Establishment of Rutting Model of Wheel-Tracking Test for Real-Time Prediction of Rut Depth of Asphalt Layers

The construction process control of asphalt layers directly affects the road service life and quality. The objective of this study was to establish a rutting model of the wheel-tracking test used for the real-time prediction of the rut depth of asphalt layers in the construction process. The gradation of asphalt mixture, asphalt content, and molding temperature were considered in the development of the new rutting model of the wheel-tracking test. The effects of these three factors on the high-temperature performance of asphalt mixture were analyzed. The order of importance of the factors affecting the high-temperature performance of asphalt mixture is the gradation of asphalt mixture, asphalt-aggregate ratio, and molding temperature. Overall, the predicted values of the rut depth of the wheel-tracking test are very close to the measured values. Furthermore, the difference between the rut depths of asphalt layers of the test group and the control group is small. These comparison results indicate that the new rutting model of the wheel-tracking test has high accuracy and good applicability for the test road.


Introduction
Rutting is one of the main early distresses in asphalt pavements, which not only significantly reduces the service quality and service life of the road but also poses a serious threat to the driving of the vehicle [1][2][3]. rough investigation, it was found that bad construction quality of the asphalt layer is one of the main reasons for the early distresses in asphalt pavement [4,5]. e construction indices are commonly used to control the construction quality of the asphalt layer [6,7], such as asphalt-aggregate ratio, gradation of asphalt mixture, and rolling temperature. However, the development of rutting is not given in the construction process of the asphalt layer, which is not conducive to reducing the early distresses in asphalt pavements. Furthermore, when the construction factors affecting the asphalt pavement performance are in an unfavourable situation, although they meet the requirements of the construction specification, the asphalt pavement performance may not meet the expected requirements. Consequently, in the construction process of the asphalt layer, it is important to predict the rut depth of asphalt pavement in real time to control the construction quality of the asphalt layer.
A variety of rutting models have been established to estimate the development of the rut depth of asphalt pavement. e resilient strain of the asphalt layer, the number of load repetitions, and the temperature were used to predict the asphalt pavement rutting in the MEPDG design method [8]. e distinguishing feature of this model was the consideration of the mechanical response of the pavement structure and the asphalt mixture performance. e format of the NCHRP 1-40B rutting model [9] is the same as that of the MEPDG rutting model. e difference between these two models is that the material properties and volumetric properties of the asphalt mixture are adopted to adjust the permanent deformation constants for the NCHRP 1-40B rutting model. e NCHRP 9-25 rutting model is based on the material properties, voids in the mineral aggregate, and compaction parameters to estimate the rutting rate [10]. Le et al. [11] proposed a rutting model for South Korean Pavement Design Guide, and the model variables are the number of loadings, temperature, and initial air voids. e rutting model proposed by Kim et al. [12] is based on the number of loads, the loading time, temperature, and the ratio of shear stress to shear strength. In China, the JTG D50-2017 rutting model is used to verify the alternative pavement structure in the design phase of road projects [13]. e model variables mainly include the permanent deformation equivalent temperature of the asphalt layer, the rut depth of the wheel-tracking test, and the number of load repetitions. Wang et al. [14] established a rutting model for the Asphalt Pavement Analyzer rutting test. e variables mainly include temperature, loading time, loading level, and air void.
To predict the rut depth of asphalt pavement in real time during construction, an accurate rutting model needs to be selected. When determining the rutting model, two principles should be considered: (1) the rutting model should have high accuracy for road construction projects; (2) the model variables can be detected or predicted in the construction process of the asphalt layer. e accuracy of the rutting models is best compared by the long-term follow-up monitoring of the actual road rut, but there are currently no corresponding complete test data. Each rutting model is based on a certain foundation, which is inseparable from the materials, pavement design, and construction methods of the corresponding countries. erefore, the applicability of the foreign rutting model in China needs further verification. In China, the pavement structure is designed according to JTG D50-2017 [13]. Its design requirements can be used for construction process control. Furthermore, the JTG D50-2017 rutting model [13] had been verified by the actual road projects of China. erefore, the JTG D50-2017 rutting model [13] was selected for real-time prediction of the permanent deformation of asphalt layers. e JTG D50-2017 rutting model [13] needs to input the permanent deformation of the wheel-tracking test. is model variable cannot be detected in real time during the actual construction of the asphalt layer. It is necessary to estimate the rut depth of the wheel-tracking test according to the real-time detection data of the asphalt layer. erefore, the model for rut depth of the wheel-tracking test should be proposed as the submodel of the JTG D50-2017 rutting model [13].
According to the NCHRP 704 report [15] and the findings by Rahman [16], the main factors affecting the hightemperature performance of asphalt pavement are the gradation of asphalt mixture, the properties of the asphalt, the effective asphalt content, the air voids, and the thicknesses of the asphalt layers. In the asphalt mixture plant, the gradation of the asphalt mixture can be predicted in real time by the digital image processing technology [17][18][19][20] or online detection [6,7]. e asphalt-aggregate ratio can be detected in real time by the online detection of the asphalt mixture plant [6]. e ground-penetrating radar can be used to estimate the air voids and the thicknesses of the asphalt layers in real time [21][22][23][24]. Based on the air voids and the related information of aggregates, the effective asphalt content can be calculated [6].
is paper aims to propose a rutting model of the wheeltracking test for monitoring the construction quality of the asphalt layer in real time. e model variables can be determined in real time during the construction of the asphalt layer. e wheel-tracking test was conducted according to T 0719-2011 of JTG E20-2011 [25]. e rutting model of the wheeltracking test was verified by road test results. e JTG D50-2017 rutting model [13] was used to predict the rutting development of the pavement structure. Furthermore, the effect of the deviation of the rutting model of the wheel-tracking test on the rut depth of pavement structure was analyzed.

Experimental Program
2.1. Raw Materials. Two types of asphalt mixtures, AC-13 and SUP-20, were used for the wheel-tracking test.

Asphalt Binder.
e SBS-modified asphalt (Ι-C) was selected for AC-13. Its properties are shown in Table 1. e requirements for the material properties of asphalt were according to JTG F40-2004 [6]. e tests shown in Table 1 were conducted based on JTG E20-2011 [25]. Table 2 presents the properties of asphalt for SUP-20, which was SBS-modified asphalt with the performance grade of PG 76-22.

Mineral Aggregate.
e sizes of the aggregates used for AC-13 were 0∼2.36 mm, 2.36∼4.75 mm, 4.75∼9.5 mm, and 9.5∼13.2 mm. e properties of these aggregates are shown in Table 3. e tests shown in Table 3 are carried out in accordance with JTG E42-2005 [31]. Five different sizes of aggregates were used for SUP-20, which were 0∼2.36 mm, 2.36∼4.75 mm, 4.75∼9.5 mm, 9.5∼13.2 mm, and 13.2∼19 mm. Table 4 lists the properties of the aggregates for SUP-20. e mineral powder is limestone flour. According to JTG F40-2004 [6], the mineral powder for the asphalt mixture must be ground from hydrophobic stone such as limestone or strong basic rock in magmatic rock, and the soil impurities in the original stone should be removed.

Design of Mix Proportion.
e designed gradations of AC-13 and SUP-20 are shown in Figure 1. For AC-13 and SUP-20, the optimum asphalt-aggregate ratios (OARs), which were 5.0% and 4.5%, were determined based on the Marshall design method and Superpave design method, respectively. e molding temperature of specimens was 160°C, which was related to the initial rolling temperature. e design results for the asphalt mixtures of AC-13 and SUP-20 are shown in Table 5. According to the location of the road construction project, the design results met the technical requirements of JTG F40-2004 [6] and AASHTO M 323 [35], respectively.

Variability Design of Construction Control Indices.
According to the requirements of construction specifications of asphalt pavements [6,7], the influencing factors of     [34] Advances in Civil Engineering the construction quality of asphalt layers mainly include raw material quality, mineral gradation, asphalt content, construction temperature, rolling passes, degree of compaction, thickness of the asphalt layer, and evenness. By analyzing these factors, it can be found that, for the construction process of the asphalt layer, the main factors affecting the construction quality can be essentially summarized as mineral gradation, asphalt content, rolling temperature, rolling passes, and thickness of the compacted asphalt layer. With the widespread use of Global Positioning System-Real-Time Kinematic (GPS-RTK) technology, the number of rolling passes is well controlled [36]. RTK is a real-time dynamic relative positioning technology using GPS carrier phase observations; the working principle of RTK is that the base station transmits its observations and station coordinate information to the mobile station through the data link. erefore, the main considered factors of construction quality were mineral gradation, asphalt content, and rolling temperature in this study, which can be determined in real time. In the asphalt mixture plant, the allowable fluctuation ranges of mineral gradation for the AC-13 and SUP-20 are shown in Figures 1(a) and 1(b), respectively [6,37]. e asphalt content should be controlled at the range of design value ±0.3% [6]. In this research, the degree of fluctuation in the molding temperature was designed to be ±15°C. e aggregate segregation and temperature differential can occur in the production, transportation, and paving processes of asphalt mixture. Previous studies have shown that aggregate segregation and temperature differential have adverse effects on the asphalt pavement performance [38][39][40][41][42]. erefore, the influence of segregation on the hightemperature performance of asphalt mixture was considered for establishing a more suitable rutting model of the wheeltracking test. In the actual construction process, aggregate segregation is very complex. In this study, the degree of segregation aggregate is mainly characterized by the percent passing of 2.36 mm sieve, which is the key sieve. e contained aggregates in the asphalt mixture are divided into two parts by the 2.36 mm sieve. Part 1 was composed of particles passing through the 2.36 mm sieve. e particles retained on the 2.36 mm sieve composed part 2. e following method was used to simulate the aggregate segregation of asphalt mixture: increasing (decreasing) the mass of each size of particles of P1 part in equal proportion and decreasing (increasing) the mass of each size of particles of P2 part correspondingly. Four different levels of aggregate segregation for AC-13 were designed in this study, which are shown in Figure 2. For the temperature differential, the set molding temperatures were 145°C and 130°C. e air voids of asphalt mixtures with different degrees of segregation were determined by the means of the Superpave gyratory  Advances in Civil Engineering compactor, and the effect of nonsegregation area on the segregation area was considered in this study [43]. Further information related to the determination of air voids can be found in [43]. e test conditions of different groups of asphalt mixtures are shown in Table 6.

Specimen Preparation and Testing Procedures.
e specimen preparation was conducted according to T 0703-2011 of JTG E20-2011 [25]. e size of the slab specimen for the wheel-tracking test is 300 mm (long) × 300 mm (wide) × 50 mm (height). First, the mesh mold was put into an oven at a temperature of 100°C for one hour. en, the mesh mold was taken out of the oven. A plain paper was laid in the mesh mold. Next, the asphalt mixture was mixed again by a spatula. e asphalt mixture was placed evenly in the mesh mold from side to center, and the middle part of the paved asphalt mixture was slightly higher than the surrounding area.
e frame was removed, and a preheated compact hammer was used to tamp the paved asphalt mixture from the edge to the middle, as shown in Figure 3. When the asphalt mixture reached the molding temperature, a plain paper was placed on the surface of the asphalt mixture. en, the mesh mold containing the asphalt mixture was put on the platform of the roller compactor. e total load used for compaction was adjusted to 9 kN. In general, the set air voids can be achieved by 24 passes according to the T 0703-2011 of JTG E20-2011 [25].
e wheel-tracking test was required by the JTG D50-2017 rutting model of the asphalt pavement, which was performed in accordance with T 0719-2011 of JTG E20-2011 [25], as shown in Figure 4. e test temperature was 60°C, and the wheel pressure was 0.7 MPa. e slab specimen together with the mesh mold was placed in an incubator with a temperature of 60 ± 1°C for 5 hours.
en, the slab specimen together with the mesh mold was placed on the test platform of the rutting test machine. e wheel reciprocates over the specimen with a travel distance of 230 ± 10 mm. e frequency of the wheel ranges from 42 ± 1 passes per minute across the specimen. e rutting test machine was started to make the test wheel travel back and forth. e rut depth was collected by the rut deformation automatic recorder.

JTG D50-2017 Rutting Model of Asphalt Pavement.
According to JTG D50-2017 [13], the rut depth of asphalt layers can be predicted using the following equations: where R a is the rut depth of the asphalt layers (mm); R ai is the rut depth of sublayer i (mm); n is the number of sublayers; T pef is the equivalent temperature for the permanent deformation of the asphalt layer (°C); N e3 is the number of equivalent load repetitions on the design lane; h i is the thickness of sublayer i (mm); h 0 is the thickness of the slab specimen for the wheel-tracking test (mm); R 0i is the permanent deformation of wheel-tracking test for the asphalt mixture of sublayer i when the number of wheel passes is 2520 (mm); k Ri is the comprehensive correction coefficient; z i is the depth of sublayer i (mm); h a is the total asphalt layers thickness (mm); p i is the vertical compressive stress of the top surface of sublayer i (MPa). Table 7 presents the results of the wheel-tracking test.

Effect of Gradation on Rut Depth of Wheel-Tracking
Test. Based on Tables 6 and 7, the influence of gradation level on rut depth of wheel-tracking test is shown in Figure 5. For the design gradation of AC-13, the rut depth is 2.603 mm, which is the average value of the rut depths of groups 10∼18. From Figure 5, it can be observed that, for the set gradation levels, the rut depth increases as the gradation level changes from the upper limit of fluctuation through the design gradation to the lower limit of fluctuation. is is because the asphalt content is at a high level for the three gradation levels. When the gradation level changes from fine gradation to coarse gradation, the specific surface area of the mineral material decreases. erefore, the free asphalt increases, which leads to the increase of the rut depth. Furthermore, when the gradation changes from the design level to the lower limit of the gradation fluctuation, the asphalt mixture becomes difficult to be compacted, causing a decrease in the high-temperature performance of the asphalt mixture.    Figure 6 presents the relationship between the asphalt content and the rut depth of the wheeltracking test according to Tables 6 and 7. For 4.8% of the asphalt content of AC-13, the rut depth is 2.771 mm, which is the average value of the rut depths of groups 4, 5, 6, 13, 14, 15, 22, 23, and 24. For the set asphalt content, the curve of the rut depth is relatively flat when the asphalt content ranges from 4.5% (4.0%) to 4.8% (4.3%). e rut depth of the wheel-tracking test increases as the asphalt content increases from 4.8% (4.3%) to 5.0% (4.6%). As the asphalt content increases, the free asphalt in the asphalt mixture increases, which leads to a decrease in the hightemperature stability of the asphalt mixture.

Effect of Molding Temperature on Rut Depth of Wheel-
Tracking Test. Figure 7 shows the effect of molding temperature on the rut depth of the wheel-tracking test on the basis of Tables 6 and 7 Figure 7: Variation in rut depth with molding temperature. 8 Advances in Civil Engineering wheel-tracking test decreases. is is mainly because the asphalt consistency is reduced, the asphalt film thickness increases, and the mixture becomes easy to be compacted. However, the rut depth of the wheel-tracking test increases as the molding temperature ranges from 160°C to 175°C. is can be attributed to the decrease of air voids, the decrease of the asphalt film thickness, and the increase of free asphalt.
On the other hand, the importance of each factor can be evaluated according to Figures 5-7. For the given factor levels, the order of factors is gradation, asphalt content, and molding temperature in accordance with the influence degree of factors from strong to weak.

Rutting Model of Wheel-Tracking Test.
According to NCHRP 704 report [15] and Rahman et al. [44], the main factors affecting the permanent deformation of the asphalt layer are cumulative percent retained on the 3/4 inch, 3/8 inch, no. 4 standard sieves, percent passing of no. 200 standard sieves, the properties of asphalt, effective asphalt content, air voids, effective binder content, and the thickness of the asphalt layer. For the properties of asphalt, Rahman et al. [44] mainly used two viscosity-temperature susceptibility parameters A and VTS to predict the rutting depth of the Hamburg Wheel-Tracking Device test. In this study, the established rutting model of the wheel-tracking test will be used to evaluate the high-temperature performance of the asphalt layer in real time. Unfortunately, the properties of asphalt and the thickness of the asphalt layer are not easy to be detected in real time.
e air voids of the asphalt layer can be estimated according to the findings by Zhao [43] or measured by the intelligent roller [45]. en, the effective binder content can be calculated based on JTG F40-2004 [6]. e gradation of asphalt mixture can be in real time obtained from the asphalt mixture plant. is paper mainly considers the effects of gradation, effective asphalt content, and air voids on the permanent deformation of the asphalt mixture. e data used to establish the rutting model of the wheel-tracking test are shown in Table 8.
According to the above analysis of the factors affecting the asphalt pavement rutting, a new rutting model of the wheel-tracking test was established based on the data shown in Table 8 (2) Based on Table 8, the estimated values of the rut depth of wheel-tracking test are shown in Figure 8, compared with the measured values. Different from the previous rut prediction model of the wheel-tracking test [44], this model can predict the rut depth of the compacted asphalt mixture in real time.

Verification of Rutting Model of Wheel-Tracking Test.
After the rutting model of the wheel-tracking test is established, it needs to be verified based on road construction projects. Figure 9 and Table 9 present the gradations and asphalt contents of the asphalt mixture sampled from a highway construction project in Jiangsu province of China by the extraction tests (ETs), respectively. e asphalt mixture was prepared according to the results of the ETs. e molding temperature is shown in Table 10, which is measured by the infrared temperature sensors. Based on the air voids of the asphalt mixture determined by the Superpave gyratory compactor, the slab specimens were molded, and the rut depths of these specimens were obtained using the wheel-tracking test. For the extraction test groups, the predicted and measured values of the rut depth of the wheeltracking test are shown in Figure 10.
e applicability of the rutting model of the wheeltracking test was evaluated by using the deviation between the estimated and the measured values of each extraction test group. According to Figure 10, the average deviation between the predicted and the measured values of rut depths of the extraction groups is 6.62%. e maximum deviation of these extraction test groups is 19.19%. Except for the 8th extraction group, the absolute values of the deviations of the other extraction groups were less than 14%. Overall, the deviation between the predicted and measured values of the rut depths of these extraction test groups is relatively small, indicating that the rutting model of the wheel-tracking test established in this study has good applicability for the test road.

Effect of Deviation of Rutting Model of Wheel-Tracking Test on Prediction Accuracy of JTG D50-2017 Rutting Model of Asphalt Layers.
e influence of the difference between the estimated and measured values of rut depths of wheeltracking test on the rut depths of asphalt layers predicted by the JTG D50-2017 rutting model [13] was investigated in this study.

Asphalt Pavement Structure and Traffic Parameters.
e pavement structure was mainly determined based on the design data of the highway construction project and JTG D50-2017 [13], which is shown in Figure 11. e traffic volume of large passenger cars and trucks on the highway section was set at 4,750 vehicles per day, with an annual growth rate of 5%. e design life of this highway was 15 years. According to the recommended value of JTG D50-2017 [13], the directional distribution factor was set to 0.55, and the lane distribution factor was set to 0.78. e vehicle class distribution factors were determined according to truck traffic classification (TTC) 1 of JTG D50-2017 [13], as shown in Table 11.

Advances in Civil Engineering
According to JTG D50-2017 [13], the proportion of not fully loaded and fully loaded vehicles of each type is shown in Table 12; the conversion factor of equivalent single axle loads is shown in Table 13. e cumulative equivalent single axle loads can be calculated by [13] where N 1 is the average daily equivalent single axle loads of the design lane; AADTT is the annual average daily truck and largesize passenger bus traffic (vehicle/d); DDF is the directional distribution factor; LDF is the lane distribution factor; m is the vehicle class number; VCDF m is the distribution factor of vehicle class m; EALF m is the conversion factor of equivalent single axle loads of vehicle class m; N e is the cumulative equivalent single axle loads of the design lane in the design service life; t is the design service life of pavement (year); c is the annual average growth rate of traffic in the design service life. e influence of the temperature condition at the location of the road project was considered by the JTG D50-2017 rutting model of the asphalt layers [13]. For the city of Nanjing and pavement structure, the equivalent temperature for the permanent deformation of the asphalt layer was 25.0°C, that is, T pef � 25.0°C. According to JTG D50-2017 [13], the asphalt mixture layers shown in Figure 11 were layered, and the thicknesses of these sublayers were 10 mm, 15 mm, 15 mm, 20 mm, 20 mm, 20 mm, and 80 mm. e vertical compressive   stress at the top of each sublayer was calculated using the elastic layer system theory. e load parameters and calculation point positions [13] are shown in Figure 12. By calculation, the rutting of the asphalt layer is 14.9 mm for the design service life, which meets the design requirement of JTG D50-2017 (≤15.0 mm) [13]. e development of rutting with the service life is shown in Figure 13.

Rutting Prediction Results of Asphalt
Layers. e cylinder specimens used for the dynamic modulus test were molded according to the air voids of the asphalt mixtures for each extraction test group. e dynamic modulus test was conducted according to T 0738-2011 of JTG E20-2011 [25], and the test conditions were 20°C and 10 Hz. For each extraction test group, the results of the dynamic modulus test are shown in Figure 14. According to the JTG D50-2017 rutting model of the asphalt layers [13], the rutting prediction results of asphalt layers are shown in Figure 15. In this paper, the predicted rut depths of asphalt layers using the measured rut depths of wheel-tracking test are classified as the control group. e rest, which are based on the predicted rut depths of wheel-tracking test, are classified as the test group.         14 Advances in Civil Engineering From Figure 15, the average deviation of the rut depths of the asphalt layers between the control group and the test group is 3.34%. For the extraction test groups 1∼10, the largest deviation is 9.52%. Furthermore, the absolute values of the deviations for these extraction test groups are all less than 10%. e results indicated that the influence of the deviation between the predicted and measured values of rut depths of wheel-tracking test on the rutting prediction results of JTG D50-2017 is small.

Conclusions
In this study, a new rutting model of the wheel-tracking test was proposed as the submodel of the JTG D50-2017 rutting model of the asphalt layers, which can be used to monitor the construction quality of the asphalt layer in real time. e gradation, asphalt-aggregate ratio, and molding temperature were considered as the factors affecting the permanent deformation of the wheel-tracking test. e new rutting model of the wheel-tracking test was verified based on a road construction project. Furthermore, the effect of using the estimated value of rut depth of wheel-tracking test instead of the measured values was analyzed in this study. Based on the results and analysis, the following conclusions can be drawn: (1) For the given factor levels, the permanent deformation of the asphalt mixture increases as the gradation level changes from the upper limit of fluctuation through the design gradation to the lower limit of fluctuation. In the asphalt mixture plant, the coarser gradation of asphalt mixture has an adverse influence on the high-temperature of the asphalt mixture if the asphalt content is at a high level. (2) For the given factor levels, increasing the asphalt content overall leads to the increase of the permanent deformation of the asphalt mixture. ere is a suitable molding temperature to obtain better hightemperature performance of asphalt mixture, which is near the designed molding temperature. (3) For the given factor levels, the influence degree of the three factors on the permanent deformation of the asphalt mixture is in such an order: gradation, asphalt content, and molding temperature. (4) Based on the results of the extraction test, the deviation between the predicted and measured values of rut depth of wheel-tracking test is small, which indicates that the new rutting model of the wheeltracking test has good applicability for SUP20. (5) e deviation between the rut depths of asphalt layers of the test group and the control group is small, which also indicates that the new rutting model of the wheel-tracking test has good prediction accuracy for SUP20.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.