The compaction of asphalt mixture is crucial to the mechanical properties and the maintenance of the pavement. However, the mix design, which based on the compaction properties, remains largely on empirical data. We found diculties to relate the aggregate size distribution and the asphalt binder properties to the compaction behavior in both the eld and laboratory com- paction of asphalt mixtures. In this paper, we would like to propose a simple hybrid model to predict the compaction of asphalt mixtures. In this model, we divided the compaction process into two mechanisms: (i) visco-plastic deformation of an ordered thickly-coated granular assembly, and (ii) the transition from an ordered system to a disordered system due to particle rearrangement. This model could take into account both the viscous prop- erties of the asphalt binder and grain size distributions of the aggregates. Additionally, we suggest to use discrete element method to understand the particle rearrangement during the compaction process. This model is cali- brated based on the SuperPave gyratory compaction tests in the pavement lab. In the end, we compared the model results to experimental data to show that this model prediction had a good agreement with the experiments, thus, had great potentials to be implemented to improve the design of asphalt mix- tures. Keywords: Hot mixed asphalt, Compaction, Discrete element method, Hybrid model Preprint submitted to Construction and Building Materials July 19, 2019 1. Introduction 1 Hot mixed asphalt is ubiquitous in pavement industry. The mechanical 2 properties and durability of asphalt mixtures are largely in uenced by the 3 porosity. High porosity usually leads to low strength and high permeability 4 of the moisture [1, 2], while low porosity may result in high temperature 5 sensibility [3, 4]. Thus, we should maintain a reasonable porosity after the 6 compaction process. 7 In the construction eld, we use roller compactorS to compact the asphalt 8 mixtures. During the compaction process, the material is subjected to both 9 normal pressure and shear stress. In the laboratory, to represent the similar 10 volume properties of the eld compaction, a variety of laboratory compaction 11 methods have been developed, among which the SuperPave gyratory com- 12 pactor (SGC) plays an important role in studying the compaction behavior 13 and mechanical properties of asphalt mixtures [5]. In this study, we use 14 the Brovold SuperPave gyratory compactor for the experimental part. The 15 compactor has one cylindrical ring, one top plate to provide gyratory mo- 16 tion, and one bottom plate (pushed by the loading system) to o er constant 17 pressure (Fig. 1 and 2). Usually, the asphalt mixtures will be compacted 18 with a gyratory speed of 30 rpm (or n= 0:5 rps) and a pressure of 600 kPa. 19 The gyratory angle is 1.25(or= (1:25=180)). We could calculate the 20 average shear rate during compaction as _ = 2n0:07. 21 Figure 1: Sketch of the Brovold SuperPave gyratory compactor. Experimentally, Consuegra et al. [6] compared di erent laboratory com- 22 2 pactors to the eld compaction and gave each compactor evaluations based on 23 their ability to produce mixtures with engineering properties similar to those 24 produced in the eld, which concluded that the gyratory compactor behaved 25 relatively better than other compaction methods. Also, Hunter et al. [7] 26 analyzed the in uence of compaction mode on the mechanical performance 27 of asphalt mixtures. They concluded that both gyratory and vibratory com- 28 paction might produce sti er specimens than the mixtures compacted in the 29 eld. To design asphalt mixture using laboratory compactor, Blankenship 30 et al. [8] proposed a rational method for laboratory compaction of hot-mix 31 asphalt. However, even the laboratory compaction process tends to be a 32 random process, and the compaction behavior is governed by a number of 33 factors, such as binder content, binder type, temperature, loading method, 34 aggregates' grain size distributions, aggregate shapes, etc.. Stakston et al. 35 [9] investigated the in uence of the angularity of ne aggregates on the com- 36 paction behavior of asphalt mixtures, which indicated that a higher ne ag- 37 gregate angularity may lead to higher resistance to compaction. Delgadillo 38 and Bahia [10], however, analyzed the in uence of both temperature and 39 pressure on the behavior of both laboratory and eld compaction, and found 40 that the compaction was not reduced dramatically when the temperature 41 was reduced from 125C to 75C. 42 Figure 2: Sketch of the compaction process using Brovold SuperPave gyratory compactor. While most of the research of the compaction behavior focused on the qualitative analysis of the factors which may in uence the gyratory com- paction behavior, few research focused on the quantitative investigation of 3 the compaction behavior. Awed et al. [11] proposed a method for predicting the laboratory compaction behavior of asphalt mixtures, which provided us a phenomenological tool for predicting the laboratory compaction. They linked the air void ratio to parameters, such as gradation scale parameter, gradation shape parameter, and asphalt content, and their model also converged to a logarithmic law shown in the following equation [11]. AV=a[ln(NG)] + b (1) whereAVis the air void ratio, and NGis the number of gyrations, and a 43 andbare parameters empirically determined by material parameters. 44 Theoretically, the asphalt mixtures, when in high temperature, can be seen as granular materials (aggregates) with interstitial viscous uid (as- phalt binder) [12]. Thus, the compaction of asphalt mixtures can follow the research of the compaction of granular materials. In the past decades, physicists were interested in the general compaction or relaxation of mono- dispersed or bi-dispersed granular materials [13]. Although the compaction behavior of mono- or bi- dispersed granular materials may di er from the be- havior of the compaction of asphalt mixtures, the underlying physics should be similar and transferable. The microscopic analyses of granular materi- als during compaction induced by tapping or vabrating have been studied [13, 14]. The relationship between collective microscopic structure and the compaction dynamics has been explained [15, 16]. Several equations or mod- els for describing the compaction behavior were proposed based on multiple- time-scale assumption [17, 14, 18]. Among these models, Knight et al. [14] proposed a logarithmic equation to better t the compaction behavior of mono-dispersed granular materials. (t) = f 1 1 +Bln (1 +t= )(2) where (t) is the volume fraction of granular materials at time t, fis the 45 nal volume fraction when time goes to in nity,  1= f 0is the 46 di erence between fand the initial volume fraction 0,B, and are tting 47 parameters. This form was motivated by, as stated in Ref. [14, 19], the 48 observation of large time intervals of logarithmically slow relaxation in the 49 time evolution of density of the compacted granular materials. 50 In this paper, we are going to link the compaction of granular materials 51 to the compaction behavior of the asphalt mixtures, at the same time, con- 52 sider the visco-plastic deformation induced by air voids, viscosity of asphalt 53 4 binder, and wide grain size distribution. To simplify the analysis of this 54 paper, we consider the asphalt mixture as a mixture of coarse aggregates 55 (aggregate with size >2:36 mm) and ne aggregate mixtures (FAM, mix- 56 ture of asphalt binder and ne aggregates). In this study, we will divide the 57 deformation of asphalt mixture during compaction into two parts: (i) the de- 58 formation caused by the viscous behavior of FAM, and (ii) the deformation 59 induced the the particle rearrangement. We will organize this paper in the 60 following way. First, after the introduction, we are going to introduce the 61 model framework for prediction the compaction behavior of asphalt mixtures. 62 Then, we will calibrate this model with several experiments obtained in the 63 laboratory. Then, the model will be validated by comparing the modeling 64 results with other experimental results. 65 2. Model Description 66 Figure 3: Two parts of the deformation during the compaction of asphalt mixtures: (1) viscous deformation; (2) particle rearrangement. The motivation of this paper is to understand the compaction behavior 67 of asphalt mixtures from the viewpoint of granular materials. However, as a 68 granular materials, asphalt mixtures are far too complicated because of the 69 complex aggregate shapes and wide range of particle sizes. To tackle such 70 problem, certain simpli cation is necessary. 71 As what we have stated, we divided the asphalt mixture into two parts, 72 one is coarse aggregates (aggregates larger than 2.36 mm), and the 73 5 other one is ne aggregate matrix (mixture of asphalt binder and ne 74 aggregate ( <2:36 mm)); 75 We consider the coarse aggregates as spherical particles with mate- 76 rial properties same as the real aggregates. The median size of coarse 77 aggregates is denoted as dc 50; 78 Then, we may regard the ne aggregate matrix as the thick coatings 79 on the surface of coarse aggregates. 80 Meanwhile, the FAM itself is a granular- uid system with average par- 81 ticle size same as the median particle size of the ne aggregates, df 50. 82 The constitutive relationship of the FAM follows the same rule as the 83 rheology proposed by Trulsson et al. in Ref [20]. 84 Firstly, one part of the deformation during the compaction processes comes from the deformation of FAM coatings when two coarse aggregates approach each other. Secondly, as the asphalt mixture approaches random loose packing, the particles would also like to rearrange themselves to form a more stable packing. Then the e ect of particle rearrangement will gradually play an important role as the compaction proceed. As we can see from Fig. 3, during the compaction process, we have two types of deformation. Usu- ally at the beginning of the compaction, the FAM serves as coatings of the coarse aggregate, which prevent two adjacent particles from coming toward each other, which brings the viscous deformation of the whole mixture. On the other hand, when the solid fraction of aggregate packing become larger and larger, the particle rearrangement starts to play important roles. The particle will oscillate during compaction, which may create free space for the other particles to move inside, which can help the whole mixture to form a denser state. Thus, we have the following equation: (t) = v(t) +  rp(t) (3) where (t) is the volume fraction of the asphalt mixture at time t, v(t) is 85 the volume fraction of the asphalt mixture due to viscous deformation at 86 timet, and  rp(t) is the change of volume fraction due to rearrangement 87 of particles at time t. Here we consider the e ect of particle rearrangement 88 as the increment on top of viscous deformations. 89 We should note that the behavior of the FAM follows the rheology of 90 granular- uid systems (or slurries) proposed by Trulsson et al in Ref. [20], 91 6 where the frictional rheology of a granular- uid system is governed by a 92 dimensionless number, K=Iv+ I2 c, andIc= _ d=p =pis called the 93 inertial number, and Iv=_ =is called the viscous number. Here, is the 94 normal stress and is the dynamic viscosity of the interstitial uid. In this 95 section, to build a reasonable model framework, we are going to discuss these 96 two compaction sources. 97 2.1. Visco-plastic deformation induced by the FAM 98 To calculate the visco-plastic deformation induced by the FAM, we sim- 99 plify the asphalt mixture to have a ordered crystal-like structure as it is shown 100 in Fig. 4. The forces acting on two adjacent aggregates can be calculated 101 based on the e ective viscosity and thickness of the FAM coatings. Because 102 we use crystal-like structure to simplify the asphalt mixture, the problem be- 103 come one-dimensional. The fundamental element of the crystal-like structure 104 is shown in Fig. 5. 105 Figure 4: Simpli cation of the viscous deformation induced by the FAM coatings on the surface of coarse aggregates. We show that the deformation can be calculated using a computational cell shown in Fig. 5. The problem becomes solving the motion of particle j under pressure = 600 kPa and Shear rate _ = 0:07. The acting loading on the particle jis introduced by the compaction pressure. We have two parts of resistance forces: (1) squeeze-induced lubrication force, and (2) shear- 7 induced resistance forces. Thus, we can obtain the following equations: md2x dt2=1 4(dc 50)2n e _  GfR2 e  6t e R2 e G2 f h0xdx dt(4a) Gf= 1h 1 +2VL Re (h0x)2i0:5 (4b) wherexis the displacement of the particle j,n e andt e are the normal and 106 tangential e ective viscosities of the FAM, VL= 83 cis the e ective volume of 107 FAM between two coarse aggregates, cis the thickness of the FAM coating, 108 which can be calculated based on the volume ratio between coarse aggregates 109 and the FAM, Gfis the e ective coecient calculated based on the e ective 110 volume of FAM, Re = (1=Ri+ 1=Rj)1is the e ective radius of adjacent 111 particles (Here, Ri=Rj= 0:5dc 50). In Fig. 5, H(t) is the distance between 112 centers of two particles at time t, andH0=H(t) is the initial value of H.h(t) 113 is the distance between the surfaces of two particles at time t, andh0=h(0) 114 is the initial value of h. 115 Figure 5: Computational cell for calculating the change of volume fraction due to the viscous deformation of the FAM coatings, based on which we can form the di erential equation for calculating the motion of particles so that we could also calculate the volume fraction versus time. We have stated that the constitutive relationship of the FAM coating follows the rheology of granular- uid systems proposed in Ref. [20, 12, 21]. 8 Thus, we could rst calculate the frictional rheology (e ective frictional coe- cient,e , and solid fraction, FAM) of the FAM with the following equations. K=Iv+ I2 c (5a) e =1+21 1 +K0=p K(5b) FAM= m 1 + kp K(5c) where, according to [12, 21], 0:03,1= 0:265,2= 2:2,K0= 0:5, m= 0:605, k= 0:8 are tting parameters. We can then calculate the normal and tangential e ective viscosities accordingly [21]. t e  _ =1 26 _  p( _ d)2+b_  ( m s)2:52(6a) n e n _ =s e (6b) wherebis the dynamics viscosity of the asphalt binder at compaction tem- 116 perature, 0:03 according to Ref. [12], 1= 0:265,2= 2:2, andK0= 0:5 117 are tting parameters. 118 Figure 6: Comparison of the volume fraction / gyration number relationship as we change the thickness of FAM coating. Based on the rheology of granular- uid systems proposed by Trulsson 119 et al. [20], we could apply the calculated normal and tangential e ective 120 viscosities to the ordinary di erential equation in Eqn. 4a, and solve it using 121 9 MATLAB internal function ode45s() . After calculation we can obtain the 122 relationship between the displacement xand timet, then we could convert 123 the displacement to volume fraction of asphalt mixtures and convert the 124 time to gyration numbers ( vp= vp(N)). To test the results of the ODE, we 125 chose three di erent coating thickness (three di erent mass ratio between the 126 FAM and coarse aggregates). Fig. 6 shows the relationship between volume 127 fraction of the ordered asphalt mixtures, , and the number of gyrations, 128 N. It shows that, as we increase the amount of the FAM (which lead to the 129 increase of FAM coating thickness), the compaction volume fraction can be 130 improved accordingly. 131 2.2. Rearrangement of aggregates 132 In the previous section, we could see that, based on the viso-plastic de- 133 formation of the FAM coating, the volume fraction of the asphalt mixture 134 could not even reach 90%, this lead us to the next step: to consider the 135 rearrangement of the particles. We approach the problem theoretically with 136 several simpli cations in the previous section, but to deal with the particle 137 rearrangement, we have no theoretical tools in hand. Thus, we use discrete 138 element method (DEM) to simulate the gyratory compaction behavior of 139 granular materials with interstitial uid. However, the asphalt mixtures has 140 wide range of particle sizes, and it is time-consuming to model every parti- 141 cle size in a mixture. Thus, certain assumptions have to be made: (1) The 142 eciency of particle rearrangement is only governed by the loading condi- 143 tions (pressure, shear rate, etc.) and particle size distribution; (2) during the 144 compaction process of asphalt mixtures, unlike bi-dispersed surface granu- 145 lar ows, no segregation occurs, which is consistent with the experimental 146 observation of the experiments [22]; (3) The overall particle rearrangement 147 e ect of di erent sizes can be summed up based on the mixture theory; (4) 148 The compaction of each size group of particles is governed by the mean size 149 of this size group. 150 Based on these assumptions, we can use discrete element method (DEM) to simulate the gyratory compaction of a monodispersed granular- uid sys- tem in a SuperPave gyratory compactor con guration shown in Fig. 1. We compacted the granular materials with particle diameters = (2 0:4) mm us- ing constant pressure of 600 kPa, gyratory speed of 30 rpm, gyratory angle of 1.25, and the viscosity of the interstitial uid is set to be equal to 250 cP. To simplify the analyses, we neglected the e ect of interstitial uid on the parti- cle rearrangement. All the dimensional parameters will be normalized using 10 Figure 7: Relationship between the solid fraction of particle rearrangement and the di- mensionless time, t average particle radius,  rp, mass of average-size particles,  m= (4=3)r3 pp, and gravitational acceleration, g. Thus, the compaction time, tcan be non- dimensionalized as ttp g=rp, wheretis the dimensionless time. In Fig. 7, we plotted the relationship between dimensionless time, t, and the change of solid fraction of granular materials during the compaction. Here, the change of solid fraction can be seen as the e ect of particle rearrangement. The compaction curve in Fig. 7 can be tted with the following equation:  i rp(t) = 0:0520:052 1 + 0:17 ln (1 +t )(7) where  i rp(t) is the change of volume fraction for a compaction of particles 151 with certain average grain size, tis the dimensionless time. This tting 152 curve is based on Eq. 2. 153 The above tting curve can only be used to quantify a monodisperse granular assembly. To obtain the total e ect of particle rearrangement of the whole grain size distribution, we have be implement mixture theory. We divide the aggregates into di erent size groups based on the sieving test. Each size group of aggregates is bounded by adjacent sieve sizes ( diand di+1), and the mean size of each size group is calculated by di=p didi+1 and ri p= 0:5di. On one hand, based on the mean size of each size group, we can calculate the compaction behavior of each size group,  i rp(t), where 11 tis a function of particle size. On the other hand, we can also obtain the mass ratio of each size group based on the sieving test, i. Then, we obtain the total particle rearrangement e ect based on the grain size distribution of aggregates.  rp(t) = Ns i=1 i i rp(t) (8) whereNsis the number of aggregate size groups in the sieving test. 154 2.3. Redistribution of particle rearrangement 155 In previous sections, we analyzed the contributions of both viscous de- 156 formation and particle rearrangement to the overall compaction process. In 157 this process, we treated the viscous contribution as the foundation of the 158 change of solid fraction, and regarded the particle rearrangement e ect as 159 the increment. However, due to the existence of the viscous e ect, the par- 160 ticle rearrangement may not happen in the same way as we have calculated, 161 thus, the two part of contributions cannot be added together directly. In this 162 section, we proposed a redistribution function of particle rearrangement to 163 reshape the the curve of  rp(t). 164 The basic idea is that at the beginning of the compaction, due to the huge e ect of viscous deformation stated in the previous section, the e ect of particle rearrangement is smaller that what we had in the DEM simulations. Thus, we would like to decrease the in uence of particle rearrangement at the beginning of the compaction, but enhance the in uence of that toward the end of the compaction. We proposed the following equation to capture the redistribution of the particle rearrangement. rp(N) = 0:5 +1 1 + rp=N(9) where rpis the balancing point, which depend on the grain size distribu- tion, andNis the gyration number. Once we know the viscosity of asphalt binder at the compaction temperature and the grain size distribution of the aggregate, the relationship between rpand the grain size distribution is the only parameter we need to calibrate. In the end, if we combine the contri- butions from both the viscous deformation and the particle rearrangement, we can obtain the following relationship between volume fraction of asphalt mixtures, vf, and the compaction time, t, to describe the whole gyratory compaction process of asphalt mixtures: vf(t) = vp(t) +rp(N(t)) rp(t) (10) 12 3. Model Calibration 165 The model we proposed require the information of the viscosity of asphalt 166 binder, and the sieving analysis results of the aggregates, based on which we 167 could obtain both the viscous deformation and the particle rearrangement 168 e ect during the compaction process of the asphalt mixtures. However, since 169 we also need to redistribute the particle rearrangement e ect, the parameter, 170 rp, needs to be calibrated using experimental study. In this section, we are 171 going to provide such experimental results to obtain a reasonable value of 172 this parameter. 173 3.1. Materials and experimental work 174 In this study, the main point is to capture the in uence of aggregate grain 175 size distributions, thus we prepared seven sets of compaction experiments 176 with di erent grain size distribution to calibrate the redistribution of the 177 particle rearrangement e ect. In these experiments, we use the same type of 178 asphalt binder (PG64-22). No additives were added to the asphalt binder. 179 As what we have stated, in the analysis of viscous deformation, we treat the 180 asphalt binder as a Newtonian uid with viscosity measured at 135C and 20 181 rpm. We measured the viscosity at such temperature and rotational speed 182 using a rotational viscometer, and obtained that the viscosity of asphalt 183 binder is approximately 250 cP. 184 Figure 8: Grain size distribution of aggregates. 13 We acquired the aggregate from two sources: river sand and quarry grav- 185 els. We show the size distribution of the seven sets of aggregates in Fig. 8. 186 Four sets of aggregate has maximum diameter of 12.5 mm, while three sets of 187 aggregate has maximum diameter of 25 mm. During the experiment, we rst 188 put all the materials into the oven, which set to be at 140C. After remaining 189 in the oven for one hour, the materials were transferred to the mixer to be 190 mixed for 180 seconds. To compact the asphalt mixtures in a laboratory, 191 we used Brovold SuperPave gyratory compactor (Fig. 1). This experimen- 192 tal apparatus can compaction the asphalt mixtures at constant pressure and 193 constant shear rate. Following the standard compaction testing procedure 194 [23], we set the compaction pressure at 600 kPa, gyratory angle at 1.25, and 195 gyratory speed at 30 rpm. 196 The height of the mixture was measured after each gyration. In order to 197 calculate the volume fraction of the asphalt mixture at each gyration number 198 based on the position of the bottom plate of the compactor, we also need 199 to measure both the the theoretical maximum speci c gravity, Gmm, and 200 the bulk speci c gravity of the mix, Gmb, which were conducted based on 201 ASTM D2041 and ASTM D2726 [24, 25]. Based on the recorded position 202 of the bottom plate, and the measured GmmandGmb, the volume fraction 203 ( mix= 1 air, where mixwas the volume fraction of the compacted asphalt 204 mixture, and airwas the air void ratio of the compacted asphalt mixture) can 205 be calculated in the software attached to the SuperPave gyratory compactor. 206 The relationship between mixand the gyration number can be obtained 207 accordingly. 208 3.2. Experimental results and model calibration 209 The markers with di erent colors in Fig. 8 show the experimental results 210 with di erent grain size distributions. It shows that the compaction behav- 211 ior can be greatly in uenced by the grain size distribution of aggregates. 212 By comparing the experimental results with the characteristic parameters of 213 the grain size distributions (mass ratio between ne aggregates and coarse 214 aggregates, median aggregate sizes, etc.), we could conclude that more ne 215 aggregates and smaller median aggregate size could result in better com- 216 paction results. 217 As what we have stated, we would like to nd the relationship between the 218 balancing point, rp, and the grain size distrbution for the model calibration. 219 Thus, we rst obtained the best t (with a speci c rp) for each experimental 220 results, plotted as solid curves with di erent colors (Fig. 9). Then, we plotted 221 14 Figure 9: Comparison between experimental results and the results obtained from the proposed hybrid model the tted balance point, rp, against the median aggregate size (radius), 222 r50(Fig. 10). We found that the relationship between rpandd50can be 223 described usingn the following parabolic equation: 224 Figure 10: The relationship between rpand median radius r50 Thus, we have associated each part of the compaction contribution to the 225 properties of asphalt binder and the grain size distributions. The calibrated 226 model could be used to predict the gyratory compaction behavior of asphalt 227 mixtures in the future. 228 15 Table 1: Mix design of the model validation experiments Sieve size 3N30 3N50 3N100 (mm) (%) (%) (%) 12.5 100 100 100 9.5 94.1 94.7 95.3 6.3 71.5 72.2 72.9 4.75 60.5 61.3 62.0 2.36 42.4 38.2 34.0 1.18 29.2 24.9 20.4 0.60 19.7 16.4 12.8 0.30 11.5 9.9 7.6 0.15 6.1 5.7 4.2 0.075 4.6 4.3 3.0 r50(mm) 1.41 1.54 1.68 rp 27.6 26.3 24.4 4. Model validation and discussions 229 This model can be validated with a set of di erent compaction experi- 230 ments (3N30, 3N50, 3N100). The maximum aggregates size of this set of 231 experiments is 12.5 mm. The overall size distributions is shown in Table 232 1. It shows that three di erent compaction tests have di erent grain size 233 distributions, di erent percentage of ne aggregate mixtures, di erent me- 234 dian radius, and di erent balance point of the particle rearrangement. Based 235 on the material information, we could implement the model we introduced 236 in previous sections. The model can be validated if the model prediction 237 matches the experimental results. 238 In Fig. 11, we showed both the experimental results (markers) and the 239 model predictions (lines). Generally, the prediction has great agreement 240 with the experimental results, which indicates that this simple model could 241 roughly capture the compaction behavior of hot mixed asphalt. 242 Besides, this model could help us with the understanding of the com- 243 paction mechanism of asphalt mixtures. Previously, we would regard the 244 compaction deformation of asphalt mixtures as the result of the squeeze of 245 16 Figure 11: Results of model validations air voids in porous media, thus simulate the process using the porous me- 246 dia mechanical models. In our model, we reverse the thinking and, instead 247 of investigating the deformation brought by the change of air voids, we put 248 priority on the solid- uid mixture itself. 249 This model con rms the importance of the grain size distribution of ag- 250 gregates on the compaction results. With this model, we could nd that 251 increasing the mass of ne aggregate matrix could help improve the com- 252 paction eciency by in uencing the visco-plastic deformations during com- 253 paction process. Also, a reasonable grain size distribution could also bene t 254 the particle rearrangement e ect. Meanwhile, we should acknowledge that 255 such model is still relatively preliminary, thus need more experimental data 256 to calibrate and validate. 257 5. Conclusions 258 This paper provides a simple hybrid model for predicting the compaction 259 behavior of asphalt mixture in a SuperPave gyratory compactor. Di erent 260 from previous phenomelogical model where the compaction curves were tted 261 using di erent forms of equations and continuum models considering the com- 262 paction as the deformation of air voids, the author divided the compaction 263 deformation into two parts: (1) viscous deformation due to the existence of 264 asphalt binder; (2) particle rearrangement due to the compaction excitation. 265 17 The viscous deformation can be solved numerically based on a theoretical dif- 266 ferential equation, while the particle rearrangement e ect can be quanti ed 267 based on DEM simulation of monodisperse granular materials and mixture 268 theory. Based on experimental results, this model can be calibrated and 269 further validated. 270 Although being preliminary, this method did bring a relatively functional 271 tool for predicting the gyratory compaction process of asphalt mixtures. 272 With this model, we could calculate the compaction deformation based on 273 the mix design of asphalt mixtures, which could be both time-saving and 274 economical for the pavement industry. Furthermore, such model has poten- 275 tials to be improved with more experimental data so that it can be applied 276 to predict the eld compaction of asphalt mixtures. 277 6. Acknowledgement 278 The author of this paper would like to acknowledge the help from Prof. 279 Kimberly Hill and Prof. Jia-Liang Le for the discussions about the model 280 framework. The author would also thank the Saint Anthony Fall Laboratory 281 at UMN for the computing resources provided. 282