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  .
2. The Raw Material Performance Test
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 Table 1  .
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 Table 2  .
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 Table 3.
Lignin fiber was used, the basic performance test results are shown in Table 4.
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 raw materials used in the test are all in line with the requirements of the road.
3. Cold-Filled Asphalt Mixture Design
The aggregate gradation design scheme and the optimum oil-stone ratio of cold-filled SMA-13 asphalt mixture are shown in Table 5  .
Table 1. No. 90 Class A asphalt test results.
Table 2. Basalt coarse aggregate technical index.
Table 3. The technical index of limestone fine aggregate.
Table 4. The technical index of lignin fiber.
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 Table 6  .
It can be seen from Table 6 that the range of fractal dimension satisfying the low-temperature bending strain is D = 2.5484 - 2.6122, Dc = 2.0172 - 2.1676, Df = 2.6695 - 2.8772.
The ternary linear regression model is established through taking εB as the dependent variable, taking D, Dc, Df as the independent variables.
Table 5. The scheme of gradation design of cold-filled SMA-13 asphalt mixture.
Table 6. The fractal dimension of cold-filled SMA-13 asphalt mixture and the low temperature test data.
Note: The second group of bending strain εB 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).
εB = −432953 − 20571.98D + 99964.86 Dnc + 104839.34 Df (1)
Regression coefficient R2 = 0.956.
The ternary linear correlation models of bending strain and three fractal dimensions are established, the correlations of data in Table 6 are analyzed by using SPSS software to obtain the correlation between the bending strain and fractal dimension, as is shown in Table 7.
It can be seen from Table 7, the correlation sequence of low temperature bending strain εB and the fractal dimension D, DC, Df from large to small is Df > D > DC, indicating that the relation between the aggregate fractal dimension and bending strain is relatively large, the correlation between εB and DC is relatively small.
The correlation model of εB and Df is established, as is shown in the formula (2).
εB = −115184 + 46204Df (2)
Regression coefficient R2 = 0.790.
The correlation model of εB and D, Df is established, as is shown in the Formula (3).
εB = −333868 + 104099D + 28508Df (3)
Regression coefficient R2 = 0.998.
Similarly, the ternary linear regression models of bending strength is established, as is shown in the Formula (4).
RB = 59 + 22.55D − 26.96Dc − 21.19Df (4)
Regression coefficient R2 = 0.940.
For the correlation between the bending failure strength and the fractal dimension, the data in Table 6 are analyzed by SPSS software. The relationship between the bending failure strength RB and the fractal dimension is shown in Table 8.
Table 7. Correlation between low temperature bending failure strain and fractal dimension of cold-filled SMA-13 asphalt mixture.
Table 8. Correlation between low temperature bending strength and fractal dimension of cold-filled SMA-13 asphalt mixture.
Table 9. The prediction model comparison of bending strain and bending strength for cold-filled SMA-13 asphalt mixture.
It can be seen from Table 8 that the correlation between the bending strength RB and the fractal dimension DC of the coarse aggregate gradation is relatively large. Therefore, a correlation model between the bending strength and the fractal dimension DC can be established. But the regression coefficient is low.
4. Model Selection
As described above, a correlation model of low-temperature bending strain, bending strength and fractal dimension is established, and the results are summarized in Table 9.
It can be seen from Table 9 that the prediction accuracy of model 1, 3 and 4 is relatively high, and the model 1 and 3 are recommended as the prediction model of low temperature bending strain and the model 4 is recommended as the prediction model of low temperature bending strength through multi-model comparison.
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.