4.2.2. Maximum Water Film Path Length (WFPLmax)
The WFPL
max of two-way eight-lane, ten-lane, and twelve-lane circular-curve sections are simulated under different linear combinations of TS and LS. The results are shown in
Table 10. At a certain value of PW and TS, WFPL
max values are positively correlated with LS. With the arch TS is 2%, WFPL of 4% LS under two-way eight lanes is 2.21 times that of 0.3% LS. WFPL of 4% LS under two-way ten lanes is 2.21 times that of 2% LS. WFPL of 4% LS under two-way twelve lanes is 2.22 times that of 2% LS. The increase in LS, although allowing for an increase in the synthetic slope of the pavement, is biased in the direction of LS, while the longitudinal length of the pavement is quite long compared to the transverse width, which increases WFPL.
Increasing TS from 2% to 2.5% for circular-curved sections with the same LS can effectively reduce the WFPLmax. This not only increases the synthetic slope but also causes the synthetic LS direction to gradually deviate from the TS direction, which makes the WFPL decrease greatly because the transverse width of the pavement is quite short relative to the longitudinal length. When LS is the same, WFPLmax continues to become longer as PW becomes larger. This is due to certain conditions of the same TS and LS. The direction of water flowing is unchanged, and the number of lanes increases so that the PW increases. The water flow is correspondingly longer, so the WFPL increases greatly.
As shown in
Table 11, it can be seen that when the number of lanes is certain, the larger the LS, the better the reduction effect of WFPL
max through changing TS from 2% to 2.5%. For a two-way eight-lane pavement, changing TS from 2% to 2.5%, the reduction of WFPL
max at 4% LS is 6.55 m, which is 82 times the decrease corresponding to 0.3% LS (0.08 m). For the two-way ten-lane pavement, changing TS from 2% to 2.5%, the reduction of WFPL
max at 4% LS is 7.86 m, which is 87 times the decrease in the corresponding 0.3% LS (0.09 m). For the two-way twelve-lane pavement, the reduction of WFPL
max at 4% LS is 9.17 m, which is 92 times the decrease corresponding to 0.3% LS. From
Table 11, it can be found that the reduction of WFPL
max, when changing TS from 2% to 2.5%, is not only obvious with the increase in LS, but is significant with the increase in PW. It can be concluded that in the case of a wide circular-curve section with limited alignment and large design LS, it can be considered to increase TS from 2% to 2.5% to reduce WFPL
max, and the wider the pavement width, the better the improvement effect.
The following linear regression analysis was carried out using SPSS to rank the effect degree of the three indicators of TS, LS, and PW on WFPL
max regarding the absolute value of the standard coefficient, and the results are shown in
Table 12. From
Table 12, it can be seen that when using the absolute value of the standard coefficient for comparison, the LS has the greatest influence on the WFPL
max, followed by the PW, and the TS has the smallest influence.
4.2.3. Maximum Water Flow Depth (WFDmax)
Results of the WFD
max, the WFD on the first lane middle line, and the WFD on the second lane middle line of circular-curve sections under different LS, TS, and PW conditions at 120 km/h are shown in
Table 13 and
Table 14. For circular-curve sections under the design speed of 120 km/h, the WFD
max and the WFD on the first/second lane middle line are not greater than 5.03 mm, are lower than the safe WFD thresholds, thus meeting the needs of traffic safety. When PW and TS are certain, the WFD
max and WFD on the first/second lane middle line increase with the increase in LS. For two-way eight lanes under 2% TS and 4% LS, the WFD
max is 3.65 mm relative to a 2% LS increase of 0.14 mm. For two-way ten lanes under 2% TS and 4% LS, the WFD
max is 3.89 mm relative to the 2% LS increase of 0.14 mm. For the two-way ten lanes under 2% TS and 4% LS, the WFD
max is 4.12 mm relative to the 2% LS increase of 0.16 mm. This is because when the TS is fixed, the increase in LS makes the synthetic slope direction favor the longitudinal direction of the pavement, the WFPL
max becomes bigger, and the retention time of the water flow on the surface becomes longer, which leads to the increase in the WFD.
When the LS is the same, increasing the TS from 2% to 2.5% can effectively reduce the WFD. As the LS and PW increase, increasing the TS has a better effect on reducing the WFD. The increase in TS can not only increase the synthetic slope of the pavement and accelerate the water drainage but also make the direction of the WFP gradually biased in the direction of TS because the length of the transverse width of the pavement is much smaller than the length of the longitudinal direction, which makes the pavement surface water in a certain width of the pavement flow through a reduced distance, and the WFPL is shortened so that the WFD is greatly reduced. Moreover, the WFDmax and the WFD on the first and second lanes become larger as the PW increases at a certain TS and LS. This is due to the fact that as the number of lanes increases, the pavement becomes wider, the WFPLmax becomes longer, the corresponding WFPL also becomes longer, and the retention time of the surface water on the pavement becomes longer, resulting in the accumulation of water film, and the WFD increases accordingly.
The relationship between the change rate of the WFD
max and LS is shown in
Figure 8. From
Figure 8, it can be seen that when LS is certain, the change rate of the WFD
max (
Figure 8a), the change rate of the WFD in the first travel lane middle (
Figure 8b), and the change rate of the WFD in the second lane middle (
Figure 8c) decrease successively, indicating that the further the distance from the central median, the smaller the change rate of the WFD affected by LS. Moreover, the change trends of the WFD
max and the WFDs in the first/second lanes with the growth of the LS are consistent, and all of them have the maximum value at LS of 2.1%. In cases where the LS is less than 2.1%, the WFD change rate becomes faster as LS increases, while in cases where the LS is greater than or equal to 2.1%, the WFD change rate becomes slower with the LS growth. In the case of LS between 1.1% and 4%, the change in LS has a greater effect on the WFD than in the case of LS between 0.3% and 1.1%. It can be concluded that it is more effective to reduce the WFD by adjusting LS when the LS is between 1.1–4%, and it is not recommended to prioritize adjusting the LS metrics to reduce the WFD
max when the LS is less than 1.1%.
Moreover, widening of two-way ten lanes to twelve lanes while adjusting TS from 2% to 2.5%, or widening of two-way eight lanes to ten lanes while adjusting TS from 2% to 2.5%, can both reduce the WFDmax, and the wider the pavement, the greater the magnitude of the reduction of the WFDmax. The maximum reduction can reach 0.08 mm. Therefore, in the design of the widening of the old road, 2.5% can be considered the minimum TS to effectively alleviate the problem of the WFD on the inside of the road becoming larger as a result of road widening.
The linear regression analysis was carried out using SPSS to rank the influence degree of the three indicators of the TS, LS, and PW on the WFD
max regarding the absolute value of the standard coefficient, and the results are shown in the table below. As can be seen from
Table 15, when using the absolute value of the standard coefficients for comparison, PW has the greatest impact on WFD
max, followed by TS and LS.