Investigating the Seepage Characteristics of an Open-Graded Friction Course Using Finite Element Modeling

Abstract

An open-graded friction course (OGFC) is an asphalt mixture designed with a large air void (AV) content that provides enhanced drainage capability at the surface. The main objectives of this study were to investigate the impacts of selected factors (i.e., the OGFC thickness and coefficient of permeability, the permeability of the underlying layer, and traffic loading) on the drainage characteristics of the OGFC, develop a quantitative tool to simulate the deterioration in the functional performance of the OGFC, and propose new guidelines for the AV content of OGFC for optimum functionality. To this end, a three-dimensional finite element (FE) model was developed to evaluate the impacts of OGFC permeability, OGFC layer thickness, underlying layer permeability, rain intensity, and traffic volume on the seepage characteristics of OGFC pavements. The impacts of these factors were evaluated by calculating the time at which the OGFC surface reaches overflow condition (T_C). Statistical analysis of the results showed that all considered factors had a significant impact on OGFC seepage characteristics, except OGFC permeability. In addition, an artificial neural network (ANN) model was developed to predict T_C without the need for FE modeling. Results indicated that the ANN model predicted T_C accurately with R² values of 0.99 and 0.98 in the training and validation stages, respectively. The results also indicated that the model accurately predicted T_C over time for OGFC pavements with a root-mean-square error of less than 5.0%. Simulation runs were conducted using the developed FE model under different OGFC AV content conditions and rain intensities. Results revealed that an OGFC layer with an AV content of 16% would provide adequate drainage performance while minimizing OGFC durability issues.

Keywords

infrastructure pavements design and rehabilitation of asphalt pavements asphalt pavement design roadway design

An open-graded friction course (OGFC) is typically designed with a large air void (AV) content (from 15% to 22%), which provides for enhanced drainage capability at the surface ( 1 , 2 ). Therefore, the possibility of hydroplaning decreases, and subsequently wet weather crashes also decrease ( 3 ). Chen et al. ( 4 ) concluded that the OGFC reduced the accident rate from 1.79 accidents per million vehicles per kilometer (ACC/MVK) to 0.28 ACC/MVK ( 4 ). Similarly, the OGFC reduced the number of fatalities by two-thirds in wet weather conditions in Japan ( 5 ). The OGFC also provides a means with which to control spray and splash during rain events, which in turn improves vision during precipitation. In Virginia, the OGFC provided the best splash and spray control compared to other types of mixes based on a qualitative evaluation of the splash and spray characteristics of these mixes ( 6 ). In Louisiana, the splash and spray performance of four OGFC projects was qualitatively compared to adjacent Superpave pavement sections ( 7 ). Results indicated that splash and spray could be effectively controlled if an OGFC layer is applied as a wearing surface course. To ensure OGFC best performance, many factors including pavement geometric design (i.e., longitudinal and transversal slopes), location characteristics (i.e., rain intensity), and OGFC layer characteristics (i.e., thickness and coefficient of permeability) should be considered.

During the last two decades, many studies have evaluated the different factors that contribute to OGFC hydraulic performance using finite element analysis (FEA). It has been concluded that the OGFC drainage capacity is strongly dependent on its porosity ( 8 , 9 ). In addition, pavement geometric design, including longitudinal and transverse slopes and pavement length, has been identified as a significant factor that affects OGFC hydraulic characteristics ( 10 , 11 ). Yet, previous studies have focused on the impacts of the OGFC layer itself and ignored the impacts of the underlying layers’ permeabilities on the drainage properties. Moreover, these studies have ignored the impact of traffic on the long-term hydraulic performance of OGFC mixes. It should be noted that permeability and seepage are different terms. Permeability is a term that describes how easily water or any other fluid flows through a porous medium. In contrast, the term seepage describes the phenomenon when water flows through a porous medium because of a difference in the water head.

In Louisiana, the AV content of the OGFC is required to be in the range of 18%–24% ( 7 , 12 , 13 ). The high AV content of the OGFC promotes its functionality by allowing the water to drain horizontally through the interconnected voids, therefore preventing hydroplaning, splash, and spray ( 14 , 7 ). However, high AV content may have detrimental impacts on OGFC durability. Because of its high AV content, OGFC mixes are easier to penetrate and are more affected by water and oxygen ( 15 ). This exposure promotes premature failure (i.e., raveling, stripping, and cracking) and clogging of the voids. Therefore, the AV content should be controlled accordingly to minimize its contribution to the durability issues in the OGFC.

Objectives

This study aims to evaluate the seepage characteristics of an OGFC using FEA and an artificial neural network (ANN). The following objectives were achieved:

evaluate the impacts of the OGFC thickness and coefficient of permeability and the permeability of the underlying layer on its seepage characteristics under different rainfall intensities;

investigate the long-term hydraulic performance of OGFC pavements by considering the impact of traffic;

develop a quantitative ANN model for the prediction of the time to reach the overflow condition (T_c) in OGFC pavements;

evaluate the current AV guidelines and propose new AV guidelines for OGFC applications in Louisiana ( 16 ).

Background

Seepage Analysis Using Finite Element Analysis

FEA is a powerful tool for solving many complex engineering and scientific problems. Among the existing numerical models, SEEP/W is a numerical finite element (FE) model that can be effectively used to simulate water flow through porous media in real-life applications. It has been used extensively to simulate many drainage problems in geotechnical engineering and other disciplines, given its accuracy ( 17 ). Mousa et al. ( 18 ) utilized the results of a calibrated SEEP/W model to introduce guidelines for using crack-sealing while minimizing water entrapment under cracks for low-volume roads.

SEEP/W was also used to simulate water flow in flexible pavement using transient analysis ( 19 ). The results of SEEP/W were compared to the results of the Drainage Requirement in Pavements (DRIP) software. Results indicated that SEEP/W is an adequate tool to evaluate pavement subsurface drainage systems. However, the DRIP software yielded conservative results as it assumes one-dimensional water flow in the fully saturated condition. In another study, Yoo et al. ( 20 ) utilized SEEP/W to simulate the flood-runoff reduction effect of four filtration strategies. The authors concluded that SEEP/W yielded reasonable results; therefore, SEEP/W was selected in the present study to simulate the seepage characteristics of a pavement section with an OGFC.

Numerical Studies of OGFC Hydraulic Characteristics

Tan et al. ( 21 ) used FE software (i.e., SEEP 3D) to investigate the impacts of the longitudinal and cross-sectional slopes on the thickness design of the OGFC. Results indicated that both cross-sectional and longitudinal slopes significantly affected the drainage performance of the OGFC layer. For example, the increase of the cross-slope by 1% increased OGFC drainage capacity by 88%. Similarly, other researchers utilized numerical analysis to determine the impacts of pavement length and cross-sectional slope on the time to reach the overflow condition under different rainfall intensities ( 10 ). Results indicated that the time required to reach the overflow condition increased when the cross-sectional slope increased. However, the increase in pavement length and rainfall intensity decreased the time required for the water to flow over the pavement surface. In another study, three-dimensional (3D) FE software (i.e., COMSOL Multiphasic) was employed to investigate the impact of the longitudinal slope on OGFC drainage capacity ( 11 ). To achieve this objective, a pavement with a width of 32 ft (10 m) and a length of 262 ft (80 m) was simulated using COMSOL. The OGFC layer was simulated with a thickness of 2.00 in. (50.08 mm) and with varying longitudinal slopes from 0% to 6%. Results indicated that the contribution of the longitudinal slope to the OGFC drainage capacity was insignificant.

OGFC Permeability Loss Caused by Traffic

OGFC mixes are designed to reduce the potential of hydroplaning and minimize splash and spray. However, because of the large AV content, the OGFC may become clogged with debris over time, resulting in a loss of permeability ( 22 ). In addition, the OGFC could be clogged because of densification under traffic loading ( 23 ). Permeability loss may also be attributed to binder creep, which starts immediately after construction, especially during hot weather conditions ( 24 ). The main conclusion of the referenced studies was that the OGFC loses most of its permeability effectiveness until a traffic loading of 2 × 10⁶ equivalent single axle loads (ESALs); the OGFC then reaches a plateau in its permeability at which it resists further densification or clogging, as illustrated in Figure 1 ( 25 ).

Relation between Air Voids and Permeability

In NCHRP 1-55, Watson et al. ( 22 ) measured the coefficient of permeability of six OGFC mixes and correlated the permeability results to the AV content of each mix. The AVs of all OGFC mixes ranged between 15.7% and 21.9%, while the permeability values ranged from 80 to 237 m/day. These data were used to develop a correlation between AV content and the coefficient of permeability of the OGFC. Results indicated a direct relationship between K_OGFC and AV (%) content with a coefficient of determination (R²) of 0.94. Equation 1 provides the relation between AV content and K_OGFC as reported by Watson et al. ( 22 ):

K_{OGFC} = 24.87 \times AV - 324.88

(1)

where K_OGFC is the OGFC permeability (m/day) and AV is the AV content (%).

Effects of Air Voids Content on OGFC Performance

In a study conducted by James et al. ( 26 ), the durability of two OGFC mixes was evaluated. Both mixes had almost the same aggregate gradation, except for sieve No. 3/8” (9.5 mm), and the same binder content. The AV contents were 15.4% and 22.2% for the good and poor mixes, respectively. The good and poor mixes had Cantabro losses of 19.3% and 37.9%, respectively. These results indicate that OGFC mixes with a high AV content are more susceptible to raveling compared to OGFC mixes with a low AV content. In addition, the good mix showed higher rutting resistance than the poor mix. The good mix required more than 20,000 passes to reach the maximum allowable rutting depth compared to about 2000 passes for the poor mix.

Mansour and Putman ( 27 ) evaluated the impacts of aggregate gradation and AV content on 10 OGFC mixes. The AV content of these mixes ranged from 10.0% to 17.7%. Results showed that the mix with the highest AV exhibited the highest Cantabro loss, indicating inferior raveling resistance. In NCHRP 1-55, six OGFC mixes with documented field performance were evaluated ( 22 ). Three mixes exhibited good field performance and the others were poor mixes. The good mixes showed lower average AV content as compared to the poor mixes. In addition, results indicated that the Cantabro loss increased with the increase in AV content. Furthermore, all the mixes exhibited acceptable rut depth at 20,000; however, the mixture with the highest AV content failed at only 3200 passes.

Contribution to the Body of Knowledge

Based on the literature review, limited studies have been conducted to investigate the seepage characteristics of OGFC pavement in full-scale applications. Therefore, the literature review revealed the following knowledge gaps.

Although a few studies evaluated the impact of pavement factors, such as longitudinal and cross-sectional slopes, on OGFC hydraulic characteristics, none of the previous studies evaluated the impacts of the permeability of the underlying layer on the seepage characteristics of the pavement section. Furthermore, field calibration of the developed models was rarely conducted.

The literature review revealed that no quantitative model is available for the prediction of the time to reach overflow conditions in OGFC pavements.

Methodology

Figure 2 shows the developed and adopted research methodology. In this study, a two-dimensional (2D) FE model previously developed by the authors using SEEP/W was considered ( 18 ). For the purpose of study, the model was re-constructed using SEEP/3D in three dimensions. Afterward, steady-state analysis was conducted to define the initial conditions of the problem. Before proceeding with the transient analysis, the developed model was calibrated. Once the model was calibrated, an OGFC layer was added to the model and a series of simulation runs was conducted to evaluate the effect of different factors on the hydraulic characteristic of OGFC pavements. As illustrated in Figure 2, the effects of the OGFC layer thickness (T_OGFC), OGFC coefficient of permeability (K_OGFC), underlying layer coefficient of permeability (K_HMA), rain intensity (R), and traffic volume on OGFC seepage characteristics were evaluated using SEEP/3D. FE results were then used to calculate the time at which water overflow occurs (T_C). Afterward, the results of the FE model were statistically analyzed to identify the factors that significantly affected T_C. The results of SEEP/3D were then used to train and validate an ANN model for the prediction of T_C without the need for FEA. In addition, the developed FE model were used to propose new AV guidelines for OGFC applications in Louisiana.

Original 2D Model Characteristics

The original 2D model consisted of three layers (i.e., dense hot mix asphalt [DGHMA] layer, base layer, and subgrade). The thickness of the DGHMA and base layers was 4.5 in. (114.3 mm) and 9.5 in. (241.3 mm), respectively. The pavement transversal slope and width were 2.5% and 24.0 ft (7.30 m), respectively. The road had two side ditches, each of which had a width of 5 ft (1.5 m) and a depth of 3 ft (0.9 m) ( 18 ).

To describe the unsaturated water flow through the pavement layers, the soil water characteristic curve (SWCC) and hydraulic conductivity function are required. Table 1 shows pavement layer properties as defined in the FE model developed by Mousa et al. ( 18 ). In the referenced study, DGHMA saturated hydraulic conductivity (K_sat) was measured in the laboratory according to FM 5-565 ( 28 ). However, typical K_sat values from previous research were assigned to the base layer and subgrade soil ( 29 ). Similarly, Mousa et al. used typical Van Genuchten fitting parameters for the DGHMA layer, base layer, and subgrade from previous studies, as presented in Table 1.

Table 1.

Material Seepage Properties ( 18 )

Property	Van Genuchten fitting parameters				K_sat (in./s)
Property	n	a	Residual moisture content	Saturated moisture content	K_sat (in./s)
DGHMA	1.09	0.489	0.0	0.06	1.35×10⁻⁶
Base (sandy loam)	1.89	1.31	0.065	0.41	4.80×10⁻⁴
Subgrade (loam)	1.56	2.725	0.078	0.43	1.14×10⁻⁴

Note: a, n = empirical shape-defining parameters of the Van Genuchten equation; DGHMA = dense hot mix asphalt.

3D FE Model Layout

In this study, SEEP/3D was used to re-construct the 2D model of the previous study using the material properties described in Table 1; see Figure 3. The cross-section of the roadway consisted of a 4.50 in. (114.3 mm) asphalt layer on top of a 9.5 in. (241.3 mm) base layer that rested on the natural subgrade soil. The natural ground was extended laterally 36 ft (11 m) on both sides beyond the side ditches, as was observed in the field. The side ditches were simulated with a bottom width of 4.90 ft (1.50 m) and a depth of 2.95 ft (0.90 m). As shown in Figure 3, the transversal slope of the main road was assumed to be 2.5%, while the side slope of the ditches was assumed to be 1:1. In total, the model consisted of 45,817 nodes and 7700 triangular elements.

Steady-State FE Analysis

A steady-state analysis was conducted to define the initial conditions of the problem. Steady-state analysis was conducted under the following boundary conditions ( 18 ).

Based on a field survey of the calibration site, the water level in the left-hand side ditch was 2.62 ft (0.80 m); therefore, a total hydraulic head (H) of 64 ft (19.5 m) was assigned to the wetted perimeter of the left-hand side ditch (H = ditch bed level [18.7 m] + head pressure [0.8 m] = 19.5 m).

The water level in the right-hand side ditch was 0.66 ft (0.20 m); therefore, a total hydraulic head (H) of 62 ft (18.9 m) was assigned to the wetted perimeter of the right-hand side ditch (H = ditch bed level [18.7 m] + head pressure [0.2 m] = 18.9 m).

To account for the vertical and lateral seepage in the entire system, two lines of zero pressure head were applied at a level of 15.6 m.

Calibration of the Steady-State FE Analysis

In the previous 2D model developed by the authors, steady-state analysis was calibrated using the volumetric water content (VWC) at the mid-depth of the base layer and at the ground water table (GWT) level. For this purpose, the VWC at the mid-depth of the base layer was calculated based on ground penetrating radar (GPR) survey data using the Topp equation ( 30 ). Results indicated that the VWC at the mid-depth of the base layer was 0.30. In addition, the GPR survey data showed a strong reflection at 0.60 m beneath the pavement surface, which was indicative of the GWT level.

The calculated VWC and GWT level were used to validate the steady-state analysis in the 3D model. The model was run under steady-state conditions and the VWC was calculated along section 1-1 (i.e., at the mid-depth of the base layer), as presented in Figure 4a. Results indicated that the average VWC at section 1-1 was 0.20, as presented in Figure 4b. In addition, the pore water pressure was calculated at section 2-2, see Figure 4a, to locate the GWT depth. The GWT corresponds to the location at which the pore pressure equals zero. Figure 4c indicates that the GWT was located at a depth of 1.2 m beneath the pavement surface. Results of the steady-state analysis under the initial boundary conditions revealed that the VWC and GWT were not consistent with the GPR test results. It was determined that inaccurate measurements of the water level in the side ditches might be the reason for these discrepancies. Therefore, several runs were conducted after changing the water level in the side ditches. After several trials, the average VWC yielded 0.30 and a pore pressure of zero was located at a depth of about 0.6 m, as presented in Figure 4, b and c , respectively. Both conditions were satisfied when total heads of 19.5 and 19.3 m were applied along the wetted perimeter of the left- and right-hand side ditches, respectively.

Transient Analysis

After the model was calibrated, an OGFC layer was added to the FE model for the purpose of this study. Typical Van Genuchten parameters (i.e., a, n) for the OGFC layer were assumed based on the results of a previous study ( 10 ). In this study, a and n were assumed to be 2.23 kPa and 1.63, respectively. Using these inputs, several runs were conducted to evaluate the impacts of K_OGFC, T_OGFC, K_HMA, R, and traffic on OGFC seepage characteristics.

Development of an Artificial Neural Network Model for T_c Prediction

ANN Model Structure and Inputs

In this study, an ANN model was developed to predict T_C using T_OGFC, K_HMA, R, and traffic volume (i.e., significant factors). This model can serve as a quick tool to predict T_C without FEA. To this end, a multilayered feed-forward backprop ANN with a LOGSIG transfer function and TRAINGDX training function was used to develop the model; see Figure 5. The input layer contained four neurons, while the output layer consisted of one neuron. The remaining two layers were hidden layers and consisted of eight neurons each.

Training and Validation of the ANN Model

A dataset consisting of 648 data points was used to develop the ANN model. This dataset was divided into two groups. The first group contained 80% of the data, which was used in model fitting. The second group consisted of 20% of the data, which was used to validate the trained ANN model with a separate dataset. These percentages were adopted since they returned the best performance of the proposed model.

Finite Element Model Inputs

OGFC Characteristics

For the K_OGFC values, three OGFC mixes were fabricated in the laboratory and their coefficients of permeability were measured according to FM 5-565 ( 15 ). Results indicated that K_OGFC was 0.06, 0.05, and 0.03 in./s for Mixes 1–3, respectively. It worth noting that all mixes satisfied the minimum requirement of OGFC permeability recommended by NCHRP 1-55 (i.e., 0.02 in./s) ( 22 ).

For T_OGFC, the OGFC is typically constructed with lift thicknesses of 0.75 and 1.25 in. in Louisiana ( 7 ). In addition, an additional thickness of 1.9 in. was considered. The 1.9 in. lift thickness was considered for two reasons. Firstly, the OGFC is typically placed with a lift thickness of 1–2 in. in Europe ( 22 ). Secondly, this thickness was considered to generate more data to develop the ANN model. Based on this assumption, three K_OGFC and T_OGFC values were considered in this study; see Table 2.

Table 2.

Overview of the Finite Element Simulation Runs

Factor	No. of cases	Values	Units
K_OGFC	3	0.03, 0.05, and 0.06	in./s
T_OGFC	3	0.75, 1.25, and 1.90	In.
Rain (R)	3	0.02, 0.04, 0.10	in./h
K_HMA	4	1.36 × 10⁻⁶, 1.18 × 10⁻³, 2.36 × 10⁻³, and 3.54 × 10⁻³	in./s
Traffic	6	0, 2, 4, 6, 8, and 10	10⁶× ESALs
Total	3 × 3 × 3 × 4 × 6 = 648

Note: ESALs = equivalent single axle loads.

Underlying Layer Characteristics

Mohammad et al. ( 31 ) conducted laboratory permeability tests on field cores extracted from 17 Superpave projects in Louisiana. Results indicated that the permeability of Superpave mixes had a maximum coefficient of permeability of 3.54 × 10⁻³ in./s. In this study, four K_HMA values were simulated (i.e., 1.36 × 10⁻⁶, 1.18 × 10⁻³, 2.36 × 10⁻³, and 3.54 × 10⁻³ in./s); see Table 2.

Rain Intensities

In this study, three rain intensities (R) were assumed based on rainfall data in Louisiana. Hourly rain intensity values were obtained from the LSU Agricultural Center website for the period from January 2020 to January 2021. To this end, a total of 8088 observations were obtained with R ranging from 0 to 1.89 in./h. In this study, the hours that experienced zero rainfall intensity were removed, resulting in a total of 720 observations of rainy hours. Afterward, these observations were used to calculate the first, second, and third quartiles (see Table 2), which were used in the analysis.

Traffic Impact Simulation

In this study, the effect of traffic was considered by applying a reduction factor to the initial permeability coefficient of the mixes. As previously noted, because of traffic and other factors, OGFC permeability decreases over time. In this study, reduction factors of 1.00, 0.50, 0.36, 0.32, 0.25, and 0.20 were applied to the initial OGFC permeability to obtain the coefficient of permeability at 0, 2 × 10⁶, 4 × 10⁶, 6 × 10⁶, 8 × 10⁶, and 10 × 10⁶ ESALs, respectively, as presented in Figure 1. An AV content that corresponds to each permeability coefficient was calculated using Equation 1. Simulation runs were then conducted to evaluate the effect of traffic on the seepage characteristics of the pavement section constructed with an OGFC layer. In all, a total of 648 runs were conducted in this study, as presented in Table 2.

Determination of the Critical Location

Before proceeding to the seepage analysis, the critical location, at which T_C is to be calculated, must be determined. In this paper, the critical location on the surface of the OGFC layer was selected based on the analysis results. Two locations were investigated, the left- and right-hand wheel paths. These locations were selected because of their frequent exposure to traffic wear compared to other locations on the pavement surface. A line that is located at 2.5 ft from the pavement centerline was identified as the left-hand wheel path, while a line at 3.0 ft from the shoulder–lane boundary represented the right-hand wheel path ( 32 ). To identify the critical location, the calibrated model was run using the following conditions:

K_OGFC = 0.06 in./s;

OGFC thickness = 0.75 in.;

K_HMA = 2.36 × 10⁻³ in./s;

R = 0.02, 0.04, and 0.1 in./h; and

traffic volume = 0 ESALs.

Results and Discussion

Critical Location

Figure 6 compares the T_C values in the left- and right-hand wheel paths for the different R values. These results indicate that the time to reach overflow conditions (T_C) was always shorter in the right-hand wheel path than that for the left-hand wheel path at all R values. Therefore, a point in the right-hand wheel path will reach saturation before a corresponding point in the left-hand wheel path. These results may be because rainfall water always moves toward the shoulder under gravitational forces. Therefore, the total amount of water that will be induced in the right-hand wheel path will be more than that in the left-hand wheel path. Based on these results, all the remaining analysis was conducted based on the T_C values in the right-hand wheel path, since it is more critical.

Effect of Selected Factors on the Hydraulic Characteristics of the OGFC

This section presents the effect of each selected factor while the remaining factors were kept constant. For instance, the effect of K_OGFC on the OGFC pavement seepage characteristics was evaluated by varying K_OGFC (i.e., 0.03, 0.05, 0.06 in./s) while the remaining factors were kept constant, as presented in Table 3.

Table 3.

Inputs to the Finite Element (FE) Model to Investigate the Impact of each Factor on Open-Graded Friction Course Hydraulic Characteristics and the Results of the Significance Test

FE input	Factor
FE input	K_OGFC (in./s)	T_OGFC (in.)	K_HMA (in./s)	R (in./h)	Traffic (ESALs)
K_OGFC (in./s)	0.03, 0.05, and 0.06	0.05	0.05	0.05	0.05
T_OGFC (in.)	1.25	0.75. 1.25, and 1.90	1.25	1.25	1.25
K_HMA (in./s)	1.18 × 10⁻³	1.18 × 10⁻³	1.18 × 10⁻³, 2.36 × 10⁻³, and 3.54 × 10⁻³	1.18 × 10⁻³	1.18 × 10⁻³
R (in./h)	0.02	0.02	0.02	0.02, 0.04, 0.01	0.02
Traffic (ESALs)	0				0, 2, 4, 6, 8, and 10 × 10⁶
Correlation with T_C	0.02	0.32	0.41	−0.52	−0.35
Prob > \|ρ\|	0.63	<0.0001	<0.0001	<0.0001	<0.0001

Note: ESALs = equivalent single axle loads.

The results of the FE model, using the input data described Table 3, are presented Figure 7. As presented in Figure 7, K_OGFC, T_OGFC, and K_HMA had a positive correlation with the time to reach the overflow condition (T_C), as presented in Figure 7, a–c, respectively. For example, T_C increased slightly from 1.80 to 1.86 h. when K_OGFC was increased from 0.03 to 0.06 in./s at R = 0.02 in./h. Similarly, T_C increased from 1.26 to 2.70 h when the OGFC thickness was increased from 0.75 to 1.90 in. In addition, T_C increased by 0.2 h (12 min) when K_HMA was increased from 1.36 × 10⁻⁶ to 3.54 × 10⁻³ in./s. These results may be attributed to the increase in the water storage capacity of the whole system because of the increase of K_OGFC, T_OGFC, and K_HMA. In contrast, the results show that the correlation between T_C and both R and traffic volume was negative—see Figure 7, d and e , respectively. In this case, T_C decreased from 2.04 to 0.98 h when the rain intensity increased from 0.02 to 0.04 in./h. Similarly, the time to reach the overflow condition decreased from 1.37 to 0.80 h when the pavement was subjected to 2 × 10⁶ ESALs after construction.

Correlation Matrix Between T_C and FE Model Input Variables

To develop the ANN model, it was critical to identify which factors are significant in determining the time to overflow (T_C) of OGFC pavements. To this end, SAS 9.4 was used to construct a correlation matrix among T_C and all the inputs of the FE model considered in this study. An analysis of variance (ANOVA) test was then conducted to evaluate the statistical significance of each FE model input on T_C by examining the following hypotheses at a 0.05 confidence level ( $α$ ):

H0 (null hypothesis): β1 = 0;

H1 (alternative hypothesis): β1 $\neq$ 0

where H0 and H1 are the null and alternative hypotheses, respectively, and β1 is the slope between each input and T_C.

Table 3 shows that T_C had a positive correlation with K_OGFC, T_OGFC, and K_HMA with Pearson correlations of 0.02, 0.32, and 0.41, respectively. Conversely, both R and traffic volume had an inverse correlation with T_C with Pearson correlations of −0.52 and −0.35, respectively. The ANOVA results indicated that H0 can be rejected for T_OGFC, K_HMA, R, and traffic volume because the P-value was less than 0.05. Therefore, it can be concluded that there is sufficient evidence at a 0.05 significance level that a linear relationship exists between T_C and T_OGFC, K_HMA, R, and traffic volume. In contrast, the results indicated that H0 cannot be rejected in the case of K_OGFC as the p-value was greater than 0.05. Therefore, it can be concluded that a linear correlation does not exist between T_C and K_OGFC at the 0.05 significance level. These results were expected, as all mixes satisfied the minimum requirement of permeability.

Results of ANN Model Training and Validation

Figure 8 shows the results of the ANN model training and validation. In general, the figure illustrates that the ANN model predicts T_C accurately with coefficients of determination (R²) of 0.99 and 0.98 in the training and validation stages, respectively. In addition, the model yielded low errors when the ANN predicted and FE calculated values were compared with root-mean-square errors (RMSEs) of 5.02% and 0.31% in the training and validation stages, respectively. For further evaluation, SAS 9.4 was used to conduct a two-tailed t-test to compare the means of T_C produced by the ANN and FE by testing the following hypotheses at $α$ = 0.05:

H₀: the average of TC_ANN = the average of TC_FE;

H₁: the average of TC_ANN $\neq$ the average of TC_FE.

In the training and validation stages, results indicated p-values of 0.926 and 0.99, respectively. Therefore, H₀ cannot be rejected, indicating that the average TC_ANN = the average TC_FE in both the training and validation stages. Based on these results, it can be concluded that the average critical time predicted by the ANN is equal to the average of the critical time produced by the FE model.

Application of the Developed ANN Model

Over time, OGFCs become clogged because of dust, binder creep, and consolidation. Therefore, routine maintenance (i.e., vacuum sweeping) for the OGFC layer is unavoidable. Until now, there has been no available tool or model for predicting the functional service life of pavement sections constructed with an OGFC layer. The developed ANN model presented in this study can fill this gap. To illustrate this application, the developed FE model was used to calculate T_C for the two cases described in Table 4 over time. In addition, the ANN was used to calculate T_C for the same cases. The predicted T_C values from both procedures were also compared.

Table 4.

Inputs to Finite Element and Artificial Neural Network Models for Real-Life Applications

Factor	Case 1	Case 2	Unit
K_OGFC	0.05		in./s
T_OGFC	1.25	1.90	in.
R	0.04		in./h
K_HMA	3.54 × 10⁻³		in./s
Traffic	0, 2, 4, 6, 8, and 10		10⁶× ESALs

Note: ESALs = equivalent single axle loads.

Figure 9 indicates that, over time, the time to reach the overflow condition decreases because of the clogging and reduction of OGFC interconnected voids. It should be noted that the drop in OGFC permeability after 2 × 10⁶ ESALs in Case 2 was significantly higher than that of Case 1. In Case 2, the OGFC thickness is 1.9 in., which may cause more consolidation than that of Case 1 that simulated a thickness of 1.25 in. for the OGFC layer. In addition, the ANN model predicted the T_C over the OGFC service life accurately with RMSE values of 4.1% and 4.9% for Cases 1 and 2, respectively, as compared to the FE model. These results imply that the developed ANN model can be used as a practical tool to model the deterioration in the functional performance of OGFC mixes. With the help of this model, state highway agencies (SHAs) can predict the time at which routine maintenance should be conducted for roadway segments constructed with an OGFC layer.

Air Void Guidelines for Open-Graded Friction Course Mixes

In this section, the developed FE model was used to evaluate and recommend new AV guidelines for OGFC mixes in Louisiana. As previously noted, a high AV content has a detrimental impact on OGFC durability ( 26 , 27 ). In Louisiana, OGFC mixes are usually produced with an AV content between 18% to 24%, which is higher than the AV content recommended by other states ( 22 ). Therefore, the developed FE model was used to evaluate the current AV guidelines in Louisiana for OGFC applications.

For this purpose, the developed FE model was used to calculate the degree of saturation (DOS) in the right-hand wheel path at R of 0.04 in./h (i.e., Q₂) after 1.00 h. The DOS was calculated for pavement sections constructed with an OGFC layer with different AV contents (i.e., 10%, 12%, 14%, 16%, 18%, 20%, 22%, and 24%), as presented in Table 5. Equation 1 was then used to predict K_OGFC for each AV content. In addition, the impact of traffic was considered by applying the reduction factors obtained from the results of this study.

Table 5.

Inputs to the Finite Element Model for Air Void (AV) Guidelines

Factor	Values	Unit
OGFC AV content	10, 12, 14, 16, 18, 20, 22, and 24	%
K_OGFC	Calculated using Equation 1	in./s
T_OGFC	1.25	in.
R	0.04	in./h
K_HMA	1.36 × 10⁻⁶	in./s
Traffic	0, 2, 4, 6, 8, and 10	10⁶× ESALs

Note: OGFC = open-graded friction course; ESALs = equivalent single axle loads.

Degree of Saturation after 1 H of Precipitation

Figure 10 presents the DOS values for OGFCs with different AV contents after different traffic loading levels. As shown in this figure, OGFC layers with AV contents of 16%, 18%, 20%, 22%, and 24% did not reach the overflow conditions even after 1 h of continuous rain (i.e., R = 0.04 in./h). This observation was also confirmed even after 10 × 10⁶ ESALs. In contrast, OGFC layers with AV contents of 10%, 12%, and 14 % were saturated after 1 h of rain at all traffic levels. Based on these results and considering the worst-case scenario, it can be recommended that the lower limit of AV requirements for OGFC mix should be decreased from 18% to 16%. Based on the literature review, high AV content always results in poor durability of the OGFC mix ( 15 ). Therefore, the high limit of AV requirements may also be decreased from 24% to 20% to enhance the durability of the mix.

Conclusions and Recommendations

This study aimed at investigating the impacts of selected factors on OGFC pavements’ seepage characteristics; developing a quantitative tool to simulate the deterioration in OGFC pavements’ functional performance; and proposing guidelines for the AV content of OGFC mixes. To achieve these objectives, a 3D FE model was developed to assess the effects of OGFC permeability, OGFC layer thickness, underlying layer permeability, rain intensity, and traffic volume on the seepage characteristics of OGFC pavements. The main findings of this study were as follows.

Results indicated that as the thickness of the OGFC, the permeability coefficient of the OGFC, and the permeability coefficient of the underlying layer increased, T_C also increased. This can be attributed to the increase in the storage capacity of the OGFC layer. In contrast, T_C decreased with the increase in rain intensity and traffic wear. In the case of an increase in rain intensity, more water is required to be drained; granted the same permeability level, the time to reach the overflow condition will decrease. With respect to traffic, the permeability of OGFC pavement decreases with traffic because of mix consolidation or binder creep. In addition, with the increase of pavement age (related to traffic), debris accumulates, which results in OGFC clogging.

Results of the developed FE model were used to train and validate an ANN model for the prediction of T_C. The inputs of this model included the thickness of the OGFC, permeability coefficient of the underlying layer, and rain intensity. Results showed that the developed ANN model was able to predict T_C accurately with R² values of 0.99 and 0.98 in the training and validation phases, respectively. In addition, statistical analysis showed that the differences between T_C values predicted by the ANN and those produced by the FE model were statistically insignificant. These results indicate that the developed ANN model can be used in lieu of the FE model to evaluate the ability of the proposed OGFC layer to drain rainfall water in an acceptable time according to the conditions in the field.

For a 60-min rainstorm of 0.04 in./h, an OGFC layer with an AV content of 16% can drain rainfall water without reaching overflow conditions even after traffic wear. Based on these results, it is recommended that the lower limit of AV requirements for OGFC mixes should be decreased from 18% to 16%. In addition, the high limit of AV requirements may also be decreased from 24% to 20% to enhance the mix durability.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: H. Abohamer, M. Elseifi; data collection: H. Abohamer, C. Mayeux; analysis and interpretation of results: H. Abohamer, M. Elseifi, C. Mayeux, S.B. Cooper III; draft manuscript preparation: H. Abohamer, M. Elseifi, C. Mayeux, S.B. Cooper III, S. Cooper, Jr. All authors reviewed the results and approved the final version of the manuscript.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The study was financially supported by the Louisiana Transportation Research Center (LTRC). Grant number 21-6B.

ORCID iDs

Hossam Abohamer

Mostafa A. Elseifi

Corey Mayeux

Samuel Cooper

The contents of this paper do not necessarily reflect the official views or policies of LTRC or LaDOTD.

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Investigating the Seepage Characteristics of an Open-Graded Friction Course Using Finite Element Modeling

Abstract

Keywords

Objectives

Background

Seepage Analysis Using Finite Element Analysis

Numerical Studies of OGFC Hydraulic Characteristics

OGFC Permeability Loss Caused by Traffic

Relation between Air Voids and Permeability

Effects of Air Voids Content on OGFC Performance

Contribution to the Body of Knowledge

Methodology

Original 2D Model Characteristics

3D FE Model Layout

Steady-State FE Analysis

Calibration of the Steady-State FE Analysis

Transient Analysis

Development of an Artificial Neural Network Model for Tc Prediction

ANN Model Structure and Inputs

Training and Validation of the ANN Model

Finite Element Model Inputs

OGFC Characteristics

Underlying Layer Characteristics

Rain Intensities

Traffic Impact Simulation

Determination of the Critical Location

Results and Discussion

Critical Location

Effect of Selected Factors on the Hydraulic Characteristics of the OGFC

Correlation Matrix Between TC and FE Model Input Variables

Results of ANN Model Training and Validation

Application of the Developed ANN Model

Air Void Guidelines for Open-Graded Friction Course Mixes

Degree of Saturation after 1 H of Precipitation

Conclusions and Recommendations

Footnotes

Author Contributions

Declaration of Conflicting Interests

Funding

ORCID iDs

References

Development of an Artificial Neural Network Model for T_c Prediction

Correlation Matrix Between T_C and FE Model Input Variables