1 Introduction
Effective pavement management systems (PMS) are crucial for preserving high-quality road infrastructure, especially since much of the global road network is already built. Surface deflection serves as a key metric for assessing the structural integrity of pavements, especially in terms of load-bearing capacity. Among the non-destructive testing methods typically used within PMS, the falling weight deflectometer (FWD) is known for its ability to apply varying load levels with precision and consistency for measuring surface deflections, providing insights into the condition of in-service pavements. Several studies have emphasized the significance of deflection basin parameters (DBPs) for evaluating the structural capacity of operational pavements based on FWD deflection measurements [
1–
3].
Pavement surface deflections are influenced by various environmental and structural factors, with pavement temperature being one of the most critical due to asphalt’s well-known temperature-dependent behavior [
4]. Adjusting measured pavement deflections to a reference temperature, usually set at 20 °C, is essential for accurately assessing a flexible pavement’s structural condition, ensuring consistency in the evaluation process [
5]. Corrective techniques often rely on graphical models with logarithmic or linear relationships. A prime example is the most commonly adopted temperature correction method in the US, which many state departments of transportation and local agencies utilize. This method is outlined in the AASHTO 1993 design guide [
6] and remains a standard approach for adjusting pavement deflections based on temperature.
Although the method described in AASHTO 1993 for correcting surface deflections is simple to implement, relying solely on asphalt layer temperature and thickness, it falls short in accuracy when accounting for the impact of temperature on FWD deflections. The method overlooks several important factors, such as temperature gradients within the pavement, daily heating and cooling cycles, and variations in pavement condition, all of which can significantly influence deflection measurements [
2,
7]. During the day, the surface temperature rises rapidly, reaching significantly higher levels than deeper pavement layers. At night, the surface cools quickly, creating sharp temperature gradients [
7–
9]. In addition, the method in AASHTO 1993 does not clearly define the asphalt layer temperature to be used, which adds some additional uncertainty to the method. The temperature gradient within the pavement depth makes it challenging to determine an effective asphalt temperature [
7,
10]. It is common practice for highway agencies to use pavement surface temperatures for simplicity since they can be obtained directly through the infrared thermometer integrated into the FWD device. However, pavement surface temperature is sensitive to air temperature and may not accurately capture changes in temperature gradients. Thus, previous studies have shown that the mid-depth temperature of the asphalt layers might be more appropriate for representing the effective temperature of the asphalt layer, providing more accurate deflection corrections when considering temperature effects on asphalt pavements [
7,
8]. Subsequent research examined the use of one-third-depth asphalt layer temperature as an alternative to mid-depth measurements but found no significant improvement in correction accuracy [
11,
12]. Other deflection correction methods, such as the one proposed by Diaz Flores et al. [
13], defined the effective asphalt layer temperature as the average of the temperature values measured at the top and bottom of the asphalt layer. However, their study did not compare the accuracy of this approach with that obtained using mid-depth or one-third-depth asphalt layer temperatures. Notably, all these methods to determine the effective asphalt layer temperature pertain to traditional asphalt pavements, whereas the present study focuses on full-depth asphalt pavements.
Full-depth asphalt pavements are a common type of flexible pavement structure in various regions, particularly in areas with extreme freeze–thaw cycles or weak subgrades, such as parts of the United States, Canada, and northern Europe. Unlike traditional asphalt pavements, these designs often have substantially greater asphalt thicknesses than more conventional flexible pavements that contain aggregate base and subbase layers. Full-depth asphalt pavements consist entirely of asphalt mixtures, with a surface layer typically ranging from 38 to 63 mm, an intermediate layer from 50 to 100 mm, and a base layer from 100 to 250 mm. This multilayered structure enhances structural integrity and load-bearing capacity [
14,
15]. In such cases, air and surface temperature variations may not uniformly affect the entire asphalt depth.
Despite previous research demonstrating that mid-depth temperature provides improved accuracy for temperature corrections in traditional asphalt pavements, research on the impact of temperature on surface deflections for full-depth asphalt pavements is more limited. Furthermore, no studies have specifically examined the effective pavement temperature for use with the AASHTO 1993 temperature correction method or assessed its accuracy for full-depth asphalt pavements. Therefore, there is a clear need to assess the most appropriate pavement temperature input for reliable deflection analysis in these thicker pavement structures. This study aims to address this gap by systematically evaluating different temperature inputs and their impact on deflection corrections for full-depth asphalt pavements.
2 Objective and scope
This study examines the effective pavement temperature for use as the input temperature in the AASHTO 1993 method for surface deflection adjustments when analyzing FWD data of full-depth asphalt pavements. Pavement temperature gradients were assessed using temperature sensors installed at various depths in three selected full-depth asphalt pavement sections in Indiana. FWD tests were conducted on these selected sections at two different temperatures on the same day, with simultaneous temperature gradient measurements. For the FWD deflections analysis, temperature correction factors (TCFs) were calculated using the AASHTO 1993 method with three different pavement temperatures as inputs: surface temperature, mid-depth temperature of the entire full-depth asphalt layer, and the temperature at the midpoint between the pavement surface and the depth where daily temperature variations were minimal. The accuracy of these TCFs was assessed based on their ability to produce consistent deflections at a reference temperature, with the most accurate TCF identified as the one that minimized variations in the corrected central surface deflection (D0) values from FWD test results at different temperatures on the same day. By evaluating the accuracy of these correction factors, the study proposes a more accurate input temperature for analyzing surface deflections in full-depth asphalt pavements, thereby minimizing the temperature effects during pavement condition analysis.
3 Methodology
3.1 Evaluation of temperature gradients in full-depth asphalt pavements
Three in-service Indiana full-depth asphalt pavement sections were selected for temperature sensor installation at various asphalt layer depths: one state route (Section A), and two US highways (Sections B and C). Table 1 summarizes the details of the selected field sections, including total asphalt pavement thickness and temperature sensor locations. Three locations were tested for each field section, resulting in nine test locations. The temperature sensors used were thermistors arranged in custom-designed bars, known as temperature trees (TTs), as shown in Fig. 1(a). Based on test section characteristics, the sensor supplier’s specifications, and the manufacturing requirements for the TTs, 305 mm TTs with 4 thermistors at different depths were used in Sections A and B. In section C, a 610 mm TT with 5 thermistors was employed, given the higher thickness of this pavement section. Table 1 also indicates the thermistor arrangement in each TT, listing the respective distance from the surface. The thermistor positions were selected based on the individual pavement layer thicknesses measured from field cores, ensuring temperature measurements at each layer interface and at the asphalt base layer mid-depth, as shown in Fig. 1(b). This approach allowed for temperature variation investigations within the entire asphalt thickness. It should be noted that the selected sections were constructed using different mixture designs and in different years, which may influence the temperature sensitivity of the asphalt layer.
Figure 1(b) shows the schematic of the TTs set up in a generic full-depth asphalt pavement section. Since none of the three sections involved new construction, installing the sensors required a destructive method. The chosen installation method involved using a 100-mm diameter field core extraction machine to create the space for vertically inserting the TTs into the pavement. Additionally, a radial saw was employed to cut a 20–30 mm depth channel from the sensor location to the shoulder to protect the cables. The sensors were positioned between the wheel path and the shoulder to avoid the wheel path. After placing the TTs in position and securing the cables in the channel, the remaining space was filled with a cold asphalt mixture manually compacted to avoid damaging the sensors. Figure 1(b) shows how thermistors 1 and 2 (Th-1 and Th-2) were designed to be installed at the layer interfaces between the surface, intermediate, and base layers.
A 4-channel data acquisition device with four input ports was used for temperature data collection, which was connected to a laptop via an Ethernet cable. Temperature data were recorded synchronously with the FWD testing, allowing for real-time monitoring, which is essential for the research. The thermistors offer a temperature range of −40 to 200 °C with an accuracy of ±2%.
3.2 Surface deflection data collection
The FWD device simulates a moving wheel loading by applying three levels of impulse loads (31, 40, and 49 kN). It measures pavement surface deflections at nine different points using geophones positioned linearly at various distances from the center of the FWD loading plate, ranging from 0 to 1500 mm. The deflection at a specific distance from the loading center is denoted as Dx; for instance, D600 refers to the deflection recorded by the geophone situated 600 mm from the loading center, as shown in Fig. 2. This study measured deflections under a 40 kN FWD load, the standard load level used for FWD data analysis.
FWD tests were conducted in Sections A, B, and C, each at two different temperatures on the same day, to capture FWD deflection data at varying temperature conditions while minimizing differences due to traffic loads. For each section, the first set of FWD tests was completed early in the morning, before 10:00 AM Eastern Time (ET), followed by a second set of testing in the afternoon, after 1:00 PM ET, thus capturing load response data at two widely different pavement temperatures. Table 2 presents detailed surface temperature readings for the nine selected testing locations, showing the temperature variations between tests. These temperature differences were not the same at all the testing locations, as the temperature was influenced by the weather conditions on each test day. Each testing location is identified by its section ID (A, B, or C) followed by a location number (1, 2, or 3); for instance, location A1 refers to the first testing location of Section A. Higher temperatures recorded during the afternoon tests are designated as T2 for each FWD testing location, while the lower temperature from early morning tests are labeled as T1. It should be noted that the surface temperatures listed in Table 2 were measured using the infrared thermometer integrated into the FWD device.
Figure 3 shows how the FWD tests were conducted at the temperature sensor locations, from which temperature information was collected at the exact moment the FWD tests were conducted. Consequently, the data set for each location includes pavement deflection basin curves, pavement surface temperatures, and pavement temperatures at varying depths.
3.3 Temperature correction of surface deflections
The temperature correction method outlined in the AASHTO 1993 design guide was used to address the temperature effects in the measured FWD deflections and assess its accuracy based on the input temperature used. This standard introduces two diagrams to offer TCF for adjusting D0, as depicted in Fig. 4. Figure 4(a) is employed for granular or asphalt-treated bases, while Fig. 4(b) is used for cement- or pozzolanic-treated bases. Due to the pavement structure of the full-depth asphalt sections, the diagram from Fig. 4(a) was used.
It is important to note that the TCFs derived from the AASHTO 1993 design guide are primarily designed to adjust the
D0. However, this approach raises several conflicting issues. For instance, previous studies have shown that other deflection values, such as D200, D300, D600, D900, and D1200, are also influenced by pavement test temperatures [
2,
8]. In some cases, the corrected
D0 values were even lower than the deflections measured 200 mm away from the loading center (D200), leading to unreasonable DBPs and compromising the accuracy of structural evaluations of in-service pavements. In 1995, Kim et al. [
7] identified several limitations of this correction method, including its tendency to overcorrect FWD deflections at high temperatures. This issue is believed to stem from the method’s inadequate consideration of pavement temperature gradients. Furthermore, there is ambiguity regarding which pavement temperature should be used as input for this standard method. In this study, the pavement-installed temperature sensors were utilized to calculate three different TCFs, using temperatures at various depths as inputs in the AASHTO 1993 method (Fig. 4(a)). These depths were:
1) TCF1: pavement surface temperature (current practice);
2) TCF2: mid-depth temperature of the entire full-depth asphalt layer;
3) TCF3: temperature at the midpoint between the surface and the pavement depth where there was no daily temperature variation. This midpoint was determined based on the analysis of the measured temperature gradients.
After temperature correction, the objective is to obtain deflections at a reference temperature, which are expected to be consistent. Therefore, the criterion for identifying the most accurate TCF and the effective temperature for use in the AASHTO 1993 temperature correction method is the TCF that minimizes the differences between the corrected D0 values. For this analysis, the relative difference, ΔD0, was calculated by dividing the absolute difference between D0 at T2 and T1 by the value of D0 at T1, as shown in Eq. (1). This approach provides a comparative measure of the variation in D0 across different cases.
4 Results and discussion
4.1 Assessment of temperature gradients in full-depth asphalt pavements
Figure 5 illustrates the temperature gradients at the various test locations, recorded with the TTs while the FWD testing was conducted. Filled markers were used to represent pavement temperature gradients during the afternoon testing (temperature gradient T2), while empty markers indicate the early morning pavement temperature gradient (T1). Different testing locations within each section were distinguished using various marker types and line styles.
The temperature gradients shown in Fig. 5 provide insights into full-depth asphalt pavement thermal profiles, particularly regarding daily variations within the pavement. As expected, the most significant temperature fluctuations occur at the surface, where environmental temperature changes have a more pronounced effect. The pavement surface temperature rises from T1 in the morning to T2 in the afternoon, with these temperature increases delayed throughout the pavement depth, a logical phenomenon. Notably, daily temperature variations diminish beyond a certain depth on all three pavements. Regardless of the total pavement layer thickness, temperatures measured at depths of 203 mm and deeper remain relatively constant at each location, while significant temperature fluctuations occur from the pavement surface down to a depth of 100 mm. The depth of full-depth asphalt pavements (300 mm or greater in these three pavements) is the primary reason that, beyond a certain depth, the temperature of the asphalt remains nearly constant throughout daily cycles. This observation led to the definition of TCF3, which represents the temperature at the midpoint between the surface and the depth where temperature stability is observed.
4.2 Effect of pavement temperature gradients on AASHTO 1993 temperature correction
Performing FWD tests on a given pavement section at two different temperatures on the same day allowed for obtaining different deflection basin curves resulting from the viscoelastic behavior of the asphalt mixtures, given there were no changes in the pavement structural condition. Since there were no significant changes in pavement condition within the test time intervals, it is expected that after correcting the FWD deflections for temperature effects, the deflections would be similar. This temperature correction accuracy is essential for appropriate pavement management and effective decision-making regarding the need for rehabilitation activities.
Since the TCFs provided by the AASHTO 1993 design guide apply only to correcting the central deflection, D0, Table 3 summarizes the absolute D0 values measured at two testing temperatures across the nine test locations. Figure 6 shows the deflection basin curves for Section A, Location A3, before and after temperature correction, as an illustrative example of the temperature correction result. In Fig. 6, the measured FWD deflections are depicted with filled markers and a continuous line, while the temperature-corrected values, adjusted using the three TCFs, are indicated by empty markers and dashed lines. The temperature of the sensor at 100 mm was used for calculating the TCF3 because the temperature remained constant below 203 mm. The deflections measured during the high-temperature gradient, T2, measured in the afternoon, are represented by circular markers, while those measured during the low-temperature gradient, T1, recorded in the morning, are shown with triangular markers. Filled markers indicate uncorrected deflections, whereas filled markers represent deflections after correction using the respective TCFs.
Figure 6 visually compares the D0 deflection values at different temperatures, both before and after temperature correction, allowing for an assessment of TCF effects. Since T2 is always higher than T1, the orange deflection basin curve, corresponding to the gradient T2, consistently shows larger FWD deflections. When correcting deflections corresponding to the gradient T1, it is evident that the corrected D0 values are always larger than the measured D0 values. This occurs because the surface, mid-depth, and 100 mm depth sensor temperatures are all lower than the reference temperature, 20 °C, causing the TCFs to exceed 1 (Fig. 4(a)), which increases the D0 values upon correction. This trend differs for deflections corresponding to the gradient T2. Although the T2 surface temperature (25.67 °C) is higher than the reference temperature, the temperatures at both mid-depth and 100 mm were lower than the reference temperature of 20 °C. Therefore, while the corrected D0 at T2 using TCF1 (based on pavement surface temperature) was lower than the measured D0, the corrected D0 at T2 using TCF2 and TCF3 were both higher than the measured D0. These results emphasize the importance of pavement temperature gradients in understanding asphalt pavement responses and behavior to loading, particularly their impact on surface deflections, and highlight the need to determine the appropriate effective temperature for more accurate temperature correction during deflection analysis.
To identify the effective temperature that provides the most accurate TCF for correcting FWD deflections, a correction was considered more accurate when the corrected D0 values within a testing location were more similar. As shown in Fig. 6, the largest absolute difference between corrected D0 values, 27.3 µm, occurred when using TCF1, which decreased to 17.9 µm using TCF2. Ultimately, TCF3 provided the most accurate correction for this location, resulting in an absolute difference of 9.6 µm between the corrected D0 values, showing more consistent corrected D0 values.
To better compare deflections and assess the accuracy of the different TCFs across the nine testing locations, the relative difference metric, ΔD0, defined in Eq. (1), was used. Table 4 summarizes this metric as a percentage for all nine testing locations, showing the ΔD0 obtained when applying the three different TCFs and the ΔD0 resulting from uncorrected D0 values for reference.
The use of TCF1, which corresponds to using the surface temperature, does not indicate clear trends according to the Δ
D0 shown in Table 4. While the use of TCF1 reduced the Δ
D0 in locations A1 and A2 compared to the Δ
D0 from uncorrected deflections, it increased it in the other locations, yielding inadequate results and making the use of surface temperature inadvisable. TCF2 corresponds to using the mid-depth temperature of the asphalt layer, which many researchers recommend as asphalt pavements’ effective temperature to be considered in the AASHTO 1993 correction method [
7,
16]. The values shown in Table 4 show a decrease in the Δ
D0 in most cases when using TCF2 compared to uncorrected deflections, except for the locations in Section C, where there are no clear trends. Even if it is logical, it is worth mentioning that using mid-depth temperature (TCF2) is not recommended for very thick asphalt pavements, as is the case for Section C. As shown in Fig. 5(c), the temperatures measured at mid-depth (around 275 mm in this section) showed minimal variation, making the TCF2 values nearly identical. This is why the Δ
D0 in uncorrected cases and after applying TCF2 remain practically unchanged (Table 4). Overall, TCF2 performed better than TCF1, reducing the Δ
D0 in most cases compared to the uncorrected case, yet it was still not effective due to the higher thickness in full-depth asphalt pavements.
The effects of using TCF3 on the ΔD0 were superior to those of TCF1 and TCF2. The ΔD0 were reduced in all locations compared to the ΔD0 in the uncorrected case, showing a great effect in Sections B and C. In all three test locations of these two sections, the use of TCF3 showed the lowest ΔD0 of the three TCFs. The effect of TCF3 in Section A was also beneficial, reducing the ΔD0 compared to the uncorrected D0 values, but not as much as in Sections B and C. This can be explained by the poorer condition of Section A’s pavement, as observed in the D0 values summarized in Table 3. Section A showed D0 values exceeding 200–250 µm, while Sections B and C barely exceeded 100 µm. The poorer condition of Section A may influence the effectiveness of the temperature correction.
Due to the greater thickness of the asphalt mixture in full-depth asphalt pavements, the mid-depth temperature often shows minimal variations in daily heating and cooling cycles, as seen in Fig. 5. This is especially true for Section C, with an asphalt thickness exceeding 500 mm and mid-depth temperature not showing significant variations (Fig. 5(c)). This makes the use of mid-depth temperature as the effective temperature inadequate, and therefore, the use of TCF2 is not recommended in full-depth asphalt pavements. The use of TCF1 is also not recommended, as surface fluctuations are too sensitive to environmental changes and cannot accurately reflect the temperature condition throughout the asphalt material thickness.
In contrast, using temperature at the midpoint within the thickness affected by temperature changes allows for calculating TCF3 and shows an adequate correction of D0 deflections using the AASHTO 1993 method. The temperature values at different depths measured in full-depth asphalt sections show that the depth of temperature influence is approximately 200 mm, and calculating the TCFs using the temperature at 100 mm shows consistent corrections of the D0 deflections. These findings indicate that a temperature at a 100 mm pavement depth may be a more effective input for the AASHTO 1993 correction method in full-depth asphalt pavements than other possible temperature location choices. Furthermore, based on these findings and to eliminate the need for temperature sensors, a new approach is recommended for correcting D0 deflections due to temperature. The approach would utilize temperature prediction models, based on easily measurable variables, to estimate the pavement temperature at a 100 mm depth, which would then serve as input for the AASHTO 1993 method. Future research will focus on evaluating and enhancing the accuracy of these models to improve their application in temperature correction for surface deflections in full-depth asphalt pavements.
5 Summary of findings and recommendations
Regardless of pavement layer thickness, temperature gradient measurements in full-depth asphalt pavement sections indicate minimal daily temperature variations at approximately 200 mm of depth.
Temperature correction factor method 1 (TCF1), calculated using the surface temperature of the asphalt pavement, generally shows the least accurate correction of D0 FWD deflections of the three TCFs studied. Differences between corrected D0 using the TCF1 were often larger than for uncorrected D0. This is because the pavement surface temperature is susceptible to environmental changes, making it an ineffective representation of the total asphalt layer temperature in full-depth asphalt pavements.
Temperature correction factor method 2 (TCF2), corresponding to the mid-depth asphalt temperature, generally showed a better correction than TCF1. However, mid-depth temperature may not be the best option for use in full-depth asphalt pavements due to their greater thickness than conventional asphalt pavements. Since temperatures below approximately 200 mm show minimal daily variation, TCF2 will not capture temperature effects on FWD deflections in thicker, full-depth asphalt pavements. This is especially noticeable in Section C, which is 550 mm thick.
Temperature correction factor method 3 (TCF3) was calculated based on the temperature at the midpoint between the pavement surface and the depth where temperature variations became minor. The temperature sensors indicate this stable point is at approximately 200 mm, so TCF3 was calculated using the temperature values measured at 100 mm. TCF3 provided a more accurate correction with smaller relative differences in D0 than the other TCFs.
Based on the findings from the pavement section analyzed in this study, it is recommended to utilize the pavement temperature at approximately 100 mm depth, the midpoint between the surface and the level where daily temperature variation becomes negligible, as the effective input temperature for the AASHTO 1993 method to correct surface pavement deflections and mitigate temperature effects. This depth may vary depending on local pavement structure and climate conditions. While improvements in the corrected D0 may reduce issues related to unreasonable DBPs in some cases, fully addressing the problem would require a correction method that accounts for temperature effects on all affected geophones, not just D0. Furthermore, rather than relying on temperature sensors, the 100-mm depth pavement temperature can be predicted through external measurements with pavement temperature prediction models, such as the BELLS3 model. Notably, the concept proposed in this study may also be extended to deflections obtained from Traffic Speed Deflectometers, where temperature correction is likewise essential. Ongoing and future research efforts aim to refine these models and develop new ones to enhance the accuracy of pavement temperature predictions. This will facilitate the proposal of a novel and practical temperature correction approach for FWD deflections explicitly designed for transportation agencies.
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