Research on Average Longitudinal Slope Length of Expressway Based on Braking Behavior

doi:10.12141/j.issn.1000-565X.230674

Abstract

Abstract:

Excessive temperature of the truck brake hub is a primary factor leading to brake failure. To enhance the safety of trucks traveling on continuous downhill sections, this study refined the average longitudinal slope design parameters and investigated the correlation between driver braking behavior and the temperature rise characte-ristics of truck brake hubs. Based on driver braking behavior, it proposed a reliability design method for longitudinal slope length. Firstly, a continuous downhill section of an expressway in the western mountainous area was selected for real vehicle test, and the road longitudinal slope parameters and driver braking behavior data were collected. Secondly, according to the measured data, the evaluation indexes were proposed: displacement intensity coefficient and brake hub temperature gradient. This study investigated the relationship between displacement intensity coefficient and road profile, both longitudinal and transverse, as well as the relationship between displacement intensity coefficient and brake hub temperature gradient through regression analysis. Finally, a reliability model was constructed based on the driver’s braking behavior and critical temperature. Using the Monte Carlo simulation, critical slope lengths corresponding to different average longitudinal slopes on continuous downhill sections were determined and compared with the specification. The results indicated that there is a weak correlation between the radius of the circular curve and the displacement intensity coefficient, while there is a significant positively correlation between the longitudinal slope gradient and the displacement intensity coefficient, and the goodness of fit r² is 0.95. When the longitudinal slope gradient is greater than 2%, the braking measures taken by drivers are mostly sustained braking, which is more different from the braking behavior of drivers mostly taking point braking when the longitudinal slope gradient is less than 2%. The displacement intensity coefficient and the temperature gradient of the braking hub are significantly positively correlated with the goodness-of-fit r² is 0.845. When the proportion of the driver braking for 85%, the braking behavior of the driver at this time with the specification of defining the conditions of the slope length is basically the same. When the reliability is 0.95, the average longitudinal slope is 2.1%~3.0%, and the critical value of the continuous slope length is 14.95~30.12 km. The given reference values take into account the randomness in the real driving environment, and provide a basis for the design of the slope length with an average slope of less than 2.5%.

Key words: road engineering, braking behavior, displacement strength coefficient, reliability, critical slope length

CLC Number:

U491.2⁺55

ZHANG Chi, GUO Tingyu, HU Ruilai, GAO Yanyang, ZHOU Yuming. Research on Average Longitudinal Slope Length of Expressway Based on Braking Behavior[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(2): 12-26.

Figures/Tables 23

Fig.1

Fig.2

Table 1

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Table 2

Results of correlation test between displacement strength coefficient and circular curve radius"

回归类型	回归函数形式	标准误差	P> $t$	r²
线性回归	y=ax+b	0.050 7	0.000	0.262 5

Table 2

Fig.8

Fig.9

Table 3

Results of correlation test between displacement strength coefficient and longitudinal slope"

回归类型	回归函数形式	标准误差	P> $t$	r²
线性回归	y=ax	0.004 9	0.000	0.950 4

Table 3

Fig.10

Table 4

Fig.11

Table 5

Results of correlation test between displacement strength coefficient and brake hub temperature gradient"

回归类型	函数形式	标准误差	P> $t$	r²
线性回归	y=ax+b	0.008 2/0.005 0	0.000/0.012	0.845
指数回归	y=ae ^bx	0.003 7/0.084 8	0.000/0.000	0.782
幂函数回归	y=ax^b	0.056 2/0.031 6	0.000/0.000	0.834

Table 5

Fig.12

Table 6

Fig.13

Table 7

Fitting results of different braking duration ratios"

制动时长比率/%	函数分布形式	参数值
80	$y = y 0 + A e - x - x c 2 2 w 2$	A=141.78，w=0.092，y₀=6.78，x_c=0.64
85		A=150.96，w=0.092，y₀=7.22，x_c=0.64
90		A=159.78，w=0.092，y₀=7.64，x_c=0.64
95		A=168.59，w=0.092，y₀=8.06，x_c=0.64
100		A=177.41，w=0.092，y₀=8.48，x_c=0.64

Table 7

Fig.14

Table 8

Table 9

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序号	试验路段桩号范围^1）	平均坡度/%	累计坡长/km	相对高差/m	连续纵坡路段间距/m
1	ZK131+790-ZK99+242	-2.44	32.030	780.873	ZK99+242-ZK89+172=10 070
2	ZK89+172-ZK62+946	-2.14	27.672	592.330	ZK99+242-ZK89+172=10 070
2	ZK89+172-ZK62+946	-2.14	27.672	592.330	ZK62+946-ZK51+764=11 182
3	ZK51+764-ZK33+134	-2.06	18.630	384.010	ZK62+946-ZK51+764=11 182

分布类型	拟合优度检验	统计	P值	在置信水平5%下的结论
正态	K-S修正检验	0.129 45	≤0.010	排除正态分布
对数	K-S修正检验	0.284 31	≤0.010	排除对数分布
威布尔分布	K-S修正检验	0.133 06	≤0.010	排除威布尔分布
伽马分布	K-S修正检验	0.236 06	≤0.005	排除伽马分布

平均坡度/%	临界坡长/km
平均坡度/%	77%^1）	80%^1）	85%^1）	90%^1）	95%^1）	100%^1）
2.1	33.06	31.76	30.12	28.88	25.97	24.56
2.2	30.98	29.02	27.67	24.86	23.67	22.48
2.3	28.32	26.87	25.12	23.34	21.79	20.46
2.4	25.39	23.81	22.75	20.45	19.76	18.83
2.5	22.03	21.74	20.18	18.83	17.75	16.97
2.6	20.49	19.73	18.92	17.76	16.93	15.87
2.7	19.92	18.98	18.04	17.13	15.97	14.91
2.8	19.00	17.89	17.25	15.97	14.72	13.76
2.9	17.99	16.88	15.97	14.93	13.94	12.68
3.0	16.85	15.77	14.95	13.79	12.90	11.74

平均坡度/%	文献［2］中的规范坡长/km	临界坡长/km
2.1		30.12
2.2		27.67
2.3		25.12
2.4		22.75
2.5	20.00	20.18
2.6	18.96	18.92
2.7	17.92	18.04
2.8	16.88	17.25
2.9	15.84	15.97
3.0	14.80	14.95

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