Development of Risk Quantification Models in Road Infrastructure Projects

Abstract

Road infrastructure is a significant factor in the development of any country, affecting economic growth, social development, and environmental sustainability. Large infrastructure projects often face significant risks and uncertainties, which can lead to delays, budget over-runs, and an insufficient quality of the completed work. These issues undermine the economic viability of projects and affect the overall efficiency of infrastructure development. For these reasons, based on a literature review and completed project analysis, the risks that lead to an increasing Contract Price (ICP) and an Extension of Time (EoT) for the construction of the project are identified. Based on the results of the completed project analysis, the values of the ICP and EoT were quantified. Also, the probability of the occurrence of each risk in new projects was calculated. Based on the obtained results, a model was defined that groups risks into clusters. Risks in the first cluster should have priority for funding, and preventive measures are defined for them. The model obtained in this way can greatly enhance project management in real-world conditions and can lead to a significant reduction in project time and budget over-runs.

1. Introduction

Risk is defined as the chance of an undesirable event occurring depending on the circumstances [1]. Risk management is a systematic approach to dealing with risk and involves making a series of decisions to ensure that the project’s implementation proceeds in a safe and efficient manner [2]. Risks arise during all phases of project execution. If these risks are not assessed and managed effectively, they can affect the project’s performance [3].

International projects in the field of road infrastructure attract companies from developing countries such as China, India, Brazil, and Turkey [1]. However, international projects bring specific risks that do not appear in domestic projects [4]. Therefore, an appropriate risk management process is needed to meet the project’s success criteria and to avoid higher-level risks during international projects [5]. The importance of risk management in international projects has been examined by several authors [4,6,7].

In addition to risk analysis, it is necessary to pay attention to incorporating environmentally friendly raw materials into construction practices, which is essential for enhancing environmental sustainability and reducing costs. Recent studies have demonstrated the potential of using crushed waste oyster shells as an eco-friendly alternative in mortar production. These materials not only contribute to reducing the environmental impact through the repurposing of waste but also enhance the mechanical characteristics and longevity of the mortar. The inclusion of supplementary cementitious materials further enhances these benefits, making the use of waste oyster shells a viable strategy for sustainable construction [8,9]. Also, when designing roads [10,11], it is necessary to pay attention to the safety of all road users [12,13,14], as well as the capacity of roads [15,16]. Therefore, integrating such materials into construction practices is crucial for promoting environmental sustainability and achieving cost-effective solutions. However, a key aspect of road infrastructure project management is risk analysis.

Risk management is an ongoing process that begins with the identification of potential risks associated with the project. Risk identification precedes risk assessment, where the potential impacts of identified risks are evaluated. Once project risks are identified and assessed, appropriate measures to mitigate the risk or responses to the risk are formulated [1]. Project performance typically depends on the appropriate mitigation measures being adopted to address the identified risks [17,18].

Extensions of Time are one of the most significant risks that must be managed [19]. Factors leading to Extensions of Time can be divided into nine groups [20]. In their study, Kim et al. [21] used a Bayesian belief network model to examine and determine the probability of Extensions of Time in two analyzed projects, obtaining results of 72% and 67%. The average Extension of Time was 10% of the total time allocated for project implementation.

However, a small number of studies examine the risks related to “Extension of Time”, while on the other hand, a significant number of studies examine the risks related to the “increasing Contract Price” of projects.

Literature Review

Defining and analyzing risks in road infrastructure projects is crucial in the early stages of a project and represents a critical success criterion [22,23]. Risk assessment and predicting cost over-runs are major challenges in many projects [24]. The assessment of contingency costs is an essential phase in risk management [25].

Contingencies are defined as identified risks and unexpected events that can occur during various phases of a project. At the beginning of the project, the likelihood of contingencies is relatively high due to greater uncertainty and gradually decreases during subsequent phases of the project [26]. In their study, Flyvbjerg and Dirk [27] noted that 90% of infrastructure projects had cost over-runs and that in road construction projects, the average cost over-run was 20%.

In their study, Afzal et al. [17] analyzed developed models for reducing project cost over-runs presented in studies from 2008 to 2018. The analyzed models were based on the following methods: Adaptive Neuro-Fuzzy Inference Systems; Bayesian belief networks; Dynamic Bayesian Networks; Fuzzy Hybrid Models; Genetic Algorithms; Fuzzy Evaluation Models; Multi-Criteria Regression Analysis; Monte Carlo Simulation, and many others. On the other hand, Valipour et al. [28], Fang et al. [29], Qazi et al. [30], Islam et al. [31], and Islam and Nepal [32] developed models based on artificial intelligence to manage risk and reduce cost over-runs. The dynamics and complexity of a project bring a series of risks that result in increased project costs [33,34,35,36].

Table 1. Key characteristics and research results based on a literature review.

Authors	The Title of the Paper	Year	Methodology	Key Research Results
Wang, Dulaimi, and Aguria [7]	Risk management framework for construction projects in developing countries	2004	Alien Eyes’ Risk Model	Twenty-eight critical risks were identified and categorized on three (state, market, and project) hierarchical levels, and their criticality was assessed and ranked.
Luu, Kim, Van, and Ogunlana [21]	Quantifying schedule risk in construction projects using Bayesian belief networks	2009	Bayesian belief networks	Sixteen factors were identified that can have a direct impact on exceeding deadlines.
Kululanga and Kuotcha [37]	Measuring project risk management process for construction contractors, with statement indicators linked to numerical scores	2010	Statistical analysis	Most of the variables in the project risk management process were positively and significantly related to the progression in size and the experience of construction contractors.
Dandage, Mantha, and Rane [38]	Ranking the risk categories in international projects using the TOPSIS method	2018	TOPSIS method	Identification of eight different types of risk categories associated with international projects.
Viswanathan, Tripathi, and Jha [1]	Influence of risk mitigation measures on international construction project success criteria—a survey of Indian experiences	2020	Factor analysis	The positive relationship between risk mitigation factors and project success (coefficient 0.8).
Issa, Mosaad, and Salah Hassan [39]	Evaluation and selection of construction projects based on risk analysis	2020	AHP, Fuzzy risk analysis model	Five criteria and seventy factors influencing the decision of the contractor were identified, and the weight and importance of each criterion were determined.
Khalilzadeh, Banihashemi, and Božanić [40]	A Step-By-Step Hybrid Approach Based on Multi-Criteria Decision-Making Methods and A Bi-Objective Optimization Model to Project Risk Management	2024	Fuzzy method	An innovative and reliable hybrid approach based on MCDM and mathematical optimization methods was proposed.
Our Study	Development of Risk Quantification Models in Road Infrastructure Projects	2024	Aggregation models; Weighted Linear Combination (WLC) method; cluster analysis.	From the literature and completed projects, 7 groups of factors, with a total of 56 factors, which influence the increase in the price and the extension of the deadline for the construction of infrastructure projects were identified. Every factor is quantified (price and number of days). Prevention measures were defined for the factors that have the greatest impact on increasing the costs and time of construction of infrastructure projects.

summarizes the most important characteristics of key papers in this area, such as their research methodology, and the key research results within the topic of interest. The studies included in Table 1 were selected for their relevance to risk management in road infrastructure projects. The objective is to offer a comprehensive overview by incorporating research with diverse methodologies, spanning various publication years, and including recent studies with varied conclusions. This selection process ensures broad representation and highlights the evolution and range of approaches in risk management research. By presenting this spectrum of methodologies and findings, the table aims to provide a nuanced understanding of the field and illustrate the progression of research over time.

2. Methodology and Tools

In this study, risks affecting delays, shown through an Extension of Time (EoT), and cost over-runs, shown through an increasing Contract Price (ICP), in road infrastructure projects are analyzed. The analysis was performed based on data from the literature and completed projects, and for each risk, the probability of occurrence in new projects was defined. To quantify each risk of EoT and ICP, aggregation models and multi-criteria decision-making methodologies (MCDMs) were used. Also, using cluster analysis, we identified the group of risks with the greatest impact on EoT and ICP, as well as the greatest probability of it appearing in future projects.

2.1. Risk Quantification

The literature and data from completed projects were analyzed to identify relevant risks. Based on this analysis, risks were grouped into seven categories.

• Multi-Criteria Decision-Making (MCDM)

The analyzed problem can be considered as a typical multi-criteria decision-making (MCDM) problem, where certain alternatives should be ranked according to several criteria [41]. The Weighted Linear Combination (WLC) method, which consists of several key steps that ensure systematic and objective decision-making, was used as the MCDM [42]. First, the data are collected for all relevant criteria that will be used in the evaluation of options. These data are then normalized to standardize the different metrics according to the same scale (between 0 and 1), allowing for a fair comparison. The next step is to determine the weights for each criterion, which reflect the relative importance of each criterion in the final decision. After that, the normalized values of each criterion are multiplied by the corresponding weights, and the resulting weighted amounts are added for each option, resulting in a total score. Finally, the options are ranked according to their overall ratings, with options with higher ratings taking precedence. This process enables structured and transparent decision-making that takes multiple aspects of performance and risk into account.

• Cluster Analysis

Cluster analysis was employed to identify the group of risks with the greatest impact on EoT and ICP and the highest probability of occurrence in future projects. This analysis allowed for the identification of key risks that require special attention in project management.

2.2. Software and Tools Used

The analysis was conducted using SPSS software (v. 28.0) for statistical analysis and Python software (v. 3.10.4) for data normalization, risk quantification, and cluster analysis.

By combining methodologies for risk quantification, MCDM, cluster analysis, and descriptive statistics, a comprehensive model for risk identification and management in road infrastructure projects was developed. This model enables more efficient project management, reduces delays and budget over-runs, and facilitates better planning of preventive measures for future projects. For a clearer presentation of the paper’s methodology, the flowchart diagram is shown in Figure 1.

3. Results

3.1. Project Dataset

The database employed in this research encompasses 28 successfully completed projects within the construction of the European Road Corridor 10, traversing the Republic of Serbia. Originating from the northern border with Hungary, the European Road Corridor 10 proceeds southward. In the vicinity of the city of Niš, Corridor 10 bifurcates into two distinct branches: the southern branch leading to the capital of Greece, Athens, and the eastern branch extending to Asia Minor via Bulgaria. All 28 contracts were meticulously executed following rigorous tender procedures that adhered to international standards and the regulations of international financial institutions.

The construction of the southern branch of Corridor 10, spanning 74.2 km, commenced in 2010 and was successfully concluded in 2024, marking the completion of all projects. This route was strategically divided into 10 distinct sections, complemented by an additional 2 sections dedicated to the development of parallel non-commercial roads. These roads were specifically designed to cater to the local population who were directly affected by the construction of the new highway, ensuring uninterrupted access and connectivity.

Furthermore, the construction of the eastern branch of Corridor 10, spanning 86.5 km, commenced in 2009 and was also successfully completed in 2024. This route encompassed a total of 16 contracts, each meticulously executed to ensure the highest standards of quality and efficiency. These projects included the construction of a full-profile highway, with the construction of seven tunnels and numerous bridges. The relevant construction contracts were signed in accordance with the Conditions of Contract for Construction, harmonized edition June 2010, for building and engineering works, designed by the Employer, the Multilateral Development Bank. The tender procedures that were applied to these open international tenders were governed by the World Bank’s Guidelines and EBRD Procurement Rules and described in the Guide to Procurement that was in force on the day of the Finance Contracts. The major procurement system used was a two-envelope system on postqualification, with only four procurements being based on the prequalification system.

The formation of the risk list applied in this research was carried out based on a review of the available literature and a specially organized expert interview called Risk Management, which was conducted during a two-day interview and discussion. A total of 14 engineers, experts from various fields with many years of experience in road infrastructure projects in Serbia and other countries, participated in the expert interview. All interviewed experts had also participated in some of the projects included in this analysis, as representatives of the Employer, engineers, or Technical Consultants. In this study, Employer’s Risk Events (EREs) were analyzed, which were the result of the realization of certain risks listed on the formed risk list. All Claims and Variation Orders, the application of the adjustment multiplier for Changes in Cost and associated coefficients, exchange rate differences due to payments in different currencies, contract terminations by the Employer, commercial interests due to delayed payments of Interim Payment Certificates, surpluses and shortages of contracted Bills of Quantities on the project, engagement of Dispute Adjudication Boards, and Amicable Settlements were analyzed. Each analyzed event resulted in additional payments that were not included in the Accepted Contract Amount, which resulted in an increasing Contract Price and/or an Extension of Time for project realization. The adopted risk list is connected to all risk events (there were 1429 in total), based on the analysis of all relevant documentation within each project, which includes the engineer’s determinations of Claims, Interim Payment Certificates, submitted Variation Orders, and Final Payment Certificates. In

Table 2. Descriptive statistics of completed projects.

	Accepted Contract Amount [EUR]	Time for Completion [Days]	The Length of the Section [km]	ICP [EUR]	EoT [Days]
Average	27,278,833.36	~610	7.23	41,343,706.21	~743
Min	3,283,504.45	120	0.17	1,537,082.86	0
Max	74,738,676.05	900	21.40	194,166,387.13	2075

, descriptive statistics for the completed projects are shown.

3.2. Identification of Factors

For the purposes of this study, a database of 28 completed projects was analyzed. An EoT was identified in 27 out of 28 projects, while an ICP was identified in all analyzed projects. Twenty-five projects were used to obtain quantified values of EoT and ICP, while three projects were used for the validation of results. Fifty-six different risks were identified, which were classified into seven risk groups. The findings highlight the key factors contributing to delays and cost over-runs in infrastructure projects, providing valuable insights for mitigating these risks and improving project outcomes. In Figure 2, seven risk groups are shown on an Ishikawa diagram.

Table 3. Presentation of systematized factors from the literature and specific projects.

Design	1.1 Non-compliance of the project with environmental conditions due to inappropriate design bases.
	1.2 Lack of details and technical specifications in the project documentation (insufficiently elaborated parts of the project documentation).
	1.3 Complex design or inappropriate construction technology.
	1.4 Non-compliance in parts of project documentation.
	1.5 Delays in the production or changes in project documentation during execution.
	1.6 Incorrect Bill of Quantities of works.
	1.7 Insufficiently examined and imprecisely determined locations, as well as available quantities of materials in borrow pits.
	1.8 Failure to provide adequate locations for deposit areas for excavated materials.
	1.9 Unresolved collisions with existing infrastructure facilities (underground installations, pipelines, local roads, railways, etc.).
	1.10 Inadequate design of riverbeds and storm water treatment.
	1.11 Inapplicable project documentation for high cuts, including tunnel portals.
External	2.1 Problems with property–legal relations (e.g., expropriation, etc.).
	2.2 Delay in obtaining permits and approvals from relevant authorities.
	2.3 Problems with obtaining a use permit.
	2.4 Local regulations regarding the construction of tunnels are insufficient.
	2.5 Changes in laws and regulations.
	2.6 Banks—compliance with the environmental and social requirements of each bank.
	2.7 Exchange rate instability and resource price spikes.
	2.8 New environmental restrictions or unforeseen circumstances (archeological sites, mines and explosives, etc.).
	2.9 Exceptionally adverse weather conditions.
	2.10 Force majeure (natural disasters, pandemic, epidemic, etc.).
Resource	3.1 Labor shortage.
	3.2 Low productivity and unskilled labor force.
	3.3 Lack of materials on the market.
	3.4 Inadequate quality of materials.
	3.5 Equipment failures and obsolete machinery.
	3.6 Lack of equipment (mechanization).
Employer	4.1 Delays in payment of Interim Payment Certificate by the Employer.
	4.2 Variation Order request.
	4.3 Slow decision-making.
	4.4 Poor communication between the Employer and other project participants.
	4.5 Lack of funds or lengthy procedure for financing unforeseen works and Variation Orders.
	4.6 Delay in handing over (parts of) the construction site to the contractor.
	4.7 A long period of additional contracting for unforeseen and subsequent works (especially due to changes during implementation).
Contractor	5.1 Re-execution of works due to errors or poor quality of the works performed.
	5.2 Poor financial condition of the contractor.
	5.3 Inefficient planning and management of works on the construction site.
	5.4 Inadequate experience of the contractor.
	5.5 Irresponsible execution of works and jeopardizing the safety of other works.
	5.6 The contractor entering the OFAC (Office of Foreign Assets Control) list of sanctioned persons and companies.
Engineer	6.1 Lack of experience and expertise on the part of the engineer.
	6.2. Insufficient number of engineering team members.
	6.3 Avoiding professional supervision to take a proactive role and issue instructions.
	6.4 Delays in reviewing and certifying the performed works.
	6.5 Delays in the review and approval of the Method Statement.
	6.6 Delays in the review and approval of materials.
Project	7.1 Inadequate duration of the project according to the contract.
	7.2 Inadequate or imprecise contract terms.
	7.3 Unsolved Claims, Variations, and VEPs.
	7.4 High complexity of the project (scope of works, topography, access restrictions, new technologies, etc.).
	7.5 Disputes between different parties involved in the project during the implementation of the works.
	7.6 Inadequate Cash Flow of the project.
	7.7 Poor Contract Management of the project.
	7.8 Termination of the contract.
	7.9 Non-compliance of the contractor’s activities on adjacent construction sites.
	7.10 Accidents on the construction site.

presents a systematized overview of the identified risks. The selected risk factors were taken from the following studies: Assaf and Al-Hejji [20]; Chan and Kumaraswamy [43]; Gondia et al. [44]; Gunduz and Yahya [45]; Rachid et al. [46]; and Santoso and Soeng [47]. Similar risks, based on their nature of occurrence and supported by the existing literature, were categorized into these seven distinct groups. This classification provides a structured framework for understanding the common origins and characteristics of risks affecting infrastructure projects, aiding in the development of targeted risk management strategies.

3.3. Risk Occurrence in Projects

For each event in a project, there is a major risk that is dominant and has the most significant impact on the outcome of that event. Depending on the type of event, there may be one or more secondary risks, which have a smaller impact than the major risk but can still contribute to the overall project risk. However, there are situations where secondary risks are not present, making the major risk the only relevant factor. In each analyzed project, to quantify the values of ICP and EoT, the major risk was first defined, while the other identified risks were designated as secondary.

Some risks appear more often in infrastructure projects, while some risks rarely appear or do not appear at all. There are risks that appear more than once within a single project. To determine the average number of occurrences of a certain risk in one project, we use the following formula:

Ai = (Σfi)/N

where the following apply:

• Ai—the average number of occurrences of risk i;
• Σfi—the sum of occurrences for each project;
• N—the total number of projects.

Table 4. Results of (a) average number of occurrences of major risk and (b) average number of occurrences of secondary risk.

Risk Group	Risks	(a) Average Number of Occurrences of Major Risk	(b) Average Number of Occurrences of Secondary Risk
Design	1.1	10.54	18.64
	1.2	3.57	2.32
	1.3	2.57	4.64
	1.4	7.04	10.54
	1.5	3.93	9.04
	1.6	3.75	3.21
	1.7	3.18	0.54
	1.8	2.57	0.68
	1.9	12.04	4.39
	1.10	8.25	2.39
	1.11	13.29	3.36
External	2.1	1.57	0.96
	2.2	2.21	5.46
	2.3	2.43	0.82
	2.4	0.32	0.07
	2.5	1.75	0.82
	2.6	1.61	0.50
	2.7	1.21	0.36
	2.8	0.36	0.32
	2.9	0.18	0.54
	2.10		0.14
Resource	3.1		5.46
	3.2	0.25	0.82
	3.3	0.07	0.07
	3.4	1.86	4.04
	3.5		0.07
	3.6		0.07
Employer	4.1	0.46	0.21
	4.2	2.25	5.07
	4.3	0.18	0.21
	4.4		0.04
	4.5	0.18	0.25
	4.6	0.32	0.79
	4.7		0.07
Contractor	5.1	0.39	0.43
	5.2	0.32	0.25
	5.3	0.11	0.11
	5.4		0.21
	5.5	0.04	0.14
	5.6	0.21	0.04
Engineer	6.1	0.11	0.11
	6.2.		0.04
	6.3		0.11
	6.4		0.14
	6.5	0.11	0.14
	6.6		0.21
Project	7.1	0.29	0.29
	7.2	1.64	2.71
	7.3	0.61	1.11
	7.4	1.82	1.61
	7.5	0.68	0.39
	7.6		0.14
	7.7	0.25	0.29
	7.8	0.36	0.18
	7.9	2.82	0.79
	7.10		0.39

shows the results for (a) the average number of occurrences of the major risk and (b) the average number of occurrences of a secondary risk.

3.4. Quantification of ICP and EoT

Each analyzed project has one or more Claims and/or Variation Orders, which have a quantified ICP and EoT, which are caused by a certain number of identified risks. To quantify the values of ICP and EoT for each risk individually and based on all analyzed projects, the major risk was first defined, while the other risks were defined as secondary. The coefficients (0.9, 0.8, 0.7, 0.6, 0.5) of risk quantification, in the formulas below, were defined by the authors, in consultation with the 14 already mentioned experts, based on their previous expertise in completed projects. Depending on the number of accompanying risks, the following formulas were used to quantify the EoT:

Major risk

Single risk:

EoT_Rmri = EoT_c

Two risks:

EoT_Rmri = EoT_c × 0.9

Three risks:

EoT_Rmri = EoT_c × 0.8

Four risks:

EoT_Rmri = EoT_c × 0.7

Five risks:

EoT_Rmri = EoT_c × 0.6

Six and more risks:

EoT_Rmri = EoT_c × 0.5

Secondary risk

Two risks:

EoT_Rsr1 = EoT_c × 0.1

Three risks:

EoT_Rsr1 = EoT_c × 0.1; EoT_Rsr2 = EoT_c × 0.1

Four risks:

EoT_Rsr1 = EoT_c × 0.1; EoT_Rsr2 = EoT_c × 0.1; EoT_Rsr3 = EoT_c × 0.1

Five risks:

EoT_Rsr1 = EoT_c × 0.1; EoT_Rsr2 = EoT_c × 0.1; EoT_Rsr3 = EoT_c × 0.1; EoT_Rsr4 = EoT_c × 0.1

Six risks:

EoT_Rsr1 = EoT_c × 0.1; EoT_Rsr2 = EoT_c × 0.1; EoT_Rsr3 = EoT_c × 0.1; EoT_Rsr4 = EoT_c × 0.1;

EoT_Rsr5 = EoT_c × 0.1

More than six risks:

EoT_Rsri = EoT_c × 0.5/n

where the following apply:

• EoT_c—total number of days of delay per Claim or/and Variation Order;
• EoT_Rmri—the major risk;
• EoT_Rsri—the secondary risks;
• n—the number of secondary risks;
• i—the index of the secondary risk, starting from 1.

In order for the formulas for major and secondary risk to be applicable for all projects, the obtained values are expressed in percentages (the major and/or secondary risk in relation to the total value of the EoT for the specified project).

According to a similar principle, the ICP can also be calculated:

Major risk

Single risk:

ICP_Rmri = ICP_c

Two risks:

ICP_Rmri = ICP_c × 0.9

Three risks:

ICP_Rmri = ICP_c × 0.8

Four risks:

ICP_Rmri = ICP_c × 0.7

Five risks:

ICP_Rmri = ICP_c × 0.6

Six and more risks:

ICP_Rmri = ICP_c × 0.5

Secondary risk

Two risks:

ICP_Rsr1 = ICP_c × 0.1

Three risks:

ICP_Rsr1 = ICP_c × 0.1; ICP_Rsr2 = ICP_c × 0.1

Four risks:

ICP_Rsr1 = ICP_c × 0.1; ICP_Rsr2 = ICP_c × 0.1; ICP_Rsr3 = ICP_c × 0.1

Five risks:

ICP_Rsr1 = ICP_c × 0.1; ICP_Rsr2 = ICP_c × 0.1; ICP_Rsr3 = ICP_c × 0.1; ICP_Rsr4 = ICP_c × 0.1

Six risks:

ICP_Rsr1 = ICP_c × 0.1; ICP_Rsr2 = ICP_c × 0.1; ICP_Rsr3 = ICP_c × 0.1; ICP_Rsr4 = ICP_c × 0.1;

ICP_Rsr5 = ICP_c × 0.1

More than six risks:

ICP_Rsri = ICP_c × 0.5/n

where the following apply:

• ICP_c—total number of days of delay per Claim or/and Variation Order;
• ICP_Rmri—the major risk; ICP_Rsri—the secondary risks;
• n—the number of secondary risks;
• i—the index of the secondary risk, starting from 1.

Table 5. Results for (a) percentage of EoT and (b) percentage of ICP of risk.

		EoT [%]		ICP [%]
Risk Group	Risks	Major Risk	Secondary Risk	Major Risk	Secondary Risk
Design	1.1	10.25	3.24	1.24	0.35
	1.2		2.77	0.41	0.30
	1.3		2.42	1.05	0.28
	1.4	9.64	3.18	1.24	0.16
	1.5	29.57	2.34	2.91	0.43
	1.6		3.28	9.75	0.56
	1.7	7.15	1.87	1.57	1.11
	1.8		2.39	1.07	0.51
	1.9	20.27	2.52	0.33	0.21
	1.10		3.16	0.55	0.18
	1.11	16.28	2.66	5.66	0.39
External	2.1	31.69	2.89	2.26	0.07
	2.2	28.03	2.97	0.83	0.49
	2.3		2.53	0.36	0.31
	2.4		4.31	0.17	0.01
	2.5		2.90	0.94	0.05
	2.6		2.81	1.12	0.67
	2.7	2.57	2.10	10.84	0.37
	2.8	10.41	1.69	0.30	0.51
	2.9	4.09	3.40	1.49	0.57
	2.10		1.47		0.40
Resource	3.1		0.35		0.18
	3.2		0.35	2.46	0.18
	3.3		2.93	0.50	0.78
	3.4		3.44	1.13	0.18
	3.5		1.63		0.02
	3.6		1.63		0.01
Employer	4.1	4.78	4.24	0.26	0.95
	4.2		2.33	0.37	0.12
	4.3	7.15	6.56	3.00	0.69
	4.4		0.56		0.03
	4.5		4.11	0.06	0.02
	4.6	24.17	3.81	3.46	0.33
	4.7		1.22		0.63
Contractor	5.1		3.43	0.37	0.54
	5.2	6.97	2.63	2.61	3.99
	5.3	2.81	1.54	9.87	0.03
	5.4		3.23		0.20
	5.5		1.01	1.24	0.34
	5.6	4.83	2.17	7.56	3.55
Engineer	6.1		1.53	0.04	0.30
	6.2.		8.12		0.03
	6.3		2.75		0.35
	6.4		1.88		0.02
	6.5		2.10	0.29	0.09
	6.6		3.10		0.35
Project	7.1		2.22	0.93	0.13
	7.2	0.69	2.35	0.40	0.19
	7.3	0.03	2.28	0.30	0.76
	7.4	0.02	2.52	5.10	0.16
	7.5	0.33	2.71	3.75	0.29
	7.6		6.11		1.45
	7.7		0.91	0.24	0.05
	7.8		8.99	21.22	0.58
	7.9	0.63	2.67	1.81	0.34
	7.10		1.64		0.81

shows the results for (a) the percentage of EoT and (b) the percentage of ICP of a risk. For example, if risk 1.1. appears in a project as the major risk, it will cause an increase in ICP of 1.24% of the contracted price of the project, while the EoT will change by 10.25% of the contracted deadline for the completion of the project.

3.5. Risk Classification

In order to be able to compare the risks, with each risk being defined by the value of the EoT and ICP and the probability of occurrence of the risk (PoR), for major and secondary cases, it is necessary to perform data normalization:

$${{{\mathrm{EoT}}_{\mathrm{major}}}^{\mathrm{norm}}}_{ }={\displaystyle \frac{EOT\mathrm{major}-min\left(EOT\mathrm{major}\right)}{\max \left(EOT\mathrm{major}\right)-min\left(EOT\mathrm{major}\right)}}$$

$${{{\mathrm{EoT}}_{\sec }}^{\mathrm{norm}}}_{ }={\displaystyle \frac{EOT\sec -min\left(EOT\sec \right)}{\max \left(EOT\sec \right)-min\left(EOT\sec \right)}}$$

$${{{\mathrm{ICP}}_{\mathrm{major}}}^{\mathrm{norm}}}_{ }={\displaystyle \frac{ICP\mathrm{major}-min\left(ICP\mathrm{major}\right)}{\max \left(ICP\mathrm{major}\right)-min\left(ICP\mathrm{major}\right)}}$$

$${{{\mathrm{ICP}}_{\sec }}^{\mathrm{norm}}}_{ }={\displaystyle \frac{ICP\sec -min\left(ICP\sec \right)}{\max \left(ICP\sec \right)-min\left(ICP\sec \right)}}$$

$${{{\mathrm{PoR}}_{\mathrm{major}}}^{\mathrm{norm}}}_{ }={\displaystyle \frac{PoR\mathrm{major}-min\left(PoR\mathrm{major}\right)}{\max \left(PoR\mathrm{major}\right)-min\left(PoR\mathrm{major}\right)}}$$

$${{{\mathrm{PoR}}_{\sec }}^{\mathrm{norm}}}_{ }={\displaystyle \frac{PoR\sec -min\left(PoR\sec \right)}{\max \left(PoR\sec \right)-min\left(PoR\sec \right)}}$$

where the following apply:

• EoT_major^norm—the major normalized EoT risk; EoT_sec^norm—the secondary normalized EoT risk;
• ICP _major^norm—the major normalized ICP risk; ICP _sec^norm—the secondary normalized ICP risk;
• PoR _major^norm—the major normalized PoR; PoR _sec^norm—the secondary normalized PoR.

Based on the weighted values shown above, an overall risk score (R_s) can be calculated:

R_s = ω₁ × EoT_major^norm + ω₂ × EoT_sec^norm + ω₃ × ICP _major^norm + ω₄ × ICP _sec^norm + ω₅ × PoR _major^norm + ω₆ × PoR _sec^norm

where ω1, ω2, ω3, ω4, ω5, and ω6 are weighting factors that reflect the relative importance of each parameter. For the given example, all factors are equally important: ω1 = ω2 = ω3 = ω4 = ω5 = ω6 = 1/6.

Table 6. Data normalization results and R_si score.

		Occurrences of Risk		Impact of Risk EoT		Impact of Risk ICP
Risk Group	Risks	Major	Secondary	Major Risk	Secondary Risk	Major Risk	Secondary Risk	Risk Score
Design	1.1	0.7931	1.0000	0.1486	0.2662	0.0301	0.0877	0.39
	1.2	0.2686	0.1245		0.2276	0.0099	0.0752	0.12
	1.3	0.1934	0.2489		0.1988	0.0255	0.0702	0.12
	1.4	0.5297	0.5655	0.1398	0.2613	0.0301	0.0401	0.26
	1.5	0.2957	0.4850	0.4287	0.1923	0.0706	0.1078	0.26
	1.6	0.2822	0.1722		0.2695	0.2365	0.1404	0.18
	1.7	0.2393	0.0290	0.1037	0.1537	0.0381	0.2782	0.14
	1.8	0.1934	0.0365		0.1964	0.0260	0.1278	0.10
	1.9	0.9059	0.2355	0.2939	0.2071	0.0080	0.0526	0.28
	1.10	0.6208	0.1282		0.2597	0.0133	0.0451	0.18
	1.11	1.0000	0.1803	0.2360	0.2186	0.1373	0.0977	0.31
External	2.1	0.1181	0.0515	0.4595	0.2375	0.0548	0.0175	0.16
	2.2	0.1663	0.2929	0.4064	0.2440	0.0201	0.1228	0.21
	2.3	0.1828	0.0440		0.2079	0.0087	0.0777	0.09
	2.4	0.0241	0.0038		0.3541	0.0041	0.0025	0.06
	2.5	0.1317	0.0440		0.2383	0.0228	0.0125	0.07
	2.6	0.1211	0.0268		0.2309	0.0272	0.1679	0.10
	2.7	0.0910	0.0193	0.0373	0.1726	0.2630	0.0927	0.11
	2.8	0.0271	0.0172	0.1509	0.1389	0.0073	0.1278	0.08
	2.9	0.0135	0.0290	0.0593	0.2794	0.0361	0.1429	0.09
	2.10		0.0075		0.1208		0.1003	0.04
Resource	3.1		0.2929		0.0288		0.0451	0.06
	3.2	0.0188	0.0440		0.0288	0.0597	0.0451	0.03
	3.3	0.0053	0.0038		0.2408	0.0121	0.1955	0.08
	3.4	0.1400	0.2167		0.2827	0.0274	0.0451	0.12
	3.5		0.0038		0.1339		0.0050	0.02
	3.6		0.0038		0.1339		0.0025	0.02
Employer	4.1	0.0346	0.0113	0.0693	0.3484	0.0063	0.2381	0.12
	4.2	0.1693	0.2720		0.1915	0.0090	0.0301	0.11
	4.3	0.0135	0.0113	0.1037	0.5390	0.0728	0.1729	0.15
	4.4		0.0021		0.0460		0.0075	0.01
	4.5	0.0135	0.0134		0.3377	0.0015	0.0050	0.06
	4.6	0.0241	0.0424	0.3504	0.3131	0.0839	0.0827	0.15
	4.7		0.0038		0.1002		0.1579	0.04
Contractor	5.1	0.0293	0.0231		0.2818	0.0090	0.1353	0.08
	5.2	0.0241	0.0134	0.1011	0.2161	0.0633	1.0000	0.24
	5.3	0.0083	0.0059	0.0407	0.1265	0.2394	0.0075	0.07
	5.4		0.0113		0.2654		0.0501	0.05
	5.5	0.0030	0.0075		0.0830	0.0301	0.0852	0.03
	5.6	0.0158	0.0021	0.0700	0.1783	0.1834	0.8897	0.22
Engineer	6.1	0.0083	0.0059		0.1257	0.0010	0.0752	0.04
	6.2.		0.0021		0.6672		0.0075	0.11
	6.3		0.0059		0.2260		0.0877	0.05
	6.4		0.0075		0.1545		0.0050	0.03
	6.5	0.0083	0.0075		0.1726	0.0070	0.0226	0.04
	6.6		0.0113		0.2547		0.0877	0.06
Project	7.1	0.0218	0.0156		0.1824	0.0226	0.0326	0.05
	7.2	0.1234	0.1454	0.0100	0.1931	0.0097	0.0476	0.09
	7.3	0.0459	0.0595	0.0004	0.1873	0.0073	0.1905	0.08
	7.4	0.1369	0.0864	0.0003	0.2071	0.1237	0.0401	0.10
	7.5	0.0512	0.0209	0.0048	0.2227	0.0910	0.0727	0.08
	7.6		0.0075		0.5021		0.3634	0.15
	7.7	0.0188	0.0156		0.0748	0.0058	0.0125	0.02
	7.8	0.0271	0.0097		0.7387	0.5148	0.1454	0.24
	7.9	0.2122	0.0424	0.0091	0.2194	0.0439	0.0852	0.10
	7.10		0.0209		0.1348		0.2030	0.06

shows all the values of the normalized parameters (EoTmajornorm, EoTsecnorm, ICP majornorm, ICP secnorm, PoR majornorm, PoR secnorm), as well as the score of each individual risk score.

For group risk scores obtained from the analyzed projects, we used k-means cluster analysis [48]. By applying this analysis, a group comprising risks with similar scores was identified, enabling a detailed understanding of the ICP and EoT in infrastructure projects. The analysis resulted in the formation of nine risk groups, where each group is defined according to the similarity of scores between members of the same group. The analysis identified the five risks with the highest scores within the formed group, providing insights into key risk factors for further project evaluation and management. The five identified risks are presented below:

• 1.1 Non-compliance of the project with environmental conditions due to inappropriate design bases (0.39);
• 1.11 Inapplicable project documentation for high cuts, including tunnel portals (0.31);
• 1.9 Unresolved collisions with existing infrastructure facilities (underground installations, pipelines, local roads, railways, etc.) (0.28);
• 1.5 Delays in the creation or changes in project documentation during execution (0.26);
• 1.4 Non-compliance in parts of project documentation (0.26).

These risks highlight the critical need for proactive risk management strategies and thorough contingency planning to mitigate their adverse impacts on project timelines and budgets in road infrastructure construction.

3.6. Model Validation

To evaluate the practical applicability of the proposed model, we compared its results with the empirical data for the EoT and ICP of completed projects, focusing on the five most significant risks. From the dataset of 28 completed projects, we selected 25 projects for risk quantification and reserved 3 projects for validation of the results. The validation was conducted for the five most significant risks, for which countermeasures were also defined. For these three validation projects, the average values of each of the five analyzed risks were used to assess the accuracy of the model. This comparative analysis aimed to validate the model’s effectiveness by examining how closely its predictions align with real-world outcomes. In this way, we can identify potential improvements and ensure that the model provides reliable guidance for managing project timelines and overhead costs in the future. For validation, the Mean Absolute Error (MAE), Mean Squared Error (MSE), and R-squared (R²) were utilized as metrics [49,50,51]. These measures are commonly employed to assess the accuracy and goodness-of-fit of predictive models, providing insights into how well the model predictions align with the actual data.

Table 7. Results of MAE, MSE, and R² for ICP.

	ICP
	Major Risk			Secondary Risk
	MAE	MSE	R2	MAE	MSE	R2
1.1	0.16	0.0186	0.9578	0.06	0.0052	0.9622
1.11	0.18	0.0349		0.04	0.0034
1.9	0.11	0.0072		0.07	0.0068
1.5	0.36	0.0729		0.08	0.0095
1.4	0.48	0.0858		0.13	0.0124

shows the results of the MAE, MSE, and R² for ICP, while

Table 8. Results of MAE, MSE, and R² for EoT.

	EoT
	Major Risk			Secondary Risk
	MAE	MSE	R2	MAE	MSE	R2
1.1	0.43	0.1647	0.9486	0.19	0.0384	0.9602
1.11	0.62	0.4141		0.12	0.0105
1.9	0.89	1.3084		0.09	0.0092
1.5	0.92	1.3481		0.21	0.0184
1.4	0.77	1.0238		0.26	0.0242

shows the results for EoT.

The validation results, including the high R-squared (R²) values and low Mean Absolute Error (MAE) and Mean Squared Error (MSE) values, indicate that the models provide a strong predictive accuracy and fit [52,53]. The validation results for the predictive models across different risk categories demonstrate consistently high R-squared values, all about 95%. It can be concluded that the model, unlike several randomly selected risks from completed projects (which were not used in the creation of the model), does not exhibit significant deviations.

This analysis underscores the reliability of the model in capturing the underlying patterns of project timelines and overhead costs. By maintaining consistency even when applied to independent project data, the model demonstrates its reliability and generalizability. The minimal discrepancies between the model’s outputs and the completed project data highlight its accuracy and potential as a practical tool for project management. This validation through real-world comparison reinforces the model’s utility in predicting project outcomes, making it a valuable asset for project planners and managers.

4. Discussion

The comprehensive model developed in this study combines risk quantification, multi-criteria decision-making, cluster analysis, and descriptive statistics. This approach enables the identification and management of critical risks in road infrastructure projects, ultimately facilitating more efficient project management. By prioritizing investment in and defining preventive measures for the highest-impact risks, the model aims to reduce the EoT and ICP, enhancing the overall success of infrastructure projects.

Prioritization of Risks and Preventive Measures

Using cluster analysis, five key risks were identified, each with a significant impact on both the Extension of Time (EoT) and increasing Contract Price (ICP):

• Risk:
• 1.1 Non-compliance of the project with environmental conditions due to inappropriate design bases.
• Preventive Measures:

• A higher or satisfactory level of geological tests to enable the most accurate preparation of the base (as few approximations as possible);
• Installation of an adequate number of piezometers to monitor the level of underground water;
• Adequate geodetic surveying to create a geodetic base (instead of relying on data from the existing inaccurate network to reduce the costs of geodetic surveying);
• Addressing all holders of public authority for them to issue location conditions;
• Detailed previous archeological research;
• Data on hydrological and climatic impacts must be regularly updated.

• Risk:
• 1.11 Inapplicable project documentation for high cuts, including tunnel portals.
• Preventive Measures:

• A higher or satisfactory level of geological research;
• Conducting basic preliminary field research in the design phase;
• An adequate number of laboratory tests during the development of project documentation;
• Greater control when creating project documentation;
• Agreed penalties for errors in projects;
• Stricter criteria in the designer selection process (requiring more references);
• Holding responsible designers accountable;
• Installation of an adequate number of piezometers to monitor the level of underground water;
• Adequate geodetic surveying to create a geodetic base (instead of relying on data from the existing inaccurate network to reduce the costs of geodetic surveying);
• Introduction of design supervision in practice (during project implementation).

• Risk:
• 1.9 Unresolved collisions with existing infrastructure facilities (underground installations, pipelines, local roads, railways, etc.).
• Preventive Measures:

• Addressing all holders of public authority, including all cable operators and local public companies, for the issuance of location conditions;
• Consistent compliance with the issued location conditions in terms of crossing with and relocation of existing infrastructure facilities;
• Identification of all collisions on the ground before the start of construction in order to determine those that are not included in the location conditions;
• Timely conclusion of contracts on relocation of installations to define mutual relations with their owners;
• Introduction of user supervision of installation owners during the execution of works;
• A contract-defined mechanism for the relocation of uncharted simple communal installations (e.g., rural water lines and sewers);
• Creation of an adequate utility synchronization plan.

• Risk:
• 1.5 Delays in the creation or changes in project documentation during execution.
• Preventive Measures:

• Determination of an adequate deadline for the preparation of project documentation;
• Greater control during the design itself;
• Performing technical control in parallel with the design process (introducing phases);
• More thorough work by members of the Revision Commission (without political influence);
• Agreed penalties for errors in projects;
• Increased responsibility for designers;
• Changes in the local laws in this area to prescribe the designer’s obligation to eliminate all deficiencies in the project documentation;
• Introduction of design supervision in practice (during project implementation).

• Risk:
• 1.4 Non-compliance in parts of project documentation.
• Preventive Measures:

• Determination of an adequate deadline for the preparation of project documentation;
• Greater control during the creation of the basic project;
• Agreed penalties for errors in projects;
• Increased responsibility for designers;
• Changes in the local laws in this area to prescribe the designer’s obligation to eliminate all deficiencies in the project documentation;
• Introduction of design supervision in practice (during project implementation).

Implementing the abovementioned preventive measures is crucial for ensuring the compliance of infrastructure projects to mitigate key risks. Adherence to these countermeasures can significantly reduce project delays and cost over-runs, ultimately leading to more sustainable and efficient project outcomes. The identification and prioritization of key risks, as achieved through our comprehensive analysis, allows for targeted investments in preventive measures, enhancing the overall resilience of a project. By proactively addressing potential risks and their impacts, we can minimize unforeseen disruptions and associated costs, leading to substantial savings in both time and budget. Furthermore, the adoption of these strategies fosters a more responsible approach to infrastructure development, aligning project objectives with broader sustainability goals and regulatory requirements. This strategic risk management protects the project’s economic viability.

5. Conclusions

The comprehensive model developed in this study combines risk quantification, multi-criteria decision-making (MCDM), cluster analysis, and descriptive statistics. This approach enables the identification and management of critical risks in road infrastructure projects, ultimately facilitating more efficient project management. By prioritizing investment in and defining preventive measures for the highest-impact risks, the model aims to reduce project delays and budget over-runs, enhancing the overall success of infrastructure projects.

Implementing the outlined preventive measures is crucial for ensuring the compliance of infrastructure projects and mitigate key risks. Adherence to these countermeasures can significantly reduce project delays and cost over-runs, ultimately leading to more sustainable and efficient project outcomes. The identification and prioritization of key risks, achieved through our comprehensive analysis, allows for targeted investments in preventive measures, enhancing the overall resilience of a project. By proactively addressing potential risks and their impacts, we can minimize unforeseen disruptions and associated costs, leading to substantial savings in both time and budget. Furthermore, adopting these strategies fosters a more responsible approach to infrastructure development, aligning project objectives with broader sustainability goals and regulatory requirements.

The criteria and risks mentioned form a model that can most likely only be applied to Serbia and the countries of the Western Balkans. However, this approach and methodology can be applied universally, with the list of risks and their quantification varying accordingly. In analyzing the identified risks in road infrastructure projects, it is important to consider the impact of regional and national factors on risk management. Different construction methods, legal frameworks, and local conditions that are specific to each country can significantly influence the frequency and severity of certain risks, potentially affecting the applicability of the proposed model in various contexts. Therefore, further analyses will focus on adapting the model to the specific conditions of different countries, thereby enhancing its universality and applicability. This approach enables more effective management of infrastructure projects, taking into account the unique conditions of each country, and opens up opportunities for future studies aimed at improving the global efficiency of such projects.

Limitations of the study include the reliance on retrospective data from the literature and completed projects, which may introduce inherent biases and limitations in data availability and quality [54,55]. The generalizability of findings to diverse geographical and project-specific contexts may also be constrained. Additionally, the complexity of accurately predicting and quantifying risks such as cost over-runs (ICP) and time extensions (EoT) in future projects remains a challenge, influenced by evolving socioeconomic conditions and unforeseen external factors. Future studies could benefit from longitudinal data collection and more robust methodologies to address these limitations and enhance the reliability and applicability of risk assessment frameworks in infrastructure projects. Also, it is necessary to analyze the aspect of modern vehicles and requirements from the aspect of traffic when creating infrastructural projects.

Future research directions could focus on enhancing the predictive accuracy and applicability of risk models in road infrastructure projects. This includes refining methodologies for quantifying risks associated with cost over-runs (ICP) and time extensions (EoT) and incorporating dynamic factors such as changing economic conditions and other impacts. Additionally, exploring advanced statistical techniques and machine learning algorithms to improve risk assessment and cluster analysis could provide deeper insights into the interdependencies among risks and their impacts on project outcomes. Moreover, investigating innovative strategies for risk mitigation and management, including early identification and proactive measures for high-priority risk clusters, could significantly enhance a project’s efficiency and sustainability in real-world infrastructure development scenarios. In addition, it is necessary to examine projects with a larger number of risks, such as, for example, political risk at the macrolevel.