5.1. The model Analysis Based on 3D Texture Data
According to the research program, the 3D texture and the friction coefficients of each specimen are respectively tested. Then, a total of 110 sets of data are obtained. However, only the test data of AC-13 using limestone is shown in
Table 2. The 3D texture reconstruction results of AC-13(L)-4 h are displayed in
Figure 5.
The multiple linear regression model is first used to analyze the relationship between pavement skid resistance (BPN, DF60) and 3D texture indicators. Regrettably, the Regression coefficient R2 is relatively low, no more than 0.5. Thus, the multiple linear regression model is unsuitable for the relationship building. Therefore, the other regression model will be further considered.
Then the multiple quadratic multinomial regression model is used. 3D texture-based indicators are firstly integrated into a synthetic vector:
.
X and
Y are the virtual variables, which represent the wear resistance of aggregates.
X = 1 means the mineral aggregate is limestone;
X = 0 means the mineral aggregate is other materials. When
X = 0 and
Y = 1, the mineral aggregate is steel slag; but when
X = 0 and
Y = 0, then the mineral aggregate is basalt. The model can be expressed as follows:
where,
F is the skid resistance indicator (it refers to
BPN or
DF60 in this article);
M is the synthetic vector;
A,
B and
C are respectively the quadratic term coefficient matrix, monomial coefficient matrix and the constant term. The matrix
A is a symmetric square matrix.
The statistical analysis software (SAS) is used to write programs for solving this regression model. Then the insignificant independent variables are removed in turn by stepwise analysis until obtaining a satisfactory regression effect. One favorable regression effect is mainly reflected in three aspects: First, the fitting degree is excellent, namely that the value of R2 is close to 1; Second, model equation satisfies the significant level, which means the inspection probability of model parameter estimation satisfies: p < 0.05; Third, there is a significant regression relationship between all independent variables and dependent variable. The probability of factor test satisfies: p < 0.05.
As for the regression model of
BPN, four indicators (
X,
MTD1,
Sk1 and
λ) are finally retained to constitute the synthetic vector:
. The regression analysis results are shown in
Table 3,
Table 4 and
Table 5. Then, the multiple quadratic multinomial regression model and the parameters
A1,
B1 and
C1 are shown in Equation (12).
In
Table 3, the
R2 is 0.8035. Data points are more densely gathered near the regression estimation, which means the fitting degree is good. In
Table 4, All the probability values of linear, quadratic, crossproduct and total model are lower than 0.05. The relationship between dependent variable and independent variables is significant, and the regression equation model is also significant. Additionally, a factor test of model independent variables is further processed, shown in
Table 5. The probability values are all smaller than 0.05, which indicate that the overall regression coefficient of each factor is highly significant.
As for the regression model of
DF60, five indicators
X,
Y,
MTD,
Sk1 and
λ are finally retained to constitute the synthetic vector
M2. Then the multiple quadratic polynomial model between
DF60 and
M2 is established. The regression analysis results are shown in
Table 6,
Table 7 and
Table 8, and the multiple quadratic multinomial regression equation and the parameters
A2,
B2 and
C2 are shown in Equation (13).
In
Table 6,
R2 is as high as 0.9255 and root
MES is only 0.0251. The fitting degree is high. Notably, the total data points can well gather near the regression estimation. The F test-based probability values of linear, quadratic, crossproduct, and total model are respectively listed in
Table 7. Although the probability value of quadratic cannot meet the requirements of below 0.05, the probability value of total model satisfies
p < 0.0001. From the perspective of overall level, the regression equation model is significant. Additionally, the significant degree of regression coefficient is provided in
Table 8. The results show that the probability values of every factor are all lower than 0.05, which means that the overall regression coefficient of each factor is highly significant.
The comparison between Equations (12) and (13) indicates that the independent variable Y appears in DF60 model but not in BPN model. The results show that compared with DF60, the requirements of mineral aggregate classification for BPN model is relative loose. Analyzing the reasons maybe that different testing speeds determine the impact and abrasion of test equipment on aggregates. Then more intense forces make DF60 more sensitive to the hardness or wear-resistant of mineral aggregates.
5.2. The Further Harmonization of Evaluation Model
At present, there are numerous types of equipment being used to test pavement skid resistance. And the evaluation standard from different test methods is not unified, which brings a lot of obstacles for the communication with each other. In order to harmonize different test methods, the Permanent International Association of Road Congresses (PIARC) proposed the PIARC model and established International Friction Index (IFI). IFI was defined as the function containing two parameters
Sp and
F60. In IFI evaluation method,
F(
S) can be calculated:
where,
F(
S) is the standard friction coefficient at any testing speed
S;
F60 is the standard friction number, which can be calculated from the friction coefficient tested by any detection equipment at any testing speed
FRS;
Sp is the speed number, which represents the morphological characteristics of macro-texture.
The relationship between
Sp and
MTD has been listed in the references [
25,
26]. The calibration parameters of
F60 corresponding to
DF60 have also been given in the reference (ASTM, 2011), Equations (15) and (16).
In
Section 5.1, the relational expression between
DF60 and 3D texture indicators has been established. Then, the harmonization of evaluation model using 3D texture data can be obtained easily, in Equation (17).
In Equation (16), the final evaluation model just needs to measure the pavement 3D texture. It is no longer necessary to test the friction coefficient in field environment that has strong conditional limitations. After testing pavement 3D texture, it directly calculates the standard friction coefficient at any testing speed F(S). Then, FRS tested by any detection equipment at any testing speed can be solved through F60. Hence, the harmonization and comparison from different test methods can be easily achieved based on the evaluation model. In summary, this evaluation model is simple to operate and implement, since the evaluation results directly depend on pavement 3D texture. It also combines with the advantages of IFI evaluation method, which is conducive to harmonize different testing results from different detection conditions.