^{1}

^{*}

^{2}

^{3}

^{1}

Sets of cold-filled SMA-13 asphalt mixture were designed by means of orthogonal design method. The bending and low temperature creep tests of the cold-filled SMA-13 asphalt mixture were carried out. The related models of the fractal dimension and the road performance evaluation index including low temperature bending failure strain ε
_{B} and bending strength RB are established by using fractal theory. The model can be used to predict the low temperature performance of cold-filled SMA-13 asphalt mixture according to the design gradation, which can reduce the test workload and improve the working efficiency, so as to provide the reference for engineering design.

The heat compensation method is not suitable for construction in a humid, low temperature environment and pollutes the environment. On the basis of the previous research results at home and abroad, the research group, combined with the characteristics of climate, transportation and materials in Northeast China, independently research and develop cold-filled asphalt mixture suitable for the freezing period and with good road performance. Cold-filled asphalt mixture low-temperature performance is an important component of road performance, especially for the northeastern region. If the correlation model between cold-filled asphalt mixture fractal dimension and low temperature performance evaluation index can be established, the low temperature performance of cold-filled asphalt mixture can be predicted through the gradation fractal dimension to reduce the amount of test work. Based on the correlation analysis between the fractal dimension and the evaluation index of low temperature performance, the low temperature performance prediction model is established and the low temperature performance prediction model of cold-filled SMA-13 asphalt mixture is recommended through the comparison of multiple models [^{ }

Liaohe petroleum asphalt grade A No. 90, which is widely used in the northeast of China and the basic performance test results are shown in ^{ }

The coarse aggregate of cold-filled SMA-13 asphalt mixture use basalt gravel produced by Jilin Dawan Quarry. The basic performance test results are shown in

The fine aggregate should be clean, dry, no weathering, no impurities, and appropriate particle size distribution. Fine aggregate use mechanism sand from limestone produced by Liaoyang Xiaotun Yongli quarries. The basic performance test results are shown in

Lignin fiber was used, the basic performance test results are shown in

The variation coefficient of test data in Tables 1-4 is less than 15%.

24 sets of cold-filled asphalt additive preparation schemes were designed, which were combined with matrix asphalt, thinner and mineral materials to form cold-filled asphalt mixture. The compaction, looseness and low-temperature workability test were tested to select the optimal one. No. 16 cold-filled asphalt liquid was selected [

The aggregate gradation design scheme and the optimum oil-stone ratio of cold-filled SMA-13 asphalt mixture are shown in

Test items | Test value | Specification requirements | |
---|---|---|---|

Penetration (25˚C, 100 g, 5 s) 0.1mm | 91 | 80 - 100 | |

Ductility (15˚C) cm | >100 | ≥100 | |

Softening Point (R & B)˚C | 44.5 | ≥44 | |

Penetration index PI | −1.36 | −1.5 - 1.0 | |

60˚C Dynamic viscosity (Pa・s) | 163 | ≥140 | |

Wax content distillation | 1.91 | ≤2.2 | |

Flash point COC (˚C) | 245 | ≥243 | |

Solubility | 99.63 | ≥99.5 | |

Film heating test 163˚C, 5 h | Quality loss (%) | −0.3 | ±0.8 |

Penetration ratio 25˚C (%) | 67.4 | ≥57 | |

Ductility 10˚C, 5 cm/min (cm) | 32 | ≥8 |

Material specification (mm) | 13.2 - 16 | 9.5 - 13.2 | 4.75 - 9.5 | |
---|---|---|---|---|

Technical index | Standard value | Test value | ||

Crushing value (%) | ≤26 | 12.4 | 13.2 | 13.2 |

Apparent relative density (T/m^{3}) | ≥2.6 | 2.94 | 2.95 | 2.96 |

Water absorption rate (%) | ≤2.0 | 0.50 | 0.86 | 1.52 |

Consistency | ≤12 | 8 | ||

Content of needle and sheet granular (%) | ≤15 | 8.2 | 7.8 | 6.6 |

<0.075 Particle content (%) | ≤1 | 0.2 | 0.2 | 0.2 |

Material specification (mm) | 2.36 - 4.75 | 1.18 - 2.36 | 0 - 1.18 | |
---|---|---|---|---|

Technical index | Standard value | Test value | ||

Apparent relative density (T/m^{3}) | ≥2.5 | 2.687 | 2.765 | 2.734 |

Content of clay (%) | ≤3 | 0.5 | 1.5 | 1.5 |

Test items | Test results | Standard |
---|---|---|

Fiber length | <6 mm | <6 mm |

Ash content | 18.6% | 18% ± 5%, Non volatile matter |

PH value | 7.7 | 7.5 ± 1 |

Oil absorption rate | 5.8 | ≥5 times quality of fiber |

Moisture content | 3.5% | <5% (Quality calculation) |

Relative density | 1.006 |

Test results

Trabecular bending test at a temperature of −10˚C were done according to the Standard Test Method of Bitumen and Bituminous Mixtures for Highway Engineering (JTG E20-2011). The experimental results and the corresponding fractal dimensions of the low temperature stability for cold-filled SMA-13 asphalt mixture are summarized in

Model building

It can be seen from _{c} = 2.0172 - 2.1676, D_{f} = 2.6695 - 2.8772.

The ternary linear regression model is established through taking ε_{B} as the dependent variable, taking D, D_{c}, D_{f} as the independent variables.

No. | Percentage of quality pass (%) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

16 | 13.2 | 9.5 | 4.75 | 2.36 | 1.18 | 0.6 | 0.3 | 0.15 | 0.075 | Oil-stone ratio | |

1 | 100 | 95 | 62.5 | 27 | 20.5 | 19 | 16 | 13 | 12 | 10 | 5.03 |

2 | 100 | 95 | 68.8 | 30.5 | 23.3 | 21.5 | 18 | 14.5 | 13.5 | 11 | 5.23 |

3 | 100 | 95 | 56.3 | 23.5 | 17.8 | 16.5 | 14 | 11.5 | 10.5 | 9 | 4.82 |

4 | 100 | 97.5 | 62.5 | 27 | 23.3 | 21.5 | 18 | 11.5 | 10.5 | 9 | 5.04 |

5 | 100 | 97.5 | 68.8 | 30.5 | 17.8 | 16.5 | 14 | 13 | 12 | 10 | 4.92 |

6 | 100 | 97.5 | 56.3 | 23.5 | 20.5 | 19 | 16 | 14.5 | 13.5 | 11 | 5.15 |

7 | 100 | 92.5 | 62.5 | 27 | 17.8 | 16.5 | 14 | 14 | 13.5 | 11 | 5.04 |

8 | 100 | 92.5 | 68.8 | 30.5 | 20.5 | 19 | 16 | 11.5 | 10.5 | 9 | 4.93 |

9 | 100 | 92.5 | 56.3 | 23.5 | 23.3 | 21.5 | 18 | 13 | 12 | 10 | 5.15 |

10 | 100 | 98.1 | 65.2 | 25.6 | 19.8 | 16.3 | 13.8 | 12.4 | 10.4 | 8.7 | 4.93 |

11 | 100 | 97.4 | 61.1 | 28.7 | 22.1 | 17.8 | 15.1 | 13 | 11.7 | 10 | 5.09 |

12 | 100 | 97.7 | 56.1 | 26.2 | 20.9 | 18.5 | 15 | 12.2 | 11.5 | 10 | 5.04 |

13 | 100 | 92.5 | 67.5 | 23.5 | 20 | 19 | 16 | 14 | 12 | 10 | 5.04 |

Gradation number | Average maximum load (N) | Average span deflection (mm) | Bending strain ε_{B} (με) | Bending strength Mpa | D | D_{c} | D_{f} |
---|---|---|---|---|---|---|---|

SMA1 | 212 | 2.8 | 14078 | 1.79 | 2.5811 | 2.0965 | 2.7723 |

SMA2 | 230 | 3.88 | 19613 | 2.00 | 2.5958 | 2.1676 | 2.7640 |

SMA3 | 183 | 1.44 | 7288 | 2.02 | 2.5643 | 2.0172 | 2.7826 |

SMA4 | 268 | 1.65 | 8227 | 2.90 | 2.5569 | 2.1493 | 2.6695 |

SMA5 | 252 | 2.78 | 14201 | 2.10 | 2.5670 | 2.0380 | 2.8325 |

SMA6 | 270 | 1.92 | 9868 | 2.34 | 2.6122 | 2.0761 | 2.8170 |

SMA7 | 204 | 3.64 | 18666 | 1.68 | 2.6005 | 2.0378 | 2.8772 |

SMA8 | 216 | 3.51 | 18153 | 1.74 | 2.5484 | 2.1150 | 2.7224 |

SMA9 | 319 | 2.55 | 13947 | 2.17 | 2.5959 | 2.1470 | 2.7193 |

SMA10 | 249 | 2.57 | 13040 | 2.18 | 2.5489 | 2.0595 | 2.7769 |

SMA11 | 574 | 1.59 | 10346 | 4.99 | 2.5737 | 2.1385 | 2.7959 |

SMA12 | 248 | 2.48 | 12903 | 2.01 | 2.5781 | 2.1043 | 2.7833 |

SMA13 | 376 | 2.07 | 10639 | 3.07 | 2.5873 | 2.0589 | 2.7722 |

Note: The second group of bending strain ε_{B} data in the table is subject to further determination. The variation coefficient of test data in the table is less than 15%.

The correlation model of the bending strain and the fractal dimension is established by the regression analysis, as is shown in Formula (1).

ε_{B} = −432953 − 20571.98D + 99964.86 D_{nc} + 104839.34 D_{f} (1)

Regression coefficient R^{2} = 0.956.

The ternary linear correlation models of bending strain and three fractal dimensions are established, the correlations of data in

It can be seen from _{B} and the fractal dimension D, D_{C}, D_{f} from large to small is D_{f} > D > D_{C}, indicating that the relation between the aggregate fractal dimension and bending strain is relatively large, the correlation between ε_{B} and D_{C} is relatively small.

The correlation model of ε_{B} and D_{f} is established, as is shown in the formula (2).

ε_{B} = −115184 + 46204D_{f} (2)

Regression coefficient R^{2} = 0.790.

The correlation model of ε_{B} and D, D_{f} is established, as is shown in the Formula (3).

ε_{B} = −333868 + 104099D + 28508D_{f} (3)

Regression coefficient R^{2} = 0.998.

Similarly, the ternary linear regression models of bending strength is established, as is shown in the Formula (4).

RB = 59 + 22.55D − 26.96D_{c} − 21.19D_{f} (4)

Regression coefficient R^{2} = 0.940.

For the correlation between the bending failure strength and the fractal dimension, the data in _{B} and the fractal dimension is shown in

ε_{B} | D | D_{c} | D_{f} | |
---|---|---|---|---|

ε_{B} | 1.000 | 0.579 | −0.115 | 0.651 |

D | 0.579 | 1.000 | 0.070 | 0.326 |

D_{c} | −0.115 | 0.070 | 1.000 | −0.818 |

D_{f} | 0.651 | 0.326 | −0.818 | 1.000 |

R_{B} | D | D_{c} | D_{f} | |
---|---|---|---|---|

R_{B} | 1 | 0.021 | 0.193 | −0.413 |

D | 0.021 | 1 | −0.061 | 0.468 |

D_{c} | 0.193 | −0.061 | 1 | −0.791 |

D_{f} | −0.413 | 0.466 | −0.791 | 1 |

Model No. | Model expression | Regression coefficient R^{2} |
---|---|---|

1 | ε_{B} = −432953 − 20571.98D + 99964.86D_{c} + 104839.34D_{f} | 0.956 |

2 | ε_{B} = −115184 + 46204D_{f} | 0.790 |

3 | ε_{B} = −333868 + 104099D + 28508D_{f} | 0.998 |

4 | R_{B} = 59 + 22.55D − 26.96D_{c} − 21.19D_{f} | 0.940 |

It can be seen from _{B} and the fractal dimension D_{C} of the coarse aggregate gradation is relatively large. Therefore, a correlation model between the bending strength and the fractal dimension D_{C} can be established. But the regression coefficient is low.

As described above, a correlation model of low-temperature bending strain, bending strength and fractal dimension is established, and the results are summarized in

It can be seen from

The correlation model recommended between the fractal dimension and the evaluation index of low temperature performance can be used to predict the low temperature performance of cold-filled SMA-13 asphalt mixture according to the design gradation, which can reduce the test workload and improve the working efficiency.

This research was financially supported by Liaoning Provincial Expressway Operation Management Co., Ltd.

The authors declare no conflicts of interest regarding the publication of this paper.

Sun, Z.H., Wang, S.M., Ma, S. and Liu, S. (2018) Low Temperature Performance Prediction Model of Cold-Filled SMA-13 Asphalt Mixture. Materials Sciences and Applications, 9, 1066-1072. https://doi.org/10.4236/msa.2018.913077