Impact of aggregate packing on dynamic modulus of hot mix asphalt mixtures using three-dimensional discrete element method

Construction and Building Materials 26 (2012) 302–309

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Impact of aggregate packing on dynamic modulus of hot mix asphalt mixtures using three-dimensional discrete element method Huanan Yu, Shihui Shen ⇑ Washington State University, Pullman, WA 99164, United States

a r t i c l e

i n f o

Article history: Received 11 February 2011 Received in revised form 27 May 2011 Accepted 18 June 2011 Available online 16 July 2011 Keywords: Voids in mineral aggregate Volumetric property Aggregate gradation Discrete element modeling Packing Dynamic modulus

a b s t r a c t Aggregates are the major component of hot mix asphalt (HMA) mixtures. The properties of aggregates and the way of aggregate packing have important influence on the performance of HMA mixtures. Because the dynamic modulus is considered as the most important HMA property influencing the field fatigue and rutting performance of a flexible pavement and are used in the mechanistic-empirical pavement design guide for determining the stress–strain responses of the pavements, a study of the impact of aggregate packing on dynamic modulus will provide insight on the HMA mix design and the material performance evaluation. This paper studies the effect of aggregate size distribution and angularity distribution on dynamic modulus using a 3D discrete element method (DEM). Angular particles are generated using an image-based ball-clumping approach which requires significantly reduced number of balls and is capable of capturing the particle shape and angularity effect. These particles are assigned to the DEM dynamic modulus specimen based on the angularity distributions of the actual experimental specimen. A 3D DEM dynamic modulus model is thus established and calibrated using experimental data. This calibrated model is further used to evaluate how the different aggregate packing due to the change of the proportions of aggregate particles and the change of aggregate angularities can result in the change of dynamic modulus. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction Pavement design is now moving toward more mechanistic based design methodologies for the purpose of producing long lasting and high performance pavements in a cost-effective manner. The recent mechanistic-empirical pavement design guide (MEPDG), introduced by the NCHRP 1-37A project, is a product under such direction and is making progress in improving current design methods. Dynamic modulus (E⁄) is proposed by the MEPDG as an important material characterization property and a key input parameter which determines the stress and strain responses in hot mix asphalt (HMA) pavements, and correlates the time–temperature dependant properties of asphalt mixtures to field fatigue cracking and rutting performance [1]. Gabriel and Thompson [2] pointed out that dynamic modulus is the most important hot mix asphalt (HMA) property influencing the structural response of a flexible pavement. The dynamic modulus of asphalt mixtures is based upon the properties of individual constituents including asphalt and aggregates and the physicochemical interactions between the two. Particularly, because aggregates are the major component ⇑ Corresponding author. Tel.: +1 509 3357455; fax: +1 509 3357632. E-mail addresses: [email protected] (H. Yu), [email protected] (S. Shen). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.06.025

and occupy 85% by volume and 95% by weight in typical densegraded HMA mixtures [3], the properties of aggregates and the way they are packed play a significant role in determining the dynamic modulus of asphalt mixtures. However, the effect of aggregates on dynamic modulus is also less understood due to the complexity of the aggregate structure. The properties of aggregates (shape, angularity, surface texture) and the nature of aggregate packing as a whole can all influence dynamic modulus. Therefore, it is the objective of this paper to investigate how the specific packing characteristics of aggregates including gradations, aggregate shape and angularities are influencing the dynamic modulus. A comprehensive evaluation of the impact of aggregate packing on dynamic modulus will be beneficial for:  Developing or improving dynamic modulus prediction models to be used in the Level II and III MEPDG analysis for a better pavement performance prediction.  Helping the designer to realize cost-effective asphalt mixtures with maximized usage of local materials and optimized binder content through a balanced aggregate structure design.  Assisting with the pavement structural design by providing insight to optimizing the dynamic modulus based on local materials and specific loading and temperature conditions.

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2. Background There are mainly three approaches to determine dynamic modulus of an HMA mixture, by experimental testing [4], by empirical regression equations [5,6], or by combined experiments and numerical simulations [7,8]. Experimental testing is the most straightforward method which gives the dynamic modulus properties of a specific mixture over a wide temperature–frequency domain with reasonable accuracy. It is yet a costly and time-consuming method which cannot provide a full assessment of the effect of individual material properties on dynamic modulus. The availability of experimental equipments can also limit the possibility of obtaining direct dynamic modulus testing results. Existing regression equations [5,6] have related some material properties to the dynamic modulus. However, due to the limitation of the regression equations which have to be based on a large representative database, current prediction equations did not clarify how the aggregate packing can affect the dynamic modulus. They mainly focus on the impact from a few sieve sizes while not considering the shape and angularity impact, both of which have been found to play significant roles in achieving a stable aggregate structure [9]. Numerical simulations, when calibrated by experimental results, are found to be promising, especially for assessing the impact of individual properties on dynamic modulus. Buttlar and Roque [10] proposed that micromechanical models can be used to predict the viscoelastic properties of asphalt mixtures. Uddin [11] studied the creep compliance of asphalt mixtures considering both the viscoelastic properties of asphalt binder and the elastic properties of aggregates. Zhu and Nodes [12] studied 2-D normal force–displacement compliance relation based on an elastic or visco-elastic binder, and the effects of aggregate angularity is incorporated in the stress–strain relations. The results showed that a higher degree of aggregate angularity results in higher structural stiffness. Discrete element method is one type of numerical simulation method which allows the finite displacement and rotation of discrete particles, making it an excellent tool to simulate the complex micro interactions between aggregate particles within an asphalt mixture [8]. A number of studies have been conducted in the field of asphalt material using the DEM approach. Zeghal [13] presented the results of numerical simulations to characterize the resilient modulus of aggregate base/subbase materials. Lowery and Zeghal [14] applied the DEM approach to study the effects of particle stiffness on the resilient behavior of asphalt mixtures. The result indicated a linear increase of resilient modulus with the increase in particle stiffness. Li and Metcalf [15] proposed a two-step approach to predict the resilient modulus of HMA mixtures, in which the asphalt mixture is represented by a large spherical aggregate particle surrounded by a spherical shell of fine aggregate-filler-binder mixture. You and Buttlar [16] simulated the resilient modulus behavior under indirect tensile loading mode using X-ray tomography and two-dimensional DEM. Spherical balls are clumped together to represent the aggregate and asphalt components obtained from an X-ray image analysis. Chang [17] used the normal contact law to simulate the elastic moduli of granular material with anisotropic random packing structure. Huang et al. [9] applied an image based DEM approach to simulate the effect of particle size, shape, and angularity on the stability of railroad ballast. An aggregate library consisting of particles with specific angularity index (AI) and flat and elongated (F&E) ratio is generated for the simulation. Hossain [18] analyzed the angular ballast breakage behavior under cyclic loading. In this study, an assembly of ballast particles with irregular shapes was considered and the angularity of the particles was modeled in two dimensions by clumping two to nine circular particles together to form single

Fig. 1. Angularity of the particles model [18].

particles of twelve different sizes, as illustrated in Fig. 1. Contact normal stiffness (kn) of the disks was set to 5.10E9 N/m, and the contact shear stiffness (ks) was set to half of the contact normal stiffness because results are not affected significantly by different ratios of kn/ks. Matsushima and Saomoto [19] simulated the angularity of aggregates using clump of balls as shown in Fig. 2. The irregular shape of the sand was represented by a set of overlapping circles in 2-D analysis. Their procedures were validated using biaxial simulations and the result indicated higher shear strength for angular particles than circular particles. In summary, DEM is found to be an effective tool for evaluating the properties of a particulate media like asphalt mixtures and will be applied in this paper to identify the effect of aggregate packing on dynamic modulus. In particular, this paper will extend the 2-D analysis to 3-D analysis using clump of balls in PFC3D program to take into account the effect of aggregate shape and angularity on packing and dynamic modulus. 3. Experimental program An experimental program was developed to evaluate the effect of aggregate properties on dynamic modulus and validate and calibrate the DEM model. The dynamic modulus test was conducted according to AASHTO TP79-09 [20]. The specimens were compacted with a Superpave gyratory compactor into 150 mm in diameter and approximately 170 mm in height. Then specimens were cored from the center into 100 mm in diameter, and approximately 10 mm were sawed from each end of the test specimen. The bulk specific gravities and air void contents for each test specimen were measured before and after the specimen was cored and cut, prior to dynamic modulus testing. Testing was conducted at four temperatures (40, 70, 100 and 130 °F) and six frequencies (25, 10, 5, 1, 0.5, and 0.1 Hz.). Four mixtures were included in this testing program. As shown in Table 1, mix C-1 is the base mixture whose mix design has been conducted following the Superpave mix design specification [21] and the Washington State DOT mix design specification [22]. Based on mix C-1, mixes C-2, C-3, and C-4 were developed by varying gradations at three sieve sizes, 9.5 mm, 4.75 mm, and 2.36 mm, highlighted as bold values in Table 1. All four mixes used the same type of aggregates and asphalt binder, and the same asphalt content, 6.2%, which is the optimum asphalt content for mix C-1. For each mixture/gradation, two replicative specimens were prepared and tested for volumetric properties and dynamic modulus.

4. Numerical analysis This paper applies the Particle Flow Code in Three Dimensions (PFC3D) commercial DEM program from Itasca Consulting Group, Inc. [23] to conduct dynamic modulus simulation. PFC3D is classified as a discrete element code based on the definition in the review by Cundall and Hart [24]. Since it allows finite displacements and rotations of discrete bodies including complete detachment, and recognizes new contacts automatically as the calculation progress, PFC3D has been viewed as a simplified implementation of the DEM because of the restriction to rigid spherical particles. PFC3D uses balls to effectively represent the aggregates with physical

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Fig. 2. Use clump of balls to simulate angularity in two dimensions [19].

Table 1 Coarse-graded gradation information. ID

19 mm

12.5 mm

9.5 mm

4.75 mm

2.36 mm

1.18 mm

0.6 mm

0.3 mm

0.15 mm

0.075 mm

C-1 C-2 C-3 C-4

100 100 100 100

94 94 94 94

79 69 79 79

46 46 56 46

29 29 29 39

20 20 20 20

15 15 15 15

11 11 11 11

8 8 8 8

6.1 6.1 6.1 6.1

properties implemented. The aggregate-to-aggregate contacts and frictions are handled appropriately, and the contact force within the mixture and the air voids are measured easily and accurately. In addition, the DEM simulation in PFC3D can easily examine the detailed ball contacts inside the model while it is difficult to observe at field and lab. The accurate information of volume, angularity, shape and texture are needed in order to reconstruct 3-D model of an aggregate particle in the computer. The University of Illinois Aggregate Image Analyzer (UIAIA), an effective tool for obtaining morphological properties of aggregates [25], is used in this study for automated measurement of particle images. Tens of balls are clumped together in PFC3D to match the 3-D images of each particle obtained from the UIAIA. Appropriate model parameters, such as contact friction angles for different aggregate textures, are assigned so that the model can simulate experimental testing results, as a model calibration process. The details about generating particles and conducting DEM simulations are discussed below.

4.1. Particle generation Eighty aggregate particles from four sieve size groups (2.36– 4.75 mm, 4.75–9.5 mm, 9.5–12.5 mm, and 12.5–19 mm) (twenty particles per group) were randomly selected from the design gradation. These particles were scanned using UIAIA, and the aggregate angularity index (AI) and flat and elongated ratio were determined based on the approach described in Pan [26]. For each particle, three orthogonal views taken by the UIAIA were utilized to compute the volume and angularity information. As shown in Fig. 3, the three images in the x–y, y–z, and z–x planes corresponded to front view, side view and top view individually. Fig. 4 showed the 3-view pictures of representative aggregates of five different AI types. The three images from top to bottom in each column represented the front view, side view and top view of one particle individually. From left to right in Fig. 4, the angularities of the particles were increasing with the most angular particles on the right.

Fig. 3. Acquiring array subsets for images [26].

Fig. 5 showed the histogram of the AI distributions for the twenty randomly selected aggregate particles from each sieve size. This distribution was considered as a representative AI distribution of the overall aggregate blend, and was used later for determining the proportions of aggregate particles in the DEM model. One particle with an average AI of each AI group was used for the 3D PFC particle generation in PFC3D. As shown in Fig. 6, 11 to 16 different sizes of balls were clumped together to match the 3D angularity and shape of each representative aggregate particle shown in Fig. 4, and their 3D views were presented in Fig. 6a–e. These generated 3D PFC particles were further used in the DEM modeling to represent aggregates of a specific AI group. 4.2. Model parameters A three-dimensional E⁄ simulation model with 100 mm in diameter and 150 mm in height were generated which was the same size as experimental dynamic modulus testing specimen. Aggregate gradations followed the experimental gradations used in Table 1. It should be noted that in DEM simulation, complete consideration of fine particles is almost impossible which not only significantly enhance the computational time and cost, but also

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AI=375-450

AI=450-525

AI=525-600

AI=600-675

AI=Above 675

Fig. 4. Three-view pictures of five AI types.

100% 90% 80% 70%

Above 675

60%

600-675

50%

525-600

40%

450-525

30%

375-450

20% 10% 0%

12.5mm

9.5mm

4.75mm

2.38mm

Fig. 5. Histogram of the AI distributions for selected aggregates.

affect the system’s capability to reach equilibrium. It is practical and reasonable to assume for coarse-graded mixes that smaller particles mainly fill in the voids created by coarse aggregates and their contributions can be indirectly taken into account by applying appropriate contact models for the asphalt mastic consisting of fine aggregates and asphalt binders. Therefore, in this study, only coarse particles larger than 2.36 mm (retained on 2.36 mm sieve) were specifically studied for their direct contribution to dynamic modulus. As the first step, all particles were generated using spherical balls and their volumetric properties can be determined using Eq. (1). The readers are referred to the previous publication by Shen and Yu [27] for the detailed approach of obtaining the porosities of aggregate packing structures.

Pn fv i V ai p ¼ Pn i¼1 ð1 þ fv i ÞV ai i¼1

ð1Þ

where fvi is the fv value for ith sieve size of the gradation which can be getting from DEM simulation or experimental results regression. Vai is the percentage of aggregate retained in the ith sieve size, and p is the porosity or VMA of the aggregate structure. Then all spherical balls were replaced with the generated 3D particles, according to the AI proportions shown in Fig. 5. For example, statistical analysis showed that for the target aggregate

gradation with size 4.75–2.36 mm, 33.3% of the particles were in the AI group of above 675. 33.3% of the spherical balls in this size range were hence replaced with the 3D particles with AI above 675 and size between 4.75 and 2.36 mm. Similarly, all particles were replaced with the 3D angular particles and the coarse aggregate structure of the dynamic modulus specimen was built, as shown in Fig. 7. After calibration, the porosity (VMA) of the coarse aggregate structure with angular particles was found to be consistent with the spherical particle structure as discussed in Shen and Yu [27], which is 0.47. Liu and You [28] stated that it is very expensive and time-consuming for traditional image-based method to simulate aggregate shape and angularity in a varied condition, hence, other techniques such as randomly generated 3-D models [28] or by applying a virtual frequency which was based on the frequency–temperature superposition on the simulation samples [29] to reduce simulation time. One other promising technique is proposed in this study which clumps a few balls together to simulate aggregate shape and angularity in three dimensions. As can be seen from both Figs. 6 and 7, significantly reduced number of spherical balls is needed to generate representative angular aggregate particles as well as a 3D dynamic modulus specimen using the image-based ball clumping approach introduced in this study. Consequently, much faster simulation time can be achieved comparing to previous models which requires hundreds to thousands balls for simulating each aggregate particle. Depending on the model properties and gradations, the typical time for a 3D dynamic modulus specimen to reach equilibrium in this study varied from 20 to 60 h for a computer with Core 2 Duo 2.4 GHz CPU and 3 Gb of RAM. In order to describe tension forces between materials like asphalt mixtures, the PFC3D provided two bonding models, a contact-bond model and a parallel-bond model. Both bonds can be viewed as a kind of glue joining the two particles. The contact-bond acts at the contact pint which can only transmit a force, whereas the parallel-bond acts over a circular cross-section between the contacted particles which can transmit both force and moment. Different from contact bonds which are typically used to simulate the effect of adhesion acting over a small contact area, parallel bonds add the effect of additional binding material adjacent to the contact area between two contact particles [23]. Studies by You [8] and Abbas [30] on asphalt mixtures suggested

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(a) (c) (e)

(b) (d)

Fig. 6. Representative 3D particle models for each angularity index (AI) group. (a) AI group: 375–450; (b) AI group: 450–525; (c) AI group: 525–600; (d) AI group: 600–675; (e) AI group: above 675.

The parallel-bonding stiffness is defined by stiffness and strength parameters. The parallel-bonding normal stiffness parameter is activated in tension and compression, and the parallel bond shear stiffness parameter is activated in shear. Furthermore, the parallel-bonding contributes to resist rotation induced by moment. The contact breaks once the tensile or shear stresses exceed the respective strength defined by the parallel-bonding. The parallel-bonding stiffness has dimensions of stress per unit displacement. The equivalent stiffness, k0 , with dimensions of force per unit displacement is k0 = k(pb)A, where A is the cross-sectional area of the parallel-bond stiffness, and k(pb) is parallel bond stiffness [24]. To choose parallel-bond stiffness, we set the equivalent stiffness, k0 , equal to the existing calibrated contact stiffness so the contacts and parallel bonds will have the same stiffness. According to the findings by Shen and Yu [27], the calibrated contact stiffness kn is 30G N/m for this mixture. Based on the gradation, the mean particle radius in this model is 4.4 mm. If we set the radius multiplier of the parallel-bond material to 0.2, then the parallel-bond stiffness is

K pb ¼

0:5  30  109

pð0:2  4:4Þ2

 6:2  109



 N : m3

ð2Þ

Fig. 7. Dynamic modulus sample in PFC3D.

that the parallel-bonding model was sufficient in simulating the bonding characteristics of asphalt mastics under non-destructive repeated loading. It was thus used in this study for dynamic modulus property simulation.

Under the dynamic loading as used in this simulation, the asphalt mastic is acting as adhesive glue that holds the discrete aggregate together. The influence of temperature for viscoelastic asphalt material is represented by a combination change of radius multiplier of the parallel-bond and friction between aggregates.

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4.3. Loading and boundary conditions

E* (MPa) 6000

The loading platens are simulated by the top and bottom walls. The simulation involves two stages: compaction and testing. Compaction is the first and necessary stage of the simulation which ensures an initial isotropic stress state and an isotropic distribution of particles with desired porosity. During the compaction stage, the velocity of the walls is controlled automatically by a numerical ‘‘servo-control’’ mechanism (implemental via a FISH function). The ‘‘servo-control’’ algorithm is as follows:

u_ ðwÞ ¼ Gðrmeasure  rrequired Þ ¼ GDr

aA w kn N c Dt

ð4Þ

3000 2000

c-1 c-1-S

1000 0

0

5

10

15

20

25

Frequency (Hz) E* (MPa) 6000 5000 4000

ðwÞ

where a is a relaxation factor, A is the wall area, kn is the average stiffness of the contacts and Nc is the total number of contacts on the wall. The confining stress of 1 MPa can be maintained through this ‘‘servo-control’’ mechanism. During the stage of loading, the top and bottom platens are released from the ‘‘servo-control’’ and a specific velocity is applied on those walls. A time step of 1  104 s is applied during each simulation test, which means 10,000 steps are needed for one loading cycle at a frequency of 1 Hz. There are 10 loading cycles at one frequency for each test. The stress and strain are calculated by a FISH function. The stresses of those samples are computed by dividing the average reaction forces by appropriate areas. The strain in the axial direction is computed using the following equation:

L  L0 2¼ 1=2ðL0  LÞ

4000

ð3Þ

where G is the servo gain parameter for axial and lateral motion and can be determined using the following equation [23]:

G¼

5000

ð5Þ

where L is the current sample length and L0 is the original sample length. 5. Results discussion and analysis 5.1. Comparison between experimental dynamic modulus and DEM results Fig. 8 compares the DEM simulation results with the dynamic modulus testing data at 70 °F, in which the solid lines are testing results for four mixes (C-1 to C-4) and the dashed lines are the corresponding DEM simulation results. As we can see from the results, the DEM simulation reasonably simulated the trend of experimental dynamic modulus. However, almost all the DEM results under-predicts the experimental value. Possible reason for this phenomenon is due to the difference between the field aggregates and the DEM simulation particles. Though aggregate angularity properties are simulated by clumps of balls, the edge of field aggregate are quite angular with sharp corner while the edge of DEM simulation is round. The angular edge will provide stronger interlocking among aggregate skeleton compared to round edge which will result in slightly higher dynamic modulus. Another reason may be related to the accuracy of using parallelbonding contact model to capture the viscoelastic behavior of asphalt mastic at particle contact interface. From Fig. 8, we can see that the simulation result is more accurate at low frequencies compared to high frequencies. Under low frequencies (or high temperatures considering the time– temperature superposition properties of asphalt mixture), the stiffness of the asphalt binder is relatively soft and its contribution to the dynamic modulus of the mixture is less significant than

3000 2000

c-2 c-2-S

1000 0

0

5

10

15

20

25

Frequency (Hz) E* (MPa) 6000 5000 4000 3000 2000

c-3

1000

c-3-S 0

0

5

10

15

20

25

Frequency (Hz) E* (MPa) 6000 5000 4000 3000 2000

c-4

1000

c-4-S

0 0

5

10

15

20

25

Frequency (Hz) Fig. 8. Experimental result and DEM simulation result.

aggregates; the aggregate skeleton plays a major role in determining the dynamic modulus of the mix. In other words, the developed DEM model is effective in predicting the contribution of aggregate structure on dynamic modulus. However, when the effect of asphalt binder and mastics is becoming more important at higher frequencies or lower temperatures, some errors can be introduced due to the contact model selection. A better model that can better describe the visocoelastic properties of asphalt materials is now studied by the authors and will be published in a later paper. 5.2. Impact of particles sizes and proportions on dynamic modulus The effect of different particle sizes and proportions on dynamic modulus was further evaluated in this study. As shown in Fig. 9 for

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H. Yu, S. Shen / Construction and Building Materials 26 (2012) 302–309

E*(MPa),log 6000

300 0

c-1 c-2 c-3 c-4

1500

900 600

300

0.

0.

0.

1

2

5

1

2

5

10

20 25

frequency (Hz),log

Fig. 9. Dynamic modulus of four gradations.

the C-4 mixture, by increasing 10% of the percent of aggregates passing 2.36 mm sieve from the basic C-1 gradation, the largest dynamic modulus was obtained. Similarly, the C-3 mixture with 10% increase of the percent of aggregates passing 4.75 mm sieve was the second highest in dynamic modulus, followed by the C-2 mixture with 10% decrease of the percent passing in 9.5 mm sieve. Of all the four mixes, the C-1 base gradation gave the lowest dynamic modulus results.

would not give additional benefit on E⁄. This simulation result was comparable with experimental findings by Pan [26] who observed that coarse aggregates with more irregular morphologies would improve the resilient modulus of the asphalt mixture. These findings emphasized the importance of particle angularity on forming a stable structure, which can be beneficial to reach a strong skeleton with higher dynamic modulus. 6. Summary findings

5.3. Impact of angularity on dynamic modulus Based on the successfully developed 3D DEM model, we were able to study the influence of aggregate angularity on dynamic modulus. Using the same C-1 mixture gradation but replacing all particles with different AI properties, different dynamic modulus values at 70 °F temperature and 1 Hz frequency were obtained, and the results were plotted in Fig. 10. The first column showed the experimental dynamic modulus of mixture, while other columns showed the simulation result. Because the particles were randomly generated in the DEM model, repetitive simulations were conducted and error bars indicating the variability of the simulation results were shown in Fig. 10. As indicated, the simulation results had shown good repeatability. The dynamic modulus is a combination effect of many factors. When only aggregate morphology was studied, the results clearly showed that with the increase of angularity, the dynamic modulus presented an increasing trend (Fig. 10). It was interesting to see that when the angularity of the particles achieved certain level (greater than 600 in this case), the aggregates of the structure appeared to reach interlocking and further increase of angularity

E*(MPa) 1500

Design Mix

1400

375-450 450-525

1300

525-600 600-675

1200

above675 1100

AI types Fig. 10. Dynamic modulus vs. AI type.

This paper conducted a 3-Dimensional discrete element analysis using the PFC3D DEM program to evaluate the effect of aggregate packing properties on the dynamic modulus of HMA mixtures. To generate angular particles and simulate the real aggregate gradation in the PFC3D, twenty particles were randomly selected from each size category, 19–12.5 mm, 12.5–9.5 mm, 9.5–4.75 mm, and 4.75–2.36 mm. These particles were scanned using the University of Illinois Aggregate Image Analyzer (UIAIA), and their angularity index (AI) and the AI distribution were obtained to represent the AI distribution of the original gradation. Within each AI group, balls were clumped together to match the three orthogonal views of the representative particles obtained from the UIAIA, and 3D angular particles were generated. These particles with specific AI values were further used to replace the spherical balls in the original PFC3D ball models according to the AI distribution of the target aggregate gradation. Four gradations were studied in this paper. One was the basic gradation whose design was obtained based on the Superpave mix design procedure. The other three had gradations varied from the basic gradation by changing the amount of particles passing certain sieve size. It was found, for the specific gradation studied, increasing 10% of the particles passing 2.36 mm and 4.75 mm sieve, respectively, or reducing the particles passing 9.5 mm sieve by 10%, increased the resulting dynamic modulus. It was found that the 3D DEM model developed in this study can effectively predict the dynamic modulus at the same time capture the effect of particle size distribution and angularity distribution on the dynamic modulus. Particle angularity had an important impact on dynamic modulus, with higher angularities resulting in higher dynamic modulus. The image-aided 3D ball-clumping approach introduced in this paper provided a promising approach to study the effect of aggregate packing on HMA properties using PFC3D DEM program. It can take into account the effect of particle angularity and shape with significantly reduced amount of spherical balls comparing with

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other ball-clumping techniques. Reasonable prediction accuracy for dynamic modulus has been achieved. It is recommended that this approach can be used to thoroughly evaluate the aggregate effect on HMA performance, and help to improve the mix design by linking aggregate packing with HMA performance. Acknowledgements The authors gratefully acknowledge the funding support by the Transportation Northwest (TransNow) through the US DOT. Special thank goes to Dr. Tutumluer at the University of Illinois at UrbanaChampaign for assisting on the aggregate image scanning and the UIAIA analysis. References [1] Dongré R, Myers L, D’Angelo J, Paugh C, Gudimettla J. Field evaluation of Witczak and Hirsch Models for predicting dynamic modulus of hot-mix asphalt. J Assoc Asphalt Paving Technol 2005;74. [2] Gabriel G, Thompson M. HMA dynamic modulus-temperature relations. Research report FHWA-ICT-07-006; 2007. [3] Christensen D, et al. A mix design manual for hot-mix asphalt. NCHRP 9-33 report; 2009. [4] AASHTO: TP 62-03. Standard method of test for determining dynamic modulus of hot-mix asphalt concrete mixture. Washington, DC: American Association of State Highway and Transportation officials; 2001. [5] Witczak MW, Fonseca OA. Revised predictive model for dynamic (complex) modulus of asphalt mixtures. Transportation research Record 1540. Washington, DC: Transportation Research Board; 1996. [6] Christensen DW, Pellinen TK, Bonaquist RF. Hirsch model for estimating the modulus of asphalt concrete. J Assoc Asphalt Paving Technol 2003;72. Lexington, KY. [7] Mahmoud E, Masad E, Nazarian S, Abdallah I. Modeling and experimental evaluation of the influence of aggregate blending on asphalt mixture strength. J Trans Rec 2010. [8] You Z. Development of a micromechanical modeling approach to predict asphalt mixture stiffness using the discrete element method. PhD dissertation. University of Illinois at Urbana–Champaign; 2003. [9] Huang H, Tutumluer E, Hashash Y, Ghaboussi J. Discrete element modeling of aggregate behavior in fouled railroad ballast. Recent advancement in soil behavior, in situ test methods, pile foundations, and tunneling. Geotechnical Special Publication 2009;192:33–41. [10] Buttlar WG, Roque R. Evaluation of empirical and theoretical models to determine asphalt concrete stiffnesses at low temperatures_with discussion. Asphalt Paving Technol 1996;65:99–141.

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