移动荷载作用下沥青路面主应力轴旋转及方向余弦研究

董鹏军; 唐伯明; 曹雪娟

doi:10.21656/1000-0887.450214

移动荷载作用下沥青路面主应力轴旋转及方向余弦研究

doi: 10.21656/1000-0887.450214

董鹏军^1,,
唐伯明^{1, 2},
曹雪娟^{2, 3, ,}

1.
重庆交通大学土木工程学院, 重庆 400074
2.
重庆交通大学交通土建工程材料国家地方联合工程研究中心, 重庆 400074
3.
重庆交通大学材料科学与工程学院, 重庆 400074

基金项目:

国家自然科学基金 52278441

重庆市研究生科研创新项目 CYB25264

详细信息

作者简介:
董鹏军(1997—), 男, 博士生(E-mail: 2855112842@qq.com)

通讯作者:
曹雪娟(1979—), 女, 教授(通讯作者. E-mail: caoxj@cqjtu.edu.cn)

中图分类号: U416
计量
- 文章访问数: 38
- HTML全文浏览量: 14
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2024-07-16
- 修回日期: 2024-12-04
- 刊出日期: 2025-09-01

Study on Principal Stress Axis Rotations and Direction Cosines of Asphalt Pavement Under Moving Loadings

DONG Pengjun^1
,,
TANG Boming^{1, 2},
CAO Xuejuan^{2, 3
, ,}

1.
School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, P. R. China
2.
National and Local Joint Engineering Research Center of Transportation and Civil Engineering Materials, Chongqing Jiaotong University, Chongqing 400074, P. R. China
3.
School of Materials Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, P. R. China

摘要

摘要:
为揭示单次和多次荷载作用下主应力大小和方向变化对沥青路面的损伤机理，该文采用有限元软件构建了沥青路面结构模型，研究了不同轴载个数作用下沥青路面结构单元的应力路径以及主应力方向余弦变化规律. 结果表明：在单次和多次荷载作用下，路面结构单元的应力路径和主应力轴旋转强度时刻发生变化. 在荷载移动的过程中，车轮每经过考察断面一次，主应力对应的方向余弦将出现正、负交替转换，且由于不同车轮之间相互作用，导致不同车轮对应的方向余弦正峰值和负峰值不同. 第一主应力的方向余弦值沿横向和纵向均发生了瞬时正、负交替转换，表明在车辆加载的过程中主应力方向发生了突变，且在多轮作用下的交替更为复杂. 在长期的循环荷载作用下，容易导致路面出现裂缝.
- 沥青路面 /
- 荷载数量 /
- 主应力轴 /
- 方向余弦 /
- 数值模拟
Abstract:
To reveal the damage mechanism of asphalt pavement under single and multiple loadings with respect to the variations in the magnitude and direction of the principal stress, an asphalt pavement structure model was constructed with the finite element method. The stress paths and the direction cosine variations of the principal stresses in asphalt pavement structural elements under different numbers of axle loads were investigated. The results show that, under both single and multiple loadings, the stress path and the rotation intensity of the principal stress axis in the pavement structural elements change over time. During the movement of the load, as the wheel passes over the examined section, the direction cosine value corresponding to the principal stress alternates between positive and negative ones. Moreover, due to the interactions between different wheels, the positive and negative peak values of the direction cosines for different wheels differ. The direction cosine values of the 1st principal stress alternately switch between positive and negative ones both in the transverse and longitudinal directions, indicating that the principal stress direction experiences abrupt changes during vehicle loading. Furthermore, the alternations become more complex under multiple wheel loadings. Under prolonged cyclic loadings, this can lead to the formation of cracks in the pavement.
- asphalt pavement /
- load quantity /
- principal axis of stress /
- directional cosine /
- numerical simulation

HTML全文

图 1 青银高速数值分析模型

Figure 1. The Qingyin expressway pavement numerical analysis model

下载: 全尺寸图片幻灯片

图 2 荷载时程曲线

Figure 2. Load time history curves

下载: 全尺寸图片幻灯片

图 3 提取应力单元位置示意图

Figure 3. Schematic diagram of the positions of the extracted stress elements

下载: 全尺寸图片幻灯片

图 4 主应力轴旋转对比

Figure 4. Comparison of principal stress axis rotations

下载: 全尺寸图片幻灯片

图 5 车辆荷载作用下路面不同深度处单元主应力轴旋转

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 5. Rotations of stress axes at different depths of the road under vehicle loads

下载: 全尺寸图片幻灯片

图 6 σ₁与坐标轴的夹角余弦值

Figure 6. The cosine values of the angles between σ₁ and the coordinate axes

下载: 全尺寸图片幻灯片

表 1 地基材料参数

Table 1. Foundation material parameters

name	thickness/m	modulus/MPa	Poisson’s ratio	density/(kg·m^-3)	damping ratio
foundation	10	50	0.35	1 800	0.05

下载: 导出CSV

表 2 道路结构层参数

Table 2. Parameters of road structure layers

name	thickness/m	modulus/MPa	Poisson’s ratio	density/(kg·m^-3)	damping ratio
upper layer	0.04	6 544	0.25	2 526	0.05
middle layer	0.05	9 191	0.25	2 480	0.05
lower layer	0.06	12 229	0.25	2 510	0.05
base	0.36	9 000	0.25	2 400	0.05
subbase	0.20	2 500	0.25	2 200	0.05
subgrade	2.00	90	0.40	1 800	0.05

下载: 导出CSV

参考文献(30)

[1]	杨成忠, 倪凯. 列车移动荷载引起的地基土应力状态变化[J]. 铁道建筑, 2017, 57(10): 85-87. YANG Chengzhong, NI Kai. Change of stress state in subsoil induced by train travelling load[J]. Railway Engineering, 2017, 57(10): 85-87. (in Chinese)
[2]	崔新壮, 包振昊, 杜业峰, 等. 考虑应力主轴旋转的路基服役性能试验系统研制及验证[J/OL]. 土木工程学报, 2024: 1-15[2024-12-04]. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=TMGC20241104001&dbname=CJFD&dbcode=CJFQ. CUI Xinzhuang, BAO Zhenhao, DU Yefeng, et al. Development and verification of subgrade service performance test system considering stress spindle rotation[J/OL]. China Industrial Economics, 2024: 1-15[2024-12-04]. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=TMGC20241104001&dbname=CJFD&dbcode=CJFQ. (in Chinese)
[3]	董彤, 郑颖人, 刘元雪, 等. 考虑主应力轴旋转的土体本构关系研究进展[J]. 应用数学和力学, 2013, 34(4): 327-335. doi: 10.3879/j.issn.1000-0887.2013.04.001 DONG Tong, ZHENG Yingren, LIU Yuanxue, et al. Research progress of the soil constitutive relation considering principal stress axes rotation[J]. Applied Mathematics and Mechanics, 2013, 34(4): 327-335. (in Chinese) doi: 10.3879/j.issn.1000-0887.2013.04.001
[4]	ARTHUR J R F, CHUA K S, DUNSTAN T. Dense sand weakened by continuous principal stress direction rotation[J]. Géotechnique, 1979, 29(1): 91-96.
[5]	熊焕, 郭林, 蔡袁强. 交通荷载应力路径下砂土地基变形特性研究[J]. 岩土工程学报, 2016, 38(4): 662-669. XIONG Huan, GUO Lin, CAI Yuanqiang. Deformation behaviors of sandy subgrade soil under traffic load-induced stress path[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(4): 662-669. (in Chinese)
[6]	沈瑞福, 王洪瑾, 周景星. 动主应力轴连续旋转下砂土的动强度[J]. 水利学报, 1996, 27(1): 27-33. SHEN Ruifu, WANG Hongjin, ZHOU Jingxing. Dynamic strength of sand under continuous rotation of dynamic principal stress axis[J]. Journal of Hydraulic Engineering, 1996, 27(1): 27-33. (in Chinese)
[7]	ISHIHARA K, TOWHATA I. Sand response to cyclic rotation of principal stress directions as induced by wave loads[J]. Soils and Foundations, 1983, 23(4): 11-26. doi: 10.3208/sandf1972.23.4_11
[8]	边学成, 胡婷, 陈云敏. 列车交通荷载作用下地基土单元体的应力路径[J]. 土木工程学报, 2008, 41(11): 86-92. BIAN Xuecheng, HU Ting, CHEN Yunmin. Stress path in soil element of ground under moving traffic loads[J]. China Civil Engineering Journal, 2008, 41(11): 86-92. (in Chinese)
[9]	王常晶, 陈云敏. 移动荷载引起的地基应力状态变化及主应力轴旋转[J]. 岩石力学与工程学报, 2007, 26(8): 1698-1704. WANG Changjing, CHEN Yunmin. Stress state variation and principal stress axes rotation of ground induced by moving loads[J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(8): 1698-1704. (in Chinese)
[10]	童朝霞, 张建民, 张嘎. 应力主轴旋转对波浪作用下堤防变形的影响分析[J]. 工程力学, 2009, 26(10): 67-73. TONG Zhaoxia, ZHANG Jianmin, ZHANG Ga. Effects of principal-stress-axis rotation on the deformation of a dam under wave loading[J]. Engineering Mechanics, 2009, 26(10): 67-73. (in Chinese)
[11]	DAREEJU B, GALLAGE C, ISHIKAWA T, et al. Effects of principal stress axis rotation on cyclic deformation characteristics of rail track subgrade materials[J]. Soils and Foundations, 2017, 57(3): 423-438. doi: 10.1016/j.sandf.2017.05.009
[12]	杜业峰, 崔新壮, 包振昊, 等. 重载铁路非饱和路基三维动力响应分析[J/OL]. 铁道学报, 2024: 1-9[2024-12-04]. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=TDXB20240228001&dbname=CJFD&dbcode=CJFQ. DU Yefeng, CUI Xinzhuang, BAO Zhenhao, et al. Three-dimensional dynamic response analysis of unsaturated subgrade of heavy-haul railway[J/OL]. China Industrial Economics, 2024: 1-9[2024-12-04]. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=TDXB20240228001&dbname=CJFD&dbcode=CJFQ. (in Chinese)
[13]	邓鹏, 郭林, 蔡袁强, 等. 循环荷载下考虑主应力旋转的软土力学响应研究[J]. 岩土力学, 2015, 36(S2): 148-156. DENG Peng, GUO Lin, CAI Yuanqiang, et al. Study on mechanical response of soft soil considering principal stress rotation under cyclic load[J]. Rock and Soil Mechanics, 2015, 36(S2): 148-156. (in Chinese)
[14]	沈扬, 周建, 龚晓南. 主应力轴旋转对土体性状影响的试验进展研究[J]. 岩石力学与工程学报, 2006, 25(7): 1408-1416. SHEN Yang, ZHOU Jian, GONG Xiaonan. Experimental progress research on influence of principal stress rotation on soils' characteristics[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(7): 1408-1416. (in Chinese)
[15]	PRASANNA R, SINTHUJAN N, SIVATHAYALAN S. Effects of initial direction and subsequent rotation of principal stresses on liquefaction potential of loose sand[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2020, 146(3): 04019130. doi: 10.1061/(ASCE)GT.1943-5606.0002182
[16]	王凯. 主应力方向余弦的计算公式[J]. 力学与实践, 2015, 37(3): 378-380. WANG Kai. Calculation formula of cosine of principal stress direction[J]. Mechanics in Engineering, 2015, 37(3): 378-380. (in Chinese)
[17]	王凯. 主应力及其方向余弦和极值切应力方向余弦计算的补遗[J]. 力学与实践, 2021, 43(5): 740-743. WANG Kai. Supplement to the calculation of principal stresses, their direction cosines and direction cosines of extreme shear stresses[J]. Mechanics in Engineering, 2021, 43(5): 740-743. (in Chinese)
[18]	王凯. 主应力及其方向余弦计算的进一步研究[J]. 重庆交通大学学报(自然科学版), 2019, 38(11): 58-62. WANG Kai. Further study on the calculation of principal stresses and their direction cosines[J]. Journal of Chongqing Jiaotong University (Natural Science), 2019, 38(11): 58-62. (in Chinese)
[19]	郭乃胜, 谭忆秋, 赵颖华. 动荷载下饱水沥青路面黏弹性分析[J]. 土木工程学报, 2012, 45(2): 184-190. GUO Naisheng, TAN Yiqiu, ZHAO Yinghua. Viscoelastic analysis of saturated asphalt pavement under dynamic load[J]. Journal of Civil Engineering, 2012, 45(2): 184-190. (in Chinese)
[20]	申爱琴, 靳欣宽, 郭寅川, 等. 耦合场下陕北地区半刚性沥青路面力学响应分析[J]. 长安大学学报(自然科学版), 2022, 42(5): 1-11. SHEN Aiqin, JIN Xinkuan, GUO Yinchuan, et al. Mechanical response analysis of semi-rigid asphalt pavement in northern Shaanxi under coupled field[J]. Journal of Chang'an University (Natural Science Edition), 2022, 42(5): 1-11. (in Chinese)
[21]	赵楷文, 张洪伟, 全蔚闻, 等. 沥青路面结构设计指标优化及合理厚度探究[J]. 公路交通科技, 2022, 39(6): 9-16. ZHAO Kaiwen, ZHANG Hongwei, QUAN Weiwen, et al. Optimization of asphalt pavement structure design indicators and exploration of reasonable thickness[J]. Highway Transportation Technology, 2022, 39(6): 9-16. (in Chinese)
[22]	李广信, 张丙印, 于玉贞. 土力学[M]. 北京: 清华大学出版社, 2022. LI Guangxin, ZHANG Bingyin, YU Yuzhen. Soil Mechanics[M]. Beijing: Tsinghua University Press, 2022. (in Chinese)
[23]	ASSOGBA O C, SUN Z, TAN Y, et al. Finite-element simulation of instrumented asphalt pavement response under moving vehicular load[J]. International Journal of Geomechanics, 2020, 20(3): 04020006. doi: 10.1061/(ASCE)GM.1943-5622.0001616
[24]	黄晓明. 路基路面工程[M]. 6版. 北京: 人民交通出版社, 2019. HUANG Xiaoming. Road Subgrade and Pavement Engineering[M]. 6th ed. Beijing: China Communications Press, 2019. (in Chinese)
[25]	丁智, 葛国宝, 魏新江, 等. 地铁列车运营引起的地基土应力状态变化分析[J]. 岩土工程学报, 2013, 35(S2): 647-651. DING Zhi, GE Guobao, WEI Xinjiang, et. al. Analysis and research of stress state variation of ground induced by running subway[J]. Journal of Geotechnical Engineering, 2013, 35(S2): 647-651. (in Chinese)
[26]	邓融. 水和荷载耦合作用下沥青路面动力响应研究[D]. 大连: 大连海事大学, 2010. DENG Rong. Study on dynamic response of asphalt pavement under coupling action of water and load[D]. Dalian: Dalian Maritime University, 2010. (in Chinese)
[27]	董泽蛟, 曹丽萍, 谭忆秋, 等. 移动荷载作用下沥青路面三向应变动力响应模拟分析[J]. 土木工程学报, 2009, 42(4): 133-139. DONG Zejiao, CAO Liping, TAN Yiqiu, et al. Analysis of the dynamic response of three directional strains in asphalt pavement under moving vehicle loads[J]. China Civil Engineering Journal, 2009, 42(4): 133-139. (in Chinese)
[28]	孙立军. 路面行为力学[M]. 上海: 同济大学出版社, 2021. SUN Lijun. Mechanics of Behavior of Asphalt Pavements[M]. Shanghai: Tongji University Press, 2021. (in Chinese)
[29]	董泽蛟, 曹丽萍, 谭忆秋. 饱水沥青路面动力响应的空间分布分析[J]. 重庆建筑大学学报, 2007, 29(4): 79-82. DONG Zejiao, CAO Liping, TAN Yiqiu. Spatial distribution analysis of dynamic response of saturated asphalt pavement[J]. Journal of Chongqing Jianzhu University, 2007, 29(4): 79-82. (in Chinese)
[30]	崔新壮, 包振昊, 郝建文, 等. 重载公路路基动力响应现场测试与三维空间分布规律[J]. 中国公路学报, 2023, 36(10): 75-83. CUI Xinzhuang, BAO Zhenhao, HAO Jianwen, et al. On site testing and three-dimensional spatial distribution of dynamic response of heavy-duty highway subgrade[J]. Chinese Journal of Highways, 2023, 36(10): 75-83. (in Chinese)