Reliability-Based Optimization of Flexible Pavement Maintenance Using Nonlinear Deterioration Models: A Case Study from Al-Najaf, Iraq

Flexible pavements are a foundational element of transportation infrastructure, facilitating mobility, commerce, and socio-economic progress. In rapidly developing and climatically harsh regions like Al-Najaf, Iraq, these pavements face accelerating degradation due to extreme heat, overloaded traffic, insufficient drainage, and erratic traffic flow. Such factors intensify pavement distress mechanisms, including rutting, fatigue cracking, and thermal shrinkage, prompting the need for predictive maintenance strategies that can optimise pavement lifespan and minimise financial waste [1]. According to AASHTO standards and modern pavement engineering research, the deterioration of pavements due to repeated loading and environmental stressors does not follow a linear pattern; instead, it tends to accelerate over time in a nonlinear manner [2, 3]. The case of Al-Najaf represents a particularly complex example of pavement deterioration, making it an appropriate context for assessing advanced modelling approaches. Over 12 million religious tourists come in and go out of the city annually; as a result, the city experiences seasonal peaks in traffic [4], in addition to bearing a daily ESAL in excess of 23,000 on its main roads, such as the Al-Kufa-Najaf Road [5]. These conditions are exacerbated by extreme climatic conditions, summer temperatures frequently exceed 47℃, and normal precipitation is less than 100 mm per year, with regular sandstorms. Together, these climatic stresses degrade the asphalt layers and the sub-base materials, causing the road to fail prematurely [6, 7]. In such a complex setting, traditional linear deterioration models fall short. Nonlinear modelling tools like Weibull and exponential functions provide better accuracy in predicting pavement performance under highly variable environmental and operational conditions [8, 9]. This study conducts an in-depth evaluation of such nonlinear deterioration models, utilising extensive field data gathered over eight years in Al-Najaf. By applying reliability analysis techniques, the research estimates the probability of failure and identifies long-term maintenance requirements. These insights are essential for infrastructure planners aiming to optimise rehabilitation timing, set investment priorities, and align maintenance efforts with budget constraints [10, 11]. The integration of empirical data and probabilistic risk analysis contributes to the advancement of pavement management practices, particularly in arid, high-demand urban environments.

The study focuses on three road corridors in Al-Najaf: urban arterials, airport highway, and religious access roads. While extensive performance data was collected between 2016 and 2024, certain subgrade and layer thickness values were estimated based on standard construction reports, which may introduce potential biases in calibration accuracy. Moreover, traffic measurement errors and the lack of spatially distributed data could affect the reliability of the models. Although sensitivity analysis was used to mitigate these issues, the limitations of relying solely on Weibull and exponential models without incorporating spatial variability should also be acknowledged.

This paper uses a systematic approach to model pavement deterioration and to optimise corresponding maintenance policies of the Al-Kufa-Najaf Road in southern Iraq. The method starts with a detailed study of the project area and moves on to the organised aggregation and treatment of performance information for the period of 2016-2024. The effect of environment and structural conditions on the pavement is then explained. Indicators of performance (IRI, rutting, cracking) are adjusted for calibration of the nonlinear models of deterioration (Weibull and Exponential). A reliability analysis is incorporated to predict the failure probability and to provide maintenance timings. The approach additionally involves a comparative simulation of five maintenance options and is then complemented with a sensitivity analysis based on the Monte Carlo method to assess the effect of uncertainty in traffic, climate, and maintenance interruptions.

5.1 Study area description

The study area is identified as Al-Kufa-Najaf Road, a major urban arterial in Al-Najaf Governorate, southern Iraq. The area has an arid climate characterised by extremely high summer temperatures (over 47℃), low annual rainfall (< 100 mm), and frequent sandstorms, which exacerbate the condition of roads. This corridor is heavily used, featuring roughly 23,000 ESALs/day due to its role in daily commuting purposes and religious tourism. The asphalt section structure of the pavement is divided into 5–6 cm of wearing layer, 12 cm of binder layer, and 25–30 cm of base layer supported by the natural roadbed.

5.2 Data collection and processing

In this study, we collected a comprehensive set of engineering and environmental data over eight years to monitor pavement performance among selected corridors in Al-Najaf. These parameters were then gathered using standardised methods of collection to ensure high levels of precision and temporal consistency. Measuring parameters:

• IRI was evaluated using the Automated Road Analyser (ARAN) longitudinal surface profiles and provided surface roughness quantifications.
• Rutting depth was measured by 3D high-precision laser Profiling, which recorded permanent deformations in the wheel paths.
• Surface cracking is manually monitored, may include photometric image analysis to obtain the CSI according to ASTM D6433 standards.
• Resilient modulus determined by the Falling Weight Deflectometer (FWD) test has an average value of about 65 MPa and shows subgrade strength.
• Traffic loads (ESALs/day) were estimated through a combination of manual vehicle counts and fixed inductive loop detectors to calculate the Equivalent Single Axle Loads (ESALs).
• Climatic data, sourced from the Iraqi Meteorological Organisation, includes the main types of environment-stress factors on pavements: annual temperature ranges and their extremes (including rainfall levels), and frequency data for sandstorms. Meeting the needs of incomplete and inconsistent data records (less than 5 per cent of all data), interpolation techniques such as cubic spline and second-order polynomial fitting were used. Finally, all data were transformed into normalised annual flat intervals for use in model development work calibration.

5.3 Engineering and environmental context

The performance of flexible pavements in Al-Najaf is heavily influenced by the region’s extreme environmental conditions and structural pavement configurations. Over the past decade, Al-Najaf has experienced a marked shift in climate, which has directly impacted the durability of road surfaces and accelerated the degradation of pavement materials.

Table 1. Climatic and environmental conditions in Al-Najaf (2016–2024)

As shown in Table 1, climatic data collected between 2016 and 2024 indicate a progressive increase in maximum summer temperatures from 46.1℃ in 2016 to 47.9℃ in 2024, paired with a consistent decline in annual rainfall, dropping from 101.4 mm to just 86.3 mm. In parallel, the number of sandstorms per year has risen sharply, increasing from 14 to 22 events over the same period. These shifts are visualised in Figure 1, which highlights the dual climatic stressors: rising temperatures and diminishing precipitation. Together, these factors intensify pavement fatigue, accelerate oxidative ageing of asphalt binders, and promote thermal cracking and surface ravelling, particularly in unshaded or poorly drained segments of the network. This environmental background necessitates the use of durable pavement structures that can withstand thermal stress and surface erosion.

Figure 1. Max temperature and rainfall of the climatic trend in Al-Najaf (2016–2024)

Table 2 summarises the typical cross-section of flexible pavements deployed in Al-Najaf’s main corridors. The surface course generally consists of a 5–6 cm layer of hot mix asphalt (HMA), which is prone to oxidation under elevated temperatures. Beneath this lies a 12 cm binder course composed of dense bituminous material that provides intermediate structural support. The load distribution is handled by a 25 cm crushed aggregate base and a 30 cm subbase of compacted granular fill resting over natural subgrade. This layered design is intended to manage the significant traffic loading typical of the region while mitigating environmental impacts.

Table 2. Structural design of pavement layers (typical cross-section)

However, as thermal gradients steepen and sandstorm frequency increases, even well-engineered pavements require advanced performance monitoring and predictive maintenance strategies. Together, Table 1, Table 2, and Figure 1 frame the environmental and structural constraints facing pavement engineers in Al-Najaf. These inputs serve as a critical foundation for the subsequent modelling of deterioration behaviour and the selection of context-appropriate maintenance strategies.

5.4 Pavement performance monitoring

Observation of pavement performance over long periods of time provides an important basis for recognising the degradation process of road structure under combined traffic-environmental action. For the Al-Kufa-Najaf corridor, 2016–2024 performance measurements indicate deterioration that is gradual, as in the stress history example, although not in a strictly linear or even manner for ride quality and structural durability.

A time-series plot containing the two most important performance measures, the IRI and rut depth, is shown in Figure 2. It can be seen from the table that IRI increased from 1.8 m/km in 2016 to 4.7 m/km in 2024, which meant that the surface smoothness was worsening and the comfort of the users became poorer. At the same time, rutting depth increased from 3.1 to 13.3 mm, which indicated that wheel paths were progressively deforming under repeated axle loads and high temperatures. Parallel increases in the two measures highlight how early intervention is required to avoid a rapid degradation path beyond affordable levels.

Figure 2. Pavement deterioration trend (IRI and rutting)

For additional context to these results, Table 3 summarises the yearly field data for the Al-Kufa-Najaf section. They are IRI, rutting depth, percentage cracking, structural condition rating, CSI, and subgrade modulus. Together, these parameters directly relate to the long-term physical health and function of the pavement system. From Table 3, it can be seen that structural ratings have declined from 9.2 in 2016 to 5.3 in 2024, in parallel with the increasing CSI, indicating worsening surface condition. The degradation is further confirmed by a steady drop in subgrade modulus, highlighting the impact of underlying soil resilience on surface performance.

Table 3. Pavement surface performance indicators (Al-Kufa-Najaf Road)

Table 4 presents the increasing trend in traffic loading, represented by ESALs, which rose from 18,500 to over 23,000 vehicles per day. The high traffic density, especially during religious events, exerts continuous stress on pavement layers, contributing significantly to rutting and cracking.

Table 4. Traffic and load data (ESALs/day)

5.5 Modelling and calibration results

In such weather and traffic conditions, nonlinear models, for the deterioration of both advanced models, were employed to predict pavement condition more accurately. These models were selected as they are sufficiently flexible to model realistic pavement deterioration processes that accelerate over time, e.g., as a result of cumulative loading and environmental ageing.

The Weibull Model: The first model considered in the analysis was the Weibull Model, whose mathematical expression is:

$IRI(t)=a\cdot {{t}^{b}}$

In this study, the calibration process yielded the parameters a = 1.42 and b = 1.63, indicating that the deterioration rate increases progressively over time. This makes the Weibull model particularly useful in simulating later-stage pavement distress.

The second model used was the Exponential Model, represented as:

$IRI(t)=a\cdot {{e}^{b\cdot t}}$

This model with the estimated parameters a = 1.81 and b = 0.257 describes a stable growth of pavement roughness IRI in time. However, it is less sophisticated and may not completely reflect the accelerated ageing behaviours in all cases. Hence, the reliability-based analysis was used to estimate the probability of the pavement’s survival over a required period. The Weibull Reliability Function used to calculate the idea may be defined as follows:

$R(t)=\exp \left( -{{(t/\eta )}^{\beta }} \right)$

where, η = 8.5 (scale parameter representing the characteristic life of the pavement before accelerated deterioration begins), and β = 2.1 (shape parameter that indicates how quickly deterioration accelerates over time). This expression calculates the probability that a pavement will be in service for a given time "t" to enable engineers to select a suitable time for maintenance or rehabilitation.

Furthermore, the Hazard Function corresponding to it was computed to illustrate the rate of the increasing hazard of failure:

$H(t)={{(t/\eta )}^{\beta }}$

This one is key in the prediction of imminent fast decline. For practical use, the intervention level was set at R(t) < 70%, indicating that the maintenance practice is recommended when the survival probability is < 70%.

Incorporating distress modelling within reliability analysis establishes a comprehensive and systematic framework for proactive, cost-efficient pavement management. The calibration process underwent rigorous robustness checks and cross-validation, employing MATLAB (infit function), R (nls and lm packages), and Excel Solver to ensure methodological accuracy and consistency of results. As already depicted in Table 5, the performance comparison of the two models against observed pavement deterioration data is shown in Figure 3.

Table 5. Calibrated model parameters and fit statistics

This is because the empirical measurements seem to converge on important periods of the object's life, and the Weibull seems preferable for predictive purposes, especially towards the end of the object's life.

Figure 3. Model fit comparison: Weibull vs. Exponential

Figure 4 illustrates the risk-adjusted degradation projection based on the Weibull reliability function. The curve demonstrates a steep drop in reliability after year 8, emphasizing the critical importance of timely maintenance actions to prevent sudden performance failure. This projection provides decision-makers with a quantitative basis for intervention planning based on acceptable levels of service reliability.

Figure 4. Risk-adjusted degradation projection

5.6 Maintenance strategy simulation

Design and application of pavement maintenance strategies are crucial to achieving sustainable and cost-effective road asset management. Under the specific environmental and operating conditions in Al-Najaf, Iraq, the choice of the most appropriate maintenance strategy is becoming more and more important. This section describes a holistic model for five different maintenance approaches over 10 years (2025–2035) of planning. The assessed policies considered in the experiments are preventive maintenance, condition-based maintenance (CBM), hybrid strategy, risk-based planning, and no-maintenance as a baseline.

The comparison is conducted with four performance measurements, i.e., cumulative cost, surface condition measured by the IRI, the anticipated service life, and the probability of structural failure. Together, these metrics provide an overall assessment of the long-term survivability of each strategy.

As shown in Table 6, the hybrid option proved to be the most efficient with the highest projected service life (12.5 years) and the lowest average IRI (3.8) at a modest cost of \$450,000. This approach is based on the use of scheduled and condition-based maintenance, allowing intervention when field conditions are observed. Likewise, the CBM model showed quite effectiveness, leading to extending the service life to 11.2 years, based on the range of the lowest accumulated cost, which was \$390,000, by carrying out the necessary maintenance at the time that it passed the performance thresholds.

Table 6. Maintenance scenarios (2025–2035)

Conversely, not maintaining resulted in the highest cost burden ($690,000) and significantly higher failure rates of 85% emphasising the negative outcomes associated with delaying or disregarding maintenance. The findings emphasise that proactive maintenance programs should be put in place as part of the PMS, as shown in Figure 5.

Figure 5. Maintenance strategy - cost vs. service life (updated)

The cost and the lifetime of each maintenance policy are compared in terms of graphs in Figure 5. The bar chart shows the cost of each alternative, and overlaid with the dotted line series is the 20-year life span for each alternative. Such a visualisation of dual axes can present policy-makers with a more sophisticated view of the cost-efficiency effect, aiding more rational policy-making.

The economic analysis was supplemented by Net Present Value (NPV) analysis. NPV is very common in infrastructure management to account for the time value of money so that future rehabilitation and failure-related costs are discounted properly. The NPV for each strategy was calculated using the following formula:

$NPV=\Sigma (Ci+Pf(i)\cdot Crehab)/{{(1+r)}^{i}},i=1,2,...,n$

where, Ci is the annual maintenance cost in year i, Pf(i) is the probability of failure in year i, Crehab is the cost of full rehabilitation (USD 110,000), and r is the discount rate (4%). This formulation allows consistent comparison of strategies by incorporating both direct and indirect costs across the analysis period.

5.7 Sensitivity analysis inputs and results

Sensitivity analysis using Monte Carlo simulation methods was performed to examine the validity of the proposed crude and maintenance models under uncertainties of a real-world situation. Overall, 1,000 simulation runs were conducted to consider the influence of critical input variables on the pavement performance, risk of failure, and economic consequences. This method allows uncertainty to be quantified and helps with risk-based decision-making in the pavement management area.

The controlled perturbation variables were comprised of the ESALs, the environmental temperature, the time of maintenance intervention, and the binder’s ageing rate. All parameters were varied in a physical range using regional traffic and climate data. More precisely, the variation of the traffic loading (ESALs) was ±15%, the temperature was ±2.5℃, the maintenance delay was ±1 year, and that of the binder ageing was ±10%. These values were chosen to encompass realistic changes occurring over an average operating time in Al-Najaf.

These findings underscore the importance of proactive decision-making under uncertainty. For road agencies, the results suggest that even modest delays or climatic shifts can impose substantial financial burdens, reinforcing the need for continuous monitoring and adaptive maintenance planning. An upward adjustment in traffic volume of 15% simulating increased freight movement, elevated the probability of early failure by 22%. Additionally, an increase in average temperature by 2℃ led to an 18% rise in surface cracking, indicating heightened sensitivity to climate-induced degradation.

Table 7 summarises the direct impact of individual parameter changes on the year in which IRI exceeds 4.0 m/km (indicating functional failure), along with the associated increase in lifecycle costs.

As evident from Table 7, the timing of performance degradation shifts forward with each perturbation. Traffic escalation and thermal loading were particularly impactful, accelerating pavement deterioration by nearly two years in some scenarios. These insights emphasize the critical role of proactive data-driven monitoring and intervention planning under conditions of climatic volatility and increased vehicular demand.

Table 7. Variable impact on pavement performance

Figure 6 presents a dual-axis representation of the sensitivity analysis results. The bar chart displays the estimated increase in lifecycle costs (left axis) for each parameter variation, while the line plot (right axis) tracks the corresponding year when the pavement’s IRI exceeds 4.0 m/km, signaling the onset of functional failure. Among the tested parameters, a one-year maintenance delay produced the highest economic burden ($110,000), while increased temperature led to the earliest threshold breach (year 7.4). This figure underscores the interplay between environmental stressors, traffic growth, and delayed intervention—each of which exerts significant influence on long-term pavement performance and cost.

Figure 6. Sensitivity analysis -cost and degradation impact

Based on the findings of this study, several recommendations are proposed to enhance the effectiveness and sustainability of pavement management practices in similar climatic and operational contexts:

• Integrate nonlinear deterioration models, such as Weibull and exponential functions, into PMSs to more accurately represent field behaviour and failure progression.
• Incorporate reliability-based tools and hazard functions in planning and evaluation processes to improve decision-making under uncertainty.
• Establish centralised databases for pavement condition, maintenance history, and environmental data to support evidence-based policy formulation.
• Implement a pilot project to evaluate the hybrid maintenance strategy in a comparable urban setting, such as Karbala, to validate the transferability and scalability of results.