基于纹理分形特性的沥青路面抗滑性能研究综述

高茜楠; 呙润华; 耿靖杰

doi:10.3963/j.jssn.1674-4861.2022.05.002

基于纹理分形特性的沥青路面抗滑性能研究综述

doi: 10.3963/j.jssn.1674-4861.2022.05.002

1.
新疆大学建筑工程学院乌鲁木齐 830000
2.
清华大学土木工程系北京 100084

基金项目:

国家自然科学基金项目 51568063

清华大学-丰田联合研究院跨学科专项项目 20203910013

详细信息

作者简介:
高茜楠（1998—），硕士研究生. 研究方向：道路资产管理研究. E-mail：785541458@qq.com

通讯作者:
呙润华（1975—），博士，副教授. 研究方向：道路工程材料、交通基础设施养护管理. E-mail：guorh@tsinghua.edu.cn

中图分类号: U416.217
计量
- 文章访问数: 646
- HTML全文浏览量: 280
- PDF下载量: 43
- 被引次数: 0
出版历程
- 收稿日期: 2022-03-16
- 网络出版日期: 2022-12-05

A Review on Anti-skid Performance Based on Fractal Characteristics of the Texture of Asphalt Pavement

1.
College of Civil Engineering and Architecture, Xinjiang University, Urumqi 830000, China
2.
Department of Civil Engineering, Tsinghua University, Beijing 100084, China

摘要

摘要: 沥青路面纹理形貌是影响道路抗滑性能的重要因素，而路面纹理具有自相似分形特性，因此借助分形特性实现路面纹理量化，对研究路面纹理与抗滑性能之间的联系具有重要意义。从宏观和微观这2个层面总结了沥青混合料纹理和集料纹理的单重、多重分形特性相关研究；分析了分形理论在路面抗滑级配设计和抗滑集料筛选中的应用，总结了基于分形理论的多种抗滑级配设计模型，提出了基于分形理论的集料优选新思路；对比分析了分形理论与参数统计法、力学解析法及有限元模拟法在路面抗滑性能预测中的结合应用。研究结果表明：分形分析为路面纹理描述提供了新思路，但其分析方法仍未突破关键瓶颈，在模型精确性、标准化、系统性方面仍有一定限制；分形理论与抗滑级配设计和抗滑集料筛选的结合应用仍处于探索阶段，需进一步加强设计方法的合理性研究，验证其在实际工程中的适用性；横向对比各类基于纹理分形特性的抗滑预测模型性能，结果表明，有限元模拟预测模型在实际应用中能更准确地还原复杂条件下的胎-路接触状态，更具发展潜力。展望了基于纹理分形特性的沥青路面抗滑性能的未来研究方向，主要包括多尺度的纹理分形特征与抗滑性能的关联规律、实际工程分形参数判别标准，以及基于分形理论的智能抗滑预测体系构建。
- 道路工程 /
- 沥青路面 /
- 纹理形貌 /
- 分形特性 /
- 抗滑性能
Abstract: Texture morphology of asphalt pavement is an important indicator of the anti-skid performance of asphalt pavement. Meanwhile, pavement texture has its fractal characteristics. Therefore, it is important to study the correlation between pavement texture and anti-skid performance by quantifying its texture with fractal properties. Single and multi-fractal properties of pavement texture and aggregate texture are studied and summarized at both the macroscopic and microscopic levels. The applications of fractal theory in the design of anti-skid gradations and selection of anti-skid aggregate for pavements are analyzed. A variety of design of anti-skid gradation models based on the fractal theory are summarized, and a new method of anti-skid aggregate selection for pavements based on the fractal theory is proposed. Finally, the utility of the fractal theory in combination with parametric statistical methods, mechanical analysis, and finite element simulation in the field of prediction of pavement anti-skid performance is compared and analyzed. Study results show that fractal feature analysis provides a new way for the description of pavement texture. However, the fractal analysis methods with a high precision are still the bottlenecks in this field. There are still limitations within the fractal models, in terms of their accuracy, standardization and systematization of their process. The application of fractal theory in combination with gradation design and aggregate selection is still in its preliminary stage. Therefore, it is recommended that design methods in engineering should be validated based on their usefulness in the practice. The performance of various types of prediction models for forecasting anti-skid performance based on texture fractal properties are compared. Study results indicate that the prediction mod-els based on finite element simulation can more accurately restore the tire-road contact state under complex conditions in practice, indicating that such prediction models have a good potential. Future research areas on anti-skid performance of asphalt pavement based on the fractal properties of texture are discussed and proposed, including the correlation between multi-scale texture fractal characteristics and anti-skid performance, criteria for specifying fractal parameters in the practice, and the development of intelligent anti-skid prediction system based on the fractal theory.
- road engineering /
- asphalt pavement /
- texture morphology /
- fractal characteristics /
- anti-skid performance

HTML全文

图 1 路面纹理几何尺度

Figure 1. Geometric scale of pavement texture

下载: 全尺寸图片幻灯片

图 2 宏微观纹理对沥青路面摩擦影响的示意图

Figure 2. Schematic diagram of the influences of macro and micro textures on friction of asphalt pavement

下载: 全尺寸图片幻灯片

表 1 路表纹理构造分类及其形成原因

Table 1. Texture structure classification and formation reasons

类型	波长/mm	振幅/mm	形成原因
微观纹理（micro-texture）	< 0.5	< 0.5	集料表面的初始粗糙度；集料对交通作用和环境因素抛光作用的抵抗力
宏观纹理（macro-texture）	0.5~50	0.1~20	粗集料的大小、级配、形状和分布；路面面层的施工方法
大纹理（mega-texture）	50~500	0.1~50	路面磨损；施工质量缺陷
不平整度（unevenness）	0.5~50		路面摊铺质量缺陷；不均匀沉降

下载: 导出CSV

表 2 分形维数计算方法

Table 2. Calculation methods of fractal dimension

名称	计算方式	相关参数	计算公式	主要特点
盒子计数法（box-counting method）	采用方格覆盖需测量的曲线或图形并统计方格数	δ为方格的边长； N(δ) 为方格数	$D = \mathop {\lim }\limits_{\delta \to 0} \frac{{\ln N(\delta )}}{{ - \ln \delta }}$	适用于轮廓曲线和纹理图像的测量
差分盒维数法（differential box-counting，DBC）	对粗糙表面进行分割，依据网格边长计算盒子高度，并统计总盒子数	r为盒子高度（r = s/M）； M为表面投影边长； s为网格边长； N(r) 为盒子总数	$D = \mathop {\lim }\limits_{r \to 0} \frac{{\ln N(r)}}{{\ln (1/r)}}$	适用于二维纹理灰度图像和三维纹理形貌的计算，具有较强稳定性
投影覆盖法（projective covering method，PCM）	采用网格覆盖物体表面，计算并累加网格4个顶点的不规则平面面积	ε为网格边长； S_ij(ε) 为第(i, j) 个网格对应的不规则平面面积； S(ε) 为不规则面积总和	$D=2-\frac{\ln S(\varepsilon)}{\ln \varepsilon}$	适用于三维纹理形貌的计算，以不规则平面面积作为研究量
立方体覆盖法（cubic covering method，CCM）	采用立方体对粗糙表面进行覆盖并统计立方体个数	λ为立方体盒子的边长； N(λ) 为覆盖表面的立方体总数	$D=-\frac{\ln N(\lambda)}{\ln \lambda}$	适用于三维纹理形貌的计算，测试尺度越小计算结果越精确

下载: 导出CSV

表 3 抗滑级配设计模型

Table 3. Design models of skid resistance gradations

文献	理论支撑	模型特点	适用范围	抗滑性能测评
杨瑞华等^[25]	分形几何理论	分别构建出集料粒径分布分形模型和集料体积分形模型，体积分维与表面形貌、级配等均密切相关	连续、间断级配	集料体积分维增大，抗滑性能呈下降趋势
刘林^[26]	分形几何理论	构建级配分形维数用于表征沥青混合料级配特征	连续级配	级配分形维数与抗滑性能和MTD呈负相关关系
赵战利等^[27]	分形理论分形级配理论	构建级配分维数和矿粉、细集料质量分数之间的关系	连续、间断集配	得出抗滑级配分维数与矿粉质量分数的合理范围
童申家等^[28]	变异函数理论分形几何理论	构建集料粒径分布分维与路面纹理分布分维之间的关系	连续集配	纹理分布分维增大，抗滑性能先上升后下降
Hou等^[29]	分形理论集料体积分形模型	构建集料体积分维与纹理图像的面积分维之间的关系	连续集配
黄宝涛等^[30]	集料外露尺寸函数分形理论	构建集料体积分维与集料外露尺寸分维之间的关系	连续、间断集配	集料外露尺寸分维增大，抗滑性能呈上升趋势

下载: 导出CSV

参考文献(52)

[1]	GUO F, PEI J, ZHANG J, et al. Study on the skid resistance of asphalt pavement: A state-of-the-art review and future prospective[J]. Construction and Building Materials, 2021(303): 124411.
[2]	YU M, YOU Z, WU G, et al. Measurement and modeling of skid resistance of asphalt pavement: A review[J]. Construction and Building Materials, 2020(260): 119878.
[3]	DONG S H, HAN S, ZHANG Q X, et al. Three-dimensional evaluation method for asphalt pavement texture characteristics[J]. Construction and Building Materials, 2021(287): 122966.
[4]	KOVAC M, BRNA M. The influence of the pavement surface texture on the pendulum test value[J]. IOP Conference Series: Materials Science and Engineering, 2021, 1015(1): 012100. doi: 10.1088/1757-899X/1015/1/012100
[5]	李智, 王刚, 陈思宇. 基于分形理论的沥青混合料抗滑耐久性评价研究[J]. 科学技术与工程, 2014, 14(31): 302-307. doi: 10.3969/j.issn.1671-1815.2014.31.058 LI Z, WANG G, CHEN S Y. Evalution of durability agains sliding on the asphalt mix fractal theroy[J]. Science Technology and Engineering, 2014, 14(31): 302-307. (in Chinese) doi: 10.3969/j.issn.1671-1815.2014.31.058
[6]	张令刚, 钱振东, 杨理广, 等. 沥青混凝土路面表面形貌及抗滑性能的分形表达研究[J]. 公路, 2013(5): 85-88. doi: 10.3969/j.issn.0451-0712.2013.05.020 ZHANG L G, QIAN Z D, YANG L G, et al. Description of surface morphology and skid resistance of asphalt concrete pavement with fractal theory[J]. Highway, 2013(5): 85-88. (in Chinese) doi: 10.3969/j.issn.0451-0712.2013.05.020
[7]	LIU C, ZHAN Y, DENG Q, et al. An improved differential box counting method to measure fractal dimensions for pavement surface skid resistance evaluation[J]. Measurement, 2021(178): 109376
[8]	周兴林, 祝媛媛, 冉茂平, 等. 基于分段变维的沥青路表纹理磨光行为分析[J]. 中国公路学报, 2019, 32(4): 187-195+242. doi: 10.19721/j.cnki.1001-7372.2019.04.016 ZHOU X L, ZHU Y Y, RAN M P, et al. Polishing behavior analysis of asphalt pavement surface texture based on piecewise variable dimension fractal[J]. China Journal of Highway and Transport, 2019, 32(4): 187-195+242. (in Chinese) doi: 10.19721/j.cnki.1001-7372.2019.04.016
[9]	MIAO Y, SONG P, GONG X. Fractal and multifractal characteristics of 3d asphalt pavement macrotexture[J]. Journal of Materials in Civil Engineering, 2014, 26(8): 04014033. doi: 10.1061/(ASCE)MT.1943-5533.0000912
[10]	钱振东, 薛永超, 张令刚. 沥青路面三维纹理分形维数及其抗滑性能[J]. 中南大学学报(自然科学版), 2016, 47(10): 3590-3596. https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201610041.htm QIAN Z D, XUE Y C, ZHANG L G. 3-D textural fractal dimension and skid resistance of asphalt pavement[J]. Journal of Central South University (Science and Technology), 2016, 47(10): 3590-3596. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201610041.htm
[11]	冉茂平, 肖旺新, 周兴林, 等. 基于三维分形维数的沥青路面抗滑性能研究[J]. 公路交通科技, 2016, 33(2): 28-32. doi: 10.3969/j.issn.1002-0268.2016.02.005 RAN M P, XIAO W X, ZHOU X L, et al. Research of skid resistance of asphalt pavement based on 3D fractal dimension[J]. Journal of Highway and Transportation Research and Development, 2016, 33(2): 28-32. (in Chinese) doi: 10.3969/j.issn.1002-0268.2016.02.005
[12]	YEGGONI M, BUTTON J W, ZOLLINGER D G. Fractals of aggregates correlated with creep in asphalt concrete[J]. Journal of Transportation Engineering, 1996, 122(1): 22-28. doi: 10.1061/(ASCE)0733-947X(1996)122:1(22)
[13]	张肖宁, 孙杨勇. 粗集料表面纹理轮廓线分形分析及不同维数算法探讨比较[J]. 公路, 2010(12): 124-128. https://www.cnki.com.cn/Article/CJFDTOTAL-GLGL201012027.htm ZHANG X N, SUN Y Y. Analysis of fractal of micro-structure curve of coarse aggregate and contrast between different dimension algorithms[J]. Highway, 2010(12): 124-128. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GLGL201012027.htm
[14]	ZHANG X, TAO L, LIU C, et al. Research on skid resistance of asphalt pavement based on three-dimensional laser-scanning technology and pressure-sensitive film[J]. Construction and Building Materials, 2014(69): 49-59.
[15]	李智, 刘涛, 刘春雷. 基于激光和真空镀膜技术的集料细观构造评价[J]. 华南理工大学学报(自然科学版), 2013, 41(2): 88-93. doi: 10.3969/j.issn.1000-565X.2013.02.014 LI Z, LIU T, LIU C L. Microscopic structure evaluation of aggregates based on laser measurement and vacuum coating technology[J]. Journal of South China University of Technology(Natural Science Edition), 2013, 41(2): 88-93. (in chinese) doi: 10.3969/j.issn.1000-565X.2013.02.014
[16]	孙杨勇. 粗集料表面微观构造分形性质探讨与沥青路面抗滑性能关系研究[D]. 广州: 华南理工大学, 2010. SUN Y Y. Research on the fractal nature of the surface micro-structure of coarse aggregate and the relationship with the anti-slide performance of asphalt pavement[D]. Guangzhou: South China University of Technology, 2010. (in Chinese)
[17]	QUAN W, WANG H, LIU X, et al. Multi-fractal analysis for pavement roughness evaluation[J]. Procedia-social and Behavioral Sciences, 2013(96): 2684-2691.
[18]	王维锋, 严新平, 肖旺新, 等. 路面纹理的多重分形特征描述与识别方法[J]. 交通运输工程学报, 2013, 13(3): 15-21. doi: 10.3969/j.issn.1671-1637.2013.03.003 WANG W F, YAN X P, XIAO W X, et al. Approach of multifractal feature description and recognition for pavement texture[J]. Journal of Traffic and Transportation Engineering, 2013, 13(3): 15-21. (in Chinese) doi: 10.3969/j.issn.1671-1637.2013.03.003
[19]	肖神清. 沥青路表纹理多重分形表征及其磨光行为研究[D]. 武汉: 武汉科技大学, 2018. XIAO S Q. Multifractal characterization of surface texture on asphalt pavement and its polishing behavior[D]. Wuhan: Wuhan University of Science and Technology, 2018. (in Chinese)
[20]	周兴林, 肖神清, 刘万康, 等. 沥青路面表面纹理的多重分形特征及其磨光行为[J]. 东南大学学报(自然科学版), 2018, 48(1): 175-180. https://www.cnki.com.cn/Article/CJFDTOTAL-DNDX201801027.htm ZHOU X L, XIAO S Q, LIU W K, et al. Multifractal characteristics and polishing behaviors of surface texture on asphalt pavement[J]. Journal of Southeast University(Natural Science Edition), 2018, 48(1): 175-180. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DNDX201801027.htm
[21]	周兴林, 李庆丰, 肖神清. 基于多重分形的沥青混合料空隙分布特征分析[J]. 重庆交通大学学报(自然科学版), 2018, 37(12): 29-35. doi: 10.3969/j.issn.1674-0696.2018.12.05 ZHOU X L, LI Q F, XIAO S Q. Voids distribution characteristics of asphalt mixture based on multifractal theory[J]. Journal of Chongqing Jiaotong University(Natural Science), 2018, 37(12): 29-35. (in Chinese) doi: 10.3969/j.issn.1674-0696.2018.12.05
[22]	RAN M P, XIAO S Q, ZHOU X L, et al. Evaluation of segregation in asphalt pavement surface using concave multifractal distribution[J]. Journal of Testing and Evaluation, 2018(46): 20160616.
[23]	XIAO S Q, TAN Y Q, XING C, et al. Scale demarcation of self-affine surface of coarse aggregate and its relationship with rubber friction[J]. Road Materials and Pavement Design, 2021, 22(8): 1842-1859. doi: 10.1080/14680629.2020.1728365
[24]	周兴林, 肖神清, 肖旺新, 等. 粗集料表面纹理粗糙度的多重分形评价[J]. 华中科技大学学报(自然科学版), 2017, 45(2): 29-33. https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201702006.htm ZHOU X L, XIAO S Q, XIAO W X, et al. Multi-fractal evaluation on roughness of coarse aggregate surface texture[J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2017, 45(2): 29-33. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201702006.htm
[25]	杨瑞华, 许志鸿. 密级配沥青混合料集料分形分维与路用性能的关系[J]. 土木工程学报, 2007(3): 98-103+109. doi: 10.3321/j.issn:1000-131X.2007.03.017 YANG R H, XU Z H. Relationship between fractal dimension and road performance of dense-gradation asphalt mixture[J]. Journal of Civil Engineering, 2007(3): 98-103+109. (in Chinese) doi: 10.3321/j.issn:1000-131X.2007.03.017
[26]	刘林. 沥青路表三维纹理构造与抗滑性能数值关系研究[D]. 乌鲁木齐: 新疆大学, 2019. LIU L. Numerical relation study on three-dimensional texture structure and skid resistance of road surface[D]. Urumqi: Xinjiang University, 2019. (in Chinese)
[27]	赵战利, 张争奇, 薛建设, 等. 基于分形理论的沥青混合料抗滑级配评价[J]. 长安大学学报(自然科学版), 2008(3): 6-10. doi: 10.3321/j.issn:1671-8879.2008.03.002 ZHAO Z L, ZHANG Z Q, XUE J S, et al. Evaluation of skid resistance gradations of asphalt mixture based on fractal theory[J]. Journal of Chang'an University(Natural Science Edition), 2008(3): 6-10. (in Chinese) doi: 10.3321/j.issn:1671-8879.2008.03.002
[28]	童申家, 谢祥兵, 赵大勇. 沥青路面纹理分布的分形描述及抗滑性能评价[J]. 中国公路学报, 2016, 29(2): 1-7. doi: 10.3969/j.issn.1001-7372.2016.02.001 TONG S J, XIE X B, ZHAO D Y. Fractal description of texture distribution and evaluation of skid-resistance performance for asphalt pavement[J]. China Journal of Highway and Transport, 2016, 29(2): 1-7. (in Chinese) doi: 10.3969/j.issn.1001-7372.2016.02.001
[29]	HOU Y, HUANG Y, SUN F, et al. Fractal analysis on asphalt mixture using a two-dimensional imaging technique[J]. Advances in Materials Science and Engineering, 2016(1): 1-7.
[30]	黄宝涛, 田伟平, 李家春, 等. 沥青路面抗滑性能定量评价的分形方法[J]. 中国公路学报, 2008, 21(4): 12-17. https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL200804002.htm HUANG B T, TIAN W P, LI J C, et al. Fractal method basedon quantitative evaluation of asphalt pavement anti-slide performance[J]. China Journal of Highway and Transport, 2008, 21(4): 12-17. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL200804002.htm
[31]	CHEN B, ZHANG X, YU J, et al. Impact of contact stress distribution on skid resistance of asphalt pavements[J]. Construction and Building Materials, 2017(133): 330-339.
[32]	甘新立, 张文利, 谢洪胜, 等. 抗滑集料颗粒形状及表面纹理特性分析[J]. 公路, 2021, 66(10): 321-325. https://www.cnki.com.cn/Article/CJFDTOTAL-GLGL202110056.htm GAN X L, ZHANG W L, XIE H S, et al. Analysis of particle shape and surface texture characteristics of sliding resistan aggregate[J]. Highway, 2021, 66(10): 321-325. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GLGL202110056.htm
[33]	VILLANI M M, SCARPAS A, BONDT A, et al. Application of fractal analysis for measuring the effects of rubber polishing on the friction of asphalt concrete mixtures[J]. Wear, 2014(320): 179-188.
[34]	LIU J, GUAN B, CHEN H, et al. Dynamic model of polished stone value attenuation in coarse aggregate[J]. Materials, 2020, 13(8): 1875.
[35]	HU L, YUN D, LIU Z, et al. Effect of three-dimensional macrotexture characteristics on dynamic frictional coefficient of asphalt pavement surface[J]. Construction and Building Materials, 2016(126): 720-729.
[36]	LI L, WANG K C P, LI Q J. Geometric texture indicators for safety on AC pavements with 1 mm 3D laser texture data[J]. International Journal of Pavement Research and Technology, 2016, 9(1): 49-62.
[37]	石月晴. 基于图像处理的沥青路面抗滑性能研究[D]. 重庆: 重庆交通大学, 2019. SHI Y Q. Study on skid resistance of asphalt pavement based on image processing[D]. Chongqing: Chongqing Jiaotong University, 2019. (in Chinese)
[38]	刘梦梅. 沥青路面多参数优化IFI模型及其在长期抗滑性能评价中应用研究[D]. 西安: 长安大学, 2021. LIU M M. Study on the Multi-parameter improved IFI model and its application in long-term skid resistance performance evaluation of asphalt pavement[D]. Xi'an: Chang'an University, 2021. (in Chinese)
[39]	王元元. 沥青路面抗滑特性与其表面粗糙特性之关系研究[D]. 南京: 东南大学, 2017. WANG Y Y. Study on the relationship between skid resistance of asphalt pavement and its surface rough characteristics[D]. Nanjing: Southeast University, 2017. (in Chinese)
[40]	PERSSON B. Theory of rubber friction and contact mechanics[J]. Journal of Chemical Physics, 2007, 115(8): 3840-3861.
[41]	MOTAMEDI M, TAHERI S, SANDU C, et al. Characterization of road profiles based on fractal properties and contact mechanics[J]. Rubber Chemistry and Technology, 2017, 90(2): 405-427.
[42]	ASSI M A, KASSEM E, NIELSEN R. Using close-range photogrammetry to measure pavement texture characteristics and predict pavement friction[J]. Transportation Research Record Journal of the Transportation Research Board, 2020, 2674(10): 794-805.
[43]	ZHONG K, SUN M, LIU Z, et al. Research on dynamic evaluation model and early warning technology of anti-sliding risk for the airport pavement[J]. Construction and Building Materials, 2020(239): 117820.
[44]	陈嘉颖. 无人驾驶条件下沥青路面纹理识别和制动策略研究[D]. 南京: 东南大学, 2019. CHEN J Y. Asphalt pavement texture recognition and braking method for autonomous vehicle[D]. Nanjing: Southeast University, 2019. (in Chinese)
[45]	刘朝旭. 基于胎路耦合的湿滑沥青路面抗滑风险模型研究[D]. 重庆: 重庆交通大学, 2020. LIU Z X. Research on anti-skid risk model of wet asphalt pavement based on tire-road coupling[D]. Chongqing: Chongqing Jiaotong University, 2020. (in Chinese)
[46]	TAN T, XING C, TAN Y. Rubber friction on icy pavement: Experiments and modeling[J]. Cold Regions Science and Technology, 2020(174): 103022.
[47]	马彬. 车路协同动力学差异特性及轮胎印迹机理研究[D]. 长春: 吉林大学, 2014. MA B. A study on dynamics differences characteristics for vehicle-road collaborative and the mechanism of tire-road frictional drag[D]. Changchun: Jilin University, 2014. (in Chinese)
[48]	张伟光. 基于路表纹理的抗滑沥青混合料设计方法研究[D]. 南京: 东南大学, 2011. ZHANG W G. Research on design method of anti-skid asphalt mixture based on road surface texture[D]. Nanjing: Southeast University, 2011. (in Chinese)
[49]	杨发. 基于胎/路耦合的沥青路面抗滑性能研究[D]. 南京: 东南大学, 2014. YANG F. Analysis of asphalt pavement skid resistance based on tire-road coupling[D]. Nanjing: Southeast University, 2014. (in Chinese)
[50]	ZHU S, LIU X, CAO Q, et al. Numerical study of tire hydroplaning based on power spectrum of asphalt pavement and kinetic friction coefficient[J]. Advances in Materials Science and Engineering, 2017(1): 1-11.
[51]	黄晓明, 蒋永茂, 郑彬双, 等. 基于路表摩擦特性的无人驾驶车辆安全制动原理与方法[J]. 科学通报, 2020, 65(30): 3328-3340. https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB202030012.htm HUANG X M, JIANG Y M, ZHENG B S, et al. Theory and methodology on safety braking of autonomous vehicles based on the friction characteristic of road surface[J]. Chinese Science Bulletin, 2020, 65(30): 3328-3340. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-KXTB202030012.htm
[52]	LIU X, CAO Q, WANG H, et al. Evaluation of vehicle braking performance on wet pavement surface using an integrated tire-vehicle modeling approach[J]. Transportation Research Record Journal of the Transportation Research Board, 2019, 2673(3): 295-307.