Risk Analysis and Simulation of Large Bridge Construction Based on System Dynamics

Abstract

To reduce risk incidents in large bridge construction, it is necessary to study the interaction mechanisms and dynamic changes among various risk factors during the construction of large bridges. First, the evolution mechanism of construction risks for large bridges is analyzed, and a risk factor structure system is established. Then, based on system dynamics theory, a causal loop diagram and flow–stock diagram are constructed, and system dynamics equations for each variable in the flow diagram are established to build a system dynamics model. Finally, taking a large bridge construction project as an example, the variable equations are assigned actual values, and the construction risk level is simulated and analyzed. The results show that, ➀ continuous investment in safety funds can effectively reduce the overall risk level of the system, ➁ changes in the management risk subsystem have a significant impact on the overall risk level of large bridge construction, and ➂ increasing the safety investment ratio in both the personnel risk subsystem and the management risk subsystem can effectively reduce the total risk level of the system.

1. Introduction

With the rapid growth of the national economy, China’s bridge construction industry has experienced unprecedented development. Due to the large scale and complex technical requirements of bridge projects, along with the continuous increase in spans and the introduction of new structures, materials, and technologies, bridges harbor many uncertainties and associated risk sources during construction, increasing the difficulty of risk management [1,2,3]. In recent years, reports of safety incidents during bridge construction, both domestically and internationally, have attracted significant societal attention. Therefore, to reduce construction risk incidents and effectively control project quality, it is imperative to conduct systematic research on risks during bridge construction [4,5].

Scholars both domestically and internationally have conducted in-depth studies on the safety risks of bridge construction from perspectives such as structure, schedule, and management using various methods. Feng et al. [6] proposed an enhanced Probability Density Evolution Method (PDEM) framework that considers multiple failure modes and limit states for the reliability analysis of structures. Cao et al. [7] assessed the dynamic and probabilistic seismic performances of precast, prestressed, reinforced concrete frames, taking into account the influence of the slab on the overall structural behavior during the process. Yuan Hongchuan et al. [8] evaluated the safety risks of bridge construction using an improved cloud model combined with the uncertain AHP method and set pair analysis. Yuan Jianbo et al. [9] established a safety risk assessment model for highway bridge construction using network analysis and validated its scientific rationality with construction cases. Wang Lei et al. [10] conducted a safety risk assessment of the substructures of bridges in loess mountainous gully terrain using the Analytic Hierarchy Process–Fuzzy Comprehensive Evaluation and proposed safety risk control measures. Tang Tianming et al. [11] assessed the safety risks of the Wuhan Qingshan Yangtze River Highway Bridge during construction using the LEC safety evaluation method and proposed corresponding risk control measures. Zhu Zhibao et al. [12] conducted a risk assessment of each construction unit of the Strait Bridge using the WBS-RBS method combined with fuzzy hierarchy synthesis. Pang Weiying et al. [13] established a risk evaluation index system for large-span bridge construction, then assessed the risks of Tonghai Bridge using the Analytic Hierarchy Process and grey clustering, determining its risk level.

The existing literature, employing a range of methods, has extensively covered different aspects of bridge construction risk, yielding a wealth of experience. Currently, research on the risk of large bridge construction primarily involves estimating risk values and subsequently conducting safety risk assessments based on these values, without examining the changes in system safety risk values throughout the construction process. In other words, most existing risk evaluation models are static, neglecting the impact of interactions and dynamic development among various risk factors within the risk system [14]. Commonly used risk evaluation methods are more suited to assessing static systems and exhibit certain limitations when applied to dynamic and evolving risk systems. Therefore, how to comprehensively consider the coupling relationships among various risk factors and apply a systematic, dynamic approach to the risk evaluation of large bridge construction is an urgent problem that needs to be addressed [15].

System dynamics is a discipline that analyzes and studies information feedback systems. The approach of system dynamics is to explore how to understand and solve problems through a cross-disciplinary and integrative method [16]. In dealing with complex system issues, system dynamics often employs a method that combines qualitative and quantitative analysis. It is a constructive analytical method that emphasizes the system’s structure, the mechanism of behavior generation, the expression of control, and the constraints of causality. Therefore, system dynamics is particularly suited to studying large bridge construction risk systems characterized by their complexity, dynamism, and time variability [17,18].

This paper begins by applying risk management theory to analyze the evolution mechanism of construction risks for large bridges, identify risk factors, and establish a risk factor structure system. Following this, an analysis of the identified risk factors is conducted using system dynamics theory. The paper then utilizes Vensim PLE 7.3.5 software to create causal loop diagrams and stock-and-flow diagrams for the risk system of large bridge construction, establishes system dynamics equations for each variable in the flow diagram, and constructs a system dynamics model. Finally, using a large bridge construction project as a case study, the paper assigns real-world values to the variable equations based on engineering information and data processing to simulate and assess the construction risk level of large bridges.

2. Risk Factor Analysis for Large Bridge Construction

2.1. Construction Risk Evolution Mechanism Analysis

The environment at large bridge construction sites is complex and constantly changing, with numerous uncertainties present throughout the construction process. These uncertainties contribute to a variety of risk factors. Moreover, the construction of large bridges typically involves extended timelines. Throughout these periods, the various risk factors continuously interact and evolve, making the construction process one characterized by dynamic risk changes [19,20].

According to accident causation theory, the occurrence of risk accidents in large bridge construction is primarily the result of the continuous evolution of unsafe human actions and unsafe conditions of objects under the combined effects of adverse environments and management defects. For example, during the foundation construction process of bridges, sudden changes in hydrogeological conditions may lead to alterations in construction plans and machinery, further impacting the schedule and quality [21]. The construction process of the bridge’s superstructure is complex and laborious; errors in monitoring schemes and data processing can affect structural and alignment control [22]. Construction quality defects and casualties caused by the technical level of personnel and their fatigue level will elevate the risk level of construction projects [23].

In the area of bridge seismic design, multiple advanced techniques have been introduced to enhance the structural safety of bridges. For instance, Wang et al. [24] investigated the use of Buckling-Restrained Braces (BRBs) in three-span RC bridges, demonstrating that BRBs have significant potential to improve the earthquake resistance of bridges. Furthermore, research by Kaviani et al. [25] revealed that the inclination angle of a bridge significantly affects its behavior during earthquakes, providing crucial insights for bridge design. Lastly, Vincenzo Gattulli et al. [26] applied a variety of dynamic tests to determine the dynamic properties of multi-span concrete arch bridges, thereby enhancing the model’s precision and reliability. Their findings offer essential theoretical and practical guidance for ensuring safety in bridge construction.

This expanded analysis incorporates a broader range of factors, including advanced technological applications, which can provide a more comprehensive understanding of the risks involved in large bridge construction. This approach ensures that both the dynamic nature of risk factors and the influence of innovative construction techniques are thoroughly addressed in the risk management process.

2.2. Risk Factor Identification

This paper, based on the analysis of the evolution mechanism of significant bridge construction risk and the summary of previous research results, combined with the statistics of bridge construction accidents in recent years and the requirements of industry norms and standards for the identification and categorization of construction risk factors, establishes the structure of risk factors for the construction of large bridges, as shown in Figure 1. The structural system is divided into three layers. The first layer is the total risk of large-scale bridge construction. If analyzed from the perspective of systems engineering, the entire risk of the building can be viewed as a complex risk system, which can be further divided into personnel risk, equipment and material risk, investigation and design risk, construction monitoring risk, environmental risk, and management risk, for a total of six sub-systems that constitute the second layer, and the third layer of the six risk sub-systems includes the specific risk factors, totaling 31. The set of each risk subsystem can be denoted as A = {A₁, A₂, …, A_n}, with Ai being the i-th subsystem, and the set of risk factors can be represented as Ai = {A_i1, A_i2, …, A_im}, with A_ij being the j-th risk factor in the i-th subsystem.

3. System Dynamics Modelling of Large Bridge Construction Risks

3.1. Boundary Determination and Underlying Assumptions

This paper focuses on the construction risk of large bridges as its research subject. It categorizes these risks into six subsystems, including personnel risk and its system dynamics model boundary. Based on risk factor analysis, the following modeling assumptions are established.

Hypothesis 1. 

Using large-scale bridge construction as the foundation, personnel, equipment and materials, investigation and design, construction monitoring, environment, and management are identified as endogenous variables. The analysis focuses solely on the interactions between internal factors of the system, while other variables are treated as exogenous and are excluded from consideration.

Hypothesis 2. 

Scenarios that omit consideration of system collapse due to force majeure factors, such as political unrest and earthquakes, are excluded from this analysis.

Hypothesis 3. 

While managers have partial control over the system, they are unable to completely mitigate the impact of other risk factors.

3.2. Causal Loop Diagrams and Flow Diagrams Based on System Dynamics

Based on the analysis of prominent risk factors in bridge construction, the causal relationships between each risk factor are established. A causal loop diagram is then illustrated using Vensim PLE 7.3.5 software, as depicted in Figure 2. To enhance the academic nature, readability, and logical consistency of the model, this study adopts a standardized variable-naming convention. Specifically, horizontal variables are named using uppercase letters prefixed with “S,” while rate variables are prefixed with “R.” Auxiliary variables are named using “I” as a prefix.

As seen in Figure 2, the total risk of large-scale bridge construction is the sum of six subsystem risks, including personnel risk. The causal loop diagram for significant bridge construction risk evolution contains 18 feedback loops. In Figure 2, three positive feedback loops are marked with a “+” symbol, indicating that each risk factor escalates the construction risk level through the self-reinforcing effect of these loops. Figure 2 shows 15 negative feedback loops, denoted by a “−” symbol, which suggest that the system’s risk level is mitigated and stabilized through increased safety measures. For instance, increased investment in personnel safety has led to a higher rate of certified special operators, thus reducing personnel risk. The escalation of management safety efforts has helped moderate the risk associated with large-scale bridge construction, as depicted in the causal loop diagram. The dynamic flow diagram model of the large- scale bridge construction risk system, created using Vensim PLE 7.3.5 software, is illustrated in Figure 3.

In the large bridge construction risk system dynamics model developed in this paper, there are 76 variables, comprising 6 level variables, 6 rate variables, 59 auxiliary variables, and 5 constants. The main model variables are outlined in

Table 1. Model variable description table.

S/N	Type	ID	Name	S/N	Type	ID	Name
1	Horizontal variable	S1	Personnel risk level	27	Auxiliary Variables	I15	Deficiencies in the current stage of design theory
2		S2	Equipment material risk level	28		I16	Inadequate surveys, forecasting errors
3		S3	Survey and design risk level	29		I17	Uncertainty about new materials and technologies
4		S4	Construction monitoring risk level	30		I18	Construction process program
5		S5	Environmental risk level	31		I19	Stress and line control
6		S6	Managing the level of risk	32		I20	Prestressing tensioning construction
7	Rate variables	R1	Amount of change in personnel risk level	33		I21	Construction of the closing section
8		R2	Amount of change in equipment material risk level	34		I22	Surveillance solutions
9		R3	Amount of change in level of survey and design risk	35		I23	Monitoring data feedback and processing
10		R4	Amount of change in the level of construction monitoring risk	36		I24	Complexity of bridge features
11		R5	Amount of change in the level of environmental risk	37		I25	Road traffic conditions
12		R6	Amount of change in the level of management risk	38		I26	Extreme climatic conditions
13	Auxiliary variables	I1	Total risk level for construction of large bridges	39		I27	Hydrogeological conditions
14		I2	Special operators licensed to work	40		I28	Setting up work environment
15		I3	Fatigue susceptibility of construction personnel	41		I29	Frequency of construction site safety inspections
16		I4	Safety awareness among construction workers	42		I30	Effectiveness of safety management regulations
17		I5	Proficiency in professional skills	43		I31	Reasonableness of security management structure
18		I6	Safety control of large equipment mounting and dismounting	44		I32	Investment in security management funds
19		I7	Availability of safety guards	45		I33	Implementation of safety education and training
20		I8	Repair and maintenance of equipment	46		I34	Security inputs
21		I9	Improper use and destabilization of construction plant	47		I35	Personnel security inputs
22		I10	Quality of entry of components	48		I36	Security inputs for equipment and materials
23		I11	Stacking and storage of building materials	49		I37	Survey and design safety inputs
24		I12	Bridge structure selection	50		I38	Construction monitoring security inputs
25		I13	Bridge material properties	51		I39	Safety inputs for environmental risks
26		I14	Design divorced from site	52		I40	Managing security inputs

.

3.3. Establishment of System Dynamics Equations

Let the set of weights W = {W₁, W₂, …, W_n} correspond to each set of risk subsystems A = {A₁, A₂, …, A_n} in Figure 1, with W_i being the weight of the i-th subsystem, and the set of weights Wi = {W_i1, W_i2, … W_im} correspond to the location of risk factors A_i = {A_i1, A_i2, …, A_im}, with W_ij being the value of weight of the j-th risk factor in the i-th subsystem. In the set of safety input proportions P = {P₁, P₂, …, P_n}, P_i is the proportion of inputs accounted for by the i-th subsystem. In the subsystem initial assignment set L₀ = {L₀₁, L₀₂, …, L_n}, L_i is the initial assignment of the i-th subsystem.

Based on the system dynamics, the SD equations are established as follows:

1. Total risk of large bridge construction

I₁ = S₁ × W₁ + S₂ × W₂ + S₃ × W₃ + S₄ × W₄ + S₅ × W₅ + S₆ × W₆.

2. Horizontal variable equation

(1) S₁= INTEG (R₁, L⁰₁).

(2) S₂ = INTEG (R₂, L⁰₂).

(3) S₃ = INTEG (R₃, L⁰₃).

(4) S₄ = INTEG (R₄, L⁰₄).

(5) S₅ = INTEG (R₅, L⁰₅).

(6) S₆ = INTEG (R₆, L⁰₆).

3. Rate variable equation

(1) R₁ = I₂ × W₁₁ + I₃ × W₁₂ + I₄ × W₁₃ + I₅ × W₁₄.

(2) R₂ = I₆ × W₂₁ + I₇ × W₂₂ + I₁₁ × W₂₃ + I₉ × W₂₄ + I₁₀ × W₂₅ + I₈ × W₂₆.

(3) R₃ = I₁₆ × W₃₁ + I₁₇ × W₃₂ + I₁₃ × W₃₃ + I₁₂ × W₃₄ + I₁₅ × W₃₅ + I₁₄ × W₃₆.

(4) R₄ = I₂₁ × W₄₁ + I₁₉ × W₄₂ + I₁₈ × W₄₃ + I₂₃ ×W₄₄ + I₂₂ × W₄₅ + I₂₀ × W₄₆.

(5) R₅ = I₂₈ × W₅₁ + I₂₆ × W₅₂ + I₂₄× W₅₃ + I₂₇ × W₅₄ + I₂₅ × W₅₅.

(6) R₆ = I₂₉ × W₆₁ + I₃₀ × W₆₂ + I₃₁ × W₆₃ + I₃₃ × W₆₄.

4. Auxiliary variable equations

(1) I₂ = Rate of Change in I₂ per Time Step − I₃₄ × P₁ × Conversion Rate to I₂.

(2) I₃ = Rate of Change in I₃ per Time Step − I₃₄ × P₁ × Conversion Rate to I₃.

(3) I₄ = Rate of Change in I₄ per Time Step − I₃₄ × P₁ × Conversion Rate to I₄.

(4) I₅ = Rate of Change in I₅ per Time Step − I₃₄ × P₁ × Conversion Rate to I₅.

(5) I₆ = Rate of Change in I₆ per Time Step − I₃₄ × P₂ × Conversion Rate to I₆.

(6) I₇ = Rate of Change in I₇ per Time Step − I₃₄ × P₂ × Conversion Rate to I₇.

(7) I₈ = Rate of Change in I₈ per Time Step − I₃₄ × P₂ × Conversion Rate to I₈.

(8) I₉ = Rate of Change in I₉ per Time Step − I₃₄ × P₂ × Conversion Rate to I₉.

(9) I₁₀ = Rate of Change in I₁₀ per Time Step − I₃₄ × P₂ × Conversion Rate to I₁₀.

(10) I₁₁ = Rate of Change in I₁₁ per Time Step − I₃₄ × P₂ × Conversion Rate to I₁₁.

(11) I₁₂ = Rate of Change in I₁₂ per Time Step − I₃₄ × P₃ × Conversion Rate to I₁₂.

(12) I₁₃ = Rate of Change in I₁₃ per Time Step − I₃₄ × P₃ × Conversion Rate to I₁₃.

(13) I₁₄ = Rate of Change in I₁₄ per Time Step − I₃₄ × P₃ × Conversion Rate to I₁₄.

(14) I₁₅ = Rate of Change in I₁₅ per Time Step − I₃₄ × P₃ × Conversion Rate to I₁₅.

(15) I₁₆ = Rate of Change in I₁₆ per Time Step − I₃₄ × P₃ × Conversion Rate to I₁₆.

(16) I₁₇ = Rate of Change in I₁₇ per Time Step − I₃₄ × P₃ × Conversion Rate to I₁₇.

(17) I₁₈ = Rate of Change in I₁₈ per Time Step − I₃₄ × P₄ × Conversion Rate to I₁₈.

(18) I₁₉ = Rate of Change in I₁₉ per Time Step − I₃₄ × P₄ × Conversion Rate to I₁₉.

(19) I₂₀ = Rate of Change in I₂₀ per Time Step − I₃₄ × P₄ × Conversion Rate to I₂₀.

(20) I₂₁ = Rate of Change in I₂₁ per Time Step − I₃₄ × P₄ × Conversion Rate to I₂₁.

(21) I₂₂ = Rate of Change in I₂₂ per Time Step − I₃₄ × P₄ × Conversion Rate to I₂₂.

(22) I₂₃ = Rate of Change in I₂₃ per Time Step − I₃₄ × P₄ × Conversion Rate to I₂₃.

(23) I₂₄ = Rate of Change in I₂₄ per Time Step − I₃₄ × P₅ × Conversion Rate to I₂₄.

(24) I₂₅ = Rate of Change in I₂₅ per Time Step − I₃₄ × P₅ × Conversion Rate to I₂₅.

(25) I₂₆ = Rate of Change in I₂₆ per Time Step − I₃₄ × P₅ × Conversion Rate to I₂₆.

(26) I₂₇ = Rate of Change in I₂₇ per Time Step − I₃₄ × P₅ × Conversion Rate to I₂₇.

(27) I₂₈ = Rate of Change in I₂₈ per Time Step − I₃₄ × P₅ × Conversion Rate to I₂₈.

(28) I₂₉ = Rate of Change in I₂₉ per Time Step − I₃₄ × P₆ × Conversion Rate to I₂₉.

(29) I₃₀ = Rate of Change in I₃₀ per Time Step − I₃₄ × P₆ × Conversion Rate to I₃₀.

(30) I₃₁ = Rate of Change in I₃₁ per Time Step − I₃₄ × P₆ × Conversion Rate to I₃₁.

(31) I₃₃ = Rate of Change in I₃₃ per Time Step − I₃₄ × P₆ × Conversion Rate to I₃₃.

4. Construction Risk Simulation for Large Bridges

4.1. Project Case Overview

This paper conducts an empirical study using a river-crossing bridge. The main bridge features a pre-stressed concrete continuous rigid structure with separate widths for up-and-down lanes, a cross slope on the box girder’s top surface, a horizontal bottom, and C55 concrete material. The superstructure employs a suspension-casting continuous rigid frame, the central pier comprises a double thin-walled dock on a pile foundation, and the transition pier utilizes a column pier foundation. Key technical standards include: a Class I highway classification with six lanes in each direction, a Class I design load, a 100-year design base period and service life, a Class I structural design safety level, and a Class II environment for the project area.

The main body of the bridge is modeled as illustrated in Figure 4:

4.2. Parameter Determination and Variable Assignment

Many parameters are involved in the modelling process, some of which are difficult to determine. This paper ascertains the parameter values based on the actual data of bridge construction safety-related indexes, integrating relevant cases, referencing laws and regulations, standards, and norms related to bridge construction safety, and utilizing survey and statistical methods, expert scoring, and so forth. Due to the different units and the variations in the magnitude of the bridge construction evaluation metrics, it is challenging to make direct comparisons. Hence, the dimensionless quantification of the indicator is determined. So, let M_j = max_i(x_ij) and m_j = min_i(x_ij). Thus, x*_ij = (x_ij − m_j)/(M_j − m_j) is dimensionless, and x*_ij ∈ [0, 1]. When m_j = 0 (j = 1,2, …,m), we have x*_ij = x_ij/M_j.

The large bridge construction risk system dynamics model was modelled in Week, with the basic parameters set to FINAL TIME = 60, INITIAL TIME = 0, and TIME STEP = 1.

(1) Determination of variable weights

In this paper, we initially utilize the expert scoring method to obtain the relative importance scale value between each risk factor depicted in Figure 1, and subsequently employ the hierarchical analysis method to ascertain the weight of each risk factor. The results are displayed in

Table 2. Model variable weight assignment table.

Weights	Volume	Weights	Volume	Weights	Volume
W1	0.203	W24	0.021	W45	0.021
W2	0.146	W25	0.016	W46	0.029
W3	0.137	W26	0.023	W51	0.021
W4	0.134	W31	0.021	W52	0.019
W5	0.094	W32	0.023	W53	0.016
W6	0.286	W33	0.026	W54	0.015
W11	0.047	W34	0.019	W55	0.023
W12	0.026	W35	0.031	W61	0.068
W13	0.067	W36	0.017	W62	0.072
W14	0.063	W41	0.019	W63	0.065
W21	0.024	W42	0.027	W64	0.081
W22	0.027	W43	0.016
W23	0.035	W44	0.022

.

(2) Determination of initial values of risk subsystem-level variables

After determining the weights of the indicators, it is also necessary to set the initial values of the variables. Most of the variables in the model are qualitative, and it is impossible to determine the actual data by reviewing historical information. Therefore, based on the documents related to bridge construction safety and the actual construction situation, the risk subsystem-level variables were evaluated by the expert scoring method to determine the initial assigned values of each subsystem, and the results are displayed in

Table 3. The horizontal variable initiates the table.

S/N	Symbol	Variable Names	Initial Assignment
1	L01	Personnel risk	0.3
2	L02	Equipment material risk	0.4
3	L03	Survey and design risks	0.3
4	L04	Construction monitoring risks	0.4
5	L05	Environmental risks	0.2
6	L06	Managing risk	0.5

.

(3) Determination of the proportion of inputs

By considering safety inputs as system inputs and categorizing them into personnel safety inputs, equipment and material safety inputs, survey and design safety inputs, construction monitoring safety inputs, environmental safety inputs, and management safety inputs, the proportion of sub-system safety inputs is calculated as sub-system safety inputs/total safety inputs × 100%. Based on the above analyses and the actual safety inputs for large bridge construction, each subsystem’s proportion of safety inputs is presented in

Table 4. Table of safety investment proportion for each subsystem.

S/N	Subsystem Name	Proportion of Inputs	Symbol
1	Personnel risk	0.15	P1
2	Equipment material risk	0.17	P2
3	Survey and design risks	0.16	P3
4	Construction monitoring risks	0.19	P4
5	Environmental risks	0.12	P5
6	Managing risk	0.21	P6

.

(4) Determination of the amount of risk change per unit time step

Based on on-site surveys, relevant data, and the research results of other scholars, and in consideration of the criteria for classifying the risk and accident rate into orders of magnitude, the accident rate, the average number of working days per week, and the number of hours per day of exposure to the risk factors for each risk factor were determined by the experts. Then, the accident probability formula was utilized to calculate the amount of risk change per unit time step for each risk factor. The accident probability formula is displayed in Equation (1), and the calculation results are displayed in

Table 5. Risk variation per unit time step of each risk factor.

Risk Factors	Unit Length Change	Risk Factors	Unit Length Change
Special operators licensed to work	0.029	Construction process program	0.056
Fatigue susceptibility of construction personnel	0.037	Stress and line control	0.065
Safety awareness among construction workers	0.046	Prestressing Tensioning Construction	0.061
Proficiency in professional skills	0.033	Construction of the closing section	0.067
Safety control of large equipment mounting and dismounting	0.057	Surveillance solutions	0.063
Availability of safety guards	0.045	Monitoring data feedback and processing	0.059
Repair and maintenance of equipment	0.038	Complexity of bridge features	0.037
Improper use and destabilisation of construction plant	0.051	Road traffic conditions	0.035
Quality of entry of components	0.026	Hydrogeological conditions	0.034
Stacking and storage of building materials	0.031	Setting up work environment	0.043
Bridge structure selection	0.023	Frequency of construction site safety inspections	0.049
Bridge material properties	0.026	Effectiveness of safety management regulations	0.042
Design divorced from site	0.029	Reasonableness of security management structure	0.036
Deficiencies in current stage of design theory	0.021	Implementation of safety education and training	0.059
Inadequate surveys, forecasting errors	0.039
Uncertainty about new materials and technologies	0.033

.

c = λt

(1)

where c is the change in risk per unit time step, λ is the accident rate, and t is the number of hours of exposure per week.

Since the impact of extreme climate on the risk level of the system varies over time, for example, the rainy season is prone to disasters such as heavy rainfall and flooding, while the winter is susceptible to disasters such as raw snowstorms and cold snaps, the shadow variable <Time> was incorporated into the system and a table function was established to model the values of these factors, and the results are as follows:

Extreme Severe Climate=WITH LOOKUP(Time,

([(0,0)-(36,0.01)],(0,0.009),(6,0.0081353),(12,0.0095619),(18,0.0067812),(20,0.0076941),(24,0. 0055164),(28,0.00472313),(30, 0.00319956),(32,0.00258793),(36,0.00129811)))

(5) Determination of input conversion rates

Construction personnel’s safety awareness, equipment repair and maintenance, and safety education and training, among other factors, will see a reduction in risk values with an increase in safety inputs and unit safety inputs, thereby decreasing the risk values of these factors. The conversion rate of safety inputs changes over time, as the level of each element decreases differently within each time step due to variations in implementation, etc. This paper established the input conversion rate as a table function. After evaluating the risk values of each factor at a unit step, the reduction was then divided by the actual safety inputs in the time step to calculate the safety input conversion rate for a unit time step, and the specific results are as follows:

Conversion rate of inputs to licensed special operators

=WITHLOOKUP(Time,([(0,0)-(36,0.022)],(0,0.003),(6,0.0103521),(12,0.0138147),(18,0.0145662),(20,0.0154558),(24,0.0159881),(28,0.0151247),(30,0.0143387),(32,0.0139223),(36,0.0155568)))

Translation of inputs into the susceptibility of construction personnel to fatigue

=WITHLOOKUP(Time,([(0,0)-(36,0.04)],(0,0.0367574),(6,0.0251156),(12,0.0232783),(18,0.0202517),(20,0.0253795),(24,0.0267431),(28,0.0228375),(30,0.0257712),(32,0.0256675),(36,0.0253747)))

Conversion rate of inputs to safety awareness among construction personnel

=WITHLOOKUP(Time,([(0,0)-(36,0.03)],(0,0.005),(6,0.00317435),(12,0.0023677),(18,0.0203514),(20,0.0225118),(24,0.002769),(28,0.00263352),(30,0.00259612),(32,0.00245647),(36,0.00298337)))

Translation of inputs into professional skill proficiency

=WITHLOOKUP(Time,([(0,0)-(36,0.04)],(0,0.0375329),(6,0.0267412),(12,0.0243368),(18,0.0216857),(20,0.0225118),(24,0.0245773),(28,0.0262265),(30,0.0202541),(32,0.0236113),(36,0.0273625)))

The conversion rate of inputs to safety controls for mounting and dismounting large equipment

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.00091225),(6,0.00136334),(12,0.00146783),(18,0.00143754),(20,0.00158776),(24,0.00141125),(28,0.00140171),(30,0.0015897),(32,0.0015452),(36,0.00131156)))

Conversion rate of inputs to the availability of safety guards

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.00101423),(6,0.00145783),(12,0.00159271),(18,0.00155412),(20,0.00169574),(24,0.00152886),(28,0.00151091),(30,0.0015675),(32,0.0015519),(36,0.00142258)))

Conversion rate of inputs to repair and maintenance of equipment

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0),(6,0.00681342),(12,0.00636157),(18,0.00517825),(20,0.00534769),(24,0.0057586),(28,0.00581321),(30,0.00579332),(32,0.00503664),(36,0.00492845)))

The conversion rate of inputs to design detached from the field

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.0014233),(6,0.00114753),(12,0.00102754),(18,0.00125761),(20,0.0011779),(24,0.00108356),(28,0.00116554),(30,0.00119814),(32,0.00121127),(36,0.00123563)))

The conversion rate of inputs to under-survey and forecast errors

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.0016237),(6,0.00133453),(12,0.00127312),(18,0.00135715),(20,0.00139826),(24,0.0012432),(28,0.00133774),(30,0.00138532),(32,0.00141252),(36,0.00145337)))

Conversion rate of inputs to stress and line control

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.0015446),(6,0.00123374),(12,0.00116625),(18,0.00121123),(20,0.00128735),(24,0.00117341),(28,0.0012583),(30,0.00127443),(32,0.00132548),(36,0.00134531)))

The conversion rate of inputs to prestressing tensioning construction

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.0015446),(6,0.00123374),(12,0.00116625),(18,0.00121123),(20,0.00128735),(24,0.00117341),(28,0.0012583),(30,0.00127443),(32,0.00132548),(36,0.00134531)))

Conversion rate of inputs to the construction of the cohesive section

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.0014324),(6,0.00112877),(12,0.00103376),(18,0.00117428),(20,0.00117641),(24,0.00106276),(28,0.00127843),(30,0.00115387),(32,0.00131125),(36,0.0012115)))

Conversion rate of inputs to monitoring programs

=WITHLOOKUP(Time,([(0,0)-(36,0.01)],(0,0.0015475),(6,0.00125641),(12,0.00115811),(18,0.00126635),(20,0.00123799),(24,0.00117882),(28,0.00137668),(30,0.00124483),(32,0.00145526),(36,0.0013577)))

Conversion rate of inputs to monitoring data feedback and processing

=WITHLOOKUP(Time,([(0,0)-(36,0.04)],(0,0.00351573),(6,0.00214846),(12,0.0019776),(18,0.00231841),(20,0.00236885),(24,0.00248112),(28,0.00227156),(30,0.0024587),(32,0.00261819),(36,0.00273355)))

Conversion rate of inputs to road traffic conditions

=WITHLOOKUP(Time,([(0,0)-(36,0.04)],(0,0),(6,0.0305117),(12,0.0279386),(18,0.0265351),(20,0.0321672),(24,0.0336936),(28,0.03711483),(30,0.0362543),(32,0.0387543),(36,0.0395127)))

Conversion rate of inputs to environment homework assignments

=WITHLOOKUP(Time,([(0,0)-(36,0.04)],(0,0),(6,0.0314257),(12,0.02882145),(18,0.0274252),(20,0.0311936),(24,0.0325873),(28,0.03544129),(30,0.037985),(32,0.0363784),(36,0.0377965)))

Conversion rate of frequency of safety inspections invested in construction sites

=WITHLOOKUP(Time,([(0,0)-(36,0.02)],(0,0.0138533),(6,0.012532),(12,0.0098665),(18,0.0103835),(20,0.0095411),(24,0.011386),(28,0.0103577),(30,0.0103258),(32,0.0112293),(36,0.0123819)))

Conversion rate of inputs to the delivery of security education and training

=WITHLOOKUP(Time,([(0,0)-(36,0.02)],(0,0.0147597),(6,0.013174),(12,0.010296),(18,0.0114759),(20,0.0102455),(24,0.012478),(28,0.0112411),(30,0.0114792),(32,0.0123163),(36,0.0134595)))

Security inputs

=WITHLOOKUP(Total risk level for construction of large bridges,([(0,0)-(1,100)],(0,0),(0.2,20),(0.4,50),(0.6,80),(0.8,90),(1,100)))

4.3. Model Simulation and Result Analysis

By substituting the parameters of a bridge identified in Section 4.2 into the dynamics equations of the large bridge construction risk system established in Section 3.3, the simulation conducted with Vensim PLE 7.3.5 software revealed the trend of its risk level, as depicted in Figure 5.

As illustrated in Figure 5, the level of risk in the construction of large bridges gradually decreased over the simulation period (60 weeks), demonstrating that the commitment to safety in the construction of large bridges is strengthened by investing in risk management at the construction site. This improvement is attributed to consistently increasing financial support for safety measures, such as acquiring safer equipment, providing more comprehensive safety training, and enhancing the work environment, which collectively contribute to effectively reducing the occurrence of accidents and thus minimizing construction risks.

To explore the degree of influence of each risk subsystem on the total risk level of large bridge construction, the initial value of each risk subsystem was increased by one-third of its original value. When the initial value of one risk subsystem was increased, the remaining subsystems were kept unchanged. Six scenarios were designed and compared with the original scenarios, and the simulation results are displayed in Figure 6.

Figure 5 illustrates that the impact of changes in the management risk subsystem on the total risk level of large bridge construction was significant. The influence of changes in other risk subsystems, such as personnel, was subtler and more difficult to distinguish. Therefore, the magnitude of the impact of changes in the initial values of each subsystem were calculated using the Table Time table. The significance of the impact level was assessed by subtracting the average of the total risk-level values for large bridge construction for each scenario group at each time step from the standard of the original designs and dividing by the average of the actual plans. The impacts of risk changes in each subsystem were 11.9%, 11.2%, 8.1%, 10.3%, 3.7%, and 28.6%, respectively. The order of the degree of impact of the six subsystems was as follows: management > personnel > equipment and materials > construction monitoring > survey and design > environment.

Different proportions of safety inputs in each risk subsystem can lead to various overall risk levels in the total system at risk. Consequently, it is essential to monitor the trend of the overall risk level of large bridge construction under varying input ratios by adjusting the safety input ratios of each subsystem and to examine the impact of these safety input ratios on the total risk of the system. With no changes in the total safety inputs, six groups of safety input ratio adjustment programs were developed, as illustrated in

Table 6. Different safety investment ratio schemes for each subsystem.

Program	Proportion of Inputs
	Personnel Risk	Equipment Material Risk	Survey and Design Risks	Construction Monitoring Risks	Environmental Risks	Managing Risk
1	0.5	0.1	0.1	0.1	0.1	0.1
2	0.1	0.5	0.1	0.1	0.1	0.1
3	0.1	0.1	0.5	0.1	0.1	0.1
4	0.1	0.1	0.1	0.5	0.1	0.1
5	0.1	0.1	0.1	0.1	0.5	0.1
6	0.1	0.1	0.1	0.1	0.1	0.5

.

The trend of risk levels for the different input scenarios is depicted in Figure 7, where it is evident that there were variations in the incremental total risk levels of large bridge construction under the scenarios over time, leading to differences in the trends of the curves. Increasing the proportion of safety inputs in the personnel risk subsystem and the management risk subsystem effectively reduced the total risk level of the system. The ranking of the scenarios in terms of the risk level value is scenario 1 > scenario 6 > original scenario > scenario 5 > scenario 2 > scenario 4 > Scenario 3. This is because the safety awareness, skills, and behaviors of personnel directly impact daily operational safety and accident rates. Initially, investing in training and education for personnel can quickly result in safer operational behaviors and fewer accidents, significantly reducing the project’s risk levels. Although risk management has a substantial impact within the system, improvements may take longer to manifest. Effective management enhancements, such as refining processes, policies, and culture, might need time to be absorbed and implemented by the staff, and to demonstrate results in safety performance. Thus, even if the highest investments are made in risk management, their immediate impact on risk reduction may not be as noticeable as direct investments in personnel. In the complex dynamics of systems models, intricate interactions exist between subsystems. At times, a specific subsystem, like personnel risk, may be the key driver for reducing risk, while at other times, the influence of other subsystems, such as management risk, may become more pronounced. Hence, the varying effects between different strategies reflect shifts in the system’s internal dynamic equilibrium. The risk level of the system varies depending on the proportions of inputs for the same amount of time with constant safety inputs. Therefore, a change in the input program can be utilized to achieve the lowest risk-level value more rapidly and efficiently.

4.4. Risk Analysis and Simulation of Large Bridge Construction with Strategies for Optimizing Safety Investments

(1) Safety level of large bridge construction. With a weekly safety investment of CNY 500,000, the parameter values identified in the previous section were input into the system dynamics equations. The development trend of the overall risk level for large bridge construction was then obtained through computer simulation (as depicted in Figure 8). Over a simulation period of 60 weeks, the total risk level for large bridge construction progressively decreased due to the ongoing safety investment, ultimately decreasing to a risk level of 0.166055 by the 60th week.

Adjustments were made to the safety investments while keeping other conditions unchanged, and the impacts of various safety investment plans on the system’s risk level were assessed. This analysis examined how these adjustments affect the safety levels in bridge construction, with the specific investment strategies outlined in

Table 7. Various safety investment strategies.

Name	Safety Investment/CNY 10,000
Program 1	30
Program 2	40
Program 3	50
Program 4	60
Program 5	70

.

The trend chart (Figure 9) demonstrates that the overall risk level of large bridge construction decreased with enhanced safety investments and increased when safety investments were diminished.

Enhancing the risk management of bridge construction is a continuous effort. By increasing safety investments, it is possible to progressively enhance the safety awareness and skills of the workforce, thereby leading to a consistent decrease in risk levels. This underscores the effectiveness of augmenting safety investments in reducing construction risks. Detailed risk-level values are presented in

Table 8. Data analysis of the overall risk level in large bridge construction.

Time	Program 1	Program 2	Program 3	Program 4	Program 5
0	0.3758	0.3758	0.3758	0.3758	0.3758
5	0.349528	0.336057	0.322586	0.309114	0.295643
10	0.333048	0.308064	0.283081	0.258097	0.233114
15	0.322133	0.28675	0.251366	0.215982	0.180599
20	0.305696	0.25881	0.211924	0.165038	0.118152
25	0.288767	0.230281	0.171796	0.113311	0.0548254
30	0.275563	0.206226	0.136889	0.0675516	−0.00178533
35	0.26148	0.181119	0.100758	0.0203965	−0.0599646
40	0.242582	0.150236	0.0578892	−0.0344572	−0.126803
45	0.22345	0.119072	0.0146935	−0.0896848	−0.194063
50	0.204318	0.0879081	−0.0285022	−0.144912	−0.261322
55	0.185186	0.0567444	−0.0716978	−0.20014	−0.328582
60	0.166055	0.0255806	−0.114893	−0.255368	−0.395841

.

The simulation results suggest that appropriately increasing safety investments can substantially reduce the risk levels across various subsystems, thereby improving the overall safety performance of the project.

As the project progresses and environmental conditions fluctuate, the system dynamics model’s flexibility and adaptability prove it to be an effective tool for understanding and managing complex engineering risks. Future efforts should focus on further optimizing risk management strategies, enhancing the allocation of safety investments, and persistently monitoring risk level changes to maintain the highest safety standards during construction. By doing so, we can expect the realization of safer and more efficient large-scale bridge construction projects.

5. Conclusions

As urban areas in our country rapidly expand, there has been a surge in the development of traffic infrastructure, particularly in large bridge construction projects. These projects not only facilitate the growth of urban transportation networks and meet the needs of the population but also expose numerous safety risks. These risks can delay project timelines and lead to significant losses in both personal safety and property. Consequently, conducting comprehensive research on safety risk management for large bridge construction is imperative. This study focuses on the safety risks associated with large bridge construction, integrating both domestic and international research and real-world case studies. Utilizing system dynamics theory and Vensim PLE 7.3.5 software for simulation, the aim was to develop effective risk assessment and management strategies. The following are key conclusions derived from this research process:

(1) Development of a risk factor structure system: This study delves deeply into the evolution mechanisms of risks in large bridge construction, identifying key risk factors impacting construction safety. It establishes a hierarchical system that includes six major risk subsystems, including personnel, equipment and materials, and management risks, among others, and 31 specific risk factors. This structured system provides a comprehensive and systematic framework for further risk assessment and management.

(2) Development and utilization of the system dynamics model: Leveraging system dynamics theory and Vensim software, this study developed causal loop and stock–flow diagrams for the risk system of large bridge construction and formulated system dynamics equations, culminating in a comprehensive system dynamics model for large bridge construction risks. The model comprises 76 variables, including 6 level variables, 6 rate variables, 59 auxiliary variables, and 5 constants. It elucidates the interactions between various risk factors and their cumulative impact on the overall risk level. This model acts as an indispensable tool for understanding and analyzing the dynamics of risk throughout the construction process of large bridges.

(3) Simulation analysis of risk change trends: Employing a specific large bridge construction project as a case study, this research entailed defining and simulating the parameters and equations within the model to analyze the trend of risk changes during the construction phase. The simulation outcomes demonstrated that the personnel and management risk subsystems exert the most substantial influence on the overall risk level. These findings provide invaluable insights and guidance for risk management in large bridge construction projects.

(4) Proposal of risk management strategies: Drawing on the simulation analysis results, this paper further explored effective risk management strategies, including enhancing personnel safety training, refining management systems, and upgrading the quality of equipment and materials. These strategies aim to fundamentally reduce construction risks and ensure the safety and seamless progression of the project.

(5) Critical role of safety investments in risk reduction: The simulation analysis utilizing the system dynamics model verified that appropriate safety investments significantly reduce risk levels in large bridge construction. The research examined various safety investment strategies, illustrating how to optimally allocate funds in response to changes in the construction environment for the best risk management outcomes.

This study delves deeply into safety risk management for large bridge construction, developing a system dynamics model to evaluate and simulate risk factors, and it introduces practical management strategies. These contributions significantly bolster the safety of large bridge projects. Nonetheless, the research identified challenges such as limitations in data collection, the imperative for model validation, the empirical testing of risk control measures, and the potential to broaden interdisciplinary research. Future efforts will focus on collecting more comprehensive data, refining model accuracy, confirming the effectiveness of management strategies, and investigating advanced technologies for intelligent risk detection and control, aiming to provide a more comprehensive contribution to safety management in large bridge construction both theoretically and practically.