# Gradation Optimization Based on Micro-Analysis of Rutting Behavior of Asphalt Mixture

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## Abstract

**:**

## 1. Introduction

## 2. Discrete Element Simulation

#### 2.1. Establishment of Material Model

#### 2.2. Interparticle Contact Model

#### 2.3. Material Parameter Calibration

#### 2.4. Establishment of Rutting Model

## 3. Simulation Results and Analysis

#### 3.1. Interparticle Correlation State Analysis

#### 3.2. Force of Particles with Different Sizes in Rutting

#### 3.3. The Force Curve of Particles in Asphalt Mixtures

#### 3.3.1. Force Curve Analysis of Particles with Different Sizes

#### 3.3.2. Comparative Analysis of Forces on Particles of the Same Size

## 4. Asphalt Mixture Gradation Optimization, Design, and Verification

#### 4.1. Gradation Optimization Design

#### 4.2. Asphalt Mixture Performance Test

#### 4.2.1. High-Temperature Rutting Test

#### 4.2.2. Low-Temperature Bending Test

#### 4.2.3. Water Stability Performance Test

## 5. Conclusions

- (1)
- In the AC-13 asphalt mixture, particles with a radius of more than 1.8 mm are the main bearing particles. In the SMA-13 asphalt mixture, the particles with a radius of more than 3.6 mm are the main bearing particles. Small particle-size particles play a filling role. The particle force limit value of the two types of asphalt mixture is proportional to the particle size.
- (2)
- When the particle radius is less than 5.1 mm, the particle force value of the AC-13 asphalt mixture is greater than that of SMA-13. When the particle radius is greater than 5.1 mm, the particle force value of the SMA-13 asphalt mixture is greater than that of AC-13. For particles with a radius of 5.7 mm and 7.3 mm, the force limit value of the SMA-13 asphalt mixture is increased by about 30% compared to that of the AC-13 asphalt mixture.
- (3)
- Through laboratory experimental research, the dynamic stability, flexural tensile strength, water immersion residual stability, and freeze-thaw splitting strength ratios of the AC-13 asphalt mixture after optimization are 8.5%, 9.2%, 1.6%, and 1.9% higher than those before optimization. The dynamic stability, flexural tensile strength, water immersion residual stability, and freeze-thaw splitting strength ratios of the SMA-13 asphalt mixture after optimization are 10.6%, 7.3%, 0.7%, and 2.1% higher than those before optimization. The road performance of the asphalt mixture after gradation optimization has improved, which shows that the gradation optimization method is feasible.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**DEM materials modeling. (

**a**) Percentage of mass of particles of different sizes; (

**b**) Shape of real and simulated particles; (

**c**) Parameters in simulation; (

**d**) Vibration models.

**Figure 3.**Comparison between the uniaxial compression test results and the uniaxial compression simulation results (

**a**) AC-13 asphalt mixture; (

**b**) SMA-13 asphalt mixture.

**Figure 5.**Particle association states occur at different moments. (

**a**–

**d**) The interaction of axial force between particles of AC-13 asphalt mixture at 0 s, 0.5 s, 1.5 s and 2.5 s; (

**e**–

**h**) The interaction of axial force between particles of SMA-13 asphalt mixture at 0 s, 0.5 s, 1.5 s and 2.5 s.

**Figure 6.**Connection of AC-13 particles with different particle sizes. (

**a**) The simulation time is 0 s; (

**b**) The simulation time is 0.5 s; (

**c**) The simulation time is 1.5 s; (

**d**) The simulation time is 2.5 s.

**Figure 7.**Connection of SMA-13 particles with different particle sizes. (

**a**) The simulation time is 0 s; (

**b**) The simulation time is 0.5 s; (

**c**) The simulation time is 1.5 s; (

**d**) The simulation time is 2.5 s.

**Figure 9.**Relationship between force and time for four different particle sizes of SMA-13 particles.

**Figure 10.**Comparison of particle force between AC-13 and SMA-13 asphalt mixtures with the same particle size. (

**a**) The force curve of particles with a particle size of 7.3 mm; (

**b**) The force curve of particles with a particle size of 5.7 mm; (

**c**) The force curve of particles with a particle size of 3.6 mm; (

**d**) The force curve of particles with a particle size of 1.8 mm.

Type of Mixture | ${\mathit{K}}_{\mathit{n}}$ (N/m^{3}) | ${\mathit{K}}_{\mathit{s}}$ (N/m^{3}) | ${\mathit{\sigma}}_{\mathit{n}}$ (Pa) | ${\mathit{\sigma}}_{\mathit{s}}$ (Pa) | ${\mathit{R}}_{\mathit{B}}$ (mm) |
---|---|---|---|---|---|

AC-13 | 2.11 × 10^{10} | 1.01 × 10^{10} | 2.31 × 10^{5} | 2.77 × 10^{5} | 0.53 |

SMA-13 | 2.32 × 10^{9} | 1.11 × 10^{9} | 1.58 × 10^{7} | 2.83 × 10^{7} | 0.86 |

Type of Mixture | Gradation Type | Dynamic Stability (Times/mm) | |||
---|---|---|---|---|---|

1 | 2 | 3 | Average | ||

AC-13 | Gradation before optimization | 4227 | 4134 | 4192 | 4184 |

Gradation after optimization | 4583 | 4502 | 4529 | 4538 | |

SMA-13 | Gradation before optimization | 5574 | 5623 | 5649 | 5615 |

Gradation after optimization | 5968 | 6276 | 6381 | 6208 |

Type of Mixture | Gradation Type | Flexural Tensile Strength (MPa) | Maximum Bending Strain (10^{−6}) | Bending Stiffness Modulus (MPa) |
---|---|---|---|---|

AC-13 | Gradation before optimization | 10.32 | 2587.2 | 3989.85 |

Gradation after optimization | 11.27 | 2896.3 | 3891.61 | |

SMA-13 | Gradation before optimization | 12.08 | 2752.8 | 4388.87 |

Gradation after optimization | 12.96 | 3021.6 | 4289.77 |

Type of Mixture | Gradation Type | Water Immersion Residual Stability (%) | Freeze-Thaw Splitting Strength Ratio (%) |
---|---|---|---|

AC-13 | Gradation before optimization | 87.9 | 79.6 |

Gradation after optimization | 89.3 | 81.1 | |

SMA-13 | Gradation before optimization | 91.7 | 86.4 |

Gradation after optimization | 92.3 | 88.2 |

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## Share and Cite

**MDPI and ACS Style**

Guo, Q.; Xu, H.; Wang, J.; Hang, J.; Wang, K.; Hu, P.; Li, H.
Gradation Optimization Based on Micro-Analysis of Rutting Behavior of Asphalt Mixture. *Coatings* **2023**, *13*, 1965.
https://doi.org/10.3390/coatings13111965

**AMA Style**

Guo Q, Xu H, Wang J, Hang J, Wang K, Hu P, Li H.
Gradation Optimization Based on Micro-Analysis of Rutting Behavior of Asphalt Mixture. *Coatings*. 2023; 13(11):1965.
https://doi.org/10.3390/coatings13111965

**Chicago/Turabian Style**

Guo, Qingliang, Hao Xu, Junjie Wang, Jiezhou Hang, Kun Wang, Peng Hu, and Hongzhen Li.
2023. "Gradation Optimization Based on Micro-Analysis of Rutting Behavior of Asphalt Mixture" *Coatings* 13, no. 11: 1965.
https://doi.org/10.3390/coatings13111965