Risk Assessment with Monte Carlo Simulation to Improve Bridge Construction Safety †
1
Department of Civil Engineering, Universitas Sebelas Maret, Surakarta 57126, Indonesia
2
Department of Industrial Engineering, Universitas Sebelas Maret, Surakarta 57126, Indonesia
*
Author to whom correspondence should be addressed.
†
Presented at the 8th Mechanical Engineering, Science and Technology International Conference, Padang Besar, Perlis, Malaysia, 11–12 December 2024.
Eng. Proc. 2025, 84(1), 56; https://doi.org/10.3390/engproc2025084056
Published: 12 February 2025
(This article belongs to the Proceedings of The 8th Mechanical Engineering, Science and Technology International Conference)
Abstract
:The safety of bridge construction has become a special concern for the Indonesian government since many bridge construction accidents occurred in 2017 and 2018. Construction projects involve a small number of contractor employees, so when conducting accident risk assessments, the results become less accurate. Monte Carlo simulation is a method that can be applied to conduct risk analysis with limited available data. This research began with the identification of potential risks that might occur in bridge construction, resulting in 24 types of risks. Risk assessment was conducted based on the list of risks identified by the contractor’s employees who were working on a bridge project. The results of the risk assessment were then analyzed and prepared for the Monte Carlo simulation process. The simulation results showed accurate outcomes with a total of 10,000 simulations. The greatest risks occur when a worker falls, which has a risk index of 12.5961, and a girder collapses during installation, which has a risk index of 16.1873.
1. Introduction
The Social Security Administration (BPJS) Employment recorded the number of work accidents in Indonesia as 234,270 cases in 2021, as presented in Figure 1. The data show an increase of 5.65% from the previous year, which had 221,740 cases. If we look at the trend, the number of workplace accident cases in Indonesia has continued to grow over the past five years. In 2017, the number of work accidents recorded was 123,040 cases. This number increased by 40.94% to 173,415 cases in 2018. The following year, work accidents rose again by 5.43% to 182,835 cases. Workplace accidents in the country increased by 21.28% to 221,740 cases in 2020. The number also increased again last year. According to BPJS, most of those accidents occurred in the workplace. They most often occur in the morning from 6:00 a.m. to 12:00 p.m.
Projects constructing bridges and elevated structures (elevated toll roads) carry a high risk of work accidents during the construction period. From 2017 to 2020, there were several work accidents on bridge constructions, flyovers, and elevated structures in Indonesia. Those work accidents caused significant losses to the projects, both in terms of material losses and non-material losses in the form of lives that cannot be measured in monetary terms. Construction projects, including bridge projects, consist of many tasks, and thus have a high potential risk of work accidents. The ILO (International Labor Organization) classifies the causes of workplace accidents into technical equipment factors, work environment factors, and human factors. The construction of a toll road necessitates a comprehensive plan to address safety and security issues during girder lifting operations [1]. Technical equipment factors are causes of accidents due to the use of equipment that does not meet standards or is unfit for use [2,3,4]. Environmental factors that cause accidents stem from the physical environment and the socio-psychological environment [2,3,5,6,7]. Humans are the highest contributing factor to workplace accidents [2,3,8], as workers do not know safe procedures (when performing hazardous activities) and do not comply with work requirements.
Construction projects have limitations in conducting work accident risk assessments, as the limited number of employees in a construction project results in insufficient data being used. Njogu et al. [9] found that a lack of worker participation stopped the enforcement of occupational safety and health rules in Kenyan healthcare institutions. According to the research, the execution of safety protocols is enhanced when employees must follow directives [9]. Bello et al. [10] studied two research institutes in Nigeria and found that employees had not been given the attention they deserve to impact the program’s workplace health and safety [10]. This means staff are not engaged in safety activities [9,10].
The background explanation above outlines the weaknesses in the assessment of bridge construction accident risks due to data assessment limitations; therefore, in this study, the use of Monte Carlo simulation is proposed. The application of Monte Carlo simulation is expected to address the data limitations in the assessment of bridge construction safety risks.
2. Literature Review
Bridge building for highway and infrastructure development is an important part of ensuring safety, which requires rigorous engineering quality and safety management for enduring technological progress and to avoid safety incidents [11]. Superior construction control performance is needed to ensure structural safety and fulfill design specifications [12] due to the intricacy of contemporary bridge construction, especially in expanding spans and increasing construction demands.
Significant improvements in the safety of bridge construction have come through the incorporation of advanced technologies and procedures. BIM technology has enhanced the quality and efficiency of construction safety management practice [13]. The implementation of prefabricated bridge components in Accelerated Bridge Construction (ABC) has reduced the risk of traffic exposure to workers by removing the need for on-site concrete construction [14].
A holistic approach is needed for bridge building to have effective safety procedures. This includes employing extensive risk assessment techniques, including analytic hierarchical process and vague synthetic judgment transitive methods [15,16], using the latest construction technology (Building Information Modeling) [13], and taking advantage of recent management techniques such as Accelerated Bridge Construction (ABC) [14]. In addition, it requires knowledge of the interconnections of risk components [17] and collaborative safety control methods.
2.1. Bridge Construction Safety Assessment
Construction Safety Assessment is an important process used to assess and improve safety protocol on construction sites. Safety performance is assessed using diverse methodologies, including analyses of accident rates, safety management indicators, and safety performance indices (SPIs) [18]. Quantification of the impact of and areas of improvement in safety measure effectiveness can be made with these metrics. Construction Safety Assessment involves the identification of possible hazards associated with many activities in construction, including human factors, equipment, materials, management practices, and the environment [19].
Safety evaluation in construction is performed through different methods including safety inspections, audits, and the application of advanced technology. Visual inspections using checklists are often part of safety evaluations, but their effectiveness depends on the experience of the safety adviser [20]. Construction Safety Assessment is the process of evaluating and augmenting safety conditions at construction sites. This process involves the systematic collecting, managing, and disseminating of safety-related data to detect potential hazards, evaluate risks, and take preventative actions [21,22].
The performance assessment is usually conducted by both cross-sectional and longitudinal methods. Evaluations that are cross-sectional look at present safety conditions, whereas longitudinal evaluations look at safety performance over time. These elements are combined in innovative methodologies such as the fluid dynamics (FD) method to provide a more complete safety assessment [21]. Construction Safety Assessment can be carried out through various methods and tools, such as safety inspections and audits [18,23], risk assessment analyses [22], hazard identification and rectification efficiency monitoring [24], and calculations of the safety performance index (SPI) [18,24].
The risk mitigation and assurance of structural integrity requires the safety assessment of bridge construction. Safety in construction activities is assessed and overseen using diverse methodologies and technology. Overseeing bridge transverse building is performed by using three-dimensional laser scanning technology applied in point layout measurement, monitoring strategies, and data analysis [25]. As described by Chen [15], it is important to perform preconstruction risk evaluation since this is a directive of the Ministry of Transport regarding the safety risk assessment for highway bridge and tunnel engineering construction.
2.2. Advantages of Monte Carlo Simulation
Monte Carlo simulation is a useful method to overcome many data constraints and uncertainty in analytical computation. Given this special ecosystem, it provides substantial advantages over conventional methods in working with intricate systems or dwindling data availability [26]. Analytical methods can be used to quickly evaluate the impact of data uncertainty on calculations performed with analytical techniques and determine the impact of lineage common cause failures [26]. The use of Monte Carlo simulation relies on its correct execution. Researchers much follow the guidelines for data creation methodology, replication selection and conditions, benchmark application, and performance assessment [27]. Input modeling for Monte Carlo simulation is a challenge in complex systems that have non-linear behavior and interdependent variables, where methods like probability distribution fitting, resampling, or using real world data where they exist [28] need to be carefully evaluated.
Monte Carlo simulation (MCS) is a highly effective method for analyzing and modeling complex systems and processes. It has several advantages over traditional deterministic methods and other statistical methods. Monte Carlo simulation is very powerful when uncertainty plays a large role in the problem. MCS differs from deterministic models with a single outcome based on fixed inputs because of the use of random sampling to yield a range of possible outcomes to improve risk and variability understanding of results. This capability is extremely effective in fields such as finance, risk assessment, and engineering, in which uncertainty plays a dominant role in making and intensifying decisions [29,30]. Nevertheless, MCS has widespread applications to many kinds of problems in different domains, such as finance, engineering, and other environmental studies. It is very versatile and can represent systems of more than one variable, and it may be difficult to use with other techniques. For instance, the utility of MCS for conducting reliability evaluation of power distribution systems has successfully been demonstrated [29,31].
Histograms, cumulative distribution functions, and several other graphical representations are available as outputs of Monte Carlo simulations. Results from other methods that provide more abstract statistical results seem less easily communicated to stakeholders than probability distributions which this visualization helps stakeholders to understand [29,32]. For instance, Monte Carlo methods for constructing confidence intervals in mediation analysis have had comparable performance to bootstrapping techniques; the former are faster, easier to use, and applicable even when summary data are the only type available. MCS is therefore an attractive option in case of limited computational resources or when traditional methods are difficult to implement [29,30]. With this, other methodologies may be combined with Monte Carlo simulation to increase its effectiveness. For instance, MCS can be combined with the Analytical Hierarchy Process (AHP) to give weighted assessments in risk analysis frameworks which improve understandings of risks deriving from different factors in information security management systems [30].
2.3. Bridge Construction Safety with Monte Carlo Simulation
The Monte Carlo simulation has become an effective instrument for evaluating safety risks in construction projects. It enables project managers to formulate proactive safety strategies by identifying probable accident scenarios and evaluating their likelihood of occurrence [33]. Hospital development is used as an example of a construction project for which the Monte Carlo simulation is used to identify potential hazards and assess risks. Identifying and assessing hazards that impact employees or the work environment [34] is aided by simulating diverse situations. It offers this to project managers such that they may formulate proactive safety strategies as well as execute preventive actions.
The Monte Carlo simulation method is utilized to evaluate the safety of structures impacted by construction operations. It has been utilized to assess the effects of twin shield tunnel construction on neighboring masonry structures. Monte Carlo simulation, by integrating the spatial variability of soil characteristics and surface deformation modes, aids in identifying potential damage zones and evaluating building safety [35]. Dust exposure concerns and cost range estimation may be evaluated with Monte Carlo simulation. The Monte Carlo simulation technique was used to create a probabilistic risk assessment model to investigate the health impacts of construction dust on workers [36].
Risk assessment and safety evaluation in bridge construction are extensively carried out by Monte Carlo simulation. The uncertainty in several parameters is evaluated, leading to a more comprehensive study than when using deterministic techniques [11]. This is due to the fact that the method can manage many variables and produce probabilistic results, making it especially useful in decision-making in complex bridge construction projects for the engineers and project manager to optimize the designs and conduct effective risk mitigation strategies [37]. The method’s adaptability facilitates its use in multiple facets of bridge safety, encompassing material characteristics and scour depth forecasting at bridge piers [11]. Monte Carlo simulation improves the dependability of safety assessments in bridge construction projects by integrating uncertainty and delivering probabilistic conclusions.
3. Research Methodology
The occupational accident risks are identified to determine the possible hazards in bridge construction. The list of occupational accident hazards identified is used for the purpose of risk assessment. Qualitative data from interviews with construction personnel and safety specialists, site observations, and evaluations of safety protocols and incident reports are used to risk assess the occurrence of occupational accidents in bridge construction.
The outcomes of the occupational accident risk evaluation were subsequently simulated using Monte Carlo methods, beginning with the calculation of the mean and standard deviation. The risk assessment results were computed for their frequency at each value of the assessment scale, and, based on this frequency, their likelihood was determined. The outcomes of the probability analysis were utilized to establish categories according to the work accident risk assessment scale by computing cumulative probability and defining probability intervals. Random numbers were created to assess their values against the predetermined probability intervals.
The risk index is analyzed from the data obtained through Monte Carlo simulation by multiplying the probability and severity of each risk. The resulting risk index can provide information about the priority of risks that need attention, with risks classified as high or extreme receiving special attention to develop their management plans. The risk assessment model in this study is presented in Figure 2.
4. Result and Discussion
In this study, 24 associated risks were identified for the concrete bridge construction risks, including human factors, equipment, and materials. Respondents for this research came from contractor employees and focus on one of the bridge construction projects. Nine employees participated as respondents, all of whom were male and ranged in age from 28 to 57 years (Table 1). The respondents’ education levels consisted of two degrees: bachelor and master. They had work experience of 8 to 22 years, but the most common experience spans were 11–13 and 20–22 years. Respondents were selected from employees with position knowledge of bridge construction safety aspects, such as project management, project engineering, quality control, HSE, and supervising.
Likelihood and severity evaluations make up risk assessment. The probability of an accident occurring is referred to as likelihood, and the magnitude of the impact of the accident is referred to as severity. A risk index was obtained by using the likelihood and severity numbers. This study used a probability and severity assessment scale with explanations for each criterion as shown in Table 2 and Table 3. The probability scale is presented in Table 2, where almost certain is the smallest scale, or rare, valued at 1, and the largest scale, or almost certain, is valued at 5. The scale of severity is rated from 1 to 5 and details catastrophic, significant, moderate, minor, and insignificant severity, with the highest value scale impact of an accident, or catastrophic, being rated at 5 and the smallest value scale, or insignificant, being rated at 1. Table 3 presents the severity scale (minor injury, can immediately continue working after receiving assistance).
Risk levels are categorized into four classifications: they denote very high, with a risk index value of 20 to 25, in red; high, with a risk index value of 10 to 19, in orange; medium, with a risk index value of 5 to 9, in yellow; and low, with a risk index value of 1 to 4, in green. The degree of the threat posed by prospective hazards is assessed using risk levels. Risks that are categorized as extremely high and high need to be subjected to meticulous planning to reduce their likelihood and provide mitigation strategies should they occur.
The risk assessment for bridge building is detailed in Table 4, encompassing 24 risks analyzed for their likelihood and severity. The sample size consisted of contractor employees engaged in a bridge construction project, resulting in a limited number of respondents; hence, a Monte Carlo simulation was performed. The risk assessment results were analyzed for their mean and standard deviation, which would be utilized in the subsequent stage, the Monte Carlo simulation.
This research applies the Monte Carlo simulation to address data limitations in a bridge construction project. The frequency and the amount of data are compared to calculate the probability of each assessment scale, and this probability is then classified into five classes according to the scale used. Monte Carlo simulation utilizes probabilistic data derived from safety risk assessment results. The probability is derived from the frequency ratio of each assessment scale relative to the total data, with the probability of each risk assessed to obtain the overall probability value for the risks under evaluation. Table 5 presents the probability analysis results for each risk in terms of likelihood and severity.
The probability data then calculate the cumulative value based on the risk class classification and then continue to analyze the interval of the cumulative risk probability according to the class, so that there are five classifications used that have risk probability intervals. We generated random numbers to select the appropriate interval for the created class, thereby obtaining the probability and severity values of the risk. Table 6 presents an analysis of class creation for risk probabilities used in the Monte Carlo simulation.
In the Monte Carlo simulation process, random numbers are generated 10,000 times, and these random numbers will be evaluated to obtain the probability and severity values of the risks. The analysis of the risk index calculation for each risk is presented in Figure 3. The risk index value is obtained by analyzing these probability and severity values. The analysis has shown that there are two risks with a high-risk rating on the index, such as a worker falling, which has a risk index of 12.5961, and a girder collapsing during installation, which has a risk index of 16.1873. Risks in the moderate category consist of a worker being trapped, workers being injured after being caught by steel reinforcements, concrete reinforcement failing, concrete formwork collapsing, a girder breaking, a girder rolling over, and a pile overturning.
The comparison between the direct assessment results and the Monte Carlo simulation analysis shows accurate results, with an average difference of 0.14%. The smallest difference is 0.02%, found in the risk of the concrete formwork collapsing, and the largest difference is 0.47%, found in the risks of a worker being punctured with a sharp object and a worker being injured by equipment. The analysis of deviation calculations for each risk is presented in Table 7.
The Monte Carlo simulation applied in this study can be implemented well due to the limited data that can be obtained in bridge construction projects. Njogu et al. [9], Bello et al. [10] and Signoret, J. P et al. [26] found the same due to the limited number of employees who understand construction safety. The number of simulations used, totaling 10,000 in this study, can produce comprehensive calculations similar to those in the investment feasibility study [38]. A more comprehensive risk and potential return understanding was gained using this approach versus traditional methods.
This research uses random numbers 10,000 times to simulate the probability and severity to obtain accurate results, as performed by [38,39]. The number of iterations performed in Monte Carlo simulations is what makes them accurate. In general, the larger the number of simulations is, the more precise the result, but of course the computational time required is also extended [39]. This tradeoff between accuracy and efficiency is a central challenge in Monte Carlo methods. The Monte Carlo simulation results in this study have high accuracy, where the highest accuracy is only a difference of 0.02%. Accuracy in Monte Carlo simulations carried out by several researchers also produced the same thing; a Hamiltonian Monte Carlo sampling method has shown comparable accuracy to state-of-the-art software products [40]. Likewise, in a study of power indices, Monte Carlo simulations were run on 10,000 coalitions, with absolute errors of less than 10(−3) [38].
This study also includes the risk of a worker falling, with a risk index of 12.5961, which is in the high-risk category, and is a special concern for contractors to plan work safety so that this risk can be avoided. Workers falling from heights is a high risk which must be given careful consideration [41]. Falls are a major occupational hazard, with important social and economic consequences for both workers and employers [42]. According to Arachchige et al. [43], in 2017 there were 227,760 workers that had fall-related injuries, with 887 workers dying due to fatal falls. These incidents not only harm employees’ health and quality of life, they also reduce workplace productivity and raise economic costs through health costs and worker compensation [43].
A high risk of girder collapse during installation is also a risk, and in Indonesia in 2017 and 2018, several bridge projects experienced this accident. In the Indonesian construction industry, in large-scale infrastructure projects, the concern of girder collapse is very significant. Recently, several cases of girder collapse and other catastrophic events, such as cranes overturning, formwork collapsing, and material landslides [44], have taken place. Girder collapse is a serious problem in construction accidents, but it is not the only risk factor. The Failure Mode Effect Analysis and Fault Tree Analysis methods have shown that the risk of a girder falling during mobilization is the dominant risk priority in girder bridge construction. Surprisingly, “daydreaming” was the most dominant cause of accidents in the construction field [45], and girder collapse in Indonesia is part of a larger pattern of construction accidents where human casualties, asset destruction, and environmental damage can result. A comprehensive approach is needed to address this problem, which includes technical and human factors.
Monte Carlo simulation is very beneficial for conducting risk assessment and analysis on a construction project, where the number of employees performing the risk assessment is small, leading to less accurate results. This risk analysis can use commonly used spreadsheet programs with simple algorithms, allowing both small and large contractors to easily apply this analysis model. There are built-in functions and tools in Excel to generate random numbers, perform calculations, and run Monte Carlo simulations. A common process in this typically involves generating a model, specifying the input variables, with probability distributions, generating random samples, and analyzing the output [46]. For example, the probabilistic nature of critical speeds and vibration amplitudes is clarified in rotor dynamic systems with the use of Excel in modeling uncertainties in bearing damping, clearance, and mass imbalance [47]. A three-loop Monte Carlo simulation framework for seismic resilience assessment of Small Modular Reactors was developed and may be beyond the capabilities of Excel [47]. In the same vein, more sophisticated tools are used for more complex structural analyses like stochastic buckling of porous functionally graded plates [47].
5. Conclusions
Site identification and literature studies revealed 24 types of risks that may occur during bridge construction. Monte Carlo simulation is an appropriate tool for generating simulations with few data points, and the simulation results are highly accurate. The analysis results indicate that the high-risk categories include workers falling, with a risk index of 12.5961, and girder collapse during installation, with risk index of 16.1873. This risk is common in construction projects, so it should be a focus in construction projects.
Author Contributions
Conceptualization, W.H., S.A.K., D.H. and W.S.; methodology, W.H. and D.H.; software, W.H.; validation, W.H., S.A.K., D.H. and W.S.; formal analysis, W.H.; investigation, W.H.; resources, W.H.; data curation, W.H.; writing—original draft preparation, W.H.; writing—review and editing, W.H.; visualization, W.H.; supervision, W.H. and D.H.; project administration, W.H.; funding acquisition, W.H. All authors have read and agreed to the published version of the manuscript.
Funding
The funding provider for this research is Universitas Sebelas Maret through Doctoral Dissertation Research Grant (Hibah PDD) contract number 260/UN27.22/HK.07.00/2021 and 254/UN27.22/PT.01.03/2022.
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Informed consent was obtained from all subjects involved in the study.
Data Availability Statement
The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author.
Acknowledgments
I extend my sincere gratitude to Sebelas Maret University for financing this research and to the students who contributed to the interview and data collection procedure.
Conflicts of Interest
The authors declare no conflicts of interest.
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Figure 1.
Accident data for Indonesia from 2017 to 2021.
Figure 2.
Risk assessment model.
Figure 3.
Risk index bridge construction safety.
Table 1.
Characterization of respondents in this research.
| No | Description | Classification | ||||||
|---|---|---|---|---|---|---|---|---|
| 1 | Gender | Male | Female | |||||
| 9 | 0 | |||||||
| 2 | Age (year) | 28–33 | 34–39 | 40–45 | 46–51 | 52–57 | ||
| 3 | 2 | 3 | 0 | 1 | ||||
| 3 | Work experience (year) | 8–10 | 11–13 | 14–16 | 17–19 | 20–22 | ||
| 2 | 3 | 0 | 1 | 3 | ||||
| 4 | Education level | S1 | S2 | |||||
| 6 | 3 | |||||||
| 6 | Job positions | JP1 | JP2 | JP3 | JP4 | JP5 | ||
| 1 | 2 | 1 | 3 | 2 | ||||
Notation: S1: bachelor; S2: master; JP1: project management; JP2: project engineering; JP3: quality control; JP4: HSE; JP5: supervising.
Table 2.
Scale for measuring the probability of accidents.
| Likelihood | Description | Scale |
|---|---|---|
| Almost certain | Accidents occur more than once a year. | 5 |
| Likely | Accidents occur once a year. | 4 |
| Possible | Accidents occur once every two years. | 3 |
| Unlikely | Accidents occur once every three years. | 2 |
| Rare | Accidents occur once every five years. | 1 |
Table 3.
Scale of measurement due to the severity of an accident.
| Severity | Description | Scale |
|---|---|---|
| Catastrophic | Death of a worker. | 5 |
| Significant | Severe injuries that cause disabilities. | 4 |
| Moderate | Severe injuries that do not lead to disability and require treatment for more than one day. | 3 |
| Minor | Moderate injury with a treatment duration of less than one day. | 2 |
| Insignificant | Minor injuries, with the ability to resume work quickly following help. | 1 |
Table 4.
Assessment of probability and severity of bridge construction risks.
| No. | Code | Risk | Probability | Severity | ||
|---|---|---|---|---|---|---|
| Mean | STD | Mean | STD | |||
| 1 | R.1. | Worker subjected to welding exposure | 1.8889 | 0.3333 | 1.6667 | 0.5000 |
| 2 | R.2. | Worker’s skin scorched due to exposure to concrete | 2.5556 | 0.5270 | 1.2222 | 0.4410 |
| 3 | R.3. | Worker punctured with a sharp object | 2.3333 | 0.5000 | 1.4444 | 0.5270 |
| 4 | R.4. | Worker struck by large equipment or vehicles | 1.5556 | 0.5270 | 3.0000 | 0.5000 |
| 5 | R.5. | Worker’s body lacerated | 2.2222 | 0.4410 | 1.6667 | 0.5000 |
| 6 | R.6. | Worker falls | 3.3333 | 0.5000 | 3.7778 | 0.4410 |
| 7 | R.7. | Worker injured by equipment | 1.4444 | 0.5270 | 2.3333 | 0.5000 |
| 8 | R.8. | Worker electrocuted | 2.2222 | 0.4410 | 2.2222 | 0.4410 |
| 9 | R.9. | Worker slips | 2.4444 | 0.5270 | 2.0000 | 0.0000 |
| 10 | R.10. | Worker trapped | 2.2222 | 0.4410 | 2.3333 | 0.5000 |
| 11 | R.11. | Worker injured by a descending item | 2.1111 | 0.3333 | 2.2222 | 0.4410 |
| 12 | R.12. | Worker injured by girder | 1.1111 | 0.3333 | 3.3333 | 0.5000 |
| 13 | R.13. | Welding sparks hit the worker’s body | 2.2222 | 0.4410 | 1.3333 | 0.5000 |
| 14 | R.14. | Hearing impairment caused by noise | 2.1111 | 0.3333 | 1.7778 | 0.4410 |
| 15 | R.15. | Worker injured after being caught by steel reinforcement | 2.3333 | 0.5000 | 2.2222 | 0.4410 |
| 16 | R.16. | Heavy equipment or vehicle overturned | 2.1111 | 0.6009 | 2.3333 | 0.5000 |
| 17 | R.17. | Equipment falls into a river | 1.8889 | 0.3333 | 1.4444 | 0.5270 |
| 18 | R.18. | Concrete reinforcement fails | 2.0000 | 0.5000 | 2.5556 | 0.5270 |
| 19 | R.19. | Concrete formwork collapses | 2.6667 | 0.5000 | 3.3333 | 0.5000 |
| 20 | R.20. | Warth wall crumbles | 2.3333 | 0.5000 | 2.0000 | 0.0000 |
| 21 | R.21. | Girder breaks | 2.0000 | 0.0000 | 2.5556 | 0.5270 |
| 22 | R.22. | Girder rolls over | 2.3333 | 0.5000 | 2.2222 | 0.4410 |
| 23 | R.23. | Girder collapses during installation | 3.5556 | 0.5270 | 4.5556 | 0.5270 |
| 24 | R.24. | Pile overturns | 2.2222 | 0.4410 | 2.6667 | 0.5000 |
Table 5.
Probability in terms of likelihood and severity risk.
| Risk Code | Probability Risk | Severity Risk | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |
| R.1. | 0.1111 | 0.8889 | 0 | 0 | 0 | 0.3333 | 0.6667 | 0 | 0 | 0 |
| R.2. | 0 | 0.4444 | 0.5556 | 0 | 0 | 0.7778 | 0.2222 | 0 | 0 | 0 |
| R.3. | 0 | 0.6667 | 0.3333 | 0 | 0 | 0.5556 | 0.4444 | 0 | 0 | 0 |
| R.4. | 0.4444 | 0.5556 | 0 | 0 | 0 | 0 | 0.1111 | 0.7778 | 0.1111 | 0 |
| R.5. | 0 | 0.7778 | 0.2222 | 0 | 0 | 0.3333 | 0.6667 | 0 | 0 | 0 |
| R.6. | 0 | 0 | 0.6667 | 0.3333 | 0 | 0 | 0 | 0.2222 | 0.7778 | 0 |
| R.7. | 0.5556 | 0.4444 | 0 | 0 | 0 | 0 | 0.6667 | 0.3333 | 0 | 0 |
| R.8. | 0 | 0.7778 | 0.2222 | 0 | 0 | 0 | 0.7778 | 0.2222 | 0 | 0 |
| R.9. | 0 | 0.5556 | 0.4444 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| R.10. | 0 | 0.7778 | 0.2222 | 0 | 0 | 0 | 0.6667 | 0.3333 | 0 | 0 |
| R.11. | 0 | 0.8889 | 0.1111 | 0 | 0 | 0 | 0.7778 | 0.2222 | 0 | 0 |
| R.12. | 0.8889 | 0.1111 | 0 | 0 | 0 | 0 | 0 | 0.6667 | 0.3333 | 0 |
| R.13. | 0 | 0.7778 | 0.2222 | 0 | 0 | 0.6667 | 0.3333 | 0 | 0 | 0 |
| R.14. | 0 | 0.8889 | 0.1111 | 0 | 0 | 0.2222 | 0.7778 | 0 | 0 | 0 |
| R.15. | 0 | 0.6667 | 0.3333 | 0 | 0 | 0 | 0.7778 | 0.2222 | 0 | 0 |
| R.16. | 0.1111 | 0.6667 | 0.2222 | 0 | 0 | 0 | 0.6667 | 0.3333 | 0 | 0 |
| R.17. | 0.1111 | 0.8889 | 0 | 0 | 0 | 0.5556 | 0.4444 | 0 | 0 | 0 |
| R.18. | 0.1111 | 0.7778 | 0.1111 | 0 | 0 | 0 | 0.4444 | 0.5556 | 0 | 0 |
| R.19. | 0 | 0.3333 | 0.6667 | 0 | 0 | 0 | 0 | 0.6667 | 0.3333 | 0 |
| R.20. | 0 | 0.6667 | 0.3333 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| R.21. | 0 | 1 | 0 | 0 | 0 | 0 | 0.4444 | 0.5556 | 0 | 0 |
| R.22. | 0 | 0.6667 | 0.3333 | 0 | 0 | 0 | 0.7778 | 0.2222 | 0 | 0 |
| R.23. | 0 | 0 | 0.4444 | 0.5556 | 0 | 0 | 0 | 0 | 0.4444 | 0.5556 |
| R.24. | 0 | 0.7778 | 0.2222 | 0 | 0 | 0 | 0.3333 | 0.6667 | 0 | 0 |
Table 6.
Probability class interval on the likelihood of girder collapses during installation.
| Class | Frequency | Probability | Cumulative | Interval |
|---|---|---|---|---|
| 1 | 0 | 0.0000 | 0 | 0–0.0000 |
| 2 | 0 | 0.0000 | 0.0000 | 0.0000–0.0000 |
| 3 | 4 | 0.4444 | 0.0000 | 0.0000–0.0000 |
| 4 | 5 | 0.5556 | 0.4444 | 0.0000–0.4444 |
| 5 | 0 | 0.0000 | 1.0000 | 0.4444–1.0000 |
Table 7.
Accuracy of the risk index from direct assessment and Monte Carlo simulation.
| No. | Risk | Accuracy |
|---|---|---|
| 1 | Worker subjected to welding exposure | 0.26% |
| 2 | Worker’s skin scorched due to exposure to concrete | 0.04% |
| 3 | Worker punctured with a sharp object | 0.47% |
| 4 | Worker struck by large equipment or vehicles | 0.19% |
| 5 | Worker’s body lacerated | 0.08% |
| 6 | Worker falls | 0.03% |
| 7 | Worker injured by equipment | 0.47% |
| 8 | Worker electrocuted | 0.10% |
| 9 | Worker slips | 0.23% |
| 10 | Worker trapped | 0.13% |
| 11 | Worker injured by a descending item | 0.01% |
| 12 | Worker injured by girder | 0.02% |
| 13 | Welding sparks hit the worker’s body | 0.20% |
| 14 | Hearing impairment caused by noise | 0.11% |
| 15 | Worker injured after being caught by steel reinforcement | 0.13% |
| 16 | Heavy equipment or vehicle overturns | 0.02% |
| 17 | Equipment falls into a river | 0.25% |
| 18 | Concrete reinforcement fails | 0.22% |
| 19 | Concrete formwork collapses | 0.02% |
| 20 | Earth wall crumbles | 0.08% |
| 21 | Girder breaks | 0.05% |
| 22 | Girder rolls over | 0.13% |
| 23 | Girder collapses during installation | 0.06% |
| 24 | Pile overturns | 0.03% |
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MDPI and ACS Style
Hartono, W.; Kristiawan, S.A.; Handayani, D.; Sutopo, W. Risk Assessment with Monte Carlo Simulation to Improve Bridge Construction Safety. Eng. Proc. 2025, 84, 56. https://doi.org/10.3390/engproc2025084056
AMA Style
Hartono W, Kristiawan SA, Handayani D, Sutopo W. Risk Assessment with Monte Carlo Simulation to Improve Bridge Construction Safety. Engineering Proceedings. 2025; 84(1):56. https://doi.org/10.3390/engproc2025084056
Chicago/Turabian StyleHartono, Widi, Stefanus Adi Kristiawan, Dewi Handayani, and Wahyudi Sutopo. 2025. "Risk Assessment with Monte Carlo Simulation to Improve Bridge Construction Safety" Engineering Proceedings 84, no. 1: 56. https://doi.org/10.3390/engproc2025084056
APA StyleHartono, W., Kristiawan, S. A., Handayani, D., & Sutopo, W. (2025). Risk Assessment with Monte Carlo Simulation to Improve Bridge Construction Safety. Engineering Proceedings, 84(1), 56. https://doi.org/10.3390/engproc2025084056