Evaluation of Resilient Modulus Prediction Models for Saturated Pavement Base Aggregates

Abstract

Given the increased frequency of heavy rainfall, there is a high probability that pavement base aggregates in the field, particularly in coastal regions, will become saturated and remain so for extended periods. The increase in moisture content can reduce the resilient modulus (M_R) of base materials. There are numerous constitutive models that help predict the resilient modulus of base aggregates based on moisture content and stress states, to assist pavement design. The performance of most of these models has been evaluated previously, but not at full saturation. This study is an evaluation of the two best performing prediction models, as determined in previous studies and current practices. The assessment was carried out using M_R test data for seven laboratory-saturated base aggregates with different properties and moisture sensitivities (high and low). The models were first calibrated based on M_R results at the optimum moisture content and then used to predict M_R of each base material at saturation. The accuracy of the prediction and the applicability to base aggregates with different moisture sensitivities formed the basis of the evaluation. The models were found to be more accurate and even conservative when predicting M_R of saturated base aggregates with low moisture susceptibility. However, the models were erroneous in their prediction and overestimated M_R at saturation of highly moisture susceptible pavement base aggregates. An adaptation solution was proposed to improve the prediction accuracy of the existing models. This study joins efforts to design our climate-vulnerable roadways more accurately and improve pavement resilience.

Keywords

infrastructure materials aggregates pavement design modeling of granular material unbound granular material

The resilient modulus (M_R) is a measure of material stiffness obtained as the ratio of the deviator stress to the recoverable or resilient strain. In the current mechanistic-empirical pavement design guide (MEPDG) ( 1 ), the resilient modulus is the most crucial and fundamental material property for characterizing unbound pavement base materials. When designing a pavement, it is important to determine the resilient modulus at the anticipated stress state of the base material in the field. To this end, numerous prediction models have been developed and proposed over the years. The first model was the k–θ model, proposed by Seed et al. ( 2 ):

M_{R} = k_{1} {(\frac{θ}{P_{a}})}^{k_{2}}

(1)

where M_R is a function of bulk stress. Later, Witczak and Uzan ( 3 ) proposed another model, commonly known as the universal octahedral shear stress model, where M_R is a function of bulk stress (θ) and octahedral shear stress ( $τ_{oct}$ ):

M_{R} = k_{1} P_{a} {(\frac{θ}{P_{a}})}^{k_{2}} {(\frac{τ_{oct}}{P_{a}})}^{k_{3}}

(2)

where θ = bulk stress = $σ_{1} + 2 σ_{3}$ ; P_a = atmospheric pressure; $τ_{oct}$ = octahedral shear stress = $\sqrt{2} (σ_{1} - σ_{3}) / 3$ ; and k₁, k₂, and k₃ are material-specific regression coefficients. The modified version of this universal model has been adopted in the MEPDG. Since then, many studies have been conducted, and other models developed, which were well summarized by Han and Vanapalli ( 4 ) for granular materials and Liang et al. ( 5 ) for cohesive soils.

Many factors, excluding stress state, influence the resilient modulus of pavement base aggregates. These factors include gradation, density, plasticity, and, especially, the degree of saturation ( 6 ). It has been well documented by previous researchers that one of the most common causes of a decrease in resilient modulus, both in the field and in the laboratory, is increased saturation ( 7 , 8 ). Therefore, several researchers have evaluated the accuracy of different constitutive prediction models that incorporate variation in moisture content of the base materials ( 4 , 9 ). For instance, Hiltunen et al. ( 10 ) evaluated the prediction ability of the MEPDG model and found that it is conservative and underpredicts the significant increase in M_R of Florida limerock base materials at moisture contents below the optimum moisture content. However, the major shortcoming of these studies is that the ability of the models to accurately predict the resilient modulus of base materials at full saturation has not yet been evaluated. Considering the potential for pavement aggregate base materials to become saturated and potentially stay saturated, whether from flooding or a rising ground water table, it would be beneficial to evaluate the accuracy of the existing design prediction models.

The objective of this study is to evaluate the ability of existing resilient modulus prediction models to accurately predict the resilient modulus of saturated pavement base aggregates. An accurate M_R prediction model at full saturation is necessary to update design standards and ensure pavement resilience against climate water stressors. This study is an evaluation and comparison of the two most accurate design prediction models for granular base materials, based on previous research findings.

Materials and Data

For this study, seven aggregate base materials were collected from different quarries located in Alabama, Florida, and Mexico. The materials, which include four limestone and three limerock materials, are on the Alabama Department of Transportation (ALDOT) list of approved aggregates. The resilient modulus test, following the AASHTO T307 standard procedure ( 11 ), was conducted in the laboratory to determine the M_R of these base materials. Since this study is focused on the evaluation of M_R prediction models for saturated base aggregates, the materials were tested for M_R at the optimum moisture content (OMC) and at full saturation. For M_R at OMC, the materials were prepared and tested according to the procedure detailed in the AASHTO T307 specifications ( 11 ). For M_R at saturation, the materials were prepared differently before testing by first compacting the samples at OMC and then saturating them using vacuum and backpressure saturation techniques in the laboratory. The test was then performed in undrained conditions following the AASHTO T307 standard procedure ( 11 ). To ensure repeatability, three replicates were tested for each material at OMC and full saturation.

As expected, the resilient modulus decreased with increasing moisture from OMC to saturation. However, the decrease in M_R was practically significant for some materials and practically insignificant for others. Practical significance is defined by ALDOT as the change in M_R that can lead to at least a 0.5 in. change in the thickness of the asphalt concrete layer in a flexible pavement design. This threshold was found to be at least 4000 pounds per square inch (psi). Therefore, the base materials in this study that exhibited a decrease in M_R greater than 4000 psi when saturated were considered to have high moisture susceptibility (MS). Those whose decrease in M_R was less significant when saturated were considered to have low MS. The AASHTO and MS classifications of the seven granular base (GB) materials are given in Table 1. The obtained properties of the seven GB materials are presented in Table 2.

Table 1.

AASHTO and Moisture Susceptibility (MS) Classifications of Materials

Material	Aggregate type	MS classification	AASHTO classification
GB1	Limerock	Low MS	A-1-a
GB2	Limerock		A-1-a
GB3	Limestone		A-1-a
GB4	Limestone		A-1-a
GB5	Limerock	High MS	A-1-b
GB6	Limestone		A-1-a
GB7	Limerock		A-1-b

Note: GB = granular base.

Table 2.

Properties of Seven Granular Base (GB) Materials

Property	GB1	GB2	GB3	GB4	GB5	GB6	GB7
Fines content, %	13	12	10	9	21	12	27
Bulk specific gravity	2.288	2.280	2.645	2.526	2.200	2.590	2.111
Coarse aggregate absorption, %	5.7	7.8	0.4	1.6	15	0.9	15.1
Fine aggregate absorption, %	4.3	0.7	2.3	3.9	1.4	2.9	0.9
Fine aggregate content, %	61	40	61	42	60	55	42
Optimum moisture content, %	8	10.4	4.7	5.5	16	5.2	16.7
Maximum dry density, lb/ft³	128	123.8	150	141.8	112.2	147.6	111.7
Fine aggregate angularity, %	42	55	43	42	61	46	62
Sand equivalency, %	45	39	63	58	30	38	21
Plastic fines content, %	55	61	37	42	70	62	79
Los Angeles abrasion, %	39	42	27	38	55	26	61

Methods

Prediction Models

To predict the variation of M_R with respect to the saturation level for the seven GB materials, two models were selected based on current practices and results from previous studies. The first model chosen for this evaluation is the model adopted by the MEPDG. In their study, Han and Vanapalli ( 4 ) evaluated three different prediction models and determined that the MEPDG model ( 12 ) was the most accurate. This model also represents current practice in predicting M_R of saturated pavement base aggregates. The second model chosen for this evaluation is the model originally developed by Lytton ( 13 ). An extensive review of the literature was conducted and many researchers found this model to be the most accurate at predicting the variation in M_R with respect to saturation. For example, Gu et al. ( 14 ) reported from their evaluations that the Lytton model predicted M_R with better accuracy at different moisture contents than the MEPDG model. Additionally, Khosravifar et al. ( 9 ) evaluated nine M_R prediction models for base and subgrade materials and concluded that the Lytton model was the most consistent model, ahead of the MEPDG model.

MEPDG Model

The MEPDG model ( 1 ) is a modified version of the universal model previously shown in Equation 2:

M_{R} = k_{1} P_{a} {(\frac{θ}{P_{a}})}^{k_{2}} {[(\frac{τ_{oct}}{P_{a}}) + 1]}^{k_{3}}

(3)

where θ = bulk stress; P_a = atmospheric pressure; $τ_{oct}$ = octahedral shear stress = $\sqrt{2} (σ_{1} - σ_{3}) / 3$ ; and k₁, k₂, and k₃ are material-specific regression coefficients ( 1 ). This is the generalized constitutive model adopted by the MEPDG Manual of Practice ( 1 ). This model is also referred to as the k₁–k₃ model and is known to have a very high goodness of fit since it can capture the bulk stress stiffening effect and the shear stress softening effect ( 15 ).

In the most recent version of the AASHTOWare Pavement mechanistic-empirical software, the values of the M_R parameters k₁, k₂, and k₃ can no longer be entered as inputs (Level 1) for pavement design. However, the model is still used externally to predict the design M_R at a specific stress state expected in the field. Since the change in moisture content resulting from seasonal variations needs to be accounted for, the MEPDG software incorporates the Enhanced Integrated Climatic Model (EICM) to predict the change in M_R at a given saturation level. The EICM adopts the following general empirical equation to predict the change in M_R resulting from a change in the degree of saturation of GB materials ( 12 ):

\log \frac{M_{R}}{M_{Ropt}} = a + \frac{b - a}{1 + \exp (\ln \frac{- b}{a} + k_{m} . (S - S_{opt}))}

(4)

where $M_{Ropt}$ is the resilient modulus at a reference moisture condition (usually at OMC); $M_{R}$ is the resilient modulus at a given degree of saturation; $M_{R} / M_{Ropt}$ is the resilient modulus ratio; $(S - S_{opt})$ is the variation in degree of saturation expressed as a decimal fraction; $a$ is the minimum of $\log (M_{R} / M_{Ropt})$ ; $b$ is the maximum of $\log (M_{R} / M_{Ropt})$ ; and $k_{m}$ is a regression parameter.

The values of $a$ , $b$ , and $k_{m}$ are constant values that are different for coarse-grained and fine-grained materials, as summarized in Table 3. These values were obtained from a regression analysis using available literature data for different coarse and fine aggregate materials and are adopted within the EICM. A maximum modulus ratio (b) of 2.5 for coarse-grained materials and 2.5 for fine-grained materials was used as a boundary during the analysis ( 12 ). In this study, Equations 3 and 4 were used to predict the M_R of the seven base aggregates at OMC and full saturation. The predictions were also made at each of the 15 bulk stresses provided by the AASHTO T307 standard procedure ( 11 ).

Table 3.

Values of a, b, and k_m for Coarse-Grained and Fine-Grained Materials ( 12 )

Parameter	Coarse-grained materials	Fine-grained materials
a	−0.3123	−0.5934
b	0.3	0.4
k _m	6.8157	6.1324

Lytton Model

This model was originally developed by Lytton ( 13 ) to incorporate not only the variation in stress state, but also the variation in moisture content of the base materials. The variation in the saturation level is accounted for in the model through the inclusion of matric suction, as

M_{R} = k_{1} P_{a} {(\frac{σ_{bulk} - 3 θ_{w} f h_{m}}{P_{a}})}^{k_{2}} {(\frac{τ_{oct}}{P_{a}})}^{k_{3}}

(5)

where $σ_{bulk}$ = bulk stress; P_a = atmospheric pressure; $τ_{oct}$ = octahedral shear stress = $\sqrt{2} (σ_{1} - σ_{3}) / 3$ ; k₁, k₂, and k₃ are material-specific regression coefficients; $θ_{w}$ = volumetric water content; $h_{m}$ = matric suction; and $f$ is a saturation factor obtained as function of $θ_{a}$ , the volumetric water content of the material at air entry, and $θ_{u}$ , the volumetric water content of the material at unsaturation:

f = [(\frac{θ_{a} - θ_{w}}{θ_{a} - θ_{u}}) + \frac{1}{θ_{w}} (\frac{θ_{w} - θ_{u}}{θ_{a} - θ_{u}})]

(6)

According to Fredlund et al. ( 16 ), the three stress variables that influence the resilient modulus are deviatoric stress, net confining pressure, and matric suction. Matric suction is the pressure, obtained as the difference between air pressure and water pressure, that attracts water through the capillary and surface adsorptive forces of unsaturated soils. Thus, matric suction is equal to zero when the material is saturated, and the Lytton model becomes the same as the original universal octahedral shear stress model of Equation 2. Fredlund et al. ( 16 ) determined that models that incorporate suction are more accurate than those without suction.

The matric suction ( $h_{m}$ ) and the volumetric water contents ( $θ_{w}$ , $θ_{a}$ , and $θ_{u}$ ) of each base material were determined from their soil water characteristic curves (SWCCs), shown in Figure 1. The SWCCs were obtained using the prediction algorithm, based on material properties developed by Zapata ( 17 ). Although the reliability of the predictive algorithm is not very high, it is nevertheless more reliable than having different operators perform suction measurements ( 17 ). It is even one of the most commonly used methods to obtain the SWCC, and is also employed in the EICM of the MEPDG. However, it still remains a source of variability in the Lytton model, similar to the parameters $a$ , $b$ , and $k_{m}$ in the MEPDG model. In this study, Equation 5 was used to predict M_R for the seven base aggregates at OMC and full saturation. The predictions were made at each of the 15 bulk stresses provided in the AASHTO T307 standard procedure ( 11 ).

Figure 1.

Soil water characteristic curves of the granular base materials.

Evaluation Process

To evaluate the prediction accuracy of the MEPDG model and the Lytton model, the laboratory-measured values of M_R for each base material were compared with the values of M_R predicted using the two models. To do this, the root mean squared error (RMSE) and the relative error (RE) of the models’ predictions were calculated for each base aggregate at both moisture conditions (OMC and saturation). The RMSE is a performance indicator for prediction models as it provides the average difference between the values predicted by a model and the actual measured values. It is an excellent estimator of model accuracy because it encompasses both systematic and nonsystematic errors. The RMSE was calculated as

\begin{matrix} RMSE = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} ({(M_{R measured} - M_{R predicted})}^{2})} \end{matrix}

(7)

and was reported in pounds per square inch, the same unit as M_R. The RE is a measure of bias of the prediction models. It was calculated as

RE = \frac{\frac{1}{n} \sum_{i = 1}^{n} (M_{R predicted} - M_{R measured})}{\frac{1}{n} \sum_{i = 1}^{n} (M_{R measured})}

(8)

and reported as a percentage.

As mentioned earlier, three replicates were tested for each base material at OMC and full saturation. For each replicate, the values of M_R measured at the 15 bulk stresses during testing at OMC were used to calibrate the k coefficients of the two models. The two calibrated models were then used to predict M_R at the same 15 bulk stresses at OMC and saturation. The RMSE and RE were calculated using predicted and measured values of M_R for each replicate at OMC and saturation. At the end, each base material had three values each of RMSE and RE at each moisture condition. The average RMSE and RE obtained for each base material at each moisture condition are presented and discussed in the following section. A single t test was performed to assess the statistical difference between the RMSEs of the two models for each base material. The overall average RMSE or RE of every model is the mean RMSE or RE value of all base materials.

Results and Discussion

First, the OMC condition was evaluated. The overall average RMSE using the MEPDG model was 2909 psi and that using the Lytton model was 3023 psi. These RMSEs are low and may be considered practically insignificant because they are below the 4000-psi practical significance threshold. This demonstrates that both models can accurately predict M_R of the base aggregates at OMC; this is expected since it is the condition under which the key parameters of each model were calibrated. The high accuracy was also confirmed by the overall low average RE of 4% for the MEPDG model and 4% for the Lytton model. Figure 2 shows the predicted M_R from the two models compared with the measured M_R at OMC. It can be seen that most of the points are on the line of equality.

Figure 2.

M _R predicted by the two models in contrast to M_R measured for all base aggregates at optimal moisture content.

At saturation, it is important to analyze the M_R prediction accuracy of the models for pavement base aggregates with low MS and high MS separately. The following paragraphs present a summary of the average RMSE and RE of the two models for each GB material (low MS and high MS) at saturation.

For the low MS base aggregates at saturation, the average RMSE of the MEPDG model varied between 7000 and 12,500 psi and that of the Lytton model varied between 3000 and 6500 psi, as shown in Table 4 and Figure 3a. The RMSEs between the two models were found to be statistically different for all materials. The overall average RMSE of the MEPDG model was 10,516 psi and that of the Lytton model was 4565 psi (Table 4). These RMSEs are high and can be considered practically significant as they are greater than 4000 psi. However, the RMSE of the MEPDG model was twice that of the Lytton model, showing that the Lytton model is more accurate at saturation for the tested low MS base aggregates. The same trend was also observed in the REs of both models. The average RE of the MEPDG model varied between 14% and 28%, with an average of 21%, while that of the Lytton model varied between 4% and 6%, with an average of 5%, as shown in Table 4 and Figure 3b. Figure 4 is a comparison of M_R predicted by the two models against M_R measured at saturation for the base aggregates with low MS. It can be seen in Figure 4 that most of the points for the Lytton model are on the line of equality. In contrast, almost all the points for the MEPDG model lie on the x-axis (measured M_R) side of the line of equality. This means that the M_R predicted by the MEPDG model for saturated low MS base aggregates is significantly lower than the actual measured M_R. Thus, the MEPDG model is more conservative than the Lytton model when predicting M_R of saturated base aggregates with low MS. This is because the EICM equation (Equation 4) in the MEPDG model contributes to significantly decrease M_R at saturation, even though M_R of low MS base materials does not change significantly at saturation. On the contrary, and as mentioned previously, the matric suction in the Lytton model is zero at saturation; thus, the model transforms into the original universal octahedral shear stress model (Equation 2), which does not significantly decrease M_R at saturation.

Table 4.

Average Root Mean Square Error and Relative Error of the Two Models for Each Low Moisture Susceptibility Base Material at Saturation

Material	Moisture susceptibility	RMSE, psi		RE, %
		MEPDG	Lytton	MEPDG	Lytton
GB1	Low	7384	3030	17	4
GB2		10004	6505	14	5
GB3		12234	3979	28	6
GB4		11751	4004	23	5
Overall average		10516	4565	21	5

Note: GB = granular base; MEPDG = mechanistic-empirical pavement design guide; psi = pounds per square inch; RE = relative error; RMSE = root mean square error.

Figure 3.

Average errors of the two models for low moisture susceptibility base materials at saturation (with standard errors): (a) root mean square error; (b) relative error.

Figure 4.

M _R predicted by the two models in contrast to M_R measured for low moisture susceptibility base aggregates at saturation.

For the high MS base aggregates at saturation, the average RMSE varied between 3000 and 9000 psi and 4500 and 12,500 psi for the MEPDG model and the Lytton model, respectively, as shown in Table 5 and Figure 5a. The RMSEs between the two models were also found to be statistically different for all materials, with the exception of the base aggregate GB6. The overall average RMSEs were 6313 psi and 9786 psi for the MEPDG model and the Lytton model, respectively (Table 5). These RMSEs are both greater than 4000 psi and are therefore considered significantly high from a practical perspective. Even though the RMSE of the MEPDG model was two-thirds of the RMSE of the Lytton model, it can be said that both models have a low accuracy when predicting M_R of the saturated high MS base aggregates, except for GB6, which is an A-1-a material (unlike GB5 and GB7, which are A-1-b materials). Similar to the RMSE trend, the average RE of the MEPDG model varied between 7% and 20%, with an average of 14%, while that of the Lytton model varied between 14% and 34% with an average of 27%, as shown in Table 5 and Figure 5b. The comparison of M_R predicted by the two models with the measured M_R at saturation for high MS base aggregates is presented in Figure 6. It can be observed in Figure 6 that nearly all points for the MEPDG model and the Lytton model are on the y-axis (predicted M_R) side of the line of equality. This means that the value of M_R predicted by both models for the saturated high MS base aggregates is significantly higher than that of the actual measured M_R. Therefore, it can be concluded that the two prediction models have a low accuracy and overpredict M_R of the saturated base aggregates with high MS. This is because, in this case, the EICM equation (Equation 4) in the MEPDG model does not contribute sufficiently to significantly decrease M_R at saturation for high MS base materials. The EICM equation contains the regression values a, b, and k_m, which are constant for all coarse or fine materials, and are not representative of high MS base materials. For the Lytton model, there is no matric suction at saturation; thus, the model with k coefficients calibrated at OMC becomes unable to predict the M_R well at saturation of high MS base materials, as it is much lower than that of low MS base materials. It should be noted, however, that the suction values used in the Lytton model to calibrate the k coefficients were predicted rather than measured. Although these predictions were made using standard practices, such as Zapata ( 17 ) correlation equations, this may have increased the model’s variability. Using measured values could lead to different results.

Table 5.

Average Root Mean Square Error and Relative Error of the Two Models for Each High Moisture Susceptibility Base Material at Saturation

Material	Moisture susceptibility	RMSE, psi		RE, %
		MEPDG	Lytton	MEPDG	Lytton
GB5	High	8592	12169	20	33
GB6		3279	4687	7	14
GB7		5915	10828	15	34
Overall average		6313	9786	14	27

Note: GB = granular base; MEPDG = mechanistic-empirical pavement design guide; psi = pounds per square inch; RE = relative error; RMSE = root mean square error.

Figure 5.

Average errors of the two models at saturation (with standard errors): (a) root mean square error; (b) relative error.

Figure 6.

M _R predicted by the two models in contrast to M_R measured for high moisture susceptibility base aggregates at saturation.

In view of the results, the use of high MS base aggregates might lead to less accurate design results and pavements that are less resilient to climate water stressors, especially in coastal regions, where the likelihood of base aggregate saturation is high. Considering the inaccuracy of existing models using common practices, it is crucial to develop a new model or adaptation solutions to improve existing models to better predict M_R at saturation of high MS base materials.

Prediction Equation Enhancement

As a solution to better predict M_R of saturated high MS base materials, in this study, the development of prediction equations is proposed for the k coefficients in the existing models based on M_R measured at saturation and using performance-related aggregate properties. To this end, a regression analysis was performed. This idea was inspired by the study of Gu et al. ( 14 ), who proposed a similar solution; however, that solution was based on M_R measured at OMC, with the aim of predicting M_R at OMC of all base materials.

For this study, a statistical regression analysis of the results for M_R was previously conducted. The analysis demonstrated that the performance-related aggregate properties that influence the MS of base aggregates at saturation are: percentage of particles passing a #200 sieve, or fines content (FC); percentage of particles passing a #4 sieve, or fine aggregate content (FAC); fine aggregate angularity (FAA); and plastic fines content (PFC). FC and FAC are determined using, respectively, washed (AASHTO T11 ( 18 )) and dry (AASHTO T27 ( 19 )) sieve analysis. FAA is obtained following the AASHTO T304 standard procedure ( 20 ). PFC is equal to 100% minus the sand equivalency value of the material, which is obtained using the method given in AASHTO T176 ( 21 ). It was also found that FC, FAA, and PFC are highly correlated and that PFC and FAC are the best independent representatives of this set of aggregate properties in a multiple regression analysis. Therefore, to obtain prediction equations for the k coefficients in this study, a multiple regression analysis was conducted to evaluate the correlation between the measured k values at saturation and the aggregate properties (PFC and FAC) of the materials. The values of PFC and FAC of each material used in the development of the prediction equations are given in Table 2.

The results of the multiple regression analysis are presented in Table 6. An important factor in Table 6 is the significance, F, which indicates the relevance or significance of the regression equation. Values of p indicate whether the independent variables have a statistically significant effect on the dependent variables. The value of R² reflects how effectively the resulting regression model represents the data. A significance, F, or p less than 0.05 indicates statistical significance at the 95% confidence level. As presented in Table 6, the significance, F, of all prediction equations except the k₂ equation for the Lytton model was less than the significance level threshold of 0.05. The values of p for some variables were less than 0.05, while those for others were greater than 0.05. When p > 0.05, it cannot be concluded that there is a significant effect of the variable. This can be attributed to the small sample size of the M_R test results measured at saturation. With more M_R tests on saturated base materials, and a larger database, more reliable regression models can be obtained.

Table 6.

Results of Regression Analysis

Objective	Variable	Coefficient value	Standard error	p	Significance, F	R ²
MEPDG
Prediction model of k₁	Intercept	3317.62	231.77	2.8 × 10⁻¹¹	3.7 × 10⁻⁶	0.86
	PFC	−14.55	2.15	2.5 × 10⁻⁶
	FAC	−14.12	3.25	0.00039
Prediction model of k₂	Intercept	0.74	0.12	4.7 × 10⁻⁵	0.010	0.63
	PFC	0.0018	0.0013	0.19
	FAC	−0.0055	0.0020	0.012
Prediction model of k₃	Intercept	−1.02	0.38	0.016	0.00090	0.74
	PFC	−0.0082	0.0035	0.032
	FAC	0.018	0.0053	0.0035
Lytton
Prediction model of k₁	Intercept	601.21	963.73	0.56	0.012	0.77
	PFC	−9.80	8.75	0.31
	FAC	17.77	8.01	0.07
Prediction model of k₂	Intercept	0.76	1.01	0.48	0.10	0.53
	PFC	0.0065	0.0092	0.50
	FAC	−0.01	0.0084	0.27
Prediction model of k₃	Intercept	−0.48	0.58	0.44	0.0061	0.82
	PFC	−0.0065	0.0052	0.26
	FAC	0.012	0.0048	0.042

Note: FAC = fine aggregate content; MEPDG = mechanistic-empirical pavement design guide; PFC = plastic fines content.

For the MEPDG model, the prediction equations of the k coefficients at saturation resulting from this analysis are

k_{1} = 3317.62 - 14.55 (PFC) - 14.12 (FAC)

(9)

k_{2} = 0.74 + 0.0018 (PFC) - 0.0055 (FAC)

(10)

k_{3} = - 1.02 - 0.0082 (PFC) + 0.018 (FAC)

(11)

Similarly, the prediction equations of the k coefficients at saturation resulting from this analysis for the Lytton model are

k_{1} = 601.21 - 9.80 (PFC) + 17.77 (FAC)

(12)

k_{2} = 0.76 + 0.0065 (PFC) - 0.01 (FAC)

(13)

k_{3} = - 0.48 - 0.0065 (PFC) + 0.012 (FAC)

(14)

The k coefficients at saturation were predicted using the regression equations of each model. The two existing models were calibrated using the predicted k coefficients and then used to predict M_R at saturation of the high MS base materials. Figure 7 is a comparison of M_R predicted by the two models against M_R measured at saturation for the base aggregates with high MS. It can be observed in Figure 7 that most of the points for the Lytton model are on the line of equality and most of the points of the MEPDG model are either on the line of equality or on the x-axis (measured M_R) side of the line of equality. Figure 7 shows the improvements achieved in the prediction accuracy of both existing models. This was confirmed by the calculated overall average RMSE and RE, which were lower for the MEPDG model and much lower for the Lytton model than the previously obtained values, as shown in Figure 8.

Figure 7.

M _R predicted by the two models using the proposed method in contrast to M_R measured for high moisture susceptibility base aggregates at saturation.

Figure 8.

Comparison of overall average errors of the two models (with standard errors): (a) root mean square error; (b) relative error.

The overall average RMSE and RE of the MEPDG model were 4991 psi and 10%, compared with 6313 psi and 14% obtained using the original method (Figure 8). Although these values are not statistically different, the prediction of the MEPDG model changed from overprediction to more conservative; this may lead to increased pavement resilience in design. The overall average RMSE and RE of the Lytton model were 2994 psi and 4%, compared with 9786 psi and 27% obtained using the original method (Figure 8). These values are statistically and practically different. It can be concluded that, despite the low reliability of some k coefficient prediction equations, the prediction accuracy of the two existing models for saturated high MS base materials has been improved. The use of a larger dataset of k coefficients obtained from M_R testing at saturation of base materials is recommended to improve pavement performance prediction, ultimately allowing for the assessment of various adaptation solutions.

Findings and Conclusions

The goal of this research study was to evaluate the performance of existing prediction models in predicting the resilient modulus of pavement base aggregates at full saturation. Seven GB materials with different properties were tested in the laboratory according to the AASHTO T307 standard procedure ( 11 ) to determine their resilient modulus under two moisture conditions (OMC and saturation). The laboratory results revealed that four of the base materials have low MS while three of them have high MS. Two prediction models, namely the MEPDG model and the Lytton model, were selected for evaluation in this study because they are the two most favored and recommended models by previous researchers. Moreover, the MEPDG model also represents the current practice. The main findings and conclusions of this study are as follows.

Findings

For all seven pavement base aggregates at OMC, both the MEPDG and Lytton models produced accurate predictions of M_R.

For the low MS base aggregates at saturation, the Lytton model was more accurate than the MEPDG model, even though the difference between values of M_R predicted by the two models and the actual measured values of M_R was significant.

For the high MS base aggregates at saturation, both the MEPDG model and the Lytton model (calibrated using predicted SWCCs) produced inaccurate M_R predictions because the difference between the values of M_R predicted by both models and the actual measured values of M_R was greatly significant.

To improve the prediction accuracy of both models for saturated high MS base materials, multiple regression analysis was used to develop k coefficient prediction equations at saturation for the two models using performance-related aggregate properties:

The obtained k coefficient prediction equations had low reliability, owing to the small sample size of M_R test results of saturated base materials.

Despite their low statistical reliability, the obtained prediction equations were successful in improving the prediction accuracy of the models for high MS base materials.

Conclusions

Overall, the Lytton model had performed slightly better in predicting the M_R of saturated pavement base aggregates than the MEPDG model.

Both the Lytton and MEPDG models overestimated the M_R of saturated base aggregates that are highly susceptible to moisture, representing a higher risk of underdesign and less climate-resilient pavements. It is essential to point out that the results of the Lytton model could vary if measured suction values are used to calibrate the model parameters, even though common practices involve using prediction algorithms for SWCCs, as applied in this study.

The proposed enhancement to the M_R models, consisting of developing prediction equations of k coefficients at saturation, is effective in improving the accuracy of the existing models used to predict M_R for saturated high MS base materials.

The results of this study can help practitioners better appreciate the performance of existing M_R prediction models at saturation and take it into account during pavement design. More M_R testing of saturated base materials and the creation of a database of the k parameters obtained from those tests are recommended to improve the adaptation solution proposed in this study, for better prediction accuracy of the existing models. For future studies, the models can be evaluated using other types of GB material, apart from limestone and limerock. In view of the inaccuracy of existing models for saturated high MS base materials, it is also crucial to develop a rapid test to evaluate the moisture susceptibility of base aggregates before selecting them for pavement design and construction.

Footnotes

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: D. G. V. V. Biessan, B. F. Bowers, and J. B. Anderson; testing: D. G. V. V. Biessan, B. F. Bowers, and J. B. Anderson; data collection: D. G. V. V. Biessan, B. F. Bowers, and J. B. Anderson; analysis and interpretation of results: D. G. V. V. Biessan, B. F. Bowers, and J. B. Anderson; draft manuscript preparation: D. G. V. V. Biessan, B. F. Bowers, and J. B. Anderson. 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 Alabama Department of Transportation (ALDOT) and Federal Highway Administration through Project ALDOT (grant number 931-052).

ORCID iDs

Don Guy V. V. Biessan

Benjamin F. Bowers

J. Brian Anderson

Data Accesibility Statement

The data obtained during the study are available from the corresponding author on reasonable request.

The data and findings represented in this paper are the opinions and findings of the authors and do not necessarily reflect the opinions and findings of the Alabama Department of Transportation and its engineers or representatives.

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