Experimental and Numerical Analysis on Mesoscale Mechanical Behavior of Coarse Aggregates in the Asphalt Mixture during Gyratory Compaction

: Compaction is a critical step in asphalt pavement construction. The objective of this study is to analyze the mesoscale mechanical behaviors of coarse aggregates in asphalt mixtures during gyratory compaction through experiments and numerical simulation using the Discrete Element Method (DEM). A novel granular sensor (SmartRock) was embedded in an asphalt mixture specimen to collect compaction response data, including acceleration, stress, rotation angle and temperature. Moreover, the irregularly shaped coarse aggregates were regenerated in the DEM model, and numerical simulations were conducted to analyze the evolution of aggregate interaction characteristics. The ﬁndings are as follows: (1) the measured contact stress between particles changes periodically during gyratory compaction, and the amplitude of stress tends to be stable with the increase of compaction cycles; (2) the contact stress of particles is inﬂuenced by the shape of aggregates: ﬂat-shaped particles are subjected to greater stress than angular, fractured or elongated particles; (3) the proportion of strong contacts among particles is high in the initial gyratory compaction stage, then decreases as the number of gyratory compactions grows, the contacts among particles tending to homogenize; (4) during initial gyratory compactions, the normal contact forces form a vertical distribution due to the aggregates’ gravity accumulation. The isotropic distribution of contact forces increases locally in the loading direction along the axis with a calibrated internal angle orientation (1.25 ◦ ) in the earlier cyclic loading stage, then the local strong contacts decrease in the later stage, while the strength of the force chains in other directions increase. The anisotropy of aggregate contact force networks tends to weaken. In other words, kneading and shearing action during gyratory compaction have a positive impact on the homogenization and isotropy of asphalt mixture contact forces.


Introduction
Gyratory compaction is one of the main preferred methods to mold asphalt mixtures. With vertical pressure and horizontal shear simultaneously applied to the specimen, gyratory compaction can simulate the wheel kneading action during the asphalt pavement construction stage and the open traffic stage. Research has shown that the features of samples formed by gyratory compaction are closest to those of on-site core samples, and aggregate cracking can be alleviated during gyratory compaction [1][2][3]. Led by the National Highway Cooperative Research Program (NCHRP), the Superpave Gyratory Compactor to their functions: a data module, a communication module and a power module. The data are collected and stored instantly in the data module, including global time, temperature, stress, Euler angles under quaternion or geodetic coordinates, and acceleration. The shell of the sensor can be made in a specified shape. The sensor used in this study was filled in a cube shell 23 × 23 × 23 mm in size, as shown in Figure 1a, of which material strength and the bonding performance with the asphalt mixture are similar to the actual aggregate of the mixture. The test data were transmitted to a portable receiver (Figure 1b) using Bluetooth Low Energy technology in the communication and power module and can be displayed and recorded in real time. As the working temperature of the sensor should be within 120 • C, a thermal insulation layer (Figure 1c) is wrapped around the particle shell. Therefore, the sensor, embedded in hot mix asphalt mixture, can work normally under high temperatures over 120 • C during compaction.

SmartRock
SmartRock is a small-size sensor developed for monitoring granular forces, deformation, stability, etc., of railway ballasted bed [31] and highway pavements. With the particle level size, all of the above studies have been extended from macroscale to mesoscale and have achieved meaningful results. The sensor system consists of three modules according to their functions: a data module, a communication module and a power module. The data are collected and stored instantly in the data module, including global time, temperature, stress, Euler angles under quaternion or geodetic coordinates, and acceleration. The shell of the sensor can be made in a specified shape. The sensor used in this study was filled in a cube shell 23 × 23 × 23 mm in size, as shown in Figure 1a, of which material strength and the bonding performance with the asphalt mixture are similar to the actual aggregate of the mixture. The test data were transmitted to a portable receiver (Figure 1b) using Bluetooth Low Energy technology in the communication and power module and can be displayed and recorded in real time. As the working temperature of the sensor should be within 120 °C, a thermal insulation layer (Figure 1c) is wrapped around the particle shell. Therefore, the sensor, embedded in hot mix asphalt mixture, can work normally under high temperatures over 120 °C during compaction. The pressure measuring principle of SmartRock is to test and convert voltage to stress value. During compaction, the compressed sensitive film in SmartRock generates a slight deformation and a change in the resistance value of the strain gauge. Furthermore, the stress on the particle can be determined based on the voltage value, and the stress value can be determined by Equation (1): where f (kPa) is the stress value; U (V) is the voltage signal recorded; U0 is the basic voltage signal before compaction; T (°C) is the temperature; A (m 2 ) is the area of the strain gauge; a, b and c are calculation coefficients. Three sensors (R1, R2, R3) were employed in this study and the calculation parameters of each sensor are listed in Table 1.  The pressure measuring principle of SmartRock is to test and convert voltage to stress value. During compaction, the compressed sensitive film in SmartRock generates a slight deformation and a change in the resistance value of the strain gauge. Furthermore, the stress on the particle can be determined based on the voltage value, and the stress value can be determined by Equation (1): where f (kPa) is the stress value; U (V) is the voltage signal recorded; U 0 is the basic voltage signal before compaction; T ( • C) is the temperature; A (m 2 ) is the area of the strain gauge; a, b and c are calculation coefficients. Three sensors (R1, R2, R3) were employed in this study and the calculation parameters of each sensor are listed in Table 1.

Preparation of SGC Testing Materials and Equipment
In order to reduce the influence of SmartRock's size on the compactability of the asphalt mixture, AC-20C mixture (the maximum particle size is close to the SmartRock's   According to the inspection results listed in Table 2 through to Table 4, all materials meet the requirements of the Technical Specification for Highway Asphalt Pavement Construction (JTG F40-2004) [32]. The gradation curve of the AC-20C mixture is shown in Figure 2.  The gradation of the AC-20C mixture is listed in Table 5, and the optim content is 4.2%. The volumetric and mechanical characteristics of the mixture in Table 6, and both meet the specification requirements.  The gradation of the AC-20C mixture is listed in Table 5, and the optimal asphalt content is 4.2%. The volumetric and mechanical characteristics of the mixture are shown in Table 6, and both meet the specification requirements. The Superpave gyratory compactor manufactured by the PINE instrument company was adopted in this test, as shown in Figure 3a

Layout and Application of SmartRocks
Several indoor experiments with SmartRock were carried out to investig paction response characteristics from a mesoscale perspective. The applicati tRocks in gyratory compaction is illustrated as follows.
Each testing specimen weighed 4.8 kg. The mixing temperature of the a

Layout and Application of SmartRocks
Several indoor experiments with SmartRock were carried out to investigate the compaction response characteristics from a mesoscale perspective. The application of SmartRocks in gyratory compaction is illustrated as follows.
Each testing specimen weighed 4.8 kg. The mixing temperature of the asphalt mixtures was set to 180 • C, and the compaction temperature ranged from 160-170 • C. To distinguish the possible impact on the compaction process caused by the SmartRock's embedded locations, three groups of tests were carried out with SmartRock up-located (Test 1), midlocated (Test 2), and bottom-located (Test 3) in the sample, respectively (see Figure 4a). After compaction and testing, the sensor was taken out at a high temperature from the demolding specimen (as shown in Figure 4b).

Layout and Application of SmartRocks
Several indoor experiments with SmartRock were carried out to investigate the compaction response characteristics from a mesoscale perspective. The application of Smar-tRocks in gyratory compaction is illustrated as follows.
Each testing specimen weighed 4.8 kg. The mixing temperature of the asphalt mixtures was set to 180 °C, and the compaction temperature ranged from 160-170 °C. To distinguish the possible impact on the compaction process caused by the SmartRock's embedded locations, three groups of tests were carried out with SmartRock up-located (Test 1), mid-located (Test 2), and bottom-located (Test 3) in the sample, respectively (see Figure  4a). After compaction and testing, the sensor was taken out at a high temperature from the demolding specimen (as shown in Figure 4b).
(a) (b) During the test, the sampling frequency for stress, acceleration and rotation angle acquisition was set to 100 Hz. The quaternion could be transformed into an Euler angle, and all gathered signals should be filtered to reduce noise interference.

Model Construction with Irregularly Shaped Aggregates
Previous studies reported that particle shape had a significant impact on the simulation of asphalt mixture compaction behavior [33]. Therefore, Gong obtained point cloud During the test, the sampling frequency for stress, acceleration and rotation angle acquisition was set to 100 Hz. The quaternion could be transformed into an Euler angle, and all gathered signals should be filtered to reduce noise interference.

Model Construction with Irregularly Shaped Aggregates
Previous studies reported that particle shape had a significant impact on the simulation of asphalt mixture compaction behavior [33]. Therefore, Gong obtained point cloud data of particle profiles with 3D laser scanning [26] and divided the overall morphological characteristics of aggregates into five categories (rounded, fractured, angular, elongated and flat) according to ASTM D 4791 and 5821 [34,35]. Based on the statistical results, most particles were fractured and angular, and only a small number of particles were elongated and flat [33]. In this study, an open-source discrete element simulation program (YADE) was used to simulate the gyratory compaction process. Considering the particle morphology distribution characteristics [33], a reconstruction method for polyhedral particles based on Voronoi tessellation [36][37][38] was employed to set up a sample library for irregularly shaped particles. For each particle, the reconstruction method is illustrated as follows: 1.
In 3D space, seed nuclei with random coordinates are firstly arranged around the center nuclei C. The 3D space is divided into multiple polyhedrons by the vertical bisector of adjacent seed nuclei, and the polyhedron containing the center nuclei C is obtained as the basic particle shape. 2. Figure 5a shows the schematic diagram in 2D. Each particle shape is further adjusted to make the grading curve of the particle sample library satisfy the gradation requirement of the asphalt mixture. As shown in Figure 5b, spindle tension and rotation are mainly utilized to adjust particle size. The final particle shape for 3D simulation is shown in Figure 5c.

3.
After generating the polyhedrons, including three shape categories-angular particles, fractured/elongated particles and flat particles-each polyhedron is filled with densely arranged spheres to form a clump, as shown in Figure 6. In addition, asphalt binder and aggregates with sizes less than 3 mm are directly simulated by spherical particles.
1. In 3D space, seed nuclei with random coordinates are firstly arranged around the center nuclei C. The 3D space is divided into multiple polyhedrons by the vertical bisector of adjacent seed nuclei, and the polyhedron containing the center nuclei C is obtained as the basic particle shape. 2. Figure 5a shows the schematic diagram in 2D. Each particle shape is further adjusted to make the grading curve of the particle sample library satisfy the gradation requirement of the asphalt mixture. As shown in Figure 5b, spindle tension and rotation are mainly utilized to adjust particle size. The final particle shape for 3D simulation is shown in Figure 5c. 3. After generating the polyhedrons, including three shape categories-angular particles, fractured/elongated particles and flat particles-each polyhedron is filled with densely arranged spheres to form a clump, as shown in Figure 6. In addition, asphalt binder and aggregates with sizes less than 3 mm are directly simulated by spherical particles.
(a) (b) (c) Figure 5. Particle reconstruction based on Voronoi tessellation: (a) basic particle shape generation; (b) spindle tension and rotation for shape adjustment; (c) 3D particle shape for simulation.

Gyratory Compaction Process Simulation
For the DEM model, aggregates were randomly generated according to the method described in the previous section and initially stacked by gravity (see Figure 7a). Then, the top plate was fixed, while the mold was rotated around the central point of the top plate until the rotation angle reached 1.25 • . During gyratory compaction, the bottom plate was under a pressure of 600 kPa. The mold rotated around the central axis at a speed of 0.5 r/s, and the final compacted model is shown in Figure 7b. The process data for the bottom plate position and the aggregate movement were recorded. In addition, asphalt binder was considered to play a lubricating role with respect to fast movement and large displacement [39], so that the linear contact model was adopted to simulate the gyratory compaction behavior, with the meso-parameters listed in Table 7. The computer used for calculation was configured with a dual core CPU with model Intel Core I7-9700 and 3.1 GHz using the Ubuntu 16.04 operating system. The total simulation time lasted about 44 h. Particle reconstruction based on Voronoi tessellation: (a) basic particle shape generation; (b) spindle tension and rotation for shape adjustment; (c) 3D particle shape for simulation. Figure 6. Clump models.

Gyratory Compaction Process Simulation
For the DEM model, aggregates were randomly generated according to the method described in the previous section and initially stacked by gravity (see Figure 7a). Then, the top plate was fixed, while the mold was rotated around the central point of the top plate until the rotation angle reached 1.25°. During gyratory compaction, the bottom plate was under a pressure of 600 kPa. The mold rotated around the central axis at a speed of 0.5 r/s, and the final compacted model is shown in Figure 7b. The process data for the bottom plate position and the aggregate movement were recorded. In addition, asphalt binder was considered to play a lubricating role with respect to fast movement and large displacement [39], so that the linear contact model was adopted to simulate the gyratory compaction behavior, with the meso-parameters listed in Table 7. The computer used for calculation was configured with a dual core CPU with model Intel Core I7-9700 and 3.1 GHz using the Ubuntu 16.04 operating system. The total simulation time lasted about 44 h.

Specimen Height Change
The height change curves for compacted specimens from three tests were recorded and compared with the DEM simulation result, as shown in Figure 8. The compaction efficiency (height change) of the DEM model was greater than the test results in the several initial rotations (before 10 cycles). In addition, the reduction rate of specimen height in the DEM model became slower in the subsequent gyratory compaction stage. Unlike Burger's contact model with a damping pot, the linear contact model used in this paper ignored

Specimen Height Change
The height change curves for compacted specimens from three tests were recorded and compared with the DEM simulation result, as shown in Figure 8. The compaction efficiency (height change) of the DEM model was greater than the test results in the several initial rotations (before 10 cycles). In addition, the reduction rate of specimen height in the DEM model became slower in the subsequent gyratory compaction stage. Unlike Burger's contact model with a damping pot, the linear contact model used in this paper ignored the viscosity of the asphalt binder, which might explain the height change rule distinction between the DEM simulation and the test results.

Specimen Height Change
The height change curves for compacted specimens from three tests w and compared with the DEM simulation result, as shown in Figure 8. Th efficiency (height change) of the DEM model was greater than the test results initial rotations (before 10 cycles). In addition, the reduction rate of specimen DEM model became slower in the subsequent gyratory compaction stage. Un contact model with a damping pot, the linear contact model used in this p the viscosity of the asphalt binder, which might explain the height change ru between the DEM simulation and the test results.  Figure 9 shows the contact stress results of particles measured by SmartRock at different locations in three testing groups. It can be seen that the measured stress changes periodically during gyratory compaction, and the stress amplitude tends to be stable asgyrations increase. The stress value range fluctuates from 350 kPa to 750 kPa. Each particle's contact stress is also tracked in the simulation model. The result indicates that the particles' contact stress evolution in the DEM model is similar to the test result. However, the particles' contact stress is discrete due to the particles' shapes. Figure 10 shows the particles' contact stress obtained in the simulation model; particles with three different shapes (angular, fractured/elongated and flat) are located in the middle layer of the specimen. As can be seen in Figure 10, the contact stress range for the angular particle (300 kPa~800 kPa) is close to that for the fractured/elongated particle (300 kPa~700 kPa).

Contact Stress of Aggregates
Nevertheless, the flat particles' contact stress (1200 kPa~1600 kPa) is significantly higher than the other particles'. Similarly, conclusions can be drawn for other particles with different shapes according to the simulation results. It can be inferred that the flat particles are easy to trap in stress concentration, resulting in their being crushed during gyratory compaction. Therefore, the proportion of flat particles in the mixture should be reduced as much as possible.
stress is also tracked in the simulation model. The result indicates that the particle stress evolution in the DEM model is similar to the test result. However, the parti tact stress is discrete due to the particles' shapes. Figure 10 shows the particles' cont obtained in the simulation model; particles with three different shapes (angu tured/elongated and flat) are located in the middle layer of the specimen. As can b Figure 10, the contact stress range for the angular particle (300 kPa~800 kPa) is clo for the fractured/elongated particle (300 kPa~700 kPa). Nevertheless, the flat parti tact stress (1200 kPa~1600 kPa) is significantly higher than the other particles'. S conclusions can be drawn for other particles with different shapes according to th tion results. It can be inferred that the flat particles are easy to trap in stress conce resulting in their being crushed during gyratory compaction. Therefore, the prop flat particles in the mixture should be reduced as much as possible.

Contact Force Network Characteristics
Previous studies have proved that the normal contact force inside granul plays a major role in bearing external loads [40]. In this paper, the average nor force <fn> is defined as the average value of the normal contact forces. In add and weak contacts among particles construct a contact force network to resist ex Strong contacts bear the major eccentric load, while almost all friction dissipati weak contacts [41]. In this paper, normal contact force less than the average no force is recorded as weak contact, with the converse holding for strong contact. Figure 11 shows the evolution of a normal contact force (force chain) net

Contact Force Network Characteristics
Previous studies have proved that the normal contact force inside granular materials plays a major role in bearing external loads [40]. In this paper, the average normal contact force <f n > is defined as the average value of the normal contact forces. In addition, strong and weak contacts among particles construct a contact force network to resist external loads. Strong contacts bear the major eccentric load, while almost all friction dissipation occurs at weak contacts [41]. In this paper, normal contact force less than the average normal contact force is recorded as weak contact, with the converse holding for strong contact. Figure 11 shows the evolution of a normal contact force (force chain) network under different compaction cycles (2, 50, 80 and 110 cycles). The distribution of normal contacts between particles becomes denser as the compaction cycle increases. Moreover, the strong contacts in the upper and middle parts of the specimen gradually increase in the compaction process. The proportions of strong contacts in the upper, middle and lower parts of the specimen vary from 21.9%, 18.3% and 19.1% to 27.8%, 20.1% and 20.5%, respectively. The maximum normal contact force of particles reaches 450 N in 110 cycle, which is located in the middle of the specimen. The probability distribution function (PDF) of contact force is often used to quantitatively study the non-uniformity of contact force networks [42]. The average normal contact force is normalized by the contact force fn in each normal direction, and the normalized f n /<f n > is obtained. The PDF of f n /<f n > under different compaction cycles (2 and 110 cycles) is shown in Figure 12. The strong contact proportion is high in the initial gyratory compaction stage. With the increase of cycles, the strong contact proportion decreases, and the contacts among particles tend to homogenize in the compaction process. The maximum normal contact force of particles reaches 450 N in 110 cycle, which is located in the middle of the specimen. The probability distribution function (PDF) of contact force is often used to quantitatively study the non-uniformity of contact force networks [42]. The average normal contact force is normalized by the contact force fn in each normal direction, and the normalized fn/<fn> is obtained. The PDF of fn/<fn> under different compaction cycles (2 and 110 cycles) is shown in Figure 12. The strong contact proportion is high in the initial gyratory compaction stage. With the increase of cycles, the strong contact proportion decreases, and the contacts among particles tend to homogenize in the compaction process.    The three-dimensional spherical histogram can be used to visually describe the spatial distribution of the normal contact force, in which each column bar (in each discrete direction) represents the normalized local average normal contact force f n / f 0 in this direction. The local average normal contact force f n is defined as the average value of the normal contact force falling in a solid angle interval. It should be noted that the term "local" is used to distinguish it from the average value <f n > ("global") of all contact forces. Besides <f n >, another global average value f 0 is introduced. f 0 equals the average of f n in all discrete directions. Therefore, <f n > is equal to f 0 for a uniformly distributed normal contact force direction. Moreover, for the isotropic normal contact force, the spherical histogram is an exact sphere with radius 1. The non-spherical histogram means the anisotropic distribution of normal contact force. Figure 13 shows the spatial distribution of the local average contact forces of the specimen under different numbers of gyrations (2, 50, 80 and 110 cycles). In the initial gyratory compaction (at two cycles), the normal contact forces form a close to vertical distribution, which is caused by the initial vertical gravity accumulation of the aggregates. In the process of gyratory compaction, the spherical histogram increases locally in the loading direction (along the axis with a calibrated internal angle of 1.25 • ), which means that strong contacts form and grow at 50 cycles. However, at 110 cycles, the local strong contacts along the axis with a calibrated internal angle of 1.25 • decrease. While the strength of the force chains in other directions increase, the anisotropy of the aggregates' contact force network tends to weaken. Combined with the previous PDF features, kneading and shearing action during gyratory compaction can have a positive effect on the homogenization and isotropy of asphalt mixture contact force. togram increases locally in the loading direction (along the axis with a calibrated interna angle of 1.25°), which means that strong contacts form and grow at 50 cycles. However, a 110 cycles, the local strong contacts along the axis with a calibrated internal angle of 1.25 decrease. While the strength of the force chains in other directions increase, the anisotropy of the aggregates' contact force network tends to weaken. Combined with the previou PDF features, kneading and shearing action during gyratory compaction can have a pos itive effect on the homogenization and isotropy of asphalt mixture contact force.

Conclusions
This study was carried out to analyze the mesoscale mechanical behaviors of coarse aggregates in asphalt mixtures during gyratory compaction. The particles' contact stress was obtained by a novel granular sensor (SmartRock), and the evolution of the normal contact network for aggregates was explored and developed in a DEM simulation model. The mechanistic results can be used to guide on-site compaction control and mix proportion design. In summary, the main findings are as follows: 1.
The measured contact stress among particles changes periodically during gyratory compaction, and the amplitude of stress tends to be stable with the increase of compaction cycles; 2.
Particles' contact stresses are discrete and influenced by the shapes of aggregates. Flat particles are subjected to greater stress than the angular and fractured/elongated particles during gyratory compaction; 3.
It can be inferred that flat particles are easy to trap in stress concentrations, resulting in their being crushed in gyratory compaction. Therefore, the proportion of particles with flat shapes in a mixture should be reduced as much as possible; 4.
According to the contact network simulated by DEM models, the proportion of strong contacts is high in the initial gyratory compaction stage and decreases with the increase of compaction cycles. The contacts among particles tend to homogenize in the compaction process.

5.
Given the gravity accumulation of the aggregates, the normal contact forces of samples form vertical distributions in the initial gyrations. Strong contacts form and grow up locally along the axis in 1.25 • orientation at earlier cyclic loading, then decrease in the later stage. The anisotropy of aggregate contact force networks tends to be weakened by kneading and shearing of the asphalt mixture.