本研究旨在利用離散元素方法評估粒料堆積程度對瀝青混凝土成效的影響。研究方法包括實驗材料、粒料的物理性質、級配設計以及成效試驗，並詳細說明離散元素方法的模擬流程及參數設定。本研究通過實驗室試驗和數值模擬，分析不同級配和瀝青含量對瀝青混凝土性能的影響，探討其體積性質和成效性能。
實驗結果顯示，不同級配的瀝青混凝土在成效試驗中的表現存在顯著差異。M1-30在實驗室試驗計算出的CT-index為18.08，而離散元素方法計算的CT-index為21.32，誤差為17.9%。M2-50的實驗室試驗CT-index平均為115.07，而離散元素方法計算的CT-index為107.34，誤差僅為6.7%。本研究的結果表明，粒料堆積程度對瀝青混凝土的抗裂性和抗變形能力有顯著影響，不同級配的粒料在堆積過程中，顆粒之間的接觸狀態和空隙分佈對整體成效有重要作用。
研究結論指出，適當的粒料堆積能夠提高瀝青混凝土的性能，高細度模數和適中的瀝青含量有助於提高材料的抗裂性和抗變形能力，並為優化配比設計提供科學依據。基於此，本研究建議在實際工程應用中應綜合考慮粒料級配和堆積程度，以提升瀝青混凝土的使用壽命和耐久性。

This study aimed to evaluate the effect of the aggregate packing degree on the performance of asphalt concrete using the discrete element method. This study uses laboratory tests and numerical simulations to analyze the effects of different gradations and asphalt contents on the performance of asphalt concrete, and explore its volumetric properties and performance.
The experimental results show that there are significant differences in the performance of asphalt concrete with different gradations. The CT-index calculated by the M1-30 in the laboratory test is 18.08, while the CT-index calculated by the discrete element method is 21.32, with an error of 17.9%. The average laboratory test CT-index of M2-50 is 115.07, while the CT-index calculated by the discrete element method is 107.34, with an error of only 6.7%. The results of this study show that the aggregate packing degree has a significant impact on the crack resistance and deformation resistance of asphalt concrete. During the different aggregate packing degree, the contact state and void distribution between particles are important to asphalt concrete performance.
The research conclusion indicate that appropriate aggregate packing degree can improve the performance of asphalt concrete, and high fineness modulus and moderate asphalt content can help improve the material's crack resistance and deformation resistance. Based on this, this study recommends that aggregate gradation and packing degree should be comprehensively considered in actual engineering applications to improve the service life and durability of asphalt concrete.

Abdullah, W. S., M. T. Obaidat, and N. M. Abu-Sa’da. 1998. “Influence of Aggregate Type and Gradation on Voids of Asphalt Concrete Pavements.” J. Mater. Civ. Eng., 10 (2): 76–85. https://doi.org/10.1061/(ASCE)0899-1561(1998)10:2(76).
Abhijith, B. S., Uma Chakkoth, and J. M. Krishnan. 2020. “Influence of Aggregate Gradation on Laboratory Rutting Performance of Hot-Mix Asphalt Mixtures.” Transportation Research, T. V. Mathew, G. J. Joshi, N. R. Velaga, and S. Arkatkar, eds., 857–867. Singapore: Springer.
Alshamsi, K. 2006. “Development of a mix design methodology for asphalt mixtures with analytically formulated aggregate structures.” Doctor of Philosophy. Louisiana State University and Agricultural and Mechanical College.
Azéma, É., F. Radjai, and F. Dubois. 2011. “Numerical simulation of granular media composed with irregular polyhedral particles: effect of particles’ angularity.”
Baghaee Moghaddam, T., and H. Baaj. 2018. “Application of compressible packing model for optimization of asphalt concrete mix design.” Construction and Building Materials, 159: 530–539. https://doi.org/10.1016/j.conbuildmat.2017.11.004.
Bagnéris, M., F. Dubois, and A. Martin. 2013. “Numerical analysis of historical masonry structures for stone degradation diagnosis : An application to the Roman Amphitheater of Nîmes.” 2013 Digital Heritage International Congress (DigitalHeritage), 521–528.
Chang, C. S., and P.-Y. Hicher. 2005. “An elasto-plastic model for granular materials with microstructural consideration.” International Journal of Solids and Structures, 42 (14): 4258–4277. https://doi.org/10.1016/j.ijsolstr.2004.09.021.
Chang, K.-N. G., and J. N. Meegoda. 1997. “Micromechanical Simulation of Hot Mix Asphalt.” J. Eng. Mech., 123 (5): 495–503. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:5(495).
Chen, J., B. Huang, F. Chen, and X. Shu. 2012. “Application of discrete element method to Superpave gyratory compaction.” Road Materials and Pavement Design, 13 (3): 480–500. https://doi.org/10.1080/14680629.2012.694160.
Chen, J., H. Li, L. Wang, J. Wu, and X. Huang. 2015. “Micromechanical characteristics of aggregate particles in asphalt mixtures.” Construction and Building Materials, 91: 80–85. https://doi.org/10.1016/j.conbuildmat.2015.05.076.
Chen, J., T. Pan, and X. Huang. 2011. “Discrete element modeling of asphalt concrete cracking using a user-defined three-dimensional micromechanical approach.” J. Wuhan Univ. Technol.-Mat. Sci. Edit., 26 (6): 1215–1221. https://doi.org/10.1007/s11595-011-0393-z.
Cundall, P. 1971. “A computer model for simulating progressive, large-scale movements in blocky rock systems.”
Cundall, P. A., and O. D. L. Strack. 1979. “A discrete numerical model for granular assemblies.” Géotechnique, 29 (1): 47–65. https://doi.org/10.1680/geot.1979.29.1.47.
Dan, H.-C., Z. Zhang, J.-Q. Chen, and H. Wang. 2018. “Numerical Simulation of an Indirect Tensile Test for Asphalt Mixtures Using Discrete Element Method Software.” J. Mater. Civ. Eng., 30 (5): 04018067. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002252.
Ding, X., F. Huang, P. Rath, Z. Ye, W. G. Buttlar, and T. Ma. 2023. “Comparative fracture resistance assessment of rubber-modified asphalt mortar based on meso-and macro-mechanical analysis.” International Journal of Pavement Engineering, 24 (1): 2265032. https://doi.org/10.1080/10298436.2023.2265032.
Donald W., C. Jr., P. Terhi, and B. Ramon F. 2003. “Hirsch model for estimating the modulus of asphalt concrete.” Asphalt Paving Technology 2003.
Dondi, G., A. Simone, V. Vignali, and G. Manganelli. 2012. “Numerical and experimental study of granular mixes for asphalts.” Powder Technology, 232: 31–40. https://doi.org/10.1016/j.powtec.2012.07.057.
Dubois, F., M. Jean, M. Renouf, R. Mozul, A. Martin, and M. Bagnéris. 2011. “LMGC90.” 10e colloque national en calcul des structures, Clé USB. Giens, France.
Fakhri, M., P. T. Kheiry, and A. A. Mirghasemi. 2012. “Modeling of the permanent deformation characteristics of SMA mixtures using discrete element method.” Road Materials and Pavement Design, 13 (1): 67–84. https://doi.org/10.1080/14680629.2011.644080.
Feng, H., M. Pettinari, B. Hofko, and H. Stang. 2015. “Study of the internal mechanical response of an asphalt mixture by 3-D discrete element modeling.” Construction and Building Materials, 77: 187–196. https://doi.org/10.1016/j.conbuildmat.2014.12.022.
Feng, H., M. Pettinari, and H. Stang. 2016. “Three Different Ways of Calibrating Burger’s Contact Model for Viscoelastic Model of Asphalt Mixtures by Discrete Element Method.” 8th RILEM International Symposium on Testing and Characterization of Sustainable and Innovative Bituminous Materials, F. Canestrari and M. N. Partl, eds., 423–433. Dordrecht: Springer Netherlands.
Gao, L., Y. Zhang, Y. Liu, Z. Wang, and X. Ji. 2023. “Study on the cracking behavior of asphalt mixture by discrete element modeling with real aggregate morphology.” Construction and Building Materials, 368: 130406. https://doi.org/10.1016/j.conbuildmat.2023.130406.
Garcia, V. M., L. Barros, J. Garibay, I. Abdallah, and S. Nazarian. 2020. “Effect of Aggregate Gradation on Performance of Asphalt Concrete Mixtures.” J. Mater. Civ. Eng., 32 (5): 04020102. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003147.
Ge, H., J. C. Quezada, V. L. Houerou, and C. Chazallon. 2021. “Three-dimensional simulation of asphalt mixture incorporating aggregate size and morphology distribution based on contact dynamics method.” Construction and Building Materials, 302: 124124. https://doi.org/10.1016/j.conbuildmat.2021.124124.
Guo, Q., H. Xu, J. Wang, J. Hang, K. Wang, P. Hu, and H. Li. 2023. “Gradation Optimization Based on Micro-Analysis of Rutting Behavior of Asphalt Mixture.” Coatings, 13 (11): 1965. https://doi.org/10.3390/coatings13111965.
Jebahi, M., D. André, I. Terreros, and I. Iordanoff. 2015. Discrete Element Method to Model 3D Continuous Materials. Wiley.
Junaid, M., and U. Gazder. 2021. “Investigating the Tensile Strength and Permanent Deformation of Asphalt Concrete using Different Gradation Methods.” 2021 Third International Sustainability and Resilience Conference: Climate Change, 259–263. Sakheer, Bahrain: IEEE.
Kim, S., R. Roque, A. Guarin, and B. Birgisson. 2006. “Identification and Assessment of the Dominant Aggregate Size Range (DASR) of Asphalt Mixture (With Discussion).” Journal of the Association of Asphalt Paving Technologists.
Kim, Y. R., R. H. Borden, and M. Guddati. 2001. “A unified approach to predicting long term performance of asphalt-aggregate mixtures.” Long Term Durability of Structural Materials, 277–288. Elsevier.
Li, J., W. Guo, A. Meng, M. Han, and Y. Tan. 2020. “Investigation on the Micro Deformation Mechanism of Asphalt Mixtures under High Temperatures Based on a Self-Developed Laboratory Test.” Materials, 13 (7): 1791. https://doi.org/10.3390/ma13071791.
Li, W., W. Cao, X. Ren, S. Lou, S. Liu, and J. Zhang. 2022. “Impacts of Aggregate Gradation on the Volumetric Parameters and Rutting Performance of Asphalt Concrete Mixtures.” Materials, 15 (14): 4866. https://doi.org/10.3390/ma15144866.
Liang, H., L. Shi, D. Wang, X. Xiao, and K. Deng. 2021. “Influence of graded coarse aggregate content and specific surface area on the fracture properties of asphalt mixtures based on discrete element simulations and indoor tests.” Construction and Building Materials, 299: 123942. https://doi.org/10.1016/j.conbuildmat.2021.123942.
Liu, C., T. Le, B. Shi, and Y. Zhu. 2020. “颗粒离散元法工程应用的三大问题探讨.” 岩石力学与工程学报, 39 (6): 1142–1152. https://doi.org/10.13722/j.cnki.jrme.2019.0977.
Liu, S., L. Zhu, H. Zhang, T. Liu, P. Ji, and W. Cao. 2021. “Effect of Gradation Variability on Volume Parameter and Key Performances of HMA.” Front. Mater., 7: 611409. https://doi.org/10.3389/fmats.2020.611409.
Liu, Y., Q. Dai, and Z. You. 2009. “Viscoelastic Model for Discrete Element Simulation of Asphalt Mixtures.” J. Eng. Mech., 135 (4): 324–333. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:4(324).
Liu, Y., J. Xie, D. Wei, and Y. Tan. 2023. “Research on the permanent deformation mechanism and dynamic meso-mechanical response of porous asphalt mixture composite structure using the discrete element method.” Construction and Building Materials, 407: 133531. https://doi.org/10.1016/j.conbuildmat.2023.133531.
Luding, S. 2008. “Introduction to discrete element methods: Basic of contact force models and how to perform the micro-macro transition to continuum theory.” European Journal of Environmental and Civil Engineering, 12 (7–8): 785–826. https://doi.org/10.1080/19648189.2008.9693050.
Ma, T., D. Zhang, Y. Zhang, and J. Hong. 2016. “Micromechanical response of aggregate skeleton within asphalt mixture based on virtual simulation of wheel tracking test.” Construction and Building Materials, 111: 153–163. https://doi.org/10.1016/j.conbuildmat.2016.02.104.
Ma, T., D. Zhang, Y. Zhang, S. Wang, and X. Huang. 2018. “Simulation of wheel tracking test for asphalt mixture using discrete element modelling.” Road Materials and Pavement Design, 19 (2): 367–384. https://doi.org/10.1080/14680629.2016.1261725.
Majidi, B., S. Taghavi, M. Fafard, D. Ziegler, and H. Alamdari. 2016. “Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures.” Materials, 9 (5): 334. https://doi.org/10.3390/ma9050334.
Martin, A. 2010. “Ecoulement confiné d’un matériau granulaire en interaction avec un gaz, application à la relocalisation du combustible nucléaire.” phdthesis. Université Montpellier II - Sciences et Techniques du Languedoc.
Masad, E., and J. Button. 2004. “Implications of Experimental Measurements and Analyses of the Internal Structure of Hot-Mix Asphalt.” Transportation Research Record, 1891 (1): 212–220. https://doi.org/10.3141/1891-25.
Meza-Lopez, J., N. Noreña, C. Meza, and C. Romanel. 2020. “Modeling of Asphalt Concrete Fracture Tests with the Discrete-Element Method.” J. Mater. Civ. Eng., 32 (8): 04020228. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003305.
Min, Z., L. Sun, Q. Wang, and Z. Yu. 2020. “Influence of Aggregate Packing on the Performance of Uncured and Cured Epoxy Asphalt Mixtures.” J. Mater. Civ. Eng., 32 (5): 04020103. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003149.
Nian, T., J. Ge, P. Li, M. Wang, and Y. Mao. 2021. “Improved discrete element numerical simulation and experiment on low-temperature anti-cracking performance of asphalt mixture based on PFC2D.” Construction and Building Materials, 283: 122792. https://doi.org/10.1016/j.conbuildmat.2021.122792.
Olard, F., and D. Perraton. 2010. “On the Optimization of the Aggregate Packing Characteristics for the Design of High-Performance Asphalt Concretes.” Road Materials and Pavement Design, 11 (sup1): 145–169. https://doi.org/10.1080/14680629.2010.9690330.
Papagiannakis, A. T., H. M. Zelelew, and E. Mahmoud. 2018. “Simulation of Asphalt Concrete Plastic Deformation Behavior.” J. Mater. Civ. Eng., 30 (3): 04018025. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002181.
Perales, F., F. Dubois, Y. Monerie, B. Piar, and L. Stainier. 2010. “A NonSmooth Contact Dynamics-based multi-domain solver: Code coupling (Xper) and application to fracture.” European Journal of Computational Mechanics, 19 (4): 389–417. https://doi.org/10.3166/ejcm.19.389-417.
Rafiee, A., M. Vinches, and F. Dubois. 2011. “The Non-Smooth Contact Dynamics method applied to the mechanical simulation of a jointed rock mass.”
Topin, V., F. Dubois, Y. Monerie, F. Perales, and A. Wachs. 2011. “Micro-rheology of dense particulate flows: Application to immersed avalanches.” Journal of Non-Newtonian Fluid Mechanics, 166 (1–2): 63–72. https://doi.org/10.1016/j.jnnfm.2010.10.006.
Vieira, D., V. M. Garcia, I. Abdallah, and S. Nazarian. 2020. “Role of Aggregate Gradation in Balancing the Performance of Asphalt Concrete Mixtures.” Transportation Research Record, 2674 (11): 184–191. https://doi.org/10.1177/0361198120942515.
Wang, H., Z. Zhou, W. Huang, and X. Dong. 2021a. “Investigation of asphalt mixture permanent deformation based on three-dimensional discrete element method.” Construction and Building Materials, 272: 121808. https://doi.org/10.1016/j.conbuildmat.2020.121808.
Wang, X., B. Li, R. Xia, and H. Ma. 2021b. Engineering Applications of Discrete Element Method: Operation Analysis and Optimization Design of Coal and Agricultural Machinery. Engineering Applications of Computational Methods. Singapore: Springer Singapore.
Weihua W., and Xibing L. 2005. “A Review on Fundamentals of Distinct Element Method and Its Application in Geotechnical Engineering.” ytgcjs, 19 (4): 177–181.
Wu, S., G. Xu, J. Yang, R. Yang, and J. Zhu. 2020. “Investigation on Indirect Tensile Test of Asphalt Mixture Based on the Discrete Element Method.” Journal of Testing and Evaluation, 48 (3): 2345–2361. https://doi.org/10.1520/JTE20190532.
Xue, B., J. Xu, J. Pei, J. Zhang, and R. Li. 2021. “Investigation on the micromechanical response of asphalt mixture during permanent deformation based on 3D virtual wheel tracking test.” Construction and Building Materials, 267: 121031. https://doi.org/10.1016/j.conbuildmat.2020.121031.
Yan, G., H. Yu, and G. McDowell. 2009. “Simulation of granular material behaviour using DEM.” Procedia Earth and Planetary Science, 1 (1): 598–605. https://doi.org/10.1016/j.proeps.2009.09.095.
Yan, T., K. Cash, M. Turos, and M. Marasteanu. 2023. “High-compactability asphalt mix design framework based on binary aggregate packing.” Construction and Building Materials, 383: 131315. https://doi.org/10.1016/j.conbuildmat.2023.131315.
You, Z., and W. G. Buttlar. 2005. “Application of Discrete Element Modeling Techniques to Predict the Complex Modulus of Asphalt–Aggregate Hollow Cylinders Subjected to Internal Pressure.” Transportation Research Record, 1929 (1): 218–226. https://doi.org/10.1177/0361198105192900126.
You, Z., and Y. Liu. 2010. “Three-Dimensional Discrete Element Simulation of Asphalt Concrete Subjected to Haversine. Loading An Application of the Frequency-Temperature Superposition Technique.” Road Materials and Pavement Design, 11 (2): 273–290. https://doi.org/10.3166/rmpd.11.273-290.
Zhang, D., S. Hou, J. Bian, and L. He. 2016. “Investigation of the micro-cracking behavior of asphalt mixtures in the indirect tensile test.” Engineering Fracture Mechanics, 163: 416–425. https://doi.org/10.1016/j.engfracmech.2016.05.020.
Zhang, H., H. Liu, and W. You. 2022a. “Microstructural behavior of the low-temperature cracking and self-healing of asphalt mixtures based on the discrete element method.” Mater Struct, 55 (1): 18. https://doi.org/10.1617/s11527-021-01876-7.
Zhang, J. 2020. “Advances in micromechanical modelling of asphalt mixtures: a review.” European Journal of Environmental and Civil Engineering, 24 (5): 583–602. https://doi.org/10.1080/19648189.2017.1410727.
Zhang, K., H. Wen, and A. Hobbs. 2015. “Laboratory Tests and Numerical Simulations of Mixing Superheated Virgin Aggregate with Reclaimed Asphalt Pavement Materials.” Transportation Research Record, 2506 (1): 62–71. https://doi.org/10.3141/2506-07.
Zhang, X., E. Chen, N. Li, L. Wang, C. Si, and C. Wang. 2022b. “Micromechanical analysis of the rutting evolution of asphalt pavement under temperature–stress coupling based on the discrete element method.” Construction and Building Materials, 325: 126800. https://doi.org/10.1016/j.conbuildmat.2022.126800.
Zhao, G., Q. Wang, and Z. Yan. 2021. “Research on Asphalt Mixture Bending Test and Micromechanical Evolution Based on 2D Discrete-Element Method.” J. Mater. Civ. Eng., 33 (8): 04021179. https://doi.org/10.1061/(ASCE)MT.1943-5533.0003804.
Zhong, K., J. Fan, X. Huang, and M. Chen. 2022. “Discrete element simulation on anti-rutting performance of PAC-13 pavement in urban roads.” Mater Struct, 55 (4): 117. https://doi.org/10.1617/s11527-022-01952-6.
Zhou, F., S. Im, L. Sun, and T. Scullion. 2017a. “Development of an IDEAL cracking test for asphalt mix design and QC/QA.” Road Materials and Pavement Design, 18 (S4): 405–427. https://doi.org/10.1080/14680629.2017.1389082.
Zhou, W., X. Huang, and L. Wang. 2017b. “Study on the void reduction behavior of porous asphalt pavement based on discrete element method.” International Journal of Pavement Engineering, 18 (4): 285–291. Taylor and Francis Ltd. https://doi.org/10.1080/10298436.2015.1065987.