4.1. Contrast of Permanent Deformation in Flat Straight Road and Curved Ramp
As illustrated in nephograms, the permanent deformations in straight and flat road as well as those in the horizontally curved and sloped section are shown in
Figure 7 and
Figure 8 respectively.
It was found that asphaltic mixtures in the pavement surface courses under two different alignments showed slow viscous flow after prolonged loading and unloading cycles, and different locations featured quite different deformations. Overall, the deformation decreased with the distance from axle center increasing. It was observed that the greatest vertical displacement occurred right below the axle load since the vertical compressive stress herein reaches the maximum value. In contrast, asphaltic mixture that is around the wheel contact area showed swelling due to considerable lateral extruding force.
However, the deformation in curved ramp showed some differences in terms of magnitude and deformation features. On the one hand, it is seen from the above two figures that the compressive deformation in curved and sloped roadway was greater than in the simple straight highway. Detailed calculation shows that the maximum vertical deformation, maximum bump height and total rutting depth in curved slope is 9.87, 0.68 and 10.55 mm respectively whereas that in simple road is 8.93, 0.46 and 9.39 mm respectively. The deformation in the first condition is about 1.1 times that in the second condition. This result is consistent with the in-situ rutting observation [
11,
28]. Another remarkable deformation characteristic is its asymmetric upheaval surrounding the rut groove, which may have resulted from the longitudinal and transverse friction force. As shown in
Figure 8, the pavement area along the downward direction showed evident upheaval due to longitudinal friction force. While the asphaltic mixture upward showed a much smaller bump. Moreover, similar deformations could be found with respect to the transverse section.
Figure 8 shows that the upheaval developed on the outside pavement of the horizontal curve seemed larger than the inner side. This is probably due to the sideway friction force.
According to current literature, Pei and Kong et al. had investigated the rutting deformation of long sloped asphalt pavements. Their field inspections revealed that most serious rutting occurred on the top area of profile, and the rutting depth in slopes was greater than in tangential flat road [
11,
28]. By comparing, it was found that the authors’ simulation agreed with the previous research. However, the downward upheaval is not obvious in actual sloped road mainly because actual loading is not applied statically within a local spot but rather a stripped dynamic load. Therefore, the longitudinal upheaval tends to be smooth under the repeated rolling of vehicles.
4.2. Influential Factor Analysis Using Orthogonal Design Method
This section presents the discussion on the influence of different factors on the deformation developed in the HMAC pavement with sloped and horizontally curved road alignment. In view of the massive calculating runs resulting from full factorial design (5
6 = 15,625), the Taguchi array was employed to reduce experimental run. The Taguchi method or orthogonal design method (ODM) developed by Dr. Genichi Taguchi in Japan is a partial fraction experiment and has found wide use in many regions [
29]. This method uses a special set of arrays called orthogonal array (OA) to choose the level combination of the variables for each experiment and to determine the minimal number of experiments to give full information of the factors that affect the objective index [
30].
This research considered the permanent deformation as the objective index and chose six main factors each with five levels to reflect their influence. The factors and their levels are shown in
Table 5.
An OA is usually denoted by
LN(
lk), where
N is the number of performed experiments,
l is the number of levels per factor and
k is the number of factors. This study selected the
L25(5
6) OA (shown in
Table 6) to design factor-level combination and to conduct trial calculations, which needs 25 experimental runs to give necessary data for further analysis. The calculated deformations under each of the 25 experiments are shown in the rightmost column of
Table 6.
The Taguchi method usually uses intuitive analysis to analyze experimental data since it could give an explicit depict of the influence of different factors. The result of intuitive analysis in this study is also shown in
Table 6. To guide the readers, several supplementary instructions to this table are presented as follows.
In
Table 6,
Kji is the sum of the deformations with factor
j at
i level (
j = P1 to P6,
i = 1 to 5) out of all trials. In addition, the average value of
Kji and the range of each parameter is calculated as follows.
According to the Taguchi method, the range of a factor could reflect its influence on the objective index. The larger the range value of a factor, the greater its effect on the process [
31]. Based on the intuitive analysis, the ranking of factors according to their effect on pavement deformation in descending order is P2 → P1 → P3 → P4 → P6 → P5. According to
Table 5, this indicates that ESAL and contact pressure showed greater impact on the deformation developed in special road, and the thickness of upper and middle asphaltic layers were also crucial to the pavement deformation whereas the binder asphalt layer and semi rigid base demonstrated less influence.
The intuitive analysis diagram that indicates the change of pavement deformation with various factors is shown in
Figure 9.
From
Figure 9a, it could be seen that the deformation (left
Y-axis) increased linearly with the rise in tire pressure (bottom
X-axis). The deformation under the pressure of 1.6 MPa was approximately five times that under 0.4 MPa. The pavement deformation (right
Y-axis) also increased linearly with the increase in ESAL (top
X-axis). The deformation under ESAL of 2800 (10
4 times) is eight times that under ESAL of 200 (10
4 times). According to the authors’ previous research on HMAC pavement rutting with simple alignment, the deformation correlated well with ESAL in a convex power function whose exponent was 0.303 [
32]. In contrast,
Figure 9a shows that the pavement deformation in horizontally curved and sloped road increased linearly with ESAL, meaning the deformation susceptibility to traffic load in special road is increased. This result further confirms that heavy duty as well as overloading poses significant negative influence on pavement performance and should be therefore strictly controlled.
Also,
Figure 9b indicates the deformation in HMAC pavement with sloped and curved alignment changed differently with the change in depth of each structural layer. In detail, the deformation (left
Y-axis) increased by 19.5% when the upper layer depth changed from three to five centimeters (bottom
X-axis), whereas it decreased by 48.3% with the depth increasing to seven centimeters further. This suggests that an upper asphaltic course no less than five centimeters in complicated road is necessary considering the anti-rutting performance of entire pavement. In contrast, the deformation (left
Y-axis) decreased by 43.3% when the middle HMAC course depth (bottom
X-axis) doubled. It could be thereof inferred that increasing thickness of the middle course contributed most to the reduction in pavement permanent deformation since the HMAC was used in this layer. Unlike the upper and middle asphalt courses, increase in the binder course depth (bottom
X-axis) had little effect on the change of permanent deformation (left
Y-axis), according to
Figure 9b. It was concluded that the upper and middle asphalt courses were crucial to the rutting resistant performance of HMAC pavement under complicated route conditions. According to the literature, Xu suggested that modified asphalt binder be used in the middle and binder asphaltic layers to relieve pavement rutting in simple alignment [
3]. However, this study shows that as far as special road is concerned, the upper and middle courses were more crucial to the pavement anti-rutting performance. This indicates that inclusion of the longitudinal and transverse shear force changed pavement deformation characteristic and the potential rutting area had a tendency to move up in curved ramp.
Similarly,
Figure 9b shows the pavement deformation (right
Y-axis) changed little with the increase in the depth of semi-rigid base (top
X-axis). Calculation shows that the deformation decreased simply by 12.3% when the base thickness doubled, which suggests that an appropriate thickness that is not too great would be suitable for semi-rigid base.