1. Introduction
Ensuring the durability of flexible pavements poses a crucial challenge for sustainable cities, particularly in countries with constrained budgets for road maintenance programs. Roads play a vital role in the development and growth of modern societies. Over time, pavements undergo gradual deterioration and specific forms of distress progress throughout their lifespan. This degradation not only impacts the ride quality but also increases the likelihood of road traffic accidents [
1]. Consequently, it undermines the overall sustainability of the pavement infrastructure. The damage rate, however, can be reduced by adopting efficient maintenance management [
2]. Urban roads do not typically receive proper attention in maintenance programs compared to rural roads due to the growing interest in the latter. As a result, the performance of urban roads is often mediocre and necessitates frequent maintenance and rehabilitation. With the typically limited funds allocated for upkeeping urban roads, transportation agencies worldwide face serious financial challenges in the maintenance and rehabilitation of flexible pavement networks [
3]. This is of particular concern in developing countries, which have extremely scarce financial resources and relatively limited collected information about road conditions needed for adequate condition detection and due rehabilitation [
4,
5]. This necessitates a continuous evaluation of depressions and other surface deformations through comprehensive field monitoring programs [
6].
The public work department in Malaysia routinely collects pavement performance data for their standard pavement maintenance management system (PMMS), but the core issue is the lack of funds for road maintenance as per the set PMMS. In Iraq, pavement condition surveys were developed to evaluate the current condition of the pavement network to assist in minimizing current distress [
7]. The survey included network evaluation, project future condition, maintenance and rehabilitation needs, assessing repair costs, and repair programs. The pavement network in this study has unacceptable surface conditions and is in a state of constant deterioration; however, a PMMS system is yet to be established due to the lack of data.
There are several pavement indices for evaluating pavement surface conditions, including the pavement condition index (PCI), falling weight deflectometer (FWD), international roughness index (IRI), and British pendulum number (BPN) [
8,
9]. PCI is, perhaps, the most universally recognized index for evaluating pavement performance and condition. PCI is an index established by the U.S. Army Corps of Engineers [
10,
11] and mathematically expressed between 0 and 100, with 0 being the worst possible pavement condition and 100 being the best possible pavement condition. While PCI rating is widely used in transportation engineering to evaluate pavement conditions, measuring it is not always convenient [
12]. PCI can be measured using either visual or automated surveys [
13]. The visual survey is based on identifying 19 different distress types and patterns [
14]. The process is tedious and lengthy as it necessitates collecting huge field data sets. Additionally, the safety of the survey participants may be compromised. The automated survey, however, requires advanced and costly equipment, and it uses a fully equipped vehicle to collect digital data on road surface conditions [
4].
1.1. Utilization of IRI in PMMS
The IRI is a measure of pavement roughness [
3,
15]. It is common to view roughness in terms of distortion of the pavement surface, which contributes to an undesirable or uncomfortable ride. As such, the IRI reflects passengers’ and drivers’ comfort and measures their experience with the pavement surface. It can also indirectly reflect the response of vehicles to road conditions [
16]. The IRI correlates well with other riding aspects, including safety, vehicle vibration, functioning speed, and fuel consumption [
3,
17]. The IRI can be measured by calculating the distortion of the pavement surface along the longitudinal profile of the vehicle wheel path [
18]. Developing IRI-based models for performance prediction is common as pavements deteriorate [
3,
19,
20]. Increasing fuel consumption, greenhouse gas emissions, decreasing vehicle efficiency, and causing traffic accidents are well-correlated with increasing pavement roughness, which collectively costs USD one million every year [
18,
21,
22,
23]. Owed to its versatility, the IRI became a key performance index in pavement management systems (PMSs) in many countries, especially for estimating vehicle operating costs [
19]. To this end, the IRI is adopted by most road agencies across the world as an indicator of pavement performance [
20,
24].
In the Swedish specifications for calculating the IRI, 20 m road segments are utilized to determine individual IRI values. The average IRI value and the standard deviation, known as sIRI, are then calculated based on 400 m road segments. IRI specifications vary with the sIRI value, such that a 400 m segment of greater sIRI value has more stringent IRI specifications. National standards define different IRI thresholds for accepting new roads at the end of the warranty period and equally for accepting reconstructed roads. Remarkable differences have been found in the IRI specifications in various countries. IRI thresholds are, for example, 1.1 mm/m in Sweden (120 km/h), 1.9 mm/m for highways and expressways in Slovakia, 1.2 mm/m for a 20 m interval of main road in Hungary, and 2.2 mm/m for 100 m intervals of first class highways in Russia [
25].
Figure 1 depicts the IRI thresholds for new or reconstructed roads in different countries. The values are plotted against the respective segment length (L) they were developed for.
1.2. PCI versus IRI
The IRI and PCI have an inverse relationship—as the pavement gets worse, PCI decreases, and IRI increases. The correlation quality captured by
drops as the pavement deteriorates [
3]. Several studies attempted to build reliable correlations between the IRI and PCI [
15]. Dewan and Smith [
26] developed a linear regression model to assess the IRI using the PCI for urban roads in the San Francisco Bay Area. The distresses include alligator cracking, longitudinal and transverse cracking, depression and rutting, patching, and utility cut patches. The mainstream of the measured IRI values was less than 3000 mm/km. Different mathematical models were used in this study to evaluate the relationship between the PCI and IRI; only the linear regression was satisfactory.
Park et al. [
27] proposed a correlation between the PCI and IRI using data collected from The DataPave 3.0 software over an extended area in the United States (Delaware, Maryland, New Jersey, New York, Vermont, Virginia) and Canada (Ontario, Quebec, and Prince Edward Island). The data based on the long-term pavement performance (LTPP) study were from the early 1980s onwards. The study was performed by the National Research Council’s Transportation Research Board (TRB), with the support of the Federal Highway Administration (FHWA) and the American Association of State Highway and Transportation Officials (AASHTO). The
value of the model was 0.66 [
27]. Adeli, Najafi moghaddam Gilani, Kashani Novin, Motesharei and Salehfard [
3] developed a regression model for which a reasonable correlation between the IRI and PCI was observed. Linear, power, and exponential regressions were used for this purpose. The latter seems to be the most successful for the used dataset.
values of 0.75, 0.76, and 0.59 were reported for IRI values of 2.5–3.5 m/km, 3.5–5 m/km, and 5–8 m/km, respectively. Hasibuan and Surbakti [
10] also reported a relationship between the PCI and IRI for a road segment in Medan City, Indonesia. The exponential correlation was adopted with an
value of 0.59.
The studies mentioned earlier had reported weak correlations between the IRI and PCI, with R2 values ranging from 0.59 to 0.75. Therefore, this study attempted to create a more reliable regression model to capture the relationship between the PCI and IRI with a relatively higher R2 value.
3. Data Collection
This study attempts to develop a simple and affordable method for estimating the PCI based on this IRI. It is intended to economically, but accurately, collect the IRI values for the study area and subsequently use them to build an enhanced correlation with the PCI. A targeted low-budget approach is appealing for use when other traditional methods are costly and inconvenient. A correlation between the IRI and PCI was being developed for the network of flexible urban roads in the study area. Data collection included visible distress in pavement surfaces from the 44 km of urban roads in the study area.
The data collection process involved two steps: desk study collection and field collection [
33]. Office data collection encompassed the utilization of available soil profiles and reports from prior studies. The data include construction dates, pavement layers, cross-section elements, significant maintenance activities with their respective dates and sizes, traffic volumes derived from permanent and temporary traffic count stations, and relevant environmental data. Field data collection, however, entailed pavement survey data, such as geometry-related data, and pavement distresses. Field data were collected by field inspectors who visually examined the pavement surface conditions considering distress type, severity, and extent. The current study utilized a paver system for distress data collection, which included specific guidelines regarding distress classification, and the quantification of severity and extent in certain measurement units (area or length or number) based on the type of distress [
34]. Detailed descriptions of the 19 distress types implemented in this paver system, along with the guidelines, are reported by Shahin, M.Y. (2005) [
17].
The conducted full field survey of the asphalt pavement distresses enabled estimating the PCI values. This was followed by measuring the IRI values using a mobile (vehicle-mounted) ultrasonic sensor. A regression model was developed to identify the potential correlation between the IRI and PCI. Several mathematical forms were considered for this purpose, including those used in the common prediction models from the literature. Performance was assessed via a robust validation process and complemented by a comparison with the reported models. The accuracy of the developed model was further investigated through detailed error analysis. Model implication on selected developed countries was performed to gauge its applicability in similar countries.
Figure 3 depicts the development process of the model alongside the performance assessment.
3.1. PCI Survey
Distress data collection (i.e., defective areas) has been carried out for the selected urban roads located in the New Beni-Suef region, as shown in
Figure 2, to estimate PCI. The identified distresses have been classified based on the 19 distress types listed in the PAVER system [
12]. The study roads have been divided into sections with consistent characteristics throughout their length. Each pavement section is divided into sample units for the purpose of pavement inspection. Each sample unit was inspected for distress type, severity, and density. Identified distresses ranged from structural failures such as fatigue cracking, potholes, and depression to functional failures like bleeding and patching.
The study area exhibits a range of distress types, including fatigue cracks, longitudinal cracks, transverse cracks, polished aggregate, bleeding, block cracking, depressions, edge cracking, patching, and potholes. The density of low-severity fatigue cracks was 0.3%, while that of medium-severity fatigue cracks was 0.4%. The density of medium-severity bleeding was 1.2%. The density of medium-severity block cracking was 0.6%, while that of high-severity block cracking was 0.5%. The densities of medium-severity depressions and low-severity polished aggregate were 0.7% and 20%, respectively. The densities of low-severity and high-severity edge cracking were 0.22% and 0.35%, respectively. The densities of low-severity and medium-severity longitudinal and transverse cracking were 1.2% and 1%, respectively. The densities of low-severity and high-severity patching were 6% and 1.5%, respectively. The densities of low-severity, medium-severity, and high-severity potholes were 0.2%, 0.15%, and 0.1%, respectively.
Table 2 summarizes the sample pavement distress types, severity, and density along the Al-Aml Road section. After data collection, data entry and processing for PCI calculation were performed using Micro PAVER software Version 3.0, which is a well-established PMS software developed by the Army Corps of Engineers, Washington, DC, USA [
12].
The pavement sections were evaluated using a PCI rating system. PCI rating is widely used in transportation and civil engineering to evaluate pavement conditions [
12,
35]. The PCI rating system in Egypt is approved by the Ministry of Transport and is considered the main system for rating flexible pavements [
36]. The identified distress types, severity, and density for the study roads were evaluated using the Micro-PAVER Version 3.0 software, and a database for the corresponding PCI deduct values was then created. Subsequently, the software was used to calculate the total and corrected deduct values, and thus, the PCI for the sample units along each road section. Since all surveyed sample units were selected randomly, the PCI of each road section was calculated by averaging the PCI of its sample units.
Figure 4 shows examples for observed sample unit distresses along the urban flexible pavement in the study area.
3.2. IRI Survey
A mobile ultrasonic distance sensor has been fabricated to capture the pavement profile, as shown in
Figure 5. The assembly—comprised of an ultrasonic sensor, Arduino board, and connecting cables—records the distance between the sensor and the surface of the pavement in millimeters. The device was charged through a fixed USB cable connected to a laptop. It was attached to the back bumper of the vehicle at a height of 420 mm from the pavement surface along with a vertical accelerometer to capture the vertical oscillation of the vehicle as it encounters road irregularities such as bumps, potholes, and cracks. The onboard processor removed these vertical oscillations from the sensor data. The IRI was calculated as the accumulated vertical motion along the pavement profile for 1km in the vehicle wheel path. The IRI measurement was conducted in both traffic directions, and the final IRI value of the road section was derived by averaging the two IRI values obtained from each direction.
The device employed in this study utilizes the same profile-based roughness mechanism used in full-scale automated vans. This approach warrants collecting IRI values of high accuracy.
Table 3 illustrates the features and specifications of the ultrasonic sensor used. The estimated total cost of the device is USD 16. To this end, in similar studies conducted in the UK by Li et al. [
37] and Psarianos, B. et al. [
38,
39], the price tag of the survey van is estimated to be USD 500,000, which is typically beyond the capacity of pavement management programs in many developing countries.
The accuracy is highly dependent on the response time of the sensor and the vehicle’s speed. Therefore, extensive testing and trials were performed to identify the speed of the vehicle at which data could be collected with minimal error and noise. Likewise, the effect of the sensor location on the quality of collected data was examined. Attaching the sensor along with the vertical accelerometer to the rear bumper of the vehicle seems to minimize vibrations and noise that could be generated due to the vehicle’s vertical oscillations. As such, the recorded vertical distance is taken after any vehicle’s shaking and bouncing is diminished. It should be noted that the vehicle is driven at a speed not exceeding 30 km/h controlled by car cruise control to minimize vibrations and thus enhance the quality of the collected data. The computer code used in measuring distances was developed using Arduino IDE. To this end, the vehicle operates at this optimal constant speed, and the timestamp was recorded to estimate the respective measurement. The accuracy of the IRI measured by the device employed in this study was checked against those obtained from the transportation authorities. These values were treated as a reference measurement. This comparison was conducted for a selected 5 km section from Ashabab Road (
Figure 6). The estimated and reference IRI values were sampled at 100 m intervals. The cumulative difference between the estimated and reference IRI values for this section was approximately 442 mm. Approximately 52% of the estimated values (26 of 50 points in this test section) slightly underestimate the IRI reference values; however, the accuracy is quite acceptable. The average ratio between the estimated and reference IRI values (
Figure 6) was approximately 0.97, which further supports the observed accuracy.
4. Model Development
Sufficient PCI and IRI data points were collected to build a robust regression and allow for subsequent validation. The database was split into two sets. The first set is for model development, which represents 70% of all data points. The second set is dedicated solely to the validation process, which represents the remaining 30% of the points. This data split is conventional for building correlations and validations and is statistically sound [
29,
40]. It is important to note that the conditions of the preselected roads for validation (as shown in
Table 1) are quite representative of the study area. The statistical evaluation results for all pavement sections are shown in
Table 4. The data appear to have a normal distribution, but they statistically fail the normality test. The correlation coefficient between the PCI and IRI is fairly high. The ratio between the standard deviation and standard error
represents the degree of scattering with respect to the line of equality. A ratio less than 0.5 generally indicates low scatter. At
value of 0.067, the data showed accurate predictions.
Error measures must be chosen wisely to assess the model’s performance. Numerous error measures have been used in the literature for this purpose. The root mean square error (RMSE) and the mean absolute error (MAE) as error measures are very common in modeling. RMSE is unit-dependent, which does not allow for error normalization. MAE is usually a good indicator of bias; however, it cannot tell the direction of the bias, nor does it come with a cap (upper limit). For that reason, these error norms are deemed insufficient for holistic error analysis [
41]. The coefficient of determination (
) is used to measure the proportion of variance in the dependent variable.
is more sensitive to outliers than to the near mean measurements, which leads to an appreciable bias toward extreme events [
42,
43]:
where
PCIm is measured
PCI, and
PCIp is predicted
PCI. Model evaluation is instrumental in gauging its utility, which requires error estimation [
41]. In addition to the use of
for developed regressions, bias (
B) and index of agreement (
) can provide more insight into error distribution. Bias refers to the tendency of the model to overestimate or underestimate the prediction relative to the corresponding metric. The bias in this study is expressed as a ratio between the predicted and measured
PCI values:
The Willmott index of agreement (
) is defined as the ratio between the mean square error (
MSE) and the potential error (
PE). The index of the agreement generally offers a better measure of the model performance since it encompasses both
MSE and
PE [
44].
Figure 7 shows the histogram of the field-collected
PCI values. As depicted in the figure, most of the
PCI values are within the 65 to 95 range, which generally indicates good pavement quality. This is expected given the age of the roads considered in the study. Approximately 40% (96/221) of the
PCI values were in the range of 85 to 95, which can be classified as excellent. More than 39% (87/221) of the pavement sections are very good (70 to 85), and the rest of the data (35/221) were in the range of 65 to 75, which can be classified as good to very good [
4].
The calculated
PCI and
IRI values for the 221 sections of the study area are shown in
Figure 8. Several mathematical forms were considered to build a robust correlation between the
PCI and
IRI values. The variety allows for identifying the most appropriate regression and warrants generality. The
PCI predictions of the models developed by Adeli, Najafi moghaddam Gilani, Kashani Novin, Motesharei and Salehfard [
3], Dewan and Smith [
26] and Arhin et al. [
45] were poor. The developed models by Ali, Hossain, Hussein, Swarna, Dhasmana and Hossain [
2], Elhadidy, El-Badawy and Elbeltagi [
4], Hasibuan and Surbakti [
10], Park, Thomas, and Wayne Lee [
27] yielded good estimates of the
PCI. Although the sigmoid function is widely used for similar applications in pavement management [
46], it does not seem to capture the relationship between the
PCI and
IRI in this study. Upon close examination of the performance of models from the literature, the logarithmic function has proven to provide the best fit. The proposed correlation between the
IRI (in mm/km) and
PCI can be expressed as follows:
El-Cornish and Al-Amal sections are mostly in excellent condition, with PCI values higher than 75%, whereas Al-Andalus and Zamazam sections represent most of the low PCI values. Ashabab sections cover a wide range of PCI values. The coefficient of determination was estimated to be 0.82, which suggests a strong correlation between PCI and IRI.
6. Conclusions and Future Direction
This study estimates IRI values for urban roads using a locally fabricated vehicle-mounted device that logs the longitudinal profile of the pavement’s surface. The calibration process of the device was carried out using IRI data obtained from the Authority of Road Sector in Beni-Suef. The proposed survey technique is simple and accurate. The collected IRI values are well correlated with the measured PCI in the study area. Several attempts were made to identify the most appropriate mathematical correlation between PCI and IRI. With a coefficient of determination of 0.82, the exponential function fits the data satisfactorily. The study advocates using the average bias and index of agreement as more profound error norms.
Model validation was performed using dedicated data sets different from those used in the development process. The results further support model accuracy. The index of agreement of the proposed model yielded a high value compared to other models from the literature. The coefficients of determination for all models, however, were very similar. The average bias for the proposed models was close to 1.0, which was also notably higher than those of the other models—signaling high accuracy. A comparison is made between the developed model and two common models developed by Elhadidy, El-Badawy, and Elbeltagi [
4] and Ali, Hossain, Hussein, Swarna, Dhasmana, and Hossain [
2]. The latter model significantly underpredicts the PCI values, while the former performed mediocrely for the entire range of the IRI. The suggested model, thus, outperforms both models. Collectively, the proposed approach is very convenient for estimating the PCI of urban roads in developing countries with arid climates– particularly given the lack of allocated funds and resources. The model applicability was tested using actual measured data from Indonesia and Iran. For Indonesia and Iran, the results indicated that the average error did not exceed 10% and 15%, respectively. The developed model can perhaps be used satisfactorily in countries that share similar management norms and finances.
To this end, the proposed model is, however, limited by the traffic conditions considered in the study. Therefore, the model should be extended to similar arid climates, provided that sufficient traffic data become available. Increasing the number and range of data collection for the study area is necessary to enhance the generality and applicability of the model. Using unmanned aerial vehicles (UAV) to measure the IRI should be considered to improve accuracy and efficiency and minimize risk. The use of UAVs eliminates errors triggered by vehicle vibrations and road imperfections. The use of Light Detection and Ranging (LiDAR) technology can have a remarkable effect on the accuracy of the collected IRI data. Employing artificial intelligence in predicting a model could be instrumental in enhancing the proposed model when large datasets are made available.