# Low-Temperature Performance and Damage Constitutive Model of Eco-Friendly Basalt Fiber–Diatomite-Modified Asphalt Mixture under Freeze–Thaw Cycles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Raw Materials

#### 2.2. Specimen Preparation

- The control asphalt mixture sample (with no additives) (AM) has an OAC of 4.78%.
- The diatomite (corresponding to the volume ratio of the diatomite to entire filler is 6.5%) modified asphalt mixture (DAM) has an OAC of 5.12%.
- The basalt fiber (0.25% by weight of the asphalt mixture) modified asphalt mixture (BFAM) has an OAC of 5.09%.
- The basalt fiber (0.25%) and diatomite (6.5%) compound modified asphalt mixture (DBFAM) has an OAC of 5.22%.

#### 2.3. Process of Freeze–Thaw

#### 2.4. Low-Temperature Indirect Tensile Test

#### 2.5. The Nonlinear Evaluation Indexes of Stress–Strain Curves

^{2}is more than 0.998, to determine the linear zone slope and boundary point location. When R

^{2}does not meet the accuracy requirement, it iteratively reduces the boundary of the zone and solves the end point of the straight segment, as shown in Figure 4. The specific steps are as follow:

^{2}is large enough. If R

^{2}> 0.998, the interval can be seen as a linear zone, and Step 5 will be executed. Otherwise, the interval is still obtained as the nonlinear zone, so Step 4 will be executed.

#### 2.6. Damage Constitutive Model of the Asphalt Mixture under F–T Cycles

- The asphalt mixture at low temperature accords with the generalized Hooke’s law.
- The strength of micro-unit conforms to the statistical law of the three-parameter Weibull:

## 3. Results and Discussion

#### 3.1. IDT Strength

#### 3.2. IDT Failure Strain

#### 3.3. Failure Stiffness Modulus

#### 3.4. Deformation Energy Density

#### 3.5. Stress–Strain Curves

#### 3.6. Linear Zone Stress Ratio and Linear Zone Strain Ratio Result

#### 3.7. Elastic Stiffness Modulus of Linear Zone Result

#### 3.8. Experiment Verification of Constitutive Model

^{2}indicates that the statistical damage constitutive model established by Equation (15) can better describe the stress–strain relationship after F–T damage. Comparisons of the experimental results and statistical damage constitutive model predictions of different asphalt mixture are shown in Figure 20, Figure 21, Figure 22 and Figure 23. The results show that the statistical damage constitutive model is suitable for different asphalt mixtures at low temperature.

## 4. Conclusions

- F–T cycles will reduce the IDT strength, stiffness modulus and strain energy density of asphalt mixture, and increase the IDT failure strain. As the number of F–T cycles increases, the variation of each index decreases.
- After adding basalt fiber, the IDT strength, IDT failure strain, and strain energy density of the mixture are improved, and the low-temperature performance is improved. After adding diatomite, the loss ratio of each index decreases under F–T cycles, and the resistance of F–T cycles is improved. The low-temperature performance and resistance of F–T cycles for asphalt mixture are improved after compound modified by basalt fiber and diatomite. The eco–friendly basalt fiber–diatomite-modified asphalt mixture is suitable in seasonal frozen regions.
- The variation law and form of the stress–strain curve before and after the F–T cycle are proposed. The stress–strain curve is divided into linear zone and nonlinear zone. Under the action of the F–T cycles, the stress ratio in the linear zone is gradually reduced, the strain ratio in the nonlinear zone is gradually increased, and the nonlinear characteristics of the stress–strain are more significant. After the addition of basalt fiber, the nonlinear zone increases significantly, which reflects the reinforcement of the fiber during the cracking stage. The nonlinear point of the stress–strain curve can be described by the nonlinear index, and the mechanism of freezing and thawing and the mechanism of material modification are better reflected.
- The statistical damage constitutive model established in this paper can describe the stress–strain relationship of the asphalt mixture at low temperature after F–T cycles well.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Guo, Q.L.; Li, L.L.; Cheng, Y.C.; Jiao, Y.B.; Xu, C. Laboratory evaluation on performance of diatomite and glass fiber compound modified asphalt mixture. Mater. Des.
**2015**, 66, 51–59. [Google Scholar] [CrossRef] - Song, Y.; Che, J.; Zhang, Y. The interacting rule of diatomite and asphalt groups. Pet. Sci. Technol.
**2011**, 29, 254–259. [Google Scholar] [CrossRef] - Cheng, Y.C.; Tao, J.L.; Jiao, Y.B.; Guo, Q.L.; Li, C. Influence of Diatomite and Mineral Powder on Thermal Oxidative Ageing Properties of Asphalt. Adv. Mater. Sci. Eng.
**2015**, 2015, 1–10. [Google Scholar] [CrossRef] - Cong, P.L.; Liu, N.; Tian, Y.; Zhang, Y.H. Effects of long-term aging on the properties of asphalt binder containing diatoms. Constr. Build. Mater.
**2016**, 123, 534–540. [Google Scholar] [CrossRef] - Cong, P.L.; Chen, S.F.; Chen, H.X. Effects of diatomite on the properties of asphalt binder. Constr. Build. Mater.
**2012**, 30, 495–499. [Google Scholar] [CrossRef] - Yang, C.; Xie, J.; Zhou, X.; Liu, Q.; Pang, L. Performance Evaluation and Improving Mechanisms of Diatomite-Modified Asphalt Mixture. Materials
**2018**, 11, 686. [Google Scholar] [CrossRef] [PubMed] - Wang, W.S.; Cheng, Y.C.; Tan, G.J. Design Optimization of SBS-Modified Asphalt Mixture Reinforced with Eco-Friendly Basalt Fiber Based on Response Surface Methodology. Materials
**2018**, 11, 1311. [Google Scholar] [CrossRef] [PubMed] - Zheng, Y.X.; Cai, Y.C.; Zhang, G.H.; Fang, H.Y. Fatigue Property of Basalt Fiber-Modified Asphalt Mixture under Complicated Environment. J. Wuhan Univ. Technol.
**2014**, 5, 996–1004. [Google Scholar] [CrossRef] - Qin, X.; Shen, A.Q.; Guo, Y.C.; Li, Z.N.; Lv, Z.H. Characterization of asphalt mastics reinforced with basalt fibers. Constr. Build. Mater.
**2018**, 159, 508–516. [Google Scholar] [CrossRef] - Zhang, X.Y.; Gu, X.Y.; Lv, J.X.; Zhu, Z.K.; Zou, X.Y. Numerical analysis of the rheological behaviors of basalt fiber reinforced asphalt mortar using ABAQUS. Constr. Build. Mater.
**2017**, 157, 392–401. [Google Scholar] [CrossRef] - Zhang, X.; Gu, X.Y.; Lv, J.X.; Zou, X.Y. 3D numerical model to investigate the rheological properties of basalt fiber reinforced asphalt-like materials. Constr. Build. Mater.
**2017**, 138, 185–194. [Google Scholar] [CrossRef] - Liu, K.; Zhang, W.H.; Wang, F. Research on cryogenic properties of different fiber asphalts and mixtures. Adv. Mater. Res.
**2011**, 146–147, 238–242. [Google Scholar] [CrossRef] - Gao, C.M. Microcosmic Analysis and Performance Research of Basalt Fiber Asphalt Concrete. Ph.D. Thesis, Jilin University, Changchun, China, 2012. [Google Scholar]
- Zhao, L.H. Study on the Influence Mechanism of Basalt Fiber on Asphalt Mixture Property. Ph.D. Thesis, Dalian University of Technology, Dalian, China, 2013. [Google Scholar]
- Cheng, Y.C.; Zhu, C.F.; Tan, G.J.; Lv, Z.H.; Yang, J.S.; Ma, J.S. Laboratory study on properties of diatomite and basalt fiber compound modified asphalt mastic. Adv. Mater. Sci. Eng.
**2017**, 3, 1–10. [Google Scholar] [CrossRef] - Davar, A.; Tanzadeh, J.; Fadaee, O. Experimental evaluation of the basalt fibers and diatomite powder compound on enhanced fatigue life and tensile strength of hot mix asphalt at low temperatures. Constr. Build. Mater.
**2017**, 153, 238–246. [Google Scholar] [CrossRef] - Özgan, E.; Serin, S. Investigation of certain engineering characteristics of asphalt concrete exposed to freeze–thaw cycles. Cold Reg. Sci. Technol.
**2013**, 85, 131–136. [Google Scholar] [CrossRef] - Yan, K.Z.; Ge, D.D.; You, L.Y.; Wang, X.L. Laboratory investigation of the characteristics of SMA mixtures under freeze–thaw cycles. Cold Reg. Sci. Technol.
**2015**, 119, 68–74. [Google Scholar] [CrossRef] - Lachance-Tremblay, É.; Perraton, D.; Vaillancourt, M.; Benedetto, H. Degradation of asphalt mixtures with glass aggregates subjected to freeze-thaw cycles. Cold Reg. Sci. Technol.
**2017**, 141, 8–15. [Google Scholar] [CrossRef] - Gong, X.B.; Romero, P.; Dong, Z.J.; Sudbury, D. The effect of freeze–thaw cycle on the low-temperature properties of asphalt fine aggregate matrix utilizing bending beam rheometer. Cold Reg. Sci. Technol.
**2016**, 125, 101–107. [Google Scholar] [CrossRef] - Islam, M.; Asce, S.; Tarefder, R.; Asce, M. Effects of large freeze-thaw cycles on stiffness and tensile strength of asphalt concrete. J. Cold Reg. Eng.
**2016**, 30. [Google Scholar] [CrossRef] - Krcmarik, M.; Varma, S.; Kutay, M.; Jamrah, A. Development of predictive models for low-temperature indirect tensile strength of asphalt mixtures. J. Mater. Civ. Eng.
**2016**, 28, 04016139. [Google Scholar] [CrossRef] - Liu, J.; Zhao, S.; Li, L.; Li, P.; Saboundjian, S. Low temperature cracking analysis of asphalt binders and mixtures. Cold Reg. Sci. Technol.
**2017**, 141, 78–85. [Google Scholar] [CrossRef] - Yi, J.Y.; Shen, S.H.; Muhunthan, B.; Feng, D.C. Viscoelastic–plastic damage model for porous asphalt mixtures: Application to uniaxial compression and freeze–thaw damage. Mech. Mater.
**2014**, 70, 67–75. [Google Scholar] [CrossRef] - Zhang, Q.; Ze, L.; Wen, Z.; Hou, Z. Research on the damage model of asphalt mixture under synergy action of freeze-thaw and loading. J. Xian Univ. Archit. Technol.
**2016**, 48, 188–194. [Google Scholar] - Huang, S.B.; Liu, Q.S.; Cheng, A.P.; Liu, Y.Z. A statistical damage constitutive model under freeze-thaw and loading for rock and its engineering application. Cold Reg. Sci. Technol.
**2018**, 145, 142–150. [Google Scholar] [CrossRef] - Chen, S.; Qiao, C.S.; Ye, Q.; Khan, M. Comparative study on three-dimensional statistical damage constitutive modified model of rock based on power function and weibull distribution. Environ. Earth Sci.
**2018**, 77, 108. [Google Scholar] [CrossRef] - JTG E20-2011. Standard Test Methods of Asphalt and Asphalt Mixtures for Highway Engineering; Ministry of Transport: Beijing, China, 2011. (In Chinese)
- Zhu, C.F. Research on Road Performance and Mechanical Properties of Diatomite-Basalt Fiber Compound Modified Asphalt Mixture. Ph.D. Thesis, Jilin University, Changchun, China, 2018. [Google Scholar]
- Tan, Y.Q.; Sun, Z.Q.; Gong, X.B.; Xu, H.N.; Zhang, L.; Bi, Y.F. Design parameter of low-temperature performance for asphalt mixtures in cold regions. Constr. Build. Mater.
**2017**, 155, 1179–1187. [Google Scholar] [CrossRef] - Tan, Y.Q.; Zhang, L.; Xu, H.N. Evaluation of low-temperature performance of asphalt paving mixtures. Cold Reg. Sci. Technol.
**2012**, 70, 107–112. [Google Scholar] [CrossRef] - Gao, C.M.; Han, S.; Zhu, K.X.; Wang, Z.Y. Research on basalt fiber asphalt concrete’s high temperature performance. Appl. Mech. Mater.
**2014**, 505–506, 39–42. [Google Scholar] [CrossRef] - Xu, H.N.; Guo, W.; Tan, Y.Q. Internal structure evolution of asphalt mixtures during freeze-thaw cycles. Mater. Des.
**2015**, 86, 436–446. [Google Scholar] [CrossRef]

**Figure 5.**Indirect tensile (IDT) strength under F–T cycles. AM, Matrix asphalt mixture; DAM, diatomite-modified asphalt mixture; BFAM, basalt fiber-modified asphalt mixture; DBFAM, diatomite–basalt fiber-modified asphalt mixture.

Property | Value | Standard |
---|---|---|

Density (15 °C, g/cm^{3}) | 1.018 | - |

Penetration (25 °C, 0.1 mm) | 92.3 | 80~100 |

Softening point T_{R&B} (°C) | 46.9 | ≥42 |

Ductility (25 °C, cm) | >150 | ≥100 |

Viscosity (135 °C, mPa·s) | 306.9 | - |

Sieve size (mm) | 13.2 | 9.5 | 4.75 | 2.36 | 1.18 | 0.6 | 0.3 | 0.15 | 0.075 |
---|---|---|---|---|---|---|---|---|---|

Apparent density (g/cm^{3}) | 2.811 | 2.805 | 2.815 | 2.817 | 2.808 | 2.805 | 2.778 | 2.777 | 2.768 |

Absorption coefficient of water (%) | 0.33 | 0.44 | 0.54 | 0.75 | - | - | - | - | - |

Property | Hydrophilic Coefficient | Apparent Density (g/cm^{3}) | Gradation | |
---|---|---|---|---|

Sieve Size (mm) | Passing (%) | |||

Value | 0.778 | 2.722 | 0.6 | 100 |

0.15 | 95 | |||

0.075 | 80 |

Property | Color | Bulk Density | Specific Gravity | pH |
---|---|---|---|---|

Value | White | 0.38 g/cm^{3} | 2.1 g/cm^{3} | 7 |

Items | Value | Standard Value |
---|---|---|

Diameter (µm) | 10–13 | - |

Length (mm) | 6 | - |

Water content (%) | 0.030 | ≤0.2 |

F–T | Parameters | AM | BFAM | DAM | BFDAM |
---|---|---|---|---|---|

0 | m | 2.47 | 3.54 | 2.48 | 3.36 |

n | 8.13 × 10^{−4} | 9.33 × 10^{−4} | 5.93 × 10^{−4} | 9.09 × 10^{−4} | |

R^{2} | 0.935 | 0.983 | 0.997 | 0.999 | |

15 | m | 1.33 | 1.2 | 1.27 | 1.28 |

n | 2.73 × 10^{−3} | 3.50 × 10^{−3} | 3.00 × 10^{−3} | 3.69 × 10^{−3} | |

R^{2} | 0.995 | 0.992 | 0.997 | 0.982 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Cheng, Y.; Yu, D.; Tan, G.; Zhu, C.
Low-Temperature Performance and Damage Constitutive Model of Eco-Friendly Basalt Fiber–Diatomite-Modified Asphalt Mixture under Freeze–Thaw Cycles. *Materials* **2018**, *11*, 2148.
https://doi.org/10.3390/ma11112148

**AMA Style**

Cheng Y, Yu D, Tan G, Zhu C.
Low-Temperature Performance and Damage Constitutive Model of Eco-Friendly Basalt Fiber–Diatomite-Modified Asphalt Mixture under Freeze–Thaw Cycles. *Materials*. 2018; 11(11):2148.
https://doi.org/10.3390/ma11112148

**Chicago/Turabian Style**

Cheng, Yongchun, Di Yu, Guojin Tan, and Chunfeng Zhu.
2018. "Low-Temperature Performance and Damage Constitutive Model of Eco-Friendly Basalt Fiber–Diatomite-Modified Asphalt Mixture under Freeze–Thaw Cycles" *Materials* 11, no. 11: 2148.
https://doi.org/10.3390/ma11112148