Comparison of Lab vs. Backcalculated Moduli of Virgin Aggregate and Recycled Aggregate Base Layers

Abstract

The resilient modulus (M_R) and the backcalculated modulus from the FWD testing (E_FWD) of the unbound layers are critical inputs in the analysis/design of pavements. Several studies have tried to develop a conversion factor between these two parameters, while the nonlinear stress dependency of unbound materials and the pavement strain response are mostly missing from the literature. This study aims to compare the laboratory-measured M_R of recycled aggregate base (RAB) materials and a virgin aggregate base using field-based E_FWD and tries to establish pavement’s responses to loading using vertical strains from both the M_R and E_FWD values of the respective materials as comparability parameters between the two. For this purpose, a control virgin aggregate (VA, limestone) and three types of RAB materials were selected to construct four test sections. The test sections were modeled in layered elastic- and finite-element-based pavement response models to calculate the vertical strains at the mid-depth of the base and top of the subgrade layers. A comparison of the lab-calculated vertical strains using M_R with actual vertical strains in the field from E_FWD showed that there was no relationship between the two stiffness parameters in all tested RABs. The vertical strains, based on the lab M_R, undermined the stiffness of the recycled aggregates in the field. In contrast, the values of E_FWD based on the vertical strains remained close to the M_R strains of limestone (VA) throughout the testing period, establishing an E_FWD vs. M_R relationship (M_R = 0.87 E_FWD). The results also show that fine RCA was a better-performing material over three years. This research not only explores how the hydration process in RABs limits the development of M_R-E_FWD correlations but also underscores the need to consider real-world conditions when assessing their performance.

1. Introduction

The stiffness characteristics of unbound layers play vital roles in the structural integrity of flexible pavements. The resilient modulus (M_R), as a measure of unbound layer stiffness, was initially introduced by the American Association of State Highway and Transportation Officials (AASHTO) Pavement Design Guide in the 1986 Edition [1] and is also used as an essential input in the pavement analysis/design procedures, such as the Mechanistic–Empirical Pavement Design Guide (MEPDG) [2]. The M_R of a material is commonly estimated in a laboratory using sensitive equipment, making it time-consuming and expensive, and requiring well-trained personnel to carry out the testing [3]. Estimating a reasonable value for the MR of unbound layers, which closely reflects the actual behavior of unbound materials in the field, is a prerequisite for an efficient pavement analysis/design. For this purpose, applying falling weight deflectometer (FWD) testing for estimating the M_R of unbound layers has gained attention among highway agencies [4,5]. This method uses the FWD test results to backcalculate the stiffness of the unbound layers (E_FWD) using the deflection basin on the pavement surface.

Several studies have compared the laboratory-measured M_R of unbound layers with their corresponding E_FWD from FWD testing. Along with considerable variation in the conversion factors, many researchers have also proposed wide ranges of values in the literature. This can be attributed to different types of materials, variations in the field and lab environment, and the difference in time between testing for the M_R in the lab and FWD in the field [6]. It is pertinent to mention that the AASHTO guide [7] allows for both modulus types and suggests a factor of 0.33 to be used with the E_FWD.

In relevant research, Chen et al. evaluated subgrade samples from the existing pavements. They found that the laboratory M_R values were almost two times greater than those backcalculated from FWD testing [8]. Von Quintus and Killingsworth studied different base and subgrade materials from the Long-Term Pavement Performance (LTPP) Program database. They proposed a conversion factor ranging from 0.1 to 3.5 between the M_R and backcalculated E_FWD values. It has been reported that the conversion factor is highly dependent on the pavement type and temperature gradient within the AC layer [9]. In another study by Nazarian et al., the mechanical properties of about three dozen specimens with considerable diversity in stiffness and material type (from clayey subgrade to high-quality bases) were studied. The results showed that using the seismic method, the conversion factor between the laboratory-measured MR and the field modulus ranged from 0.1 to 1.0 [10]. Ping et al. reported a conversion factor of 1.6 between the laboratory-measured M_R and the backcalculated E_FWD of granular materials [11]. In another study using the LTPP database, it was reported that the backcalculated E_FWD values were, on average, about 1.7 and 1.9 times greater than the laboratory-measured M_R values for fine-grained and coarse-grained soils, respectively [12].

While every study presents a related reasoning behind the suggested conversion factors, more deliberation and research are still required to correlate the two values of different magnitudes, i.e., the M_R and E_FWD. Conversion between the two may only be validated if the pavement layers, with particular M_R and E_FWD values, show a similar extent of strain response to loading in both cases. A more realistic conversion can be expected because such responses are the key parameters for calculating the damage accumulation in the mechanistic–empirical (ME)-based pavement analysis/design procedures. In addition, almost all pavement analysis/design procedures (including the MEPDG) use a single modulus value to represent the stiffness of the unbound layers; therefore, the nonlinear stress-dependent behavior of unbound materials has not been considered in calculating the conversion factors in the literature. As the nonlinear stress-dependent behavior of unbound materials is already measured in laboratory testing by varying the applied confined and deviatoric stress, multi-load FWD testing is an alternative method to capture such nonlinear behavior in the field.

The main objective of this study is to compare the laboratory-measured M_R of unbound recycled aggregate base (RAB) and virgin aggregate base (VA) layers (at the optimum moisture content) at the time of construction with their corresponding backcalculated E_FWD over three years of their service life. The analysis is based on the vertical strain response of four test sections under a singular load level, using the finite element (FE) and layered-elastic analysis (LEA) approaches. This approach offers a fresh perspective by analyzing how the pavement response under linear and nonlinear models, both in laboratory and field settings, can impact the correlations between the M_R and E_FWD, especially for RABs. The current study takes the nonlinear behavior of unbound layers into account through the FE-based pavement response model and multi-load FWD testing.

2. Methodology

Four test sections were used in this study. The base layers of these test sections were constructed with three different RAB materials, including coarse recycled concrete aggregate (RCA), fine RCA, and a blend of recycled asphalt pavement (RAP) with RCA, which is abbreviated as RCA + RAP in the following text. In addition, one natural aggregate (limestone) base was used in one of the test sections, regarded as VA. The M_R of the unbound materials was measured in the laboratory at room temperature in samples collected during construction. Multi-load FWD tests were conducted over three years, starting two years after construction. Later, the nonlinear stress-dependent behavior of the unbound layers was modeled using the NCHRP 1-37A model, and the pavement strain response under singular loading was analyzed using the LEA- and FE-based approaches.

2.1. Test Sections

Four test sections (Cells 185, 186, 188, and 189) were constructed on a two-lane Minnesota Road Research Project Low-Volume Road (MnROAD LVR) testing facility. Each section had a 3.5-inch asphalt layer with a 12-inch base layer. A 3.5-inch sand subbase was also placed between each section’s base and subgrade layers. Another type of sand was used as a subgrade material under the coarse and fine RCA base layers, while clay loam was used under the limestone and RCA + RAP base layers. The cross-sections of these test sections are shown in Figure 1. The properties of the materials used in these test sections are shown in

Table 1. Properties of materials used in test sections.

Material	Gravel 1 (%)	Sand 2 (%)	Fine 3 (%)	Cu 4	Cc 5	LL 6 (%)	USCS 7	MDU 8 (pcf)	OMC 9 (%)	Abp.10
Coarse RCA	61.7	34.9	3.4	34.49	1.75	N/A 11	GW	126.10	9.5	6.97
Fine RCA	38.3	54.6	7.1	33.93	1.12	32.7	SW-SM	119.24	11.1	8.65
Limestone	52.3	32.6	15.1	211.3	1.91	17.9	GM	140.46	6.3	1.72
RCA + RAP	41	50.4	8.6	49.41	0.98	27.4	SP-SM	123.61	10.0	4.34
Sand (subgrade)	27.6	59.8	12.6	33.12	1.24	19.9	SM	134.84	5.6	1.84
Clay loam	3.1	37.2	59.7	N/A	N/A	36.3	CL	122.36	10	N/A
Sand (subbase)	31.1	56.5	12.4	30.30	1.10	18.9	SM	137.34	5.3	1.53

¹ Percent of gravel (%), measured based on ASTM D6913 (2004) [14]. ² Percent of sand (%), measured based on ASTM D6913 (2004). [14] ³ Percent of fine RCA (%), measured based on ASTM D6913 (2004) [14]. ⁴ Coefficient of uniformity, measured based on ASTM D2487 (2017) [15]. ⁵ Coefficient of curvature, measured based on ASTM D2487 (2017) [15]. ⁶ Liquid limit (%), measured based on BSI 1377-2 (1990) [16]. ⁷ Unified soil classification system, classified based on ASTM D2487 (2017) [15]. ⁸ Maximum dry unit weight (pcf), measured based on ASTM D1557 (2020) [17] and ASTM D4718 (2015) [18]. ⁹ Optimum moisture content (%), measured based on ASTM D1557 (2020) [17] and ASTM D4718 (2015). [18] ¹⁰ Absorption, calculated by taking the weighted average of the absorption of the coarse and fine fractions (based on ASTM C127 (2015) [19] and ASTM C128 (2015) [20]) of the materials. For the clay load, the ASTM D854 (2014) [21] was used. ¹¹ Not applicable (N/A). Unit conversion: 1 pcf = 0.157 kN/m^3.

[13]. It is also noted that a 36.3-tonne truck was used for traffic simulation on the inside lanes of these test sections.

2.2. Testing Plan

The M_R of the unbound materials was measured in the laboratory (AASHTO T 307 [22]) at room temperature. The results of the laboratory-measured M_R were extracted from a previous study [23]. It is noted that the average values of both the M_R and fitted nonlinear models are reported for the unbound materials used in the FE-based analysis approach.

Multi-load FWD testing was carried out on each test section, and deflections corresponding to sequential loads of 6000, 9000, and 12,000 lb were measured by the sensors located at 0, 8, 12, 18, 24, 36, 48, 60, and 72 inches away from the loading plate. Deflection data were collected over three years, starting two years after construction, to study the long-term behavior of the test materials. Only data from the traffic lane, i.e., inside lane, were included to assess the maximum damage.

2.3. Nonlinearity of Unbound Materials

Cyclic triaxial testing is usually used to evaluate the stiffness of unbound materials [22]. During this test, the unbound materials generally exhibited a plastic deformation in the initial cycles, which later stabilized at a certain level. This phenomenon is usually referred to as shakedown, after which a steady state and elastic response is expected from the unbound materials. The M_R at a certain applied load level is then defined as the ratio of applied deviatoric stress (σ_d) to the recoverable elastic strain (ε_r) after the shakedown, as shown in Equation (1):

$$M_R={\displaystyle \frac{{\sigma }_d}{{\epsilon }_r}}$$

(1)

where M_R is the resilient modulus (psi), σ_d is the deviatoric stress (psi), and ε_r is the recoverable peak-to-peak strain after the shakedown.

Several models have been proposed in the literature to capture the nonlinear stress-dependency of the MR to the stress state within the unbound materials caused by different applied load levels. These include models such as the K-θ model developed by Hicks and Monismith [24] and the universal model developed by Witczak and Uzan [25]. Later, the universal model was modified during the NCHRP 1-37A project [2], as shown in Equation (2). This model has become the most commonly used model to describe the nonlinearity of unbound materials.

$$M_R=k_1.p_a{\left({\displaystyle \frac{\theta }{p_a}}\right)}^{k_2}{\left({\displaystyle \frac{{\tau }_{oct}}{p_a}}+1\right)}^{k_3}$$

(2)

where θ is the bulk stress (psi), τ_oct is the octahedral shear stress (psi), p_a is the atmospheric air pressure (~14.706 psi), and k₁, k₂, and k₃ are the model coefficients. The θ and τ_oct parameters in the two-dimensional (2D) axisymmetric system can be defined as in Equations (3)–(5):

$$\theta ={\sigma }_r+{\sigma }_z+{\sigma }_t$$

(3)

$${\tau }_{oct}=\sqrt{{\displaystyle \frac{2}{3}}{J}_2}$$

(4)

$$J_2={\displaystyle \frac{1}{6}}\left[{\left({\sigma }_r-{\sigma }_z\right)}^2+{\left({\sigma }_r-{\sigma }_t\right)}^2+{\left({\sigma }_t-{\sigma }_z\right)}^2\right]$$

(5)

where σ_r, σ_z, and σ_t are the radial, vertical, and tangential shear stress components (psi), and J₂ is the second invariant of the stress (psi²).

The NCHRP 1-37A model for unbound materials was used to model the unbound layers’ nonlinearity under the multi-load FWD testing. The model coefficients were calibrated using the FWD test results [26], as shown in Equation (6):

$$E_{FWD}=k_{1FWD}.p_a{\left({\displaystyle \frac{\theta }{p_a}}\right)}^{k_{2FWD}}{\left({\displaystyle \frac{{\tau }_{oct}}{p_a}}+1\right)}^{k_{3FWD}}$$

(6)

The current study used the NCHRP 1-37A model to evaluate the nonlinearity of the unbound layers in the test sections. The model’s coefficients were laboratory-measured using the summary M_R (SMR) and backcalculations from the multi-load FWD testing.

2.4. Analysis Method

The FWD test results were used to backcalculate the layer modulus (E_FWD) of the test sections using the Modulus 7.0 computer program. This program was developed by the Texas A&M Transportation Institute (TTI) and uses deflections from seven sensors for backcalculation procedures. Therefore, deflection data from the 0, 8, 12, 18, 24, 36, and 60-inch sensors were used as the input. Furthermore, the base and subbase layers were modeled as a single layer with a thickness of 15.5 inches [13].

The nonlinear stress-dependent behavior of the unbound materials was captured using the NCHRP 1-37A model, the coefficients of which were estimated for the unbound materials in the laboratory using the M_R test results [23]. Additionally these model coefficients were also calibrated each time the multi-load FWD test was carried out in the field. The stresses for the model were found at 9.5 inches (from the surface) for the base and 25 inches (from the surface) for the subgrade modulus using a linear elastic solution (KENLAYER) [27].

The pavement strain responses were calculated in the next step by inputting the laboratory-measured M_R and backcalculated E_FWD coefficients of the NCHRP 1-37A model into the MatFEA program as a nonlinear pavement response. In addition, as the current ME-based pavement analysis/design procedures use LEA-based pavement response models, the KENLAYER program was also used to obtain the strain response of the test sections. In this regard, the flowchart of such an analysis is shown in Figure 2. It is noted that MatFEA is a 2D FE-based pavement response model developed at Michigan State University to analyze pavement structures with nonlinear stress-dependent unbound layers. This program uses a dynamically adjustable mesh size algorithm to improve the runtime efficiency of the program while maintaining the accuracy of the FE approach in calculating the pavement responses. The nonlinearity of the unbound layers was captured through an iterative process until the average error in the elemental moduli was reduced to less than 2% with 95% reliability. More details about the MatFEA program can be found elsewhere [28].

An additional step of the analysis method was the validation of the NCHRP 1-37A model coefficients, which were calibrated using the multi-load FWD testing. For this purpose, the test sections were modeled using the MatFEA program with the calibrated NCHRP 1-37A model coefficients, and the nonlinear pavement responses at the mid-depth of the unbound layers were obtained to calculate the corresponding modulus. It is noted that the MatFEA program uses the same modulus value to generate the stiffness matrix for a specific element at the mid-depth of the unbound layer under the loading center. The calculated modulus from the MatFEA program was compared with the backcalculated E_FWD value for that layer to validate the calibrated NCHRP 1-37A model coefficients.

Finally, the pavement responses, as the vertical strains at the middle of the base (9.5 inches) and top of the subgrade layer (20 inches), were compared to assess if a workable conversion between the lab M_R and the E_FWD exists.

3. Results and Discussion

This section includes the results and a discussion of the FWD test results, a comparison between the laboratory-measured M_R and backcalculated E_FWD, the nonlinear strain responses, validation of the calibrated NCHRP 1-37A model coefficients using the FWD test results, and a comparison of the vertical strain responses.

3.1. FWD Test Results

Figure 3 shows the interpreted results of the multi-load FWD testing on the test sections of this study. In Figure 3a, for Cells 185 and 186, higher E_FWD values were observed for the coarse RCA and fine RCA, with both achieving their highest values by the end of the last testing year (2022). The high layer modulus in both is attributed to cement hydration with presumably more retention of unhydrated cement in the fine RCA, causing it to have a higher value than the other RAB materials. Both the coarse and fine RCA also contained aggregates with higher angularity and, therefore, increased interlocking. It is noted that this observation agrees with the reviewed literature [13,23].

On the other hand, the backcalculated E_FWD values for the RCA + RAP base layer showed relatively lower values than those constructed with RCA. This is attributed to the lower aggregate interlocking due to the asphalt coating around the RAP aggregates. Also, the stiffening effect in the RAP aggregates due to asphalt aging was much smaller than the hydration process in the RCA aggregates, resulting in a relatively steady increase in the backcalculated E_FWD values over time in the RCA + RAP base layer. Finally, the lowest backcalculated E_FWD values were observed for section 188 with the VA base layer, which indicates it had the lowest aggregate interlocking rate compared to the RAB layers. Also, no significant stiffening effect over time was observed in the VA base layer, further validating the hydration and aging process in the RCA and RAP materials.

Figure 3b shows that the moduli of the different subgrades remained almost constant over the three years. Typically, sand showed a consistently higher value than clay loam.

Finally, Figure 3c shows the distribution of the maximum surface deflection under the loading center. According to the layered elastic theory, surface deflection (as a system response) is a nonlinear function of pavement layers and their loading properties [27]. Therefore, the stiffness of the underlying layers, including the base and subgrade layers, is expected to affect the surface deflection basin adversely. In this regard, Cell 188, which had the VA base layer with the lowest base and subgrade moduli, showed the highest surface deflection values. On the other hand, Cell 186, with the fine RCA base layer and sandy subgrade, showed the lowest surface deflections.

3.2. Comparison of Laboratory-Measured M_R against Backcalculated E_FWD

Table 2. Average model coefficients based on lab M_R tests and multi-load FWD tests.

Material	Lab Tests				Multi-Load FWD Tests
	k1	k2	k3	SMR (ksi)	k1-FWD	k2-FWD	k3-FWD	EFWD (ksi)
Coarse RCA	913	0.44	−0.07	18.1	4125	0.24	−0.03	58.28
Fine RCA	882	0.45	−0.06	17.8	7616	0.17	−0.03	107.7
VA	762	0.32	−0.05	13.9	894	0.14	−0.05	12.08
RCA + RAP	803	0.51	−0.12	16.5	1310	−0.01	−0.06	19.75
Sand subgrade	947	0.75	−0.42	11.3	1558	0.07	−0.05	20.4
Clay loam	1005	0.33	−2.59	8.6	810	−0.08	−0.06	13.35

Unit Conversion: 1 ksi = 6.895 MPa.

shows the average values of the NCHRP 1-37A model coefficients based on the lab M_R and multi-load FWD testing of the different unbound materials used in this study. The actual distribution of the obtained model coefficients is also shown in Figure 4. It is noted that the samples of the laboratory-measured data were collected at the time of construction, while the FWD-based data were averaged more than 10 times, as multi-load FWD tests were carried out for three years. This can explain the significantly wider range of the model coefficients (k_i values) obtained from the multi-load FWD tests, especially for the base layers.

A comparison of the average modulus values of the different unbound layers in Table 2 shows that the backcalculated E_FWD values were generally higher than the laboratory-measured M_R values, except for the VA base layer. This observation further highlights the stiffening effect of hydration and the aging process of the RAB materials over time. According to this table, the RCA base layers were stiffer than the other unbound materials, which is in agreement with the previous findings. Also, the fine RCA was observed to achieve the highest E_FWD value, by an adequate margin, in the field; however, the lab results for M_R present the coarse RCA as a better material. This is generally due to less breakage of the hydration materials during the compaction of the fine RCA in the lab compared to that in the field [13].

The E_FWD values were around 3.2, 6.1, 0.9, and 1.2 times those of the lab M_R for the coarse RCA, fine RCA, limestone, and RCA + RAP, respectively. For the sand and clay loam subgrades, the E_FWD values were 1.8 and 1.6 times the M_R values.

Figure 4a shows the distribution of the k₁ coefficients from the lab M_R and backcalculated FWD test results. As this figure shows, the magnitude of the k₁ coefficients obtained from the FWD data has a direct correlation with the backcalculated E_FWD values, where the RCA base layers possessed the highest values. The authors expected such a correlation as the k₁ coefficient is a direct multiplier in the NCHRP 1-37A model. However, the lab M_R presented a base + subbase k₁ of the coarse and fine RCA higher than that of the VA and RCA + RAP, but the difference was significantly smaller than the observed difference in the field. This is mainly due to the hydration of cementitious materials over an extended period, resulting in an increased modulus in the field compared to the limited hydration in the lab environment. Figure 4b shows similar results for the two subgrade soils, where the variation in the k₁ coefficient is considerably lower than those of the base layers. This is attributed to a higher stress state at the base layers and their stiffer behavior due to the higher angularity and aggregate interlocking.

Figure 4c shows the distribution of the k₂ coefficient in the NCHRP 1-37A model, which is the exponent of the bulk stress (θ) term and an indicator of the material behavior with a change in the stress state. As this figure shows, all bases showed positive k₂ coefficients in the laboratory, indicating the stress-hardening behavior. However, the magnitude of the calibrated k₂ coefficients from the FWD test results was lower than those measured in the laboratory, which means the stress sensitivity of the materials in the field over time was reduced. In the case of the subgrade materials, Figure 4d shows that both the sandy and clayey subgrades had stress-hardening behavior in the laboratory. In contrast, the clay loam subgrade showed less stress sensitivity. Meanwhile, the FWD-based data presented significantly lower values of the k₂ coefficients. Also, the clay loam subgrade had stress softening (negative k₂ coefficient) in the field, which might be expected for clayey materials.

The distribution of the k₃ coefficients of the different base and subgrade layers is shown in Figure 4e,f. As these figures show, the obtained k₃ coefficients based on the field data were very close to zero, which neglects the shear-softening term of the NCHRP 1-37A model. This observation can be attributed to the low magnitude of the shear stress at the mid-depth of the unbound layers. Therefore, the shear sensitivity of the model could not be captured during the calibration process. However, the material experienced a wide range of shear stresses in the laboratory to evaluate the effect of shear stresses on the M_R. This can explain the significantly lower k₃ coefficient of the clay loam subgrade based on the laboratory data, compared to the obtained values of almost zero based on the FWD test results.

Finally, a comparison of the results for Cells 185 and 186 for the sandy subgrade and Cells 188 and 189 for the clay loam subgrade, in Figure 4b,d, and f, shows a reasonable reproducibility for the calibrated model coefficients (k_i values) from the multi-load FWD test data. In other words, although the base layer in all test sections was completely different, almost reproducible model coefficients were obtained for the sandy subgrade in Cells 185 and 186 and the clay loam subgrade in Cells 188 and 189.

3.3. Distribution of Nonlinear Vertical Strain Responses

Figure 5 shows the distribution of the vertical strain responses for all test sections modeled using the MatFEA program. As the multi-load FWD test results were analyzed using the Modulus 7.0 program, where a single layer was used for both the base and subbase layers, a similar structure was modeled in MatFEA. The calibrated coefficients of the NCHRP 1-37A model were obtained from the corresponding FWD test results and inputted into the MatFEA for the base + subbase and subgrade layers. It is also noted that the AC layer was modeled as linear–elastic, and a 9000 lb single axle was used to simulate the traffic loading on the test sections. It is also pertinent to mention that almost all test sections experienced their highest strains in the specified month of each year, as shown in Figure 5.

A comparison of the vertical strain responses in this figure shows that the highest magnitude of the vertical strains was generated in Cell 188 with the VA base layer, which is in agreement with the previous findings; VA materials have the lowest stiffness. Similarly, the lowest strain responses were observed in Cell 186 with the fine RCA base and sandy subgrade layers. Both types of material also showed the highest stiffness based on previous findings. A visual inspection of this figure suggested the following ranking of the base layer materials based on the induced vertical strains in the pavement sections: fine RCA, coarse RCA, RCA + RAP, and VA.

3.4. Validation of FWD-Based Calibrated NCHRP 1-37A Model

As mentioned earlier, the multi-load FWD test results were analyzed using the Modulus 7.0 program to estimate the stiffness of the pavement layers, which was later inputted into the KENLAYER program to calibrate the NCHRP 1-37A model coefficients for the unbound layers. Both the Modulus 7.0 and KENLAYER programs are LEA-based analysis tools. Therefore, the nonlinear NCHRP 1-37A model’s coefficients were calibrated using a linear–elastic analysis procedure. To validate these calibrated coefficients, the test sections were modeled using the MatFEA program (as a nonlinear pavement response model), and the calibrated coefficients of the NCHRP 1-37A model were used as the inputs for the unbound layers. Later, the modulus of the specific element located at the mid-depth of the unbound layer (9.5, and 20 inches from pavement surface for the base and subgrade layers) and under the loading center was extracted from the MatFEA program and compared to the backcalculated E_FWD from the Modulus 7.0 program. The comparison was performed using the relative difference (RD) concept, as shown in Equation (7). It is noted that the proximity of the RD index to 1 is an indicator of a lower difference.

$$RD=1-\left({\displaystyle \frac{M_{R\_MatFEA}-E_{FWD}}{M_{R\_MatFEA}}}\right)$$

(7)

where RD is the relative difference, M_{R_MatFEA} is the modulus extracted from the MatFEA program (psi), and E_FWD is the backcalculated stiffness extracted from the Modulus 7.0 program (psi).

Table 3. Average relative differences between field-based backcalculated E_FWD values and MatFEA-based M_R values.

Material	Relative Difference (EFWD)
	Base + Subbase	Subgrade
Cell 185 (coarse RCA base, sandy subgrade)	0.99	0.85
Cell 186 (fine RCA base, sandy subgrade)	0.96	0.92
Cell 188 (VA base, clay loam subgrade)	0.97	1.12
Cell 189 (RCA + RAP base, clay loam subgrade)	0.99	1.10

summarizes the relative differences between the base + subbase and subgrade layers of different test sections. According to this table, the relative differences for the base + subbase layer in all test sections were within the 4% range close to 1.0, which can be used as a validation fact for the calibrated coefficients of the base + subbase layer based on FWD test data. In addition, though higher relative differences were observed for the subgrade layer, they were still within a 15% range of 1.0, which is a reasonable range for the relative difference of the materials in the field. One reason for the poorer match in the subgrade layer can be attributed to the significantly lower stress state at the 20-inch depth from the pavement surface, at which the modulus values were small; the tiny differences could have caused higher relative errors.

3.5. Comparison of Vertical Strains

In this section, the vertical strain responses of the test sections at the mid-depth of the base layer (9.5-inch depth) and the top of the subgrade layer (20-inch depth) are calculated and compared. For this purpose, the coefficients of the NCHRP 1-37A model for the base + subbase and subgrade layers were inputted into the MatFEA program (FE approach) using the lab-measured M_R and multi-load FWD test data. In addition, the test sections were also modeled using the KENLAYER program (LEA approach) with the backcalculated E_FWD values from the field E_FWD test data. It must be noted that the FWD-based data represent the field conditions over three years, starting two years after construction, while the laboratory-based data represent the conditions of the pavement layers at the time of construction.

Figure 6 shows a comparison of the calculated vertical strain at the mid-depth of the base layer. It was observed that the vertical strains calculated by the M_R-based coefficients for the coarse and fine RCA were much higher than those calculated from the E_FWD based coefficients (Figure 6a,b). Both materials exhibited stiffer behavior in the field, as indicated in the deflection and E_FWD data earlier, the extent of which could not be ascertained using lab testing during construction. Also, from the EFWD-based coefficients, vertical strains in the RCA + RAP blend were found near the projected vertical strains (lab M_R based coefficients) initially. Still, significant variations were observed during the latter years (Figure 6d).

Obtaining a field representative stiffness value for any material in the lab can be challenging, but the same is becoming more complex for RABs. The presence of unhydrated cement in RABs makes hydration a critical attribute of their performance. As it occurred gradually over time, the lab M_R was found to be insufficient to assess the degree of performance of RABs in the field. No workable relationship existed between the lab M_R and the E_FWD due to the drastically different behaviors of the recycled aggregate bases in the field and the lab.

The vertical strains in limestone obtained from the FWD data using the FE approach tended to have values near the projected vertical strains from the lab M_R (Figure 6c). LEA also exhibited a similar trend in the middle of the limestone base. Therefore, a correlation of the lab M_R with the E_FWD was deemed possible for the unbound materials (base and subgrade) in the VA (limestone) section.

Similarly, Figure 7 shows a comparison of the calculated vertical strain at the top of the subgrade layer for the different test sections. As this figure shows, different materials in the base layer significantly affected the calculated strain response at the top of the subgrade layer. The laboratory-based coefficients of the NCHRP 1-37A model for Cells 185 and 186, with the RCA base layers, presented higher vertical strains compared to those calibrated based on the field FWD test data. Similar trends with Figure 6 were also observed for Cells 188 and 189 with the VA and RCA + RAP base layers.

Furthermore, while both the FE approach and LEA projected closer values of strains for the VA and RCA + RAP at a 9-inch depth (Figure 6c,d), the FE approach presented higher strains at a 20-inch depth than the LEA (Figure 7c,d). The trends were mostly opposite at a 20-inch depth for the coarse and fine RCA sections, i.e., LEA showed more strains than the FE approach at 20 inches (Figure 7a,b). As the response of unbound layers and fine-grained soil is nonlinear under traffic loads [29,30], LEA deviated from a realistic representation of strains with increasing depth (

Table 4. Relationship between strains obtained using E_FWD (FE approach and LEA) and lab M_R (FE approach).

Test Section	Average Relative Difference between EFWD and MR Strains at 9 Inches		Average Relative Difference between EFWD and MR Strains at 20 Inches
	FE	LEA	FE	LEA
Cell 185 (coarse RCA base, sandy subgrade)	0.45	0.43	0.40	0.45
Cell 186 (fine RCA base, sandy subgrade)	0.30	0.30	0.26	0.47
Cell 188 (VA base, clay loam subgrade)	0.93	0.96	0.91	0.63
Cell 189 (RCA + RAP base, clay loam subgrade)	0.76	0.76	0.72	0.56

). Table 4 presents the relative differences (RD) between the strains from the lab M_R and E_FWD values, as shown in Equation (8):

$$\mathrm{RD}=1-\left({\displaystyle \frac{\mathrm{Lab} M_R \mathrm{Strains} \mathrm{from} \mathrm{FE}-{\mathrm{E}}_{\mathrm{FWD}} \mathrm{Strains} \mathrm{from} \mathrm{FE} \mathrm{or} \mathrm{LEA}}{\mathrm{Lab} M_R \mathrm{Strains} \mathrm{from} \mathrm{FE}}}\right)$$

(8)

4. Summary and Conclusions

Developing a correlation between the laboratory-measured resilient modulus (M_R) and the backcalculated layer modulus (E_FWD) depends on various factors. The responses of a pavement’s unbound layers (as vertical strains to an applied load) in virgin aggregate (VA) base and recycled aggregate base (RAB) test sections were studied to ascertain any relationship between the lab M_R and E_FWD values. After reviewing the strain distribution in different pavement cells, calibrated using finite element (FE) and layered elastic analysis (LEA)-based approaches, the following conclusions can be drawn:

• The application of fine recycled concrete aggregate (RCA) materials in the base layer showed the best results in the field with their high stiffness and low strain responses, followed by coarse RCA, the blend of RCA and recycled asphalt pavement (RAP) (RCA + RAP), and VA materials.
• Laboratory-measured M_R values and their corresponding coefficients of the NCHRP 1-37A model cannot represent the stiffness state of RAB material in the field. They could result in overdesigning the pavement structure. This is attributed to the aging and hydration processes of the mortar components in RAB materials.
• A comparison of the vertical strain responses between the mid-depth of the base and the top of the subgrade layer presented no correlation between the laboratory-measured M_R and the field-based backcalculated E_FWD for the RAB materials. However, such a correlation seems reasonable for Cell 188, with the VA base (limestone) and clay loam subgrade layers, as the laboratory-based and field-based vertical strains were reasonably close to each other. Therefore, the following conversion factors are proposed by the authors:
  M_R = 0.87 E_FWD (for limestone aggregate in the base layer);
  M_R = 1.55 E_FWD (for clay loam material in the subgrade layer).
• Field-calibrated coefficients of the NCHRP 1-37A model, which were obtained using the LEA approach and multi-load FWD test data, were validated with the nonlinear FE-based pavement response.
• The difference between the vertical strains obtained using the FE-based approach and those calculated via LEA tended to increase with depth. The FE approach remained conservative by giving higher strains for limestone and RCA + RAP at 20in. The opposite was observed for the coarse and fine RCA.
• By generating the pavement’s response through nonlinear parameters or stress dependencies, obtained by using E_FWD in the NCHRP model, the FE-based approach provided a better solution to avoid conversions of the modulus and obtain the best estimate of material in the field.
• This study examined the linear and nonlinear pavement responses to a single load level of 9000 lbs, establishing a foundation for future analyses of pavement responses under varying loads and their effects on the correlation between lab M_R and E_FWD.