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Abstract

This study intends to compare deflections obtained from traffic speed deflection devices (TSDDs) with the deflections of the falling weight deflectometer (FWD). For this purpose, deflections were measured on five sections of three roads in the Norwegian road network using traffic speed deflectometer (TSD) and rapid pavement tester (Raptor). Deflections were also measured using FWD at three different temperatures and the curves of FWD deflections versus temperature (FWD temperature-dependent deflection curves) were obtained. These curves were used to correct the effect of temperature difference. It was shown that both TSD and Raptor have the potential to detect structural deficiencies; however, TSD had better consistency with FWD with regard to deflection values and deflection basin parameters. A refinement was then made to make the Raptor data more consistent with FWD data. Calculating bearing capacity before and after refinement revealed that refining Raptor data can substantially increase the consistency between Raptor and FWD.

Keywords

deflection measurement falling weight deflectometer Traffic speed deflectometer rapid pavement tester structural evaluation

The falling weight deflectometer (FWD) has been the standard equipment for structural evaluation of pavements for more than 40 years. As an impulse deflection device, it drops a stationary load from a certain height to the pavement, and measures deflections at different radial distances from the load center. By using the deflection basin obtained from the FWD as well as the pavement layer thicknesses, the elastic moduli of the layers can be calculated through a back-calculation process ( 1 ). There are some challenges with regard to the utilization of the FWD. Firstly, it provides discrete measurements commonly at 25 or 50 m intervals. As a result, weak spots between two consecutive drop sites might not be detected. Secondly, the lane must be closed to traffic when the FWD operates. This may induce problems related to traffic congestion and can also be dangerous for the operators. Thirdly, the dropping weight of the FWD does not seem to accurately simulate continuous traffic loads. And finally, the FWD is slow and not efficient for network-level applications ( 2 – 4 ).

Traffic speed deflection devices (TSDDs) are state-of-the-art equipment for the structural evaluation of pavements. TSDDs have several advantages over FWD. Providing continuous measurements, moving at traffic speed, not needing road closure, and applying the load in a manner to better resemble the service condition of roads are some advantages of using TSDDs over FWD. Two current types of TSDDs include traffic speed deflectometer (TSD) and rapid pavement tester (Raptor), as shown in Figure 1.

Figure 1.

Two current types of traffic speed deflection devices: (a) traffic speed deflectometer and (b) rapid pavement tester.

Traffic Speed Deflectometer

The TSD is manufactured by Greenwood Engineering as of 2004. In the TSD trailer, dozens of Doppler laser sensors are mounted on a rigid beam, measuring the deflection velocity of the pavement. A 100 kN loading is applied through dual tires of a rear axle to the pavement surface. However, it should be noted that whatever the TSD actually measures is affected by all truck axles. By dividing deflection velocity by the instantaneous horizontal speed of the vehicle, deflection slopes are obtained ( 5 ). Deflection values at any arbitrary point can then be calculated by employing computational methods such as the area under the curve (AUTC) method and the Euler–Bernoulli (EB) method ( 6 ). TSD is the most widely used TSDD, and many studies related to its applicability are found in the literature. To date, TSD has been on missions in many countries including Denmark, Great Britain, Australia, Italy, Poland, South Africa, USA, China, Norway, and Germany ( 7 ). From Greenwood’s perspective, the main advantages of using the TSD include:

The potential of measuring at both project and network levels.

Providing high-resolution continuous data and detailed information about discontinuities.

The possibility of measuring at various load levels, as the ballast load is replaceable.

The possibility of using two measuring beams to inspect at both wheel paths.

The possibility of integrating sub-systems like surface imaging systems with artificial intelligence (AI) automated crack detection, ground-penetrating radar (GPR), right-of-way imaging cameras, and road profiler to the TSD.

The potential of finding the strength of concrete joints and detecting cracked plates.

A long service life for the vehicle.

Rapid Pavement Tester

The Raptor was designed by Dynatest in 2018. In 2020, Ramböll acquired the Raptor project from Dynatest ( 8 ). The measuring beam of Raptor is placed in a semi-trailer and equipped with twelve line laser sensors for measuring distances. This beam, made of fiber, is adjacent to the rear axle single wheel, and for countries in which right-side driving is practiced, it is placed on the right-hand side of the vehicle. The sensors measure more than 1,280 points along a 200 mm line transversal to the moving direction of the vehicle ( 9 ). An image recognition technique is then used to locate the position of the laser sensors. As a result, Raptor deflection indices (RDIs) are determined. These indices can be ultimately converted to deflection values through a back-calculation procedure. Raptor is gaining worldwide acceptance, and it has been used in several countries including Norway, Switzerland, Italy, Lithuania, Finland, Sweden, Denmark, the Netherlands, USA, Austria, Belgium, and France so far. According to Ramböll, there are several advantages in using Raptor including:

A fast onboard calibration system, to determine the position and alignment of the lasers with respect to each other.

Fast and simple loading and unloading of ballast.

Scanning the entire deflection bowl, not only discrete points.

The measuring beam material is carbon fiber, providing superb stiffness and temperature stability.

Has the potential to inspect between 150 and 400 lane-kilometers of road network per day.

Is equipped with twelve laser sensors, which is more than enough for covering the deflection bowl, and even if one of the sensors fails, the vehicle is still operational.

Literature Review

Despite the advantages of using TSDDs, the FWD can provide accurate deflection measurements and has been in service for many years ( 10 , 11 ). To date, no standard protocol has been provided for incorporating deflection data from TSDDs into pavement management systems. One reasonable doubt might be about the consistency between TSDDs and FWD. Although TSDDs are different from FWD in loading characteristics and measuring principles, any emerging technology for structural evaluation must be able to detect pavement sections with different resilient responses. Therefore, it would be beneficial to investigate levels of agreement between these devices in determining pavement structural characteristics.

Elseifi and Zihan compared TSD and FWD for a road in Louisiana State, USA. They observed that deflection values are statistically different, and that surface roughness might be an influential factor in TSD measurements. They developed an Artificial Neural Network model to predict corresponding FWD deflections from TSD deflections ( 10 ). Morovatdar et al. compared TSD and FWD measurements on a state highway in Wisconsin, and concluded that deflection basin indices obtained from TSD and FWD are in good agreement; however, FWD deflections are generally 12 to 37% higher than TSD deflections for the same positions of the road ( 12 ). Nielsen and Jensen used TSD for the structural evaluation of two runways at Copenhagen Airport. They compared the measurements of TSD with those of a heavy weight deflectometer (HWD). They also obtained the surface curvature index ( $SC I_{300}$ ) values from TSD and HWD. The $SC I_{300}$ parameter is the difference of deflections measured at the center of the loading plate and 300 mm from the center, and represents the structural condition of the surface layer. They showed that the $SC I_{300}$ values from TSD and HWD were comparable ( 13 ). In another study, Nielsen et al. showed that there is consistency between TSD measurements and deflections obtained from an instrumented road test site in Finland. They also observed a very good agreement between strains predicted from TSD and the strains obtained from the transducers of the instrumented site ( 14 ). Abdel-Khalek et al. developed a new structural number (SN) formula based on deflections obtained from a rolling wheel deflectometer (RWD). Although the proposed model had no terms related to pavement layer thicknesses and properties, a good agreement between SN values from this formula and SN values obtained from FWD was observed ( 15 ). Elseifi et al. compared RWD with FWD and observed a good agreement between deflection measurements. They concluded that both technologies can reflect the structural integrity of the pavements; however, the condition of the pavement surface is deterministic in comparing the scattering and uniformity of the data obtained from these devices ( 16 ). Antonsen and Mork found that both maximum deflection and $SC I_{300}$ were comparable for TSD and FWD in both deflection values and variation patterns. They used the bearing capacity calculated from FWD deflections as a reference for analyzing TSD measurements, and determined a revised bearing capacity formula based on the TSD term ( 17 ). In a recent paper, Katicha et al. summarized the research studies on TSD in the last decade. They concluded that there is generally a good correlation between FWD and TSD, and the information that can be obtained from FWD can also be obtained from TSD ( 5 ). There are also other studies that have tried to evaluate the consistency between TSD and FWD ( 11 , 18 , 19 ). However, temperature correction of TSDDs measurements has not been thoroughly investigated yet ( 5 ). On the other hand, Raptor is a newer technology and has seen limited research on its applicability. Madsen and Pedersen proposed a dynamic viscoelastic model to simulate the effect of impact and moving loads. They used back-calculation of Raptor measurements to find RDIs. Then, they used forward calculation (using the equations based on FWD) to find the corresponding FWD measurements. They claimed that $D_{0}$ and $D_{150}$ for the corresponding FWD deflections are comparable with measured FWD deflections at the same positions ( 20 , 21 ).

Importance of the Study

There are fundamental differences between TSDDs and FWD in loading mechanisms, load-transferring materials and measuring principles. However, a comparative study can still be beneficial for the following reasons:

1- Any emerging technology for structural evaluation of pavements must be able to differentiate between pavement sections with different resilient responses. For using data obtained from pavement structural evaluation in the pavement management system, different sections should be prioritized based on a structural index (such as structural number). The FWD has been used for more than 40 years for this purpose and has shown promising results. Therefore, the data produced by a new device must in some degree be consistent with the FWD data. As was mentioned, Raptor is a new technology manufactured in 2018, and few studies about its applicability are found in the literature. Without conducting a comparative study, it is impossible to comment on the practicality of the new technologies. Yet, regardless of fundamental differences, consistent and comparable values from a TSDD hold promise for practical use, potentially replacing FWD as the standard equipment of pavement evaluation for many years. This is the reason why the initial studies on Raptor at the NCAT testing facility in Auburn ( 8 ) were focused on comparing its measurements with FWD deflections.

2- The bearing capacity is a structural index that is traditionally used in Norway to prioritize different pavement sections based on their structural stiffness. In 2020, the Norwegian Public Roads Administration (NPRA) considered the possibility of using Raptor for deflection measurements at the network level. However, thousands of kilometers of roads had previously been measured with FWD. It was of great interest to NPRA to check if the bearing capacity values produced using Raptor deflections are comparable with FWD deflections, or if any revisions should be made to Raptor data. Also, it was uncertain if the temperature correction factor that was in use for correcting FWD deflections was also applicable to Raptor deflections. Moreover, NPRA aimed to assess whether TSD or Raptor provides better consistency with FWD, adding TSD to deepen the understanding and facilitate advanced research in pavement evaluation methodologies.

3- There are generally two methods for pavement layers' moduli from TSDD data: First, using comparison measurements under various different conditions and finding a correlation between TSDDs and FWD, and then using traditional back-calculation computer programs (that were initially developed based on FWD deflections) to obtain elastic moduli of pavement layers; second, developing new procedures for analyzing TSDD data, for example, a viscoelastic back-calculation procedure. However, a significant amount of time and effort is required for this purpose, and it might not be as practical as the first method. The correlations between TSDDs and FWD are not generic, and depend on various factors such as pavement structure, temperature, and vehicle speed. However, difficulties in developing methodologies specific to analyzing TSDD data underlie the importance of finding a consistency between deflections obtained from TSDDs and FWD.

Research Objectives

TSDDs are sophisticated and expensive tools compared with the FWD, requiring careful evaluation of their cost-effectiveness for pavement management systems. Selecting a reliable TSDD technology is of interest to road administrations and practitioners. As a means to study their application for Norway’s conditions, the NPRA conducted field tests using TSD and Raptor measurements, along with FWD measurements at different temperatures. The curves of FWD deflections versus temperature (that are called FWD temperature-dependent deflection curves in this study) were obtained for temperature correction, and GPR was used for layer thickness data. Graphical, statistical, and structural comparisons were performed between FWD and TSDDs. A proposed refinement aimed to enhance the consistency of Raptor data with FWD in determining bearing capacity. The significance of the study lies in addressing the need for reliable and cost-effective alternatives to FWD for pavement structural evaluation. By investigating the repeatability of TSDDs and evaluating their consistency with FWD, this study aims to contribute valuable insights into the applicability and potential integration of TSDDs into pavement management systems. Considering the aforementioned reasons, it would be beneficial to check levels of consistency between TSDDs and FWD.

The main objectives of this study can be summarized below:

Investigating the repeatability of TSDD measurements.

Comparing deflections obtained from TSDDs and FWD.

Obtaining a temperature correction factor in determining bearing capacity based on FWD data.

Proposing a refinement to Raptor data to make the bearing capacity obtained from Raptor and FWD comparable.

Experimental Design

Measurements were performed at five sections of three roads in the Norwegian road network using TSD, Raptor, FWD, and GPR. The roads were in a dry condition during the measurements. The FWD measurements were conducted on June 29, July 4, and July 5, 2022. The model of the FWD equipment was Dynatest 8012-044, and it measured at 25 or 50 m intervals (see Table 1). The air and surface temperatures were also recorded point by point at the same intervals during the FWD measurements. The FWD sensors were placed at nine radial distances, namely 0, 20, 30, 45, 60, 90, 120, 150 and 180 cm from the center of the load. The applied load was 50 kN and the plate diameter was 300 mm. Table 1 summarizes the name of the selected roads, locations, measured lanes, average surface temperature ( $° C$ ), number of measurements, measuring intervals, and the number of utilized data points for each road.

Table 1.

Summary of Falling Weight Deflectometer measurements

Name	Location	Lane	Avg. surface temp. ( $° C$ )	Number of measurements	Interval (m)	Utilized data points
EV14 S1D1	Stjørdal–Hofstad	Outbound	17.1	21	25	20
			28.4	20	25
			34.0	21	25
EV14 S2D1	Stjørdal–Hofstad	Outbound	19.3	161	25	161
			27.5	161	25
			30.8	161	25
EV14 S3D1	Hegramo–Forra	Outbound	20.9	131	25	66
			27.3	66	50
			28.6	131	25
		Inbound	19.9	131	25	66
			24.4	66	50
			31.5	131	25
FV704 S2D1	Skjøla–Tanem	Outbound	15.8	17	25	17 and 30
			15.9	110	25
			20.2	112	25
			28.6	30	50
FV705 S1D1	Hell–Leira	Outbound	18.5	81	25	41
			28.9	41	50
			33.1	81	25

Note: Avg. = average; temp. = temperature.

Raptor measurements were conducted in two directions on the same roads (see Table 2) on June 29, 2022. The equipment was Ramböll’s Raptor (serial No. 9100-002), and the normalized averaging length was set to 10 m. The air and surface temperatures were recorded continuously, and normalized at the same 10 m intervals. The average surface temperature was between 21.6 and 22.5 $° C$ for FV704 S2D1, and between 27.7 and 30.8 $° C$ for the other road sections. Raptor measurements were conducted at two different speed levels, around 60 and 80 km/h, to evaluate the effect of vehicle speed on deflection measurements. The reason behind choosing these particular speed levels was primarily based on their alignment with the typical traffic conditions observed on the Norwegian national road network, as they are among the most commonly used speed limits for Norwegian roads. The TSD measurements were conducted using Greenwood’s TSD on June 29, 2022, the same day as the Raptor measurements. However, the surface temperature when TSD was operating was around 5 $° C$ lower than when Raptor was on mission. As shown in Table 2, TSD measured the outbound lanes of the same roads as the Raptor (measurement was repeated at one section), and the normalized averaging length was again 10 m. Measurements were also performed at the road sections using a 1 GHz horn antenna GPR on July 1, 2022, and the thickness of the surface layer was specified. The heights of the ground and horn antenna above the surface were 30 and 40 cm, respectively, and the measurements were conducted in the right wheel path (considering that in Norway, right-side driving is practiced). The normalized averaging length of the GPR measurements was 10 m. Table 2 summarizes the measured FWD, Raptor, TSD, and GPR data. Air temperature and pavement temperature at zero depth (on the pavement surface) as well as the geographical data including latitude and longitude were also recorded by each device, and were normalized at 10 m or 25 m intervals. For Raptor and TSD, the second round of measurement was conducted immediately after the first round. Also, the instantaneous speed of the truck was recorded during the operation of the TSDDs.

Table 2.

Summary of measurements conducted by Falling Weight Deflectometer (FWD), Rapid Pavement Tester (Raptor), Traffic Speed Deflectometer (TSD) and Ground-penetrating Radar (GPR)

Name	Location	Lane	FWD	Raptor	TSD	GPR
EV14 S1D1	Stjørdal–Hofstad	Outbound	✓	x	x	✓
EV14 S1D1	Stjørdal–Hofstad	Inbound	x	x	x	✓
EV14 S2D1	Stjørdal–Hofstad	Outbound	✓	✓✓	✓✓	✓
EV14 S2D1	Stjørdal–Hofstad	Inbound	x	✓✓	x	✓
EV14 S3D1	Hegramo–Forra	Outbound	✓	✓✓	✓	✓
EV14 S3D1	Hegramo–Forra	Inbound	✓	✓✓	x	✓
FV704 S2D1	Skjøla–Tanem	Outbound	✓	✓✓	✓	x
FV704 S2D1	Skjøla–Tanem	Inbound	X	✓✓	x	x
FV705 S1D1	Hell–Leira	Outbound	✓	✓✓	✓	✓
FV705 S1D1	Hell–Leira	Inbound	x	✓✓	x	✓

Note: The shaded rows were considered for comparison purposes.

With reference to Table 2, data obtained from three sections have all four measurements (i.e., FWD, Raptor, TSD, and GPR), and they were chosen for comparison purposes. Data points for EV14 S1D1 were used as part of the data for developing a temperature correction factor based on FWD data, which will be discussed later. Also, data points of the inbound lane of EV14 S2D1, the inbound and outbound lanes of FV704 S2D1, and the inbound lane of FV705 S1D1, which were absent in the comparative study, were usable for evaluating the repeatability of Raptor data. A map showing the location of the three sections for the comparative study is shown in Figure 2. These include:

Dataset 1: EV14 S2D1, between Stjørdal and Hofstad, outbound lane, 4 km total length, 25 m intervals for FWD data, 161 data points for comparison.

Dataset 2: FV705 S1D1, between Hell and Leira, outbound lane, 2 km total length, 50 m intervals for FWD data, 41 data points for comparison.

Dataset 3: EV14 S3D1, between Hegramo and Forra, outbound lane, 3.2 km total length, 50 m intervals for FWD data, 66 data points for comparison.

Figure 2.

Location of road sections considered in this study for comparing traffic speed deflection devices with falling weight deflectometer.

Method

Temperature Correction

To accurately compare deflections of TSDDs with FWD, the effect of temperature should be considered first. Different methods for correcting this effect have been employed by researchers ( 9 , 22 –24). Correcting $D_{0}$ values for both TSDDs and FWD by using the method provided by the AASHTO design guideline ( 22 ), and adjusting $SC I_{300}$ values for TSD to a reference temperature ( 23 ) are two examples. In this study, relationships between surface temperature and FWD deflections were established. Figure 3 shows FWD deflections for a sample of twenty points at EV14 S1D1 (point numbers 48–68). As shown in Figure 3a, for each data point, $D_{0}$ was measured at three different temperatures (in this figure, the numbers on the outer circles specify the point numbers from 48 to 68, and the values inside each rectangle denote surface temperatures in °C). These three temperatures are for convenience called high, mid, and low, and are specified with different colors. For each point, a separate curve can be defined to fit the deflection values, that is, temperature-dependent deflection curves for each point can be obtained. Using these curves, $D_{0}$ values at any arbitrary temperature can be determined. As shown in Figure 3b, almost similar trends were observed for the other radial distances at the same data points (the numbers on the outer circle specify the point numbers, and the concentric circles denote deflection values in µm). Therefore, FWD temperature-dependent deflection curves can also be determined for the other radial distances.

Figure 3.

Falling weight deflectometer deflections (micrometer) for point numbers 48–68 at EV14 S1D1: (a) $D_{0}$ at three different temperatures (high, mid, and low) and (b) $D_{0}$ to $D_{180}$ at low temperature.

Figure 4 represents the schematic of the nine FWD temperature-dependent deflection curves (corresponding to nine radial distances) for each data point. As a result, deflections at any arbitrary temperature can be obtained using interpolation or extrapolation. As the surface temperature is recorded during TSDD measurements, the surface temperature of a corresponding data point from TSDDs can be replaced in the FWD temperature-dependent deflection curves of the same point. As a result, the equivalent FWD measurements at that point can be calculated. These equivalent deflections can now be compared with the measured TSDD deflections. It is worth mentioning that in this process, TSD data cannot be compared directly with Raptor data; however, both can be compared with their equivalent FWD data at the same temperature as for the TSDDs.

Figure 4.

Schematic falling weight deflectometer (FWD) temperature-dependent deflection curves for each data point, and finding equivalent FWD deflections for traffic speed deflection devices (TSDDs).

To obtain the FWD temperature-dependent deflection curves, polynomial second-degree models were used (Equation 1). For each data point, values of regression coefficients X_i, $Y_{i}$ , and $Z_{i}$ were obtained. Considering nine radial distances, nine models were developed for each data point.

\begin{array}{l} D_{i - t e m p . d e p e n d e n t . d e f} = X_{i} \times T^{2} + Y_{i} \times T + Z_{i} \Rightarrow D_{i, F W D - e q u i v .} = X_{i} \times {T_{T S D D}}^{2} + Y_{i} \times T_{T S D D} + Z_{i} \\ i = 0, 20, 30, 45, 60, 90, 120, 150, 180 \end{array}

(1)

where T is the surface temperature ( $° C$ ), and i is the radial distance (cm) of the FWD sensor from the load center.

Deflection Basin Indices and Structural Parameters

As there might be a correlation between the structural capacity of a pavement section and deflection basin indices calculated from the measured deflections at that section, it would be beneficial to consider them for comparing FWD and TSDDs. Rada et al. list 77 indices related to the deflection bowl ( 25 ). In this study, a set of five indices was considered for comparison. The formulas for determining these indices are provided in Equations 2 to 6:

SC I_{300} = D_{0} - D_{30}

(2)

BCI = D_{90} - D_{120}

(3)

ARE A_{36} = \frac{6}{D_{0}} \times (D_{0} + 2 \times D_{30} + 2 \times D_{60} + D_{90})

(4)

F - 1 = \frac{D_{0} - D_{60}}{D_{30}}

(5)

SLOPE = \frac{1}{60} \times (3 D_{0} + 3 D_{20} - 2 D_{30} - 2 D_{60} - 2 D_{180})

(6)

The $SC I_{300}$ parameter is the surface curvature index (µm) and represents the structural condition of the surface layer. The $SC I_{300}$ is the difference of deflections measured at the center of the loading plate ( $D_{0}$ ) and 30 cm from the center ( $D_{30}$ ). The BCI parameter is the base curvature index (µm) and represents the structural condition of the base layer. The BCI is defined as the difference of the deflections measured in 90 and 120 cm from the loading center. The $ARE A_{36}$ parameter is the area under a certain part of the deflection basin (dimensionless) and represents the normalized area of a vertical slice through a deflection basin at varying radial distances from the load center ( 12 ). Also, the F-1 is the Shape factor (dimensionless) and represents the amount of deflection basin curvature. The F-1 is inversely proportional to the ratio of the pavement stiffness to the subgrade stiffness ( 12 ). Finally, the SLOPE parameter is the deflection basin slope ( $10^{- 4} m$ ) and represents the sum of individual deflection slopes between every two consecutive radial distances. In Equations 2 to 6, $D_{i}$ is the deflection (µm) at i cm radial distance from the center of the load.

Also, two structural parameters, namely bearing capacity (BC) and structural factor (SF) were additionally defined.

Bearing Capacity

In the Norwegian pavement design standard, BC is used as a traditional indicator of how heavy vehicles affect a road. More precisely, BC is a structural index representing the largest axle load a road can carry over a period of time, without inducing excessive damage or necessitating major maintenance measures ( 26 ). BC is obtained according to Equation 7:

BC = 64 \times {AADT}_{H}^{- 0.072} \times DI M^{- 0.6}

(7)

where BC is the bearing capacity (tons), $AAD T_{H}$ is the average annual daily traffic for heavy vehicles, and DIM is a parameter related to deflections at inner radial distances, obtained from Equation 8:

DIM = {[457.94 \times D_{0} \times (D_{0} - D_{20})]}^{0.5} \times p^{- 1}

(8)

where $D_{0}$ and $D_{20}$ are deflections (mm) at 0 and 20 cm distances from the load center, and p is the contact pressure (MPa) of the loading plate. For a circular loading plate with 300 mm diameter and subjected to a 50 kN load, p = 0.707 MPa. To avoid obtaining unrealistic results from Equation 7, $AAD T_{H}$ values should be higher than 30. According to the Norwegian specifications, the BC values are normally higher than 20 tons for roads built in accordance with today’s road standards, whereas older roads typically have a bearing capacity of 10–14 tons in the summer season ( 27 ).

Structural Factor

A new parameter called the structural factor ( $SF$ ) was defined. This parameter was inspired by the structural number (SN) in the AASHTO design guideline for two-layer systems, with the difference that structural coefficients $a_{1}$ and $a_{2}$ are reproduced based on some empirical formulas. The charts of these formulas can be found elsewhere ( 28 ). As the GPR was unable to accurately detect the thickness of the lower layers, only the thickness of the surface layer is entered into the equation. The SF is calculated according to Equation 9:

SF = (0.0067 \times {E_{1}}^{0.5216} + 0.249 \times \log (E_{2} \times 145.038) - 0.977) \times h

(9)

where SF is the structural factor (dimensionless), $E_{1}$ and $E_{2}$ are elastic moduli (MPa) of the surface layer and sublayer, respectively, and h is the thickness of the surface layer (cm). To avoid producing unrealistic results, the $E_{1}$ parameter should be between 690 and 3450 MPa, and the $E_{2}$ parameter should be between 100 and 275 MPa. Also, this equation is valid only when the sublayer is an untreated base course ( 28 ). For obtaining $E_{1}$ and $E_{2}$ , an elastic back-calculation software system, called EBS, which was recently developed at the Norwegian University of Science and Technology, was employed. In this software, a synthetic three-layer pavement system is defined, and the forward calculation scheme for obtaining deflections is based on modeling by the KENLAYER software.

Results and Discussion

Considering a total number of 268 FWD data points (in Datasets 1, 2, and 3) and nine radial distances, 2,412 FWD temperature-dependent deflection curves were developed. A programming code in Python 3.9 was used to facilitate the process of finding model coefficients. Deflection measurements and corresponding surface temperatures were entered as input files in .txt format, and the coefficients of the models (Equation 1) were obtained.

Ramböll uses a post-processing software system to obtain deflections from RDIs ( 8 , 9 ), and can report deflections at any arbitrary distance. This software system was developed on the basis of studies conducted by Madsen and Pedersen ( 20 , 21 ). In this study, Ramböll was asked to provide deflection values at the same nine radial distances as for the FWD. To obtain deflections from TSD data, four methods are found in the literature including the EB beam method ( 29 ), AUTC method ( 30 ), the Weibull fit method ( 31 ), and Greenwood’s method. Among these, only the latter is capable of detecting the lag distance between the point below the loading axle and the point sustaining the maximum deflection. Greenwood’s method was originally developed by Pedersen ( 32 ). This method uses a parametrized synthetic model, and the model coefficients are obtained using optimization techniques. More precisely, simulated deflection slope curves are initially developed using a finite element method and Laplace transform. The obtained simulated data are then validated using the ViscoRoute software. Finally, the Gaussian and Stable distribution functions are utilized to fit the deflection slopes ( 33 ). It is worth noting that a fifth method has been recently introduced, which is based on fitting critical damping curves to the deflection slopes of the TSD ( 34 ). In the current study, Greenwood Engineering was asked to provide deflections at the same radial distances as the FWD sensors.

Deflections of TSDDs were normalized at 10 m, and the intervals for FWD deflections were 25 or 50 m. So, FWD data points were considered as reference points. Then, the geographical coordinates of points for the TSDDs were checked one by one and compared with the coordinates of the FWD data points, to select the corresponding points as close as possible to each other. In the second repetition of TSD for Dataset 1, problems in measuring surface temperatures were reported. For this reason, only one repetition of TSD and two repetitions of Raptor were compared with their equivalent FWD deflections.

FWD Temperature-dependent Deflection Curves

Figure 5 shows the FWD temperature-dependent deflection curves for a sample point in Dataset 1. As shown, the effect of temperature on the deflections is more pronounced for the inner radial distances, and temperature correction does not have a significant effect on the deflections of the outer radial distances (say $D_{120}$ , $D_{150}$ , and $D_{180}$ ). It is worth noting that the approximate range of surface temperature for which polynomial second-degree equations can be used for obtaining equivalent FWD deflections from all three datasets is between 16.5 and 28.0°C. To explain the reason for low dependency of deflections to the surface temperature at outer radial distances, it can be argued that the area under the load center experiences the highest stress, resulting in significant deflections. As the asphalt layer is affected by temperature changes, this area shows increased deflection with higher temperatures. At outer radial distances, the load is distributed over a larger area, and the stresses and strains diminish rapidly. The deflections in these regions are influenced more by the stiffness of the pavement layers rather than just the surface layer properties. Consequently, the dependency between the deflections and surface temperature at inner radial distances is expected to be higher compared with this dependency at the outer radial distances.

Figure 5.

Falling weight deflectometer temperature-dependent deflection curves for a sample data point in Dataset 1 considering second-degree polynomial regressions.

Repeatability of TSDDs

The repeatability of TSDDs was evaluated for Dataset 1. In this evaluation, the effect of temperature and/or speed was not normalized. As mentioned, the surface temperature was not recorded correctly for the second repetition of TSD. However, as these two TSD runs were conducted immediately after each other, they were compared with each other for deflections at different radial distances. Figure 6 shows two repetitions on the same chart for four radial distances of Raptor and TSD.

Figure 6.

Repeatability of traffic speed deflection devices in relation to similarity in measuring deflections for two short-term repetitions: (a) $D_{0}$ for Raptor, (b) $D_{30}$ for Raptor, (c) $D_{90}$ for Raptor, (d) $D_{180}$ for Raptor, (e) $D_{0}$ for TSD, (f) $D_{30}$ for TSD, (g) $D_{90}$ for TSD and (h) $D_{180}$ for TSD.

The graphical comparison shows that both TSD and Raptor show repeatable results, and Raptor deflections are closer to each other at inner radial distances than the outer ones. For a statistical evaluation, Pearson’s correlation coefficient was calculated according to Equation 10:

ρ_{X, Y} = \frac{cov (X, Y)}{σ_{X} σ_{Y}} = \frac{E [(X - μ_{X}) (X - μ_{Y})]}{σ_{X} σ_{Y}}

(10)

where $ρ_{X, Y}$ is the Pearson’s correlation coefficient, $cov (X, Y)$ is the covariance between two repetitions X and Y, $μ_{x}$ and $μ_{Y}$ are the means of X and Y, respectively, $σ_{x}$ and $σ_{Y}$ are the standard deviations of X and Y, respectively, and $E$ is the expectation. Values of $ρ_{X, Y}$ for TSD were 0.99 for $D_{0}$ , descending to 0.97 for $D_{180}$ . For Raptor deflections, $ρ_{X, Y}$ was 0.93 for $D_{0}$ , and between 0.97 and 0.91 for $D_{20}$ to $D_{180}$ . These high values clearly suggest that both TSD and Raptor produce repeatable results. It is also concluded that for the outer radial distances, $ρ_{X, Y}$ is generally lower compared with the inner radial distances. The good repeatability of Raptor deflections also shows that the influence of vehicle speed (between 50 and 80 km/h) in measuring deflections is almost negligible. It is worth mentioning that the thickness of the surface layer varied between 15.0 and 43.0 cm for Dataset 1, between 14.1 and 22.7 cm for Dataset 2, and between 16.1 and 43.4 cm for Dataset 3. The good repeatability of TSDDs is in accordance with some other studies ( 8 , 18 , 22 , 35 ).

Comparing Deflection Values

Deflection basins were compared for some random data points. As shown in Figure 7, Raptor 1 and Raptor 2 are the two repetitions of Raptor, TSD shows the TSD deflections, FWD-R1 and FWD-R2 denote the equivalent FWD deflections at the temperatures of the first and second rounds of Raptor, respectively, and FWD-T denotes the equivalent FWD deflections at the temperature of the TSD measurements. With regard to deflection values, it is evident that TSD generally shows more consistency with FWD compared with Raptor. Also, the consistency between FWD and TSDDs is more pronounced at the inner radial distances. The average relative error in predicting the equivalent FWD deflections for different radial distances is also determined for TSD and the two repetitions of Raptor. The results are shown in Figure 8 for each dataset separately. As shown, the relative error in determining equivalent FWD deflections is lower for TSD measurements, especially for the inner radial distances.

Figure 7.

Deflection basin comparisons for sample points for: (a) Point 100 (Dataset 1), (b) Point 120 (Dataset 1), (c) Point 5 (Dataset 2), (d) Point 15 (Dataset 2), (e) Point 31 (Dataset 3) and (f) Point 50 (Dataset 3).

Figure 8.

Average relative error of deflection values for traffic speed deflection devices and their equivalent falling weight deflectometer deflections for: (a) Dataset 1, (b) Dataset 2, and (c) Dataset 3.

Mixing data from three data sets in a single chart (Figure 9) and using statistical comparison approves again the higher levels of consistency between TSD and the equivalent FWD than for Raptor. At inner radial distances, this consistency is even higher. Also, TSD data points are seemingly more dispersed than Raptor data points. It is also shown that the two repetitions of Raptor produce comparable results, and at outer radial distances, the difference between Raptor and equivalent FWD deflections is more considerable.

Figure 9.

Comparing deflection values for traffic speed deflection devices (TSDDs) and their equivalent falling weight deflectometer (FWD) deflections for four different radial distances: (a) $D_{0}$ , (b) $D_{30}$ , (c) $D_{90}$ , and (d) $D_{180}$ .

Comparing Deflection Indices

Deflection basin parameters including $SC I_{300}$ , $BCI$ , $ARE A_{36}$ , $F - 1$ , $SLOPE$ , $BC$ , and $SF$ were calculated for each case, and are shown in Figure 10. Pearson’s correlation coefficients for these curves are depicted in Figure 11.

Figure 10.

Comparison of traffic speed deflectometer devices and the equivalent falling weight deflectometer (FWD) deflections for deflection basin parameters and structural indices: (a) $SC I_{300}$ for Raptor and FWD, (b) $SC I_{300}$ for traffic speed deflectometer (TSD) and FWD, (c) $BCI$ for Raptor and FWD, (d) $BCI$ for TSD and FWD, (e) $ARE A_{36}$ for Raptor and FWD, (f) $ARE A_{36}$ for TSD and FWD, (g) $F - 1$ for Raptor and FWD, (h) $F - 1$ for TSD and FWD, (i) $SLOPE$ for Raptor and FWD, (j) $SLOPE$ for TSD and FWD, (k) $BC$ for Raptor and FWD, (l) $BC$ for TSD and FWD, (m) $SF$ for Raptor and FWD and (n) $SF$ for TSD and FWD.

Figure 11.

Pearson’s correlation coefficients for rapid pavement tester and traffic speed deflectometer for different structural indices.

According to Figures 10 and 11, the following conclusions can be made with regard to each structural index:

SCI ₃₀₀: Pearson’s correlation coefficient is higher for TSD compared with Raptor, and both repetitions of Raptor provide similar levels of consistency. There is a good consistency between TSD and FWD; however, Raptor generally provides higher ${SCI}_{300}$ values compared with FWD.

BCI : Considering $ρ_{X, Y}$ , TSD and both repetitions of Raptor show good consistency. A closer look at Figure 10c and 10d, reveals that Raptor underestimates and TSD overestimates this index compared with FWD.

AREA ₃₆: TSD and one repetition of Raptor provide high correlation coefficients. However, the correlation coefficient for TSD is not as high as it was for $SC I_{300}$ , and for Raptor it is not as high as it was for $BCI$ .

F–1: Almost similar to $ARE A_{36}$ , TSD and one repetition of Raptor provide high correlation coefficients. However, the correlation coefficient is not as high as it was for $SC I_{300}$ (with regard to TSD) or $BCI$ (with regard to Raptor).

SLOPE : For this index, trends are almost similar to those for $SC I_{300}$ . TSD shows a better correlation with FWD, and the two repetitions of Raptor show similar levels of consistency.

BC : Both repetitions of Raptor provide $ρ_{X, Y}$ values lower than 0.60, whereas the correlation coefficient for TSD is higher than 0.80. Looking at Figure 10k, it is verified that Raptor overestimates bearing capacity.

SF : TSD and both repetitions of Raptor provide $ρ_{X, Y}$ higher than 0.90. Looking at Figure 10m and 10n, it is also revealed that both Raptor and TSD are showing good agreements with FWD, and although there are some differences between the exact values, the general trends between TSDDs and FWD are almost similar.

To summarize, $ρ_{X, Y}$ is generally higher for TSD compared with Raptor. For the second repetition of Raptor, for the three parameters $BCI$ , $ARE A_{36}$ , and $F - 1$ , Raptor is comparable to TSD; however, in determining $SC I_{300}$ , $SLOPE$ , and $BC$ , TSD performs far better. It is shown that, Raptor does not show a high level of agreement with FWD for several parameters, although both FWD and Raptor show almost similar trends. With regard to bearing capacity, Raptor overestimates BC values compared with FWD whereas TSD shows good agreement with FWD. As the most notable point, both TSD and Raptor (both repetitions) provide $SF$ values close to their equivalent FWD values, with Pearson’s correlation coefficients higher than 0.90. According to Equation 9, SF is composed of the elastic moduli of the pavement layers as well as the thickness of the surface layer. From this viewpoint, it seems to be a more accurate parameter in reflecting the resilient response of the pavement structure and therefore a more reliable index in distinguishing between sections with high and low resilient responses. Looking at Figure 10m and 10n, it is also acknowledged that both devices are good at detecting peaks and valleys, and therefore, both can detect sections with different resilient responses. This observation shows that both TSD and Raptor seem to be capable of prioritizing different pavement sections based on their structural condition at network level in a pavement management system.

Correcting Bearing Capacity Values

One of the side objectives of this study was to evaluate the possibility of using Raptor data for determining bearing capacity according to the Norwegian definition. According to Figure 10k and 10l, BC values obtained from Raptor are significantly higher than BC values obtained from the FWD. In other words, because Raptor underestimates FWD deflections (Figures 7 and 9), it overestimates the bearing capacity. However, a closer look at deflections obtained from Raptor and its equivalent FWD deflections suggests that there might be a shift between FWD and Raptor data, and Raptor deflections might possibly be converted to FWD deflections. In this part, a temperature correction factor was obtained for BC values based on FWD measurements. Then, Raptor data were modified, and a temperature correction factor was also defined based on Raptor measurements.

Temperature Correction Factor Based on the FWD

For FWD deflections, a factor for correcting the effect of temperature on BC can be defined according to Equation 11:

TC F_{FWD} = \frac{B C_{corrected, FWD}}{B C_{initial, FWD}} = {(\frac{DI M_{corrected, FWD}}{DI M_{initial, FWD}})}^{- 0.6} = {(\frac{D_{0 - corrected, FWD} \times [D_{0 - corrected, FWD} - D_{20 - corrected, FWD}]}{D_{0 - initial, FWD} \times [D_{0 - initial, FWD} - D_{20 - initial, FWD}]})}^{- 0.3}

(11)

where $TC F_{FWD}$ is the temperature correction factor of BC values based on FWD deflections, and DIM can be obtained from Equation 8. The reference temperature is set to $T = 20$ °C, and Equation 1 is solved for $i = 0, 20$ to obtain corrected values of $D_{0}$ and $D_{20}$ for each data point ( $D_{0 - corrected, FWD}$ and $D_{20 - corrected, FWD}$ ). For the available FWD data at three different temperatures, these corrected values were substituted into Equation 11. Therefore, a total of 1,203 points were obtained as shown in Figure 12. As the surface temperature was between 20 and 25°C in a small number of FWD measurements, the data in the figure appear as two clusters. However, it seems that if more measurements are taken, a continuous pattern will be obtained.

Figure 12.

Temperature correction of bearing capacity (BC) for falling weight deflectometer deflections.

As shown in Figure 12, considering a linear regression model results in a coefficient of determination as high as 0.74, justifying a linear relationship between the variables. As a result, Equation 12 is obtained for correcting the values of BC:

TC F_{FWD} = \frac{1}{1.2777 - 0.0146 \times T_{surface}}

(12)

where $TC F_{FWD}$ is the temperature correction factor and $T_{Surface}$ is the surface temperature ( $° C$ ).

Temperature Correction Factor Based on the Raptor

Similarly, the temperature correction factor for BC values based on Raptor deflections can be obtained according to Equation 13:

TC F_{Raptor} = \frac{B C_{corrected, Raptor}}{B C_{initial, Raptor}} = {[\frac{D_{0 - corrected, Raptor} \times (D_{0 - corrected, Raptor} - D_{20 - corrected, Raptor})}{D_{0 - initial, Raptor} \times (D_{0 - initial, Raptor} - D_{20 - initial, Raptor})}]}^{- 0.3}

(13)

To find $D_{0 - corrected, Raptor}$ and $D_{20 - corrected, Raptor}$ , deflection values were cleaned by removing outliers. Thereafter, two linear regression models between Raptor and FWD for $D_{0}$ and $D_{20}$ were developed (Figure 13). As the coefficients of determinations for linear regressions were as high as 0.70, the linear relationship between variables could be justified. These models are according to Equations 14 and 15. It is worth noting that the proposed equations are valid when the FWD deflection at zero radial distance from the load center ( $D_{0 - FWD})$ is between 163 and 764 µm, and at 20 cm radial distance from the load center ( $D_{20 - FWD})$ is between 125 and 625 µm.

Figure 13.

Linear regression models between rapid pavement tester and falling weight deflectometer deflections for: (a) $D_{0}$ and (b) $D_{20}$ .

D_{0 - Raptor} = 0.5331 \times D_{0 - FWD} + 83.301

(14)

D_{20 - Raptor} = 0.5761 \times D_{20 - FWD} + 69.671

(15)

Values of $D_{0 - FWD} (μ m)$ and $D_{20 - FWD} (μ m)$ were determined for each data point using the FWD temperature-dependent deflection curves by considering $T = 20 ° C$ as the reference temperature. Therefore, the ratio of initial to corrected BC values (Equation 13) was plotted in a chart (Figure 14). Finally, a correction factor for BC values based on Raptor data was obtained according to Equation 16:

TC F_{Raptor} = \frac{1}{1.3842 - 0.0171 \times T_{surface}}

(16)

where $TC F_{Raptor}$ is the temperature correction factor for BC values based on Raptor data, and $T_{Surface}$ is the surface temperature ( $° C$ ). As the coefficient of determination is 0.21, there is a poor correlation between the surface temperature and the proportion of the initial and the corrected BC. Therefore, proposing a linear correction factor does not seem to be a robust method in this regard. As a result, improving the proposed method for correcting the effect of temperature on BC based on the Raptor measurements seems to be a necessity.

Figure 14.

Temperature correction of bearing capacity (BC) for Raptor deflections.

Figure 15 shows the BC values for a sample of forty-five random points before and after applying the temperature correction factor to the Raptor data. Applying the correction factor can substantially increase the consistency between FWD and Raptor in determining BC by decreasing the relative error from 30% to around 10%.

Figure 15.

Bearing capacity (BC) before and after refining Raptor deflections.

Summary and Conclusions

This study provides a comparison between TSDDs (i.e., TSD and Raptor) with regard to the consistency with their equivalent FWD deflections. For this purpose, measurements were carried out on some roads in the middle part of Norway using FWD, TSD, Raptor, and GPR. FWD measurements were conducted at three different temperatures, and FWD temperature-dependent deflection curves were obtained to correct the effect of temperature. The main findings of this study are as follows:

Both Raptor and TSD provide repeatable deflections, especially in determining deflections at inner radial distances.

From a graphical and statistical viewpoint, the consistency between TSD and FWD is higher than the consistency between Raptor and FWD.

For three structural indices, namely $BCI$ , $ARE A_{36}$ , and $F - 1$ , one repetition of the Raptor provides comparable results with the TSD. However, the TSD is generally more consistent with the FWD in determining deflection basin parameters and structural indices.

Both TSD and Raptor are capable of detecting sections with low resilient responses.

A correction for Raptor data was proposed. Applying this correction enhances the consistency between Raptor and FWD in determining bearing capacity.

TSDDs do have many advantages over FWD, which promotes interest in using them for network-level structural evaluation. This study showed that between TSD and Raptor, the TSD shows higher levels of consistency with FWD, and Raptor deflections should be refined to correlate better with FWD deflections. However, there are fundamental differences between TSDDs and FWD that should certainly be considered. TSD determines the pavement response under the maximum load, Raptor uses the measured distance between deflected and undeflected conditions of roads, and FWD measures the maximum deflection for different time histories of loading. Besides, FWD applies an impact load on a circular plate, and the TSDDs apply a dynamic load by single (in the case of Raptor) or dual (in the case of TSD) tire loadings. Another remark is concerning the symmetry of the deflection basin. Whereas the FWD deflection basin is symmetrical around the loading center, the deflection basin obtained from a moving device is not symmetrical, and the maximum deflection occurs behind the loading axle ( 34 ). As the measuring principles and loading mechanisms are different, they should not necessarily produce similar deflection values.

The TSD has been studied for more than 10 years, and now it can be incorporated into pavement management systems. On the other hand, Raptor represents a new technology, and conducting more research studies on Raptor is recommended by the authors. However, both TSD and Raptor seem to have the potential to distinguish between sections with different resilient responses. Finally, although the findings of this study verify that there is a correlation between TSDDs and FWD, the regression models developed here were based on a limited number of data points.

Limitations of the Study

There are several limitations in the current study. To obtain deflections from TSDDs, this study relies on models developed by the device manufacturers. Although the engagements with industry experts in the manufacturers’ companies suggest ongoing methodological refinements, the reliability of deflections provided by manufacturers is a valid concern. As another limitation, the structural indices discussed in this study need improvements, as they are unable to reflect the effect of moisture in the granular layers. With regard to the temperature correction factor of bearing capacity, it should be recognized that local conditions, such as soil type, moisture content, and temperature, can significantly influence deflection measurements and consequently, bearing capacity. The selected roads in this study were chosen to be most representative of the Norwegian climate, road and pavement structure, traffic loading and patterns, and geological conditions. This careful selection ensures that the developed relationships for deflections are highly relevant and accurate for the local context. However, it is essential to acknowledge that there are limitations when applying this methodology to other countries with different parameters. To generalize the findings of this study to other roads with different geographical locations, a more comprehensive study needs to be conducted. Another issue concerns the effect of pavement roughness on TSDD measurements. It is believed that pavement irregularities might affect data measured by TSDDs. The effect of highway geometry on TSDD measurements is another issue that needs to be elaborated in a separate study.

Future Perspective

Although this study provides pretty accurate comparisons of deflection measurement between different deflection devices, the treatment selection algorithms for pavement maintenance have much lower levels of sensitivity to variations in the input data than direct correlations. Future research could focus on predicting the maintenance regimes for the same section of roads using the results from the three devices. In this regard, the NPRA has employed the Raptor for the entire national road network of Norway. There are also FWD data for most of the national road network. These data, collected over several years, are processed, and are usable now in an internal GIS-based template called ‘Baereevne_raadata_Dashboard’ (dashboard for bearing capacity data). Among a variety of possibilities in this dashboard such as checking the bearing capacity data determined by Raptor, one can assess the condition of the roads using the calculated surface curvature index, base curvature index, and the available classifications in the Norwegian road manuals. The GIS-dashboard also enables the detection and determination of road stretches classified as “weak” (with low bearing capacity values, shown in red), facilitating the planning of appropriate treatments. The dashboard is available for the internal use only, but data can be found in the National Road Data Bank (NVDB) or via vegkart.no.

To find a generalized formula for correlating TSDDs and FWD, a more comprehensive research study considering different variables (including different pavement structures, weather conditions, soil types, vehicle speeds, etc.) should be conducted. Developing new analysis methods for TSDDs independent of FWD, defining new structural parameters reflecting the structural integrity of pavements, calibration, and validation of these new indices, proposing new protocols for data collection, and more in-depth research on temperature correction procedures of TSDDs are some other research topics that can be pursued in future studies.

Footnotes

Acknowledgements

The authors thank Stine Skov Madsen, Martin Wiström, and Søren Rasmussen from Ramböll (Malmö Office), and Marshall Arokia, Nikolaj Ravn, and Karsten Jensen from Greenwood Engineering (Copenhagen Head Office) for their sincere help in organizing technical meetings about TSDDs.

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: A. Hamidi, A. F. Mirhosseini, K. R. B. Grannes, P. O. Aursand; data collection: A. F. Mirhosseini, K. R. B. Grannes, P. O. Aursand; analysis and interpretation of results: A. Hamidi, A. F. Mirhosseini, I. Hoff, H. Mork; draft manuscript preparation: A. Hamidi, I. Hoff, H. Mork, A. F. Mirhosseini. 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: This research was funded by the Norwegian University of Science and Technology (NTNU) and the Norwegian Public Roads Administration (NPRA).

ORCID iDs

Ali Foroutan Mirhosseini

Inge Hoff

Data Accessibility Statement

Data utilized in this study are confidential and cannot be shared. The programming code can be provided on request.

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Comparative Evaluation of Falling Weight Deflectometer,Traffic Speed Deflectometer and Rapid Pavement Tester in Deflection Measurement

Abstract

Keywords

Traffic Speed Deflectometer

Rapid Pavement Tester

Literature Review

Importance of the Study

Research Objectives

Experimental Design

Method

Temperature Correction

Deflection Basin Indices and Structural Parameters

Bearing Capacity

Structural Factor

Results and Discussion

FWD Temperature-dependent Deflection Curves

Repeatability of TSDDs

Comparing Deflection Values

Comparing Deflection Indices

Correcting Bearing Capacity Values

Temperature Correction Factor Based on the FWD

Temperature Correction Factor Based on the Raptor

Summary and Conclusions

Limitations of the Study

Future Perspective

Footnotes

Acknowledgements

Author Contributions

Declaration of Conflicting Interests

Funding

ORCID iDs

Data Accessibility Statement

References