Road surfaces can be classified into two categories based on their surface nature: paved and unpaved (gravel) roads. Gravel roads are unimproved roads with surfaces constructed from natural soil and stones [1] . Federal Highway Administration (FWHA) records show that the United States owns and maintains approximately 1,370,000 miles of unpaved roads, which form 35% of the total roads network length. The records show that the total mileage of gravel roads in the United States decreased in the last few decades. Figure 1 shows historical changes in gravel roads total length in the U.S. [1] .

Gravel roads form about 90% of the local roads network in the state of Wyoming. This percentage of gravel roads is considered significantly high. These gravel roads serve various land use purposes. Gravel roads in Wyoming are located in residential, agricultural, and industrial areas. This variety in land use results in considerable differences in traffic loads. Heavy traffic loads lead to higher deterioration rates and reduce the service life of gravel roads. Therefore, developing an advanced and integrated Gravel Roads Management System (GRMS) has become a necessary need. Gravel roads, like most local roads, are usually managed by local agencies. Most of the time, the local agencies have good experience in maintenance procedures, but not in roads management. Because of that, any work in developing a GRMS should consider local agencies’ needs.

Wyoming Technology Transfer Center (WYT2/LTAP) has recently started a process to develop a new gravel roads management system (GRMS). This new in-progress GRMS aims to help local agencies in managing their gravel roads in a simple and cost-effective way [2] . Data collection and building the database are the most challenging parts when developing gravel road management systems [3] . Therefore, the WYT2/LTAP is in process of introducing a holistic gravel roads data collection approach using smartphone applications and sensors [2] . However, one of the most used terms in gravel roads condition assessment is the Riding Quality Rating Guide (RQRG). Using a single term to demonstrate the overall gravel road condition reduces the data collection cost and time, and it helps in managing roads with limited resources [3] . RQRG is a subjective method to evaluate the gravel roads condition by determining the riding quality level. Many agencies have developed their own riding quality manuals to guide their inspector in evaluating the gravel roads. Since RQRG is a subjective method, the results still depend on the inspector’s personal judgment.

In this study, an objective method to determine the RQRG is introduced. The RQRG is similar to the Present Serviceability Rating (PSR) on paved roads since in both rating systems the evaluation is based on road users’ judgment and comfort. Thus, two factors are expected to have the strongest effect on riding quality: road roughness and surface corrugation. Modern smartphones’ accelerometers and cameras were utilized in collecting gravel road roughness and corrugation data for the purpose of this study. The data in this study were collected using an Android mobile application called “Roadroid”. This android application collects the roughness data by utilizing the mobile built-in accelerometer, while the corrugation data is collected by capturing photos using the mobile camera and classifying them using a sophisticated image classifier on the “Roadroid” cloud. The introduced method aims to provide pavement inspectors and evaluators with a unique method to determine riding quality. Utilizing such a method will eliminate biases due to the evaluator’s judgment on the riding quality rating, resulting in the riding quality data being more consistent when used for planning and prioritization of gravel roads maintenance. In addition, local agencies will have a solid justification for their riding quality data.

Gravel roads condition evaluation methods are mainly categorized into two groups: objective evaluation for each distress, and subjective evaluation for the riding quality. Many agencies developed their own techniques to evaluate gravel roads conditions by assessing existing distresses individually [4] . One of the earliest manuals is the U.S. Army Corps of Engineers assessment system (USACE). The USACE procedure has an index called Unsurfaced Road Condition Index (URCI). This index value depends on the existing distress severity level and area. The distress severity level and area is used to calculate a deduct value. After that, all the calculated deduct values are used in calculating an overall URCI for the gravel road segment [4] - [6] .

There are more recent studies involving systems for evaluating gravel road quality. In 2012, Bhoraskar et al. carried out a study to introduce a Gravel Road Condition Index (UPCI) based on existing surface distresses [7] . In addition, the World Bank has developed several procedures to evaluate gravel road conditions such as the Roads Economics Decision Model and the Deterioration of Unpaved Roads Model (DETOUR) [8] . The DETOUR model predicts the gravel road segment condition based on the environmental condition, road geometry and the gravel road structural characteristics [1] [8] . In another study, the University of New Hampshire and FHWA developed the Road Surface Management System (RSMS). RSMS evaluates gravel roads based on the existing distresses. The main feature of the RSMS is that the inspector evaluates the gravel road segment directly without assigning a score for each distress [9] . CSIR Transportek has also developed a Standard Visual Assessment Manual (SVAM) for unpaved roads. The SVAM has three categories for roads data. The first category is the basic data for road management and includes data about the existing distresses and their severity. The second category provides information about the extent of the existing distresses. The distresses extension is estimated by calculating the ratio between the distress area and the total road segment area. The third category is the advanced level data which includes the layers’ thicknesses, material characteristics of the gravel layer, and geometric features of the road [10] . Another rating system called the Subjective Rating System (SRS) has been developed by Central Federal Lands Highway Division. This Subjective Rating System evaluates gravel road conditions by considering five distresses and assigning a condition rate for each segment. The condition rating is based on a scale from 0 to 10, where 10 is the best condition and 0 is the worst [11] . However, most manuals evaluate gravel road distresses individually and very few provide an overall rating for road segments and mostly those manuals are complicated and require a massive number of resources. This complicity in the available methods and manuals make it difficult for local agencies for adapt and use them. Gravel roads are usually managed by local agencies with limited resource and fund. In addition, location agencies are good in maintenance work than management and evaluation. Usually, the overall assessment for gravel roads is a subjective rating determined by evaluating the riding quality.

Riding quality is a very popular indicator for gravel road conditions since most pavement distortion and distresses, including cracking, unevenness, corrugation, potholes, and rutting, affect the riding quality directly. However, this study considered only the gravel roads roughness and corrugation in order to predict and estimate the riding quality. This decision was made based on the previous experience with gravel roads. Generally, the most common distortion in gravel roads are the corrugation. In addition, the roughness is considered since it is the most distortion related to riding quality. The formation of distresses on gravel roads over time increase the road segment roughness, which leads to reduced driving quality. As a result, the road service life is decreased [12] . Road roughness and riding quality have a direct impact on vehicle operating costs (VOCs) since the rough surface of the road generates vibrations that transfer through the suspension and tires to the vehicle body [13] . The generated vibrations cause damage to vehicle parts and significantly increase overall fuel consumption [13] [14] . Recently, many road management agencies have developed their own gravel roads visual assessment manuals, such as the manual developed by the South African Council for Scientific and Industrial Research (CSIR) and the PASER manual, which was developed the by Wisconsin Department of Transportation. Even though the PASER rating system is the most used method in evaluating gravel roads in the U.S., its short scale negatively affects the road inspector’s judgment. Usually, collecting evaluation data utilizing a short scale results in two types of errors: errors of leniency, and central tendency [1] . Therefore, the WYT2/LTAP modified and expanded the PASER system to a new rating system called Riding Quality Rating Guide (RQRG) that uses a scale range from 1 to 10. The rating range expansion aims to enhance evaluation data by increasing the predicted accuracy and liming the error sources. In addition, the RQRG demonstrates the road user’s satisfaction in terms of their riding comfort over a gravel road segment [15] [16] . As a result, the RQRG is highly affected by road surface distortions such as corrugation, unevenness and potholes. In the RQRG rating system 10 represents the best condition and 1 represents the worst. Table 1 shows the Riding Quality Rating Guide summary [15] [17] .

Evaluating gravel road roughness and determining the effects of road irregularities on vehicles can be carried out using several procedures [18] . In such procedures, the surface roughness defined as a kind of pavement distortion occurs in a perpendicular direction to the pavement surface plane. Roughness could be determined by several methods such as International Roughness Index (IRI) or Unevenness Index (UI). Most of the modern procedures evaluate roughness in terms of International Roughness Index (IRI) [19] . In the last few decades, many research institutes have worked to develop advanced equipment to measure IRI. Cybernetics Corporation developed a tool called the Longitudinal Profiling System to measure road roughness by utilizing an infrared laser and accelerometer. The Longitudinal Profiling System measures the roughness in terms of IRI under the wheel path [20] . Another tool called Opti-Grade was developed to collect gravel road roughness data by the Forest Engineering Research Institute of Canada (FERIC). The Opti-Grade includes three components; an accelerometer, a GPS, and a data processing system. Opti-Grade has been tested on a small network, and its capability to collect data from large gravel road networks such as county road has not been verified yet [21] . Zhang and Elaksher introduced another approach to utilize unmanned aerial vehicles (UAV) in recognizing surface defects. This method is able to identify the density and severity of surface defects by analyzing a three dimensional model of the gravel road surface using image algorithms [19] [22] . In another study conducted by Alhasan et al., gravel roads roughness was calculated using a laser scanner. Such laser scanners are typically employed to generate three dimensional maps for the road surface. Afterward, statistical analysis was utilized to predict the IRI [23] [24] .

Despite of these advances, there is still a lack in developing an objective method to determine the riding quality on gravel roads. Most of the available objective methods are impractical and can be helpful only in research [25] . In addition, the available objective methods require a significant amount of resources, which lead them to be too expensive. Moreover, the measurements of these methods have a certain level of subjectivity, especially in collecting distresses data. Therefore, many agencies still prefer to use visual inspections [26] . Thus, utilizing smartphones features and capabilities attracted researchers in the gravel roads field. Employing smartphones in the gravel roads data collection process is a very promising practical and cost-effective method.

Utilization of smartphones in gravel roads data collection is still limited. Most of the previous research was carried out on paved roads. The dynamic nature of gravel roads make them considerably different from paved roads. However, smartphone accelerometers can be used to detect vehicle vibrations caused by road roughness [27] [28] . Another smartphone feature is the ability to use the built-in GPS to automatically referencing the evaluated segments [29] [30] . In 2017, Harikrishnan and Gopi utilized the threshold technique with the Gaussian model to recognize and evaluate pavement potholes and bumps. Vehicle vibrations were measured using a smartphone’s built-in accelerometer. Then, an advanced filter was used to minimize the abnormal data points. The overall accuracy of this model reached 90% [31] . In another study, a modern mobile application called “Smart-Patrolling” was developed to collect road surface data in terms of potholes and bumps. The smartphone was fixed in different locations inside the vehicle to study the effect of the smartphone’s placement on the collected data. The application showed an accuracy level of 89% [32] . Another mobile application, “Road Data Collector,” was developed in 2017 by Allouch et al. in order to employ machine learning concepts in road data collection. The built-in mobile accelerometer and gyroscope were used for the pothole data collection process. Several machine learning methods were applied in this study such as Decision Tree and Naïve Bayes [33] . More recently, a crown sensing-based system was built to be utilized in road surface data collection using smartphones. The mobile accelerometer and GPS were utilized to collect spatial data of the road surface. The results of this study showed that the crown sensed data can be efficient in road surface evaluation [34] .

In conclusion, current efforts to automate the data collection of gravel roads is still impractical and needs more development to be a convenient resource for gravel road agencies. In addition, there is a need to have an objective method to determine the riding quality of gravel roads. Therefore, this study is introducing a new computational method to determine the riding quality of gravel roads in consideration of the capabilities and resources of local agencies. The proposed method is a cost-effective approach and can deal with the dynamic nature of gravel road conditions.

In this study, an Android application called “Roadroid” was utilized to collect gravel road data. The application collected IRI and corrugation data. In addition, the gravel road rating system (GRRS) was used to determine the riding quality for the tested gravel road segments. Later on, the collected data was statistically analyzed to develop a computational formula for the riding quality. Afterward, IRI classification limits were introduced. Four hundred and twenty-eight gravel road segments were evaluated in Laramie County, Wyoming for the purpose of this study.

ANN architecture is one of the most important steps in developing sufficient ANN model. Thus, a massive effort has been spent to determine the suitable architecture. Essentially, developing ANN model includes three main components: the architecture that define the connection between input and output layers, the learning method, and the neuron activation function. The ANN model architecture that used in this study consists of three layers: input layer, hidden layer, and output layer as shown in Figure 8 . Extensive literature review and many trails were carried out to determine the optimum neurons number. For the purpose of this study, 10 neurons was found to be the optimum neuron number to achieve the highest accuracy without making the models complicated and time consumers.

After determining the ANN architecture, MATLAB software was used to analyze the data and develop the prediction models. The available data was randomly divided into two groups: 70% of the data was used to train and develop the model, and the remaining 30% was used for testing and validating the model. The validation and testing set was used to evaluate the models accuracy and reduce the model overfitting. A two-layer feed-forward network trained with Levenberg-Marquardt was utilized in the training process to maximize the models prediction ability by adjusting the connection weights between the layers. Generally, the ANN learning methods are classified into supervised and unsupervised methods. The supervised learning methods depends on the available data to develop inferences about the relations between the input and output variables [40] . The calculated error between the predicted output and the measured values are used to conduct adjustments on the connection weights between the model inputs and outputs. On the other hand, in the unsupervised learning process, the connection weight is adjusted based on stimuli inputs with no desired output provided in order to cluster the input values to similar features [38] .

The Levenberg-Marquardt (LM) training method is considered one of the most popular techniques for employing the feed-forward neural networks because of its superior efficiency in enhancing the training precision. This method has been tested on various function approximation problems, and was compared with a conjugate gradient algorithm [34] . Basically, this method consider the neuron as the process basic element. The neuron assumed to have a bias “b” related to the input “n” and input weight “w”. The bias can be expressed by Equation (2).

$a={\displaystyle {\sum }_{j=1}^R{w}_j{p}_j+b=Wp+b}$ (2)

Newton’s method was the base point in developing the Levenberg-Marquardt method, that give the advantage of reducing the nonlinear function sum of squares. This reduction was achieved by optimizing a performance index called F. The complexity in understanding the relationships between variables cause that the ANN models still known as “black box” technique, this complexity increase the difficulties in developing and making inferences about the effect of the individual independent variables on the response variable [15] [39] . This difficulty is considered as a disadvantage in the ANN method comparing to traditional statistical methods. Combination between both ANN and traditional statistical modelling methods, such as linear regression in this study, can limit the weakness and produce a significantly accurate model with proper understanding about the relationships between the considered variables.

The developed ANN model shows a significant high capability in predicting the riding quality on gravel roads based on the IRI condition. The developed ANN prediction model performance were compared to the developed linear regression model. Coefficient of determination (R²) was used to compare the accuracy among the two methods. The overall R² for the developed ANN model is 92.5%; while the R² reached 95% during the testing phase. Comparing the R2 of the two developed model shows that adapting the ANN method resulted in a model with 12.5% enhancement in the prediction accuracy. Figure 9 and Figure 10 represent the function fit and model performance, respectively.

Classifying the IRI into multiple categorical groups can significantly enhance the gravel roads maintenance budgeting and planning process. Even though many road authorities have developed their own IRI thresholds for paved roads, there is no suggested IRI threshold for gravel roads in the literature. Gillespie and Paterson described the roughness of different types of roads in terms of IRI and defined IRI ranges for each road type. They stated that usually the rough unpaved roads IRI range is between 507 and 1267 in/mile [33] . Figure 11 represents the expected IRI ranges in Gillespie and Paterson study [38] . The developed riding quality model, shown in Equation (1), was used to suggest and choose the gravel road IRI thresholds. This study suggests that the IRI could be classified into 3 categories; smooth, acceptable, and rough. In order to suggest a reasonable threshold for IRI on gravel roads the developed linear regression was employed. The linear regression was used to develop an IRI prediction model based on the ride quality. In order to determine the smooth category threshold, the IRI value was calculated using Equation (1) and substituting the ride quality with 7. The substituted valued was 7 for the riding quality since it is the minimum value to have good or better rating as shown in Table 1 . This means the study assumed that to have a smooth IRI level, a gravel road should have good ratings in riding quality and corrugation. In the same way, the ride quality was substituted by 5, to determine the IRI threshold for the acceptable category. The substituted value was 5 for the riding quality since it is the minimum value to have fair or better rating as shown in Table 1 . The gravel road section condition will be classified as a poor section in term of roughness when it has riding quality of less than 5. Table 7 represents the suggested IRI threshold for gravel roads.

The WYT2 center is in the process of developing a holistic GRMS. One part of the proposed GRMS is developing an integrated fully automated data collection technique. Riding quality is one of the most used terms in GRMS decision-making. Thus, the main goal of this study was to develop a computational method for the riding quality of gravel roads by utilizing a smartphone data collection technique. The developed method can limit subjectivity in the riding quality rating. In addition, this computational method will support local agencies in justifying their gravel road assessment findings. Utilizing smartphones to collect data made the developed computational method practical and cost-effective. In order to develop the computational model for the riding quality, 428 gravel road segments were evaluated and tested. The evaluation results showed that in terms of corrugation, 61.7% of the segments are in good or better condition and 9.1% of the segments are in poor or very poor condition. In addition, the riding quality assessment showed that 75.23% of the segment are in good or better condition and only 4.91% are in poor or worse condition. In conclusion, the developed riding quality model is statistically significant and has the ability to estimate the riding quality using corrugation and roughness data. The coefficient of determination of the developed model is about 82% which is sufficient for the GRMS purposes. Furthermore, thresholds for gravel roads IRI were developed and suggested in this study. There are no such ranges for gravel roads IRI in the literature. The introduced thresholds consider that a gravel road is smooth in terms of IRI if it is less than 295 in/mile, and acceptable if the IRI is between 295 and 509 in/mile, while the road is considered in rough condition if the IRI is more than 509 in/mile.

Based on the statistical analysis and results of this study, it is recommended that local agencies implement the developed riding quality model in their gravel roads management systems. In addition, further research efforts should be invested to enhance the developed thresholds for the gravel roads IRI by increasing the number of classes and utilizing advanced mathematical methods such as Tylor’s series and Fourier’s Series to determine the threshold values.

The authors would like to gratefully thank the Mountain Plains Consortium (MPC) for supporting this study. In addition, the author would like to acknowledge the contribution of Mr. Lars Froslof, the Roadroid CEO and Founder, in this study.