes an evaluation index system for the coupling of safety risks, calculates the comprehensive weight values of the risk indicators using the AHP-entropy weight method, and constructs a risk coupling degree model by combining the inverse cloud model and efficacy function. Subsequently, based on the principles of system dynamics, a causal relationship diagram and a system dynamics simulation model for the coupling of “human-material” risks in construction are established using Vensim PLE software. Finally, the case study of the underground excavation section of Chengdu Metro Line 2 is employed to perform dynamic simulation using the established model. By adjusting the relevant risk coupling coefficients and simulation duration, the impact of the coupling of various risk factors on the safety risk level of the human-material coupling system is observed. The simulation results demonstrate that: 1) Heterogeneous coupling of human and material risks has a particularly significant effect on the system’s safety risks; 2) Violations by personnel and initial support structure defects are key risk coupling factors. The findings of this study provide new insights for decision-makers to assess the safety risk of shallow-buried excavation construction in subway tunnel.

Keywords

Shallow-buried excavation method risk coupling coupling degree model system dynamics simulation analysis

1 Introduction

The rise of urban subways has led to the growing commonality of newly built tunnels in certain areas passing through existing roads or buildings at short distances, with most of these tunnels being shallow-buried and having an overlying soil layer thickness less than twice the diameter of the tunnel [1]. As one of the shallow tunnel excavation methods, the shallow-buried excavation method has become an inevitable choice and is widely used in tunnel construction due to its flexible construction methods, diverse cross-section forms, relatively low cost, and compared with the shield tunneling method, it is more suitable for special excavation sections (such as weak and uneven strata) [2]. Although the construction technology of the shallow-buried excavation method for tunnels is relatively mature, engineering accidents can also occur due to improper construction design, unclear geological exploration, or untimely support [3]. The occurrence of construction safety accidents can lead to severe economic losses, casualties, and negative societal information impact. For example, in December 2019, a tunnel collapse occurred during the shallow-buried excavation at Shahe Station of Guangzhou Metro Line 11, resulting in the death of 3 individuals and direct economic losses of approximately 20.047 million yuan. Subway tunnels involved in shallow-buried excavation exhibit characteristics such as complex and changing environmental conditions, diverse and intersecting work processes, long construction periods, large-scale engineering, multiple participating entities, and high levels of unpredictability and suddenness. Therefore, the construction process is characterized by a high degree of uncertainty and significant safety hazards [4].

The shallow-buried excavation phase of subway tunnel construction constitutes a complex ecological system, primarily encompassing subsystems such as personnel, mechanical equipment, management, and the environment. The occurrence of accidents is not solely attributable to a single factor within a specific system, nor is it merely the simple sum of various factors; rather, the emergence of risks often results from the coupling of multiple factors [5]. Due to variations in construction environments across different regions, there is currently no standardized construction technique for shallow-buried excavation methods, and the associated construction practices also differ. These methods are influenced by various factors such as geological conditions and management levels during the construction process. Additionally, new risk factors may emerge both internally and externally within the construction safety system at any time. Different risk factors can intersect and interact in terms of time and space, leading to an increasing trend in the risk level of shallow-buried excavation method construction. The coupling effect of risk factors also raises the probability and severity of safety risk accidents. Therefore, a thorough analysis of the coupling effects and evolutionary mechanisms among different risk factors is of significant importance in enhancing the overall safety risk management level throughout the entire process of subway tunnel construction using shallow-buried excavation methods.

However, the first type of risk management research on the construction phase of metro projects is to use numerical and physical simulation experimental methods to calculate and analyze the safety and reliability of tunnel structure and geological soil layer structure system [6, 7], and the other type is to identify, analyze or evaluate the construction risk system of metro projects based on the empirical judgment of engineering technology experts as the scoring [8, 9]. The former takes safety analysis as the core of the study, without considering risk indicators with human factors such as construction technology, operation level, management level, etc., and there is uncertainty in the selection of models and the adoption of construction methods. The latter uses the AHP, expert investigation method, fuzzy theory, and other technical methods to quantitatively analyze the qualitative risk factors, without dynamically considering the interactions between the risk factors, which all lead to the deviation between the calculation results and the actual situation of the project, and can not carry out risk management research on the construction process of the metro project in a more comprehensive way.

In summary, in order to study the dynamic coupling relationship among various risk factors in the shallow-buried excavation construction process of subway projects more accurately and comprehensively, this paper adopts a risk-coupling perspective to identify risk factors from four aspects: human, material, management, and environment, and constructs a risk evaluation index system. A risk coupling model for subway tunnel shallow-buried excavation construction is established to calculate the magnitude of coupling between various risk factors. Causal relationship diagrams are drawn to analyze the coupling relationship among various risk factors within the “human-material” system. Based on this analysis, a corresponding system dynamics simulation model is constructed. The constructed simulation analysis model is applied to practical engineering cases, and by adjusting relevant coupling coefficients and simulation duration, the changes in the system’s risk level are analyzed to identify key risk coupling factors, thereby enhancing the scientificity and flexibility of safety management in the shallow-buried excavation construction phase.

2 Literature review

2.1 Qualitative and quantitative research on underground engineering risks

In the initial stage of research, qualitative studies on underground construction safety risks and related theories were mainly conducted using methods such as case studies and expert surveys. American scholar H.H. Einstein is a representative figure in tunnel engineering risk analysis research, having authored several influential articles on engineering risk management that provide principles and methods for objectively analyzing risk characteristics in underground projects [10, 11]. R.J. Smith proposed a process for allocating construction risks in underground projects and discussed the principles and methods of risk allocation [12]. D.S. Xie established the concept of safety risk management for subway projects and identified the key points and challenges by studying and analyzing relevant theories of safety risk management and typical accident cases in subway projects [13]. L.G. Zhou et al. conducted a detailed study and analysis of the safety risk management hierarchy, assessment system, control standards, and monitoring plans in the field of subway construction based on the distribution of construction risks in Chinese subway projects [14]. According to research experience in underground construction projects, Einstein H.H. summarized the stages involved in assessing and analyzing construction safety risks, including risk accident collection, information processing, model establishment, and calculation evaluation [15].

As research progresses, quantitative analysis models and statistical methods have gradually been applied to various aspects of risk identification, analysis, and assessment in underground engineering. In terms of risk identification, L.Y. Ding et al. developed a safety risk identification system using subway construction drawings, which achieved automatic identification of safety risks [16]. Z.P. Zhou utilized a Bayesian Network model and conducted a sensitivity analysis of safety factor values for construction personnel based on changes in the Gini index, aiming to identify the key factors of construction safety risks [17]. In terms of risk analysis, W. Liu et al. collected and analyzed past safety accident cases that occurred during the shield tunnel construction phase of subway projects, using the ISODATA algorithm to analyze the causes of safety accidents [18]. V.H. Franco combined the mixed point evaluation and finite element theories to conduct a multi-factor numerical risk analysis on the construction environment of subway projects, studying the influence of subway construction on the safety risk coefficient of surrounding surface structures [19]. In terms of risk assessment, H. Yan et al. proposed a fuzzy matter-element model for risk assessment by employing fuzzy set and matter-element theories, based on data regarding uncertain safety risks and inconsistent evaluation factors during the subway construction phase [20]. Based on establishing a risk assessment index system, S.S. Zhou introduced the Projection Pursuit Classification (PPC) method for objective weight quantification and conducted a comprehensive evaluation of subway construction safety by constructing a D-S evidence theory risk assessment model [21].

2.2 Research on safety risk management of shallow-buried excavation construction in metro tunnels

The construction of shallow-buried and mined subway tunnels involves many uncertainties and risk factors. Currently, research on risk management in shallow-buried and mined subway tunnel construction can be divided into two different perspectives: qualitative and quantitative. In the qualitative research aspect, Y.M. Zhu elaborated on the characteristics of shallow-buried excavation construction technology for subway tunnels and proposed targeted risk control measures regarding the various risks faced in practical construction [22]. Based on a collapse accident of surrounding rock in a shallow-buried excavation station in a certain rail transit project, H.P. Xue analyzed the construction risks of shallow-buried excavation stations and proposed corresponding management measures regarding project risks and practical management experience [23]. J.L. Feng systematically elaborated on the risks and hazards faced during the construction process of tunnel engineering using the shallow-buried excavation method. This includes surrounding environmental factors, pipeline leakage factors, and construction quality factors, while also proposing targeted control measures [24].

In quantitative research, Chen M. investigated the impact of shallow-buried underground tunneling on nearby high-speed railway viaducts. By constructing a three-dimensional numerical model to simulate the excavation process of the underground segment, the deformation characteristics of the existing pile foundation of the high-speed railway viaducts during tunneling were revealed. Corresponding risk control measures were then proposed [25]. Z.Y. Ou et al. proposed a comprehensive risk assessment method for shallow-buried excavation tunnel engineering construction. This method integrates fuzzy logic, fault tree analysis, and analytic hierarchy process-data envelopment analysis, enabling the reflection of the impact of construction risk factors on individual injury, property loss, construction progress, and the environment [26]. M. Ge established an index evaluation system and a fuzzy comprehensive evaluation model for the construction risk of urban subway tunneling in concealed excavation method, and carried out risk analysis and evaluation of the concealed excavation construction process of an interval [27].

2.3 Risk coupling research

The concept of risk coupling refers to the existence of dependency and correlation to some extent among two or more risk factors. This concept was initially applied in the aviation field and has gradually extended to areas such as ecology, computer science, and construction engineering management with ongoing research on this theory. Currently, commonly used models in risk coupling research include the coupling degree model, N-K model, and system dynamics model. H. Shyur employed safety indicator data and coupling models to quantitatively analyze safety risks caused by personnel factors in aviation accidents and investigate the extent of the influence of personnel factors [28]. G. Felder et al. established a hydraulic model of flood-affected areas based on coupling model theory to study and analyze the runoff variation of catchment areas in response to precipitation input and to evaluate and mitigate flood-related safety risks [29]. D. Fan summarized and analyzed risk factors in the supply chain of manufacturing enterprises based on 190 safety risk accidents and 400 environmental accidents, studying the influence of supplier risk coupling on risk accidents from the perspective of HSE [30]. H. Pan et al. constructed a coupling degree model to analyze the impact of coupled risk factors in subway engineering projects on construction safety, and they found that the psychological quality of construction personnel and management factors significantly affect construction risks, leading them to propose relevant risk decoupling measures [31]. J. Fang et al. used data from 231 subway construction safety risk accidents in China to construct an N-K model and study the coupling patterns of risks in subway tunnel construction [32].

The study found that risk management research and application in the field of underground engineering are relatively extensive, with a wealth of theoretical ideas, quantitative analysis models, and methods in risk identification, risk analysis, risk assessment, forming a rich risk management system. When it comes to research related to risk management in shallow-buried excavation construction of subway tunnels, although there have been numerous research achievements, both qualitative and quantitative studies have mainly focused on a single dimension. There is a lack of research on the relationships and pathways of interaction between risk factors, making it difficult to clearly understand the coupling relationships between risk factors when accidents occur. Therefore, there are issues such as the relative lag in risk analysis methods for shallow-buried excavation construction of subway tunnels, a lower level of risk management research, and the need to improve the accuracy of risk assessment results. On one hand, research related to risk coupling has expanded to many industries, and studies on the mechanism, effects, and risk decoupling resulting from risk coupling have gradually matured. However, research on the coupling of risk factors in the shallow-buried excavation process of subway tunnel projects is relatively limited. On the other hand, there is a lack of research on the dynamic variability of the coupling effects between various risk factors, meaning the inability to dynamically predict the extent of the impact of changes in the coupling relationships of risk factors on system risk. In conclusion, the current research on risk management in shallow-buried excavation construction of subway tunnels faces the following limitations, which represent a progressively deepening issue:

(1)
The mutual interaction relationships between various risk factors during the construction process were not considered.
(2)
The dynamic variability of the interaction relationships between various risk factors during the construction process was not comprehensively taken into account.

Given the deficiencies in the above two aspects, it is necessary for the shallow-buried excavation construction of subway tunnels to analyze the dynamic mechanisms and evolution of interactions between risks in a more scientific manner. This involves exploring the pathways of risk propagation and interactive coupling effects during construction, reducing the accumulation of risk factors, and thereby preventing or mitigating construction safety accidents.
3 Methods

3.1 Construction of risk coupling degree model

The coupling degree model is a concept in system dynamics used to describe the degree of interconnection between various subsystems or components within a system. This interconnection level is typically referred to as coupling degree, reflecting the connections, influences, and dependencies among different parts within the system. The coupling degree model aims to aid in understanding the complexity of the internal structure of a system and the impact of interactions between different parts on the overall system behavior. This paper constructs a model for the coupling degree of risks in shallow-buried tunnel excavation for metro construction, quantitatively calculating and analyzing the coupling relationships among various risk factors in the construction safety system (with a focus on the human-material risk coupling system). The specific process of establishing the risk coupling degree model is as follows: First, establish an evaluation index system for the risk coupling of shallow-buried excavation construction. Second, use the AHP-entropy method to quantify the evaluation index system and determine the weight values of each index factor. Third, introduce the inverse generator of the cloud model to calculate the digital characteristics of each index factor. Fifth, use the efficacy function and coupling degree function to calculate the degree of coupling between various risk factors.

3.1.1 Establishment of risk indicator system

When constructing the construction risk index system of the subway shallow-buried excavation method, the characteristics of the subway shallow-buried excavation construction should be considered, and principles such as wholeness, hierarchy, representativeness, rigor, and comparability should be followed. Based on the research issues and objectives, a hierarchical analysis is conducted on the various factors of the safety system during the construction phase according to their importance. The target layer is the goal that this study or this project needs to achieve. The criterion layer is the path, method, and other means required to achieve goals. The indicator layer is extended and refined based on the standards of the criterion layer to obtain detailed factors that affect the final goal.

Based on the above three levels, and drawing from the systematic theory of safety engineering (“WuLi - ShiLi –RenLi’’) and the systematic methodology of harmonious management of engineering projects (“Ren - Shi –Wu’’) [33, 34], together with the safety risk management practice and related research of shallow-buried excavation construction of subway tunnels, the risk factors of shallow-buried excavation construction of subway tunnels are summarized into four categories: human factors, material factors, management factors, and environmental factors. Using the accident causation theory, combined with the relevant literature and case studies, identify the specific influencing factors (30 secondary indicators) of risk coupling in shallow-buried excavation construction of subway tunnels from the four first-level risk indicators of human, material, management, and environment, and construct a risk indicator system for shallow-buried excavation construction of subway tunnels, as shown in Table 1.

Table 1
Risk indicator system for shallow-buried excavation construction of subway tunnels

Target layer Criterion layer Indicator layer

Safety risks of shallow-buried excavation method in subway tunnel construction C human factors C1 Insufficient awareness of safety risks C11 Insufficient experience in tunnel construction C12 Poor on-site strain capacity C13 Substandard professional technical level C14 Poor psychological and physical fitness C15 Personnel irregularities C16

Material factors C2 Tunnel with oversized diameter or small soil cover thickness C21 Substandard quality of construction materials C22 Unreasonable construction of inverted arch C23 Initial support structure defects C24 Unstable secondary lining template and support system C25 Insufficient grouting behind the initial support and secondary lining C26 Inadequate concrete curing C27 Defective laying of waterproof board C28 Aging wear and tear or malfunction of mechanical equipment C29

Management factors C3 Insufficient pre-construction exploration and detection work C31 Inadequate monitoring work at the construction site C32 Unclear transportation planning for materials and equipment C33 Improper arrangement of construction processes C34 Insufficient risk emergency plan C35 Incomplete safety protection measures C36 Incomplete management system C37 Lack of safety training and education C38

Environmental factors C4 Complex engineering geological and hydrogeological conditions C41 Existing underground engineering obstacles C42 Complex surrounding buildings or structures C43 Ground traffic or adjacent construction disturbance C44 Surface subsidence may exceed the limit C45 Poor working environment C46 Natural calamities C47

Target layer	Criterion layer	Indicator layer
Safety risks of shallow-buried excavation method in subway tunnel construction C	human factors C1	Insufficient awareness of safety risks C11 Insufficient experience in tunnel construction C12 Poor on-site strain capacity C13 Substandard professional technical level C14 Poor psychological and physical fitness C15 Personnel irregularities C16
	Material factors C2	Tunnel with oversized diameter or small soil cover thickness C21 Substandard quality of construction materials C22 Unreasonable construction of inverted arch C23 Initial support structure defects C24 Unstable secondary lining template and support system C25 Insufficient grouting behind the initial support and secondary lining C26 Inadequate concrete curing C27 Defective laying of waterproof board C28 Aging wear and tear or malfunction of mechanical equipment C29
	Management factors C3	Insufficient pre-construction exploration and detection work C31 Inadequate monitoring work at the construction site C32 Unclear transportation planning for materials and equipment C33 Improper arrangement of construction processes C34 Insufficient risk emergency plan C35 Incomplete safety protection measures C36 Incomplete management system C37 Lack of safety training and education C38
	Environmental factors C4	Complex engineering geological and hydrogeological conditions C41 Existing underground engineering obstacles C42 Complex surrounding buildings or structures C43 Ground traffic or adjacent construction disturbance C44 Surface subsidence may exceed the limit C45 Poor working environment C46 Natural calamities C47

3.1.2 Calculation of indicator weights based on AHP-Entropy weight method

This article uses the Analytic Hierarchy Process (AHP) to determine subjective weights and references Saaty’s 1–9 scale method to compare the importance of various evaluation indicators. Based on this, a judgment matrix $M = {[\begin{matrix} m_{ij} \end{matrix}]}_{n \times n}$ is constructed. Use the feature root method to solve the eigenvalue λ_max of the judgment matrix and the corresponding eigenvector W, calculate the weight value w_ij of each indicator factor, and finally calculate CR for consistency testing.

Due to the subjectivity and susceptibility of the Analytic Hierarchy Process (AHP) to the influence of people’s experience and level of knowledge, it is necessary to introduce the entropy weight method in this study to determine objective weights and reduce the bias caused by subjective weighting. Based on the judgment matrix M scored by experts in the hierarchical indicator model, establish a decision matrix A = M = [a_ij] _m×n, perform normalization processing, and calculate the entropy weight e_ij of the indicator. Combine AHP and entropy weight method to calculate the combination weight:

ω = \frac{w_{ij} e_{ij}}{\sum_{j = 1}^{n} w_{ij} e_{ij}}

3.1.3 Construction of inverse cloud model

The inverse cloud generator is a model that can transform a set of random quantitative data into qualitative fuzzy concepts with cloud model characteristics. This article uses an inverse cloud generator to verify the rationality of experts’ ratings of risk factors and quantify the risk indicators. Assuming the capacity of sample value X_i(i =1, 2, ... , n) is N, the specific calculation steps for the inverse cloud generator are as follows:

(1)
Input: sample value X_i(i =1, 2, ... , n);
(2)
Output: a cloud model for qualitative concepts of reaction(E_x, E_n, H_e);
(3)
Calculation: according to sample data X_i, calculate sample mean $\bar{X}$ , sample variance S², expected value E_x, entropy E_n, and super entropy H_e.

3.1.4 Establishment of efficacy function

The efficacy function refers to the degree of quantification of expectations determined by calculating the efficacy coefficient, and the upper and lower limits of its index range represent its metric guidelines. And the efficacy function coefficient U_ij is calculated as follows:

\begin{matrix} U_{ij} = \\ {\begin{matrix} (E_{xij} - B_{ij}) / (A_{ij} - B_{ij}), Has positive effects \\ (A_{ij} - E_{xij}) / (A_{ij} - B_{ij}), Has negative effects \end{matrix} \end{matrix}

In the formula, A_ij and B_ij represent the upper and lower limits of the order parameter scoring. E_xij represents the quantitative expected value of the j-th factor under the i-th factor of the shallow-buried excavation construction risk of subway tunnels. U_ij represents the coefficient of the efficacy function, U_ij∈(0, 1), when U_ij tends to 0 indicating a lower degree of consistency between the indicators and the target value, and U_ij tends to 1 indicating a higher degree of consistency between the indicators and the target value. Next, calculate the orderly contribution degree of order parameters in each subsystem to the entire system:

U_{i} = \sum_{j = 1}^{m} ω_{ij} U_{ij}

In the formula, U_i represents the orderly contribution degree, and ω_ij represents the combined weight.

3.1.5 Determination of coupling degree function

According to the above calculation formula, assuming that the number of subsystems participating in coupling in the system is m, the coupling degree model of the system is as follows:

C_{m} = {[(u_{1} \cdot u_{2} \cdot \dots \cdot u_{m}) / (\prod (u_{i} + u_{j}))]}^{1 / m}

In the equation, C_m∈ [0, 1] represents the coupling strength. According to the classification level of coupling states in physics: when C_m =0, it indicates the weakest level of coupling strength; if C_m∈(0, 0.3], the coupling strength is at a low level; if C_m∈(0.3, 0.7], the coupling strength is at a moderate level; if C_m∈(0.7, 1), the coupling strength is at a high level; if C_m =1, the coupling strength is at its strongest level.

3.2 Construction of SD simulation system model

The simulation model of system dynamics primarily considers the object of study as a system, and through a combination of qualitative and quantitative methods, models, simulates, and predicts the system with the goal of designing reasonable strategies to improve the system’s behavior. This model suggests that a system is not simply a simple accumulation of its constituent units. With the inflow of external information, the system may maintain dynamic equilibrium or undergo various complex variations. Therefore, this approach emphasizes the feedback of constituent units on the system. Before establishing the system dynamics model, it is necessary to clarify what specific issues the model aims to address. Determine the system boundaries based on the research objectives, analyze the relationships between various risk factors in the research system, create a causal diagram, and specify the variable codes for fluid flow rate indicators. Subsequently, establish the mathematical relationships between variables within the system and construct an SD simulation model. The next step involves dynamic simulation and analysis of the system using Vensim PLE to investigate how different sensitivities of related variables within the system affect the risk level of the simulation system. Finally, based on the specific conditions of the simulated system, propose targeted measures to reduce the level of safety risks within the system.

3.2.1 Determination of system boundaries and construction of causal diagram

According to the above, this paper conducts a simulation study on the risk coupling of human and material subsystems in the shallow-buried excavation construction of subway tunnels. The system boundary of the system dynamics simulation study is the human risk subsystem, the material risk subsystem, and various risk factors in the safety system of shallow-buried excavation construction of subway tunnels. According to the established risk assessment index system for shallow-buried excavation construction of subway tunnels, combined with the analysis of human-material subsystem risk coupling, the causality diagram of human-material risk coupling is drawn, as shown in Fig. 1.

Fig. 1

Causal relationship diagram of human-material risk coupling.

3.2.2 Determination of fluid flow rate index for simulation system

Based on the causal diagram, the state variables, rate variables, auxiliary variables, and constants of the human-material risk coupling system are determined. The mathematical expectation of the inverse cloud generator serves as the initial value for the state variable indicators, while the coupling values calculated by the coupling model are used as the risk coupling coefficients introduced into the variable set to enhance its completeness. It should be noted that the values of the rate variables in the variable set are not only related to the risk factors causing coupling effects but are also influenced by the degree of coupling. The establishment of fluid flow rate indicators is outlined in Table 2.

Table 2
Code for various fluid flow rate Indices

Types Variable code

State variables L(t) LR(t) LW(t) LR-1(t)

LR-2(t) LR-3(t) LR-4(t) LR-5(t)

LR-6(t) LW-1(t) LW-2(t) LW-3(t)

LW-4(t) LW-5(t) LW-6(t) LW-7(t)

LW-8(t) LW-9(t)

Rate variables RR-1 RR-2 RR-3 RR-4

RR-5 RR-6 RW-1 RW-2

RW-3 RW-4 RW-5 RW-6

RW-7 RW-8 RW-9

Constants CR1-R3 CR5-R3 CR5-R1 CR2-R1

CR1-R4 CR2-R6 CR1-R6 CR4-R6

CW2-W4 CW7-W4 CW7-W3 CW2-W3

CW4-W8 CW2-W8 CW2-W5 CW9-W6

CR4-W4 CR6-W4 CR6-W7 CR6-W3

CR4-W3 CR6-W8 CR6-W5 CR6-W6

CR6-W9

Auxiliary variables RYFXZ WDFXZ

Types	Variable code
State variables	L(t)	LR(t)	LW(t)	LR-1(t)
	LR-2(t)	LR-3(t)	LR-4(t)	LR-5(t)
	LR-6(t)	LW-1(t)	LW-2(t)	LW-3(t)
	LW-4(t)	LW-5(t)	LW-6(t)	LW-7(t)
	LW-8(t)	LW-9(t)
Rate variables	RR-1	RR-2	RR-3	RR-4
	RR-5	RR-6	RW-1	RW-2
	RW-3	RW-4	RW-5	RW-6
	RW-7	RW-8	RW-9
Constants	CR1-R3	CR5-R3	CR5-R1	CR2-R1
	CR1-R4	CR2-R6	CR1-R6	CR4-R6
	CW2-W4	CW7-W4	CW7-W3	CW2-W3
	CW4-W8	CW2-W8	CW2-W5	CW9-W6
	CR4-W4	CR6-W4	CR6-W7	CR6-W3
	CR4-W3	CR6-W8	CR6-W5	CR6-W6
	CR6-W9
Auxiliary variables	RYFXZ	WDFXZ

3.2.3 Model parameter assignment and equation formulation

Based on the establishment of each fluid flow rate index, combined with the construction risk characteristics of shallow-buried excavation, the flow-stock model equations for human-material risk coupling are established as shown below:

RR - j = (\sum C_{m} \cdot LR - k) \cdot φ

RW - j = (\sum C_{m} \cdot LW - k) \cdot φ

LR - j = INTEG (RR - j, P_{ij})

LW - j = INTEG (RW - j, P_{ij})

In the equation, RR - j and RW - j are the rate variables of the factors in the human risk system and the material risk system, respectively. LR - j and LW - j are the risk levels of the factors in the human risk system and the material risk system, respectively. LR - k and LW - k are the cause-level variables of LR - j and LW - j, respectively, and C_m is the corresponding risk coupling coefficient. P_ij is the initial level value of each secondary risk indicator. φ is the impact coefficient, which is determined in this paper based on the collected raw data and the opinions of experts in related fields.

RYFXZ = \sum ω_{ij} \cdot RR - j

WDFXZ = \sum ω_{ij} \cdot RW - j

LR (t) = INTEG (RYFXZ, P_{i})

LW (t) = INTEG (WDFXZ, P_{i})

In the equation, RYFXZ and WDFXZ are rate variables corresponding to human risk factors and material risk factors, respectively. LR (t) and LW (t) are the risk levels of human risk factors and material risk factors, respectively. ω_ij is the combined weight of each secondary risk indicator, and P_i is the initial level value of each primary risk indicator.

\begin{matrix} L (t) = [ω_{i} / (ω_{i} + ω_{j})] \\ \cdot LR (t) + [ω_{j} / (ω_{i} + ω_{j})] \cdot LW (t) \end{matrix}

In the equation, L (t) is the overall risk level of the human-material coupling system, ω_i is the combined weight of human risk factors, and ω_j is the combined weight of material risk factors.

3.2.4 Building SD simulation system model (flow-stock diagram)

Based on the causal relationship diagram, established fluid flow rate index codes, and model equations, the flow-stock diagram was constructed using Vensim PLE software. It represents the risk-coupling simulation system model for subway tunnel shallow-buried excavation involving humans and materials, as depicted in Fig. 2. Using this model as a foundation, simulations were conducted, involving adjustments to indicator variables and simulation duration, followed by analysis of the simulation results.

Fig. 2

SD simulation system model for human-material risk coupling.

4 Example analysis

4.1 Project overview

The East Square Station of Chengdu Metro Line 2 is located beneath the intersection of the East Fifth Section of the Third Ring Road and a planned road in Chengdu, Sichuan Province, China. It is arranged in an east-west direction, with the west end connecting to the Shahebao East Square section and the east end connecting to the East Square Donghong Road section. The station’s underground excavation section crosses the Third Ring Road, with a length ranging from YDK39 + 971.70 to YDK40 + 048.30, a total width of 23.78 meters, and a total length of 160 meters. The excavation section is divided into two tunnels, each 80 meters long. The main tunnel consists of two sections, each with a height of 9.3 meters and a width of 9.4 meters, forming a horseshoe-shaped tunnel, with two 4-meter-wide connecting passages. The construction of the platform tunnel adopts the CRD method, while the connecting passages adopt the short bench method. Based on the established coupling degree model and system dynamics simulation model, a dynamic simulation study is conducted on the construction safety risks of the underground excavation section of Chengdu Metro Line 2. By adjusting the coupling coefficients and simulation duration appropriately, the changes in the risk level of the coupling system are analyzed, and targeted recommendations are proposed based on the analysis results.

4.2 Application of coupling degree model

4.2.1 Calculation of indicator weights

Fifteen experts closely related to the topic of this study are invited to score using a questionnaire (the experts’ units: metro groups, survey units, construction units, universities, and research institutions). Ten pieces of raw data are obtained through the steps of questionnaire distribution, collection, and screening. With the help of MATLAB, each judgment matrix is calculated to get the preliminary relevant weights, the validity of the expert judgment is tested, and the unreasonable values are eliminated and re-scored. According to the steps for calculating the weights of indicators, the weights of the combination of indicators at all levels are obtained as shown below.

(1)
Combination weight values ω₁ ∼ ω₄: 0.2446, 0.3878, 0.1702, 0.1974.
(2)
Combination weight values ω₁₁ ∼ ω₁₆: 0.1792, 0.1554, 0.1397, 0.1812, 0.0968, 0.2477.
(3)
Combination weight values ω₂₁ ∼ ω₂₉: 0.1203, 0.1428, 0.0916, 0.2257, 0.0641, 0.0744, 0.1197, 0.1082, 0.0532.
(4)
Combination weight values ω₃₁ ∼ ω₃₈: 0.1542, 0.1495, 0.0773, 0.1416, 0.1259, 0.1054, 0.1507, 0.0954.
(5)
Combination weight values ω₄₁ ∼ ω₄₇: 0.2081, 0.1590, 0.1183, 0.1075, 0.1727, 0.0922, 0.1422.

4.2.2 Relevant calculations of inverse cloud model

After determining the combined weights of the risk indicators, the actual numerical characteristic values of each risk indicator were calculated using the inverse cloud model. In order to evaluate the risk factors in the shallow-buried excavation process of subway tunnels more objectively and reasonably, reference was made to the “Code for Risk Management of Urban Rail Transit Underground Engineering Construction” (GB 50652-2011) issued by the Ministry of Housing and Urban-Rural Development of China. The risk level of the excavation section of Chengdu Metro Line 2 tunnels was delineated, with risk levels categorized into five levels from low to high. The definitions of risk levels for each level are presented in Table 3.

Table 3
Definition of construction safety risk classification

Risk level Level range Principles of disposal

Level I 0, 20) Mild risk, normal construction.

Level II 20, 40) Low risk, risk defense system can be implemented normally.

Level III 40, 60) Moderate risk, acceptable when conditions permit, but must be monitored to prevent escalation of the risk.

Level IV 60, 80) High risk, effective measures should be taken, and the cost of implementing the measures should be lower than the losses that would occur if the risk occurs.

Level V 80, 100) Extremely high risk, immediate control measures should be taken to reduce the risk, and the risk should be reduced to at least Level II.

Risk level	Level range	Principles of disposal
Level I	0, 20)	Mild risk, normal construction.
Level II	20, 40)	Low risk, risk defense system can be implemented normally.
Level III	40, 60)	Moderate risk, acceptable when conditions permit, but must be monitored to prevent escalation of the risk.
Level IV	60, 80)	High risk, effective measures should be taken, and the cost of implementing the measures should be lower than the losses that would occur if the risk occurs.
Level V	80, 100)	Extremely high risk, immediate control measures should be taken to reduce the risk, and the risk should be reduced to at least Level II.

According to the scoring criteria in Table 3, employing the Delphi method to invite 15 experienced engineering experts to conduct a questionnaire survey. The experts rated the risk situation of the project’s secondary indicators by collecting on-site data, engineering information, and conducting interviews with relevant personnel. Using the inverse cloud model to calculate the experts’ ratings, if the super-entropy H_e is a complex number, it indicates that the expert’s rating is unreasonable, and a re-rating of the risk indicators is necessary. After multiple rounds of expert ratings, the numerical characteristics (E_x, E_n, H_e) of each risk indicator are obtained, as shown in Table 4.

Table 4

Numerical characteristics of various risk indicators

Index	Expert scoring of inverse cloud model															E _x	E _n	H _e
C11	35	28	30	37	24	33	45	35	20	25	36	30	22	32	38	31.3333	6.7400	0.4883
C12	18	20	15	12	20	27	18	10	15	22	14	16	20	15	12	16.9333	4.4228	0.2773
C13	25	38	32	28	22	30	20	28	25	20	18	22	30	25	24	25.8000	5.2138	0.9939
C14	32	30	27	40	25	33	28	30	26	35	27	25	25	20	28	28.7333	4.6122	1.5381
C15	38	28	34	30	35	42	25	33	30	46	35	38	27	30	28	33.2667	5.8711	0.4105
C16	25	28	26	35	30	25	40	38	30	24	26	30	32	25	20	28.9333	5.4255	0.8797
C21	22	25	30	27	24	33	35	28	25	20	32	35	46	41	25	29.8667	7.1745	0.7121
C22	30	22	18	28	25	24	35	32	20	22	40	28	25	20	26	26.3333	5.8488	1.4739
C23	28	30	35	31	25	30	35	28	20	22	32	30	26	27	22	28.0667	4.4339	0.8322
C24	30	38	35	42	50	40	32	38	45	44	53	30	36	40	46	39.9333	6.7735	1.2135
C25	35	38	25	35	30	27	24	26	28	35	54	30	40	42	38	33.8000	7.7873	1.8404
C26	45	48	42	50	34	44	40	47	48	52	50	46	43	52	42	45.5333	4.8016	0.9621
C27	25	30	36	35	32	40	30	34	28	35	39	45	36	38	40	34.8667	5.0467	1.4434
C28	47	42	38	35	30	39	44	45	43	35	35	40	42	40	38	39.5333	4.4674	0.7714
C29	18	15	23	25	15	12	20	18	14	17	16	15	10	12	14	16.2667	3.9103	1.1607

4.2.3 Calculation of human-material risk system coupling value

Using the efficacy function and coupling function, the coupling risk factor values of the “Human” and “Material” coupling risk system are calculated. Taking C11 and C13 in the human system as examples, the coupling value between these two risk factors is calculated. Here, E_xij represents the risk expectation value calculated using the inverse cloud model; A_xij and B_xij are the upper and lower limits of the risk expectation, with values of 100 and 0. The specific process is as follows:

\begin{matrix} U_{11} = (E_{x 11} - B_{11}) / (A_{11} - B_{11}) \\ = (31.3333 - 0) / (100 - 0) = 0.3133 \\ U_{13} = (E_{x 13} - B_{13}) / (A_{13} - B_{13}) \\ = (25.8000 - 0) / (100 - 0) = 0.2580 \\ C_{11 - 13} = \sqrt{(U_{11} \cdot U_{13}) / {(U_{11} + U_{13})}^{2}} = 0.4976 \end{matrix}

Similarly, the coupling values of other risk factors in the “human-material” risk system can be obtained, as shown in Table 5.

Table 5
Coupling value of risk factors

Coupling factors Coupling Value Coupling factors Coupling Value

CR1-R3 0.4976 CW2-W8 0.4899

CR5-R3 0.4960 CW2-W5 0.4961

CR5-R1 0.4998 CW9-W6 0.4404

CR2-R1 0.4772 CR4-W4 0.4933

CR1-R4 0.4995 CR6-W4 0.4936

CR2-R6 0.4826 CR6-W7 0.4978

CR1-R6 0.4996 CR6-W3 0.4999

CR4-R6 0.5000 CR4-W3 0.5000

CW2-W4 0.4894 CR6-W8 0.4940

CW7-W4 0.4989 CR6-W5 0.4985

CW7-W3 0.4971 CR6-W6 0.4874

CW2-W3 0.4997 CR6-W9 0.4800

CW4-W8 0.5000

Coupling factors	Coupling Value	Coupling factors	Coupling Value
CR1-R3	0.4976	CW2-W8	0.4899
CR5-R3	0.4960	CW2-W5	0.4961
CR5-R1	0.4998	CW9-W6	0.4404
CR2-R1	0.4772	CR4-W4	0.4933
CR1-R4	0.4995	CR6-W4	0.4936
CR2-R6	0.4826	CR6-W7	0.4978
CR1-R6	0.4996	CR6-W3	0.4999
CR4-R6	0.5000	CR4-W3	0.5000
CW2-W4	0.4894	CR6-W8	0.4940
CW7-W4	0.4989	CR6-W5	0.4985
CW7-W3	0.4971	CR6-W6	0.4874
CW2-W3	0.4997	CR6-W9	0.4800
CW4-W8	0.5000

4.3 Simulation application of system dynamics models

4.3.1 System simulation

Based on the SD simulation system model built, the simulation time boundary selects the construction period of Chengdu Metro Line 2 for 8 months (construction time for shallow-buried excavation), and the simulation step is 1 month. Based on the establishment of the fluid flow rate index in the simulation system, the relevant data results calculated above are incorporated into the SD simulation model. The relevant data and corresponding indicator codes are shown in Table 6 (Initial value: the expected value E_x of expert scores calculated by the inverse cloud model; Assignment: the coupling values of risk factors calculated by the efficacy function and coupling function).

Table 6
Values of relevant variables

Variable code Initial value Variable code Assignment

LR-1(t) 31.3333 CR1-R3 0.4976

LR-2(t) 16.9333 CR5-R3 0.4960

LR-3(t) 25.8000 CR5-R1 0.4998

LR-4(t) 28.7333 CR2-R1 0.4772

LR-5(t) 33.2667 CR1-R4 0.4995

LR-6(t) 28.9333 CR2-R6 0.4826

LW-1(t) 29.8667 CR1-R6 0.4996

LW-2(t) 26.3333 CR4-R6 0.5000

LW-3(t) 28.0667 CW2-W4 0.4894

LW-4(t) 39.9333 CW7-W4 0.4989

LW-5(t) 33.8000 CW7-W3 0.4971

LW-6(t) 45.5333 CW2-W3 0.4997

LW-7(t) 34.8667 CW4-W8 0.5000

LW-8(t) 39.5333 CW2-W8 0.4899

LW-9(t) 16.2667 CW2-W5 0.4961

LR(t) 27.4441 CW9-W6 0.4404

LW(t) 33.8079 CR4-W4 0.4933

CR6-W4 0.4936

CR6-W7 0.4978

CR6-W3 0.4999

CR4-W3 0.5000

CR6-W8 0.4940

CR6-W5 0.4985

CR6-W6 0.4874

CR6-W9 0.4800

Variable code	Initial value	Variable code	Assignment
LR-1(t)	31.3333	CR1-R3	0.4976
LR-2(t)	16.9333	CR5-R3	0.4960
LR-3(t)	25.8000	CR5-R1	0.4998
LR-4(t)	28.7333	CR2-R1	0.4772
LR-5(t)	33.2667	CR1-R4	0.4995
LR-6(t)	28.9333	CR2-R6	0.4826
LW-1(t)	29.8667	CR1-R6	0.4996
LW-2(t)	26.3333	CR4-R6	0.5000
LW-3(t)	28.0667	CW2-W4	0.4894
LW-4(t)	39.9333	CW7-W4	0.4989
LW-5(t)	33.8000	CW7-W3	0.4971
LW-6(t)	45.5333	CW2-W3	0.4997
LW-7(t)	34.8667	CW4-W8	0.5000
LW-8(t)	39.5333	CW2-W8	0.4899
LW-9(t)	16.2667	CW2-W5	0.4961
LR(t)	27.4441	CW9-W6	0.4404
LW(t)	33.8079	CR4-W4	0.4933
		CR6-W4	0.4936
		CR6-W7	0.4978
		CR6-W3	0.4999
		CR4-W3	0.5000
		CR6-W8	0.4940
		CR6-W5	0.4985
		CR6-W6	0.4874
		CR6-W9	0.4800

Table 7

Coupling coefficient adjustment plan

Adjustment plan and coupling Types	Simulation code	Adjustment range
Plan 1: Homogeneous coupling (Human system)	CR1-R3	Increase by 50%
	CR5-R3	Increase by 50%
	CR5-R1	Increase by 50%
	CR2-R1	Increase by 50%
	CR1-R4	Increase by 50%
	CR2-R6	Increase by 50%
	CR1-R6	Increase by 50%
	CR4-R6	Increase by 50%
Plan 2: Homogeneous coupling (Material system)	CW2-W4	Increase by 50%
	CW7-W4	Increase by 50%
	CW7-W3	Increase by 50%
	CW2-W3	Increase by 50%
	CW4-W8	Increase by 50%
	CW2-W8	Increase by 50%
	CW2-W5	Increase by 50%
	CW9-W6	Increase by 50%
Plan 3: Heterogeneous coupling (Human-Material system)	CR4-W4	Increase by 50%
	CR6-W4	Increase by 50%
	CR6-W7	Increase by 50%
	CR6-W3	Increase by 50%
	CR4-W3	Increase by 50%
	CR6-W8	Increase by 50%
	CR6-W5	Increase by 50%
	CR6-W6	Increase by 50%
	CR6-W9	Increase by 50%

By running the software, the trend of construction risk level development and the corresponding risk level values for each step in the “human-material” risk coupling system can be visually observed, as shown in Fig. 3. Through the simulation, we can also get the trend of each systemic risk level and the rate variable that affects the change of each systemic risk level in the “human-material” risk coupling system, as shown in Figs. 4–6. For specific analysis results, please refer to Section 4.4.1 (1).

Fig. 3-4

The trend of risk level changes in human-material coupling systems and their subsystems.

Fig. 5-6

Key rate variables affecting changes in LR(t) or LW(t) risk levels.

4.3.2 Adjustment of coupling coefficient variable changes

In the modeling and simulation described above, there are multiple complex coupling relationships among the “human-material” coupled system. To study the key risk factors affecting the degree of coupling in the “human-material” risk system during shallow-buried tunneling construction in subway tunnels, the coupling coefficients in the system are adjusted. Only one risk coupling coefficient is adjusted each time, while the values of other coupling coefficients remain unchanged, and the adjustment magnitude is 50% each time.

There are three main adjustment plans as follows: plan 1 (adjusting the risk coupling coefficient for homogeneous human system); plan 2 (adjusting the risk coupling coefficient for homogeneous material system); plan 3 (adjusting the risk coupling coefficient for heterogeneous human-material system).

Adjusting according to each of the three plans, the trend change in the risk level of the coupled human-material system is obtained as shown in Figs. 7–9. For specific analysis results, please refer to Section 4.4.1 (2).

Fig. 7

Change trend of the risk level of human-material coupling in plan 1.

Fig. 8

Change trend of the risk level of human-material coupling in plan 2.

Fig. 9

Change trend of the risk level of human-material coupling in plan 3.

4.3.3 Adjustment of simulation duration changes

To further examine the influence of different coupling factors on the risk level of the human-material coupling system, we selected coupling coefficients that demonstrate a significant impact on the level of human-material coupling risk. These coefficients include: CR1-R6, CR4-R6, CW7-W4, CW2-W4, CR6-W4, and CR4-W4. To adjust these six different types of risk coupling coefficients, we increased them by 50% and extended the simulation duration. The adjustment plan is shown in Table 8.

Table 8
Adjustment scheme for simulation duration of coupled systems

Coupling type Simulation code Adjustment range Simulation duration

Homogeneous coupling (Human system) CR1-R6 Increase by 50% Increase by 7 months

CR4-R6 Increase by 50% Increase by 7 months

Homogeneous coupling (Material system) CW7-W4 Increase by 50% Increase by 7 months

CW2-W4 Increase by 50% Increase by 7 months

Heterogeneous coupling (Human-Material system) CR6-W4 Increase by 50% Increase by 7 months

CR4-W4 Increase by 50% Increase by 7 months

Coupling type	Simulation code	Adjustment range	Simulation duration
Homogeneous coupling (Human system)	CR1-R6	Increase by 50%	Increase by 7 months
	CR4-R6	Increase by 50%	Increase by 7 months
Homogeneous coupling (Material system)	CW7-W4	Increase by 50%	Increase by 7 months
	CW2-W4	Increase by 50%	Increase by 7 months
Heterogeneous coupling (Human-Material system)	CR6-W4	Increase by 50%	Increase by 7 months
	CR4-W4	Increase by 50%	Increase by 7 months

The adjustment plan involved extending the original simulation time from 8 months to 15 months while keeping the time step unchanged. Additionally, the risk system in its original state was retained as a reference for comparison. The simulation was run seven times, and the results are shown in Fig. 10. For specific analysis results, please refer to Section 4.4.1 (3).

Fig. 10

The trend of human-material coupling risk level changes after adjusting the coupling coefficient and simulation duration.

4.4 Analysis of simulation results and suggestions

4.4.1 Result analysis

Based on the simulation results of the “human-material” coupling risk system of Chengdu Metro Line 2 mentioned above, it can be concluded that:

(1) The system’s risk level under the initial state conditions (Figs. 3 to 6).

In practical construction projects, the safety level is influenced by the coupling relationship between various secondary risk indicators. By determining the numerical formulas for coupling coefficients and other variables, the risk level of the “human-material” coupling system gradually increases from the first to the eighth month. The simulated initial risk value in the first month is 31.35, indicating a level II low risk. The risk level value in the sixth month reaches 41.36 under the influence of coupling, surpassing the low-risk threshold. In the final month of simulation, the coupling risk level reaches 45.15, indicating a level III moderate risk.

From the trend chart of the risk system of each primary indicator obtained through simulation, it can be observed that the growth rate of material-related risk level exceeds that of human-related risk level. In the fourth month of simulation, the risk level of the material-related indicator reaches level III moderate risk, indicating that the secondary indicators related to materials have a significant influence on the overall risk safety level.

The rate charts analyzing the impact on the risk variation of each primary indicator demonstrate that the increasing trends of risk levels in violation of personnel operations (RR-6), lack of safety risk awareness (RR-1), initial support structure defects (RW-4), inadequate waterproof board installation (RW-8), and unreasonable construction of inverted arch (RW-3) are evident in the changes of primary risk indicators, and they possess irreversible characteristics. Over the short-term duration of the project, it can be observed that the construction safety defense mechanism of the Chengdu Metro Line 2 tunnel excavation project has a certain capability to resist risks. However, considering the irreversibility of risk coupling and the actual construction process of the project, the overall risk level is continuously increasing.

(2) The system’s risk level after adjusting the coupling coefficients (Figs. 7 to 9).

Adjusting the coupling coefficients of different types of risks will increase the “human-material” coupled risk level. A 50% increase in the coupling coefficient of risk reveals that insufficient safety risk awareness combined with personnel violation operation (CR1-R6) and the coupling coefficient of substandard professional technical level linked to personnel violation operation (CR4-R6) significantly contribute to the coupled risk level of human-material within homogeneous human risk factors coupling.

In the coupling of risk factors for homogeneous material, the adjustment of the coupling coefficient between inadequate concrete maintenance and initial support structure defects (CW7-W4) and the coupling coefficient between substandard construction material quality and initial support structure defects (CW2-W4) has a significant impact on the coupled risk level of human-material. It should be noted that, whether in homogeneous human factors or homogeneous material factors, after adjusting the coupling coefficients of secondary indicators, the coupled risk level of human-material gradually reaches Level III, indicating a moderate risk, starting from early May.

In the coupling coefficient of heterogeneous human-material factors, after increasing the coupling coefficient between personnel violation operation and initial support structure defects (CR6-W4), as well as the coupling coefficient between substandard professional technical level and initial support structure defects (CR4-W4) by 50%, the coupled risk level of human-object reaches 50, which is in the middle stage of Level III moderate risk. This indicates that adjustments and changes in the coupling of heterogeneous human-material factors have a significant impact on the safety level of the “human-material” coupled risk system.

(3) The situation of system risk level after adjusting the simulation duration (Fig. 10).

Selecting the relatively significant risk coupling coefficients among different coupling types, upon adjusting one risk coupling coefficient at a time, the duration of system simulation is extended to 15 months. Under these conditions, the risk level of human-material coupling consistently remains at Level IV, indicating a high risk level.

Among the heterogeneous human-material coupling types, the adjustment of the coupling coefficient between personnel violation operation and initial support structure defects (CR6-W4) has the greatest impact on the coupled risk level between humans and materials.

Adjusting the risk coefficients of other coupling types also significantly affects the coupled risk level between humans and materials, ranked in ascending order of impact as follows: CR4-R6, CR1-R6, CW2-W4, CR6-W4, and CW7-W4. From a systemic risk perspective, when the construction duration is prolonged, the original risk defense mechanism of the project fails to withstand the strong influence of coupled risks, leading to a high likelihood of construction safety accidents.

4.4.2 Suggestions

In summary, during the shallow-buried excavation construction process of metro projects, risk factors exhibit initially low impact and limited scope, thus failing to breach the defense system of metro project construction risk management. However, as construction progresses, risk factors may slowly escalate over time and even propagate to other risk factors within the system, thereby expanding the overall risk of the safety system. To mitigate the overall system risk, the following recommendations are proposed regarding key risk factors in the human-material coupling risk system of the case project:

(1)
Emphasize the importance of employee safety education and training, instill a safety production mindset, and conduct regular construction risk safety drills to enhance employees’ awareness of safety production.
(2)
Evaluate the experience, technical proficiency, and qualification credentials of construction personnel and enhance their professional technical training to ensure their expertise meets job requirements.
(3)
Establish a qualified, experienced, and independent quality inspection department responsible for inspecting the safety and quality aspects of materials, mechanical equipment, and completed projects to minimize risk coupling pathways.
(4)
Strengthen monitoring of unsafe behaviors among construction personnel, promptly correct any violations, and assign additional on-site management personnel for guidance to reduce the probability of risk coupling.
(5)
In cases where effective management is lacking during initial support construction, it is necessary to enhance stability inspections. Upon detecting abnormal deformations in the support system, shorten the measurement intervals, identify the causes of the abnormalities, and promptly reinforce the support to weaken the impact of risk factor transmission on subsequent construction.

5 Conclusion

This paper conducts a relevant study on the theory of construction risks associated with shallow-buried excavation in subway tunnel projects. It analyzes the mechanisms and relationships of risk factors in shallow-buried excavation construction from a coupling perspective, establishing a construction risk coupling evaluation index system based on human, material, management, and environmental factors. The paper combines the Analytic Hierarchy Process (AHP), entropy weight method, inverse cloud model, efficacy function, and coupling degree function to construct a risk coupling model. Furthermore, employing principles from system dynamics theory, causal diagrams depicting the coupling paths of various risk factors are drawn, analyzing the coupling effects of homogeneous single factors and heterogeneous dual factors, and establishing flow-stock diagrams for human-material systems. Lastly, dynamic simulation studies are conducted on specific cases to obtain the human-material coupling risk level in shallow-buried excavation construction safety systems. Key coupling risks are analyzed by adjusting the coupling coefficients of different risk coupling types and simulation durations. This study reveals the impact of the coupling effects among various risk sources in the safety system of subway tunnel shallow-buried excavation construction on the overall system safety level. The research aids project units in evaluating the safety risk levels of risk systems and their subsystems, identifying, preventing, and controlling safety risks within the system, thereby reducing the occurrence of unsafe accidents, lowering accident rates, and mitigating disaster losses.

Footnotes

Acknowledgments

This work has been partially supported by two projects: the research and development project of the ministry of housing and urban rural development (project number: 2020-K-129); the research project of philosophy and social sciences in Hubei province colleges and universities (project number: 21Y039).

References

Zhang

Z.X.

Liu

Huang

, et al., Three-dimensional finite-element analysis on ground responses during twin-tunnel construction using the URUP method, Tunnelling and Underground Space Technology58 (2016), 133–146.

Wang

M.S.

, Outline of tunnel construction by means of method of undercutting with shallow overburden, Tunnel Construction26(05) (2006), 1–4.

Cui

J.J.

Cui

X.Q.

, Risk control and management of subway engineering construction, Construction Technology40(10) (2011), 1–9.

Dong

Y.Z.

Xiao

Wang

, On safety risk management in shallow tunneling method metro tunnel building, Value Engineering33(21) (2014), 126–128.

Hou

G.Y.

Liu

, et al., Vulnerability analysis of the subway construction safety system with coupled multiple risk factors, China Civil Engineering Journal55(02) (2022), 111–119.

Voznesensky

A.A.

Mazein

S.V.

, Studying the variation of rotor pressing forces and horizontal soil pressure during shield tunneling, Journal of Mining Science48(02) (2012), 233–240.

Peila

, Soil conditioning for EPB shield tunneling, Ksce Journal of Civil Engineering18(03) (2014), 831–836.

Q.F.

Wang

Z.P.

L.F.

, et al., Construction risk evaluation of poor geological channels based on cloud model-improved AHP–matter–element theory, Sustainability13(17) (2021), 9632.

Wang

Y.Q.

Wang

J.B.

, et al., Risk assessment and risk control measures of tunnel construction techniques, Highway60(06) (2015), 259–263.

10.

Einstein

H.H.

, Risk and risk analysis in rock engineering, Tunneling and Underground Space Technology11(02) (1996), 141–155.

11.

Einstein

H.H.

Grasso

, et al., Decision aids in tunneling, World Tunneling4 (1998), 157–159.

12.

Smith

R.J.

, Risk management for underground projects: Cost-saving techniques and practices for owners, Tunnelling and Underground Space Technology7(02) (1992), 109–117.

13.

Xie

D.S.

Qian

Q.H.

Rong

X.L.

, Risk management in rail transit construction, Journal of Civil Engineering and Management29(01) (2012), 61–67.

14.

Zhou

L.G.

Wang

H.X.

, Evaluation and control on environmental safety risk in construction of urban metro and underground engineering, Railway Investigation and Surveying (06) (2007), 91–94.

15.

Einstein

H.H.

, Risk assessment in rock engineering, New Generation Design Codes For Geotechnical Engineering Practice —Taipei (2015).

16.

Ding

L.Y.

H.L.

, et al., Safety risk identification system for metro construction on the basis of construction drawings, Automation in Construction27 (2012), 120–137.

17.

Zhou

Z.P.

Liu

H.N.

, Mitigating subway construction collapse risk using Bayesian network modeling, Automation in Construction143 (2022), 104541.

18.

Liu

Zhao

T.S.

Zhang

Y.J.

, et al., Analysis of risk factors and countermeasures for metro shield construction, China Safety Science Journal27(10) (2017), 130–136.

19.

Franco

V.H.

Gitirana

G.DeF.N.

Deassis

A.P.

, Probabilistic assessment of tunneling-induced building damage, Computers and Geotechnics113 (2019), 103097.1–103097.15.

20.

Yan

Gao

Elzarka

, et al., Risk assessment for construction of urban rail transit projects, Safety Science118 (2019), 583–594.

21.

Zhou

S.S.

Zhang

X.J.

, Metro construction risk assessment based on PPC-D-S evidence theory, Modern Tunnelling Technology58(01) (2021), 75–83.

22.

Zhu

Y.M.

, Study on construction technology and risk of shallow-buried undercut subway tunnel, Henan Science and Technology39(29) (2020), 127–129.

23.

Xue

H.P.

, Discussion on collapse accident analysis and risk control of the shallow excavated subway station with large section, Chinese Journal of Underground Space and Engineering8(S2) (2012), 1788–1790+1795.

24.

Feng

J.L.

, Analysis on construction control points of urban shallow buried underground tunnel, Construction & Design for Engineering (07) (2022), 159–161.

25.

Chen

, Risk analysis of shallow-buried subway tunnels passing through high-speed railway grand bridge, Railway Investigation and Surveying49(01) (2023), 126–131.

26.

Z.Y.

H.L.

Huang

, et al., .Comprehensive risk assessment method for shallow underground tunnel construction, Journal of Railway Science and Engineering16(09) (2019), 2368–2377.

27.

Yan

Z.J.

, Fuzzy comprehensive evaluation of risk in urban subway tunneling through pile foundation of viaduct, Journal of Dalian University39(03) (2018), 21–26.

28.

Shyur

, Quantitative model for aviation safety risk assessment, Computer and Industrial Engineering54(01) (2008), 34–44.

29.

Felder

Gómez-Navarro

J.J.

Zischg

A.P.

, et al., . From global circulation to local flood loss: Coupling models across the scales, Science of the Total Environment635 (2018), 1225–1239.

30.

Fan

C.K.Y.

Zhou

, Sustainability risk in supply bases: The role of complexity and coupling, Transportation Research Part E: Logistics and Transportation Review145 (2021), 102175.

31.

Pan

Gou

Wang

Z.H.

, et al., Research on coupling degree model of safety risk system for tunnel construction in subway shield zone, Mathematical Problem in Engineering2019 (2019), 1–19.

32.

Fang

Guo

P.W.

Zhu

, et al., Coupling evolution analysis of subway tunnel construction safety risk based on N-K model, China Safety Science Journal32(06) (2022), 1–9.

33.

Liu

J.G.

Kong

Y.D.

Zhou

, et al., Methodology of supply chain risk management based on WSR theory, Journal of Systems Engineering33(03) (2018), 298–307.

34.

Wang

Q.K.

Zuo

W.W.

Q.Y.

, Engineering harmony under multi-constraint objectives: the perspective of meta-analysis, Journal of Civil Engineering and Management26(02) (2020), 131–146.