基于解析方法的半刚性基层沥青路面裂缝反射问题研究
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摘要
针对沥青路面半刚性基层开裂且裂缝逐渐反射的问题,基于解析的方法开展开裂路面的力学响应研究。以断裂力学理论为基础,建立开裂沥青路面的理论分析模型,通过傅里叶积分变换求解偏微分方程组,引入位错密度函数表征裂缝力学特性,留数定理计算复杂积分,获得奇异积分方程,应用Lobatto-Chebyshev求积公式对奇异积分方程进行求解,求得路面内任一点位移、应力及应力强度因子的解析表达式及数值解。以工程实例为基础,分析影响基层裂缝反射的主要因素。计算结果表明:在车辆荷载作用下,剪切破坏是裂缝扩展的主要形式;半刚性基层的弹性是影响裂缝反射的主要因素。研究成果可为半刚性基层沥青路面的设计和施工提供理论参考依据。
Aiming at the cracking of semi-rigid base of asphalt pavement and the gradual reflection of cracks,the mechanical response research on the cracked pavement was carried out on the basis of analytical method. Firstly,based on the theory of fracture mechanics,a theoretical analysis model of the cracked asphalt pavement was established. Then,the system of partial differential equations was solved by Fourier integral transform,and dislocation density function was introduced to characterize fracture mechanics. The residue theorem was used to calculate complex integrals and singular integral equations were obtained. Lobatto-Chebyshev quadrature formula was applied to solve singular integral equations. Finally,the analytical expressions and numerical solutions of displacement,stress and stress intensity factors at any point of the road were obtained. Based on the engineering example,the main factors affecting the crack reflection of the base course were analyzed. The calculation results show that: under the action of vehicle load,shear failure is the main form of crack propagation,and the elasticity of semi-rigid base is the main factor affecting crack reflection. The research results can provide theoretical reference for the design and construction of semi-rigid base asphalt pavement.
Aiming at the cracking of semi-rigid base of asphalt pavement and the gradual reflection of cracks,the mechanical response research on the cracked pavement was carried out on the basis of analytical method. Firstly,based on the theory of fracture mechanics,a theoretical analysis model of the cracked asphalt pavement was established. Then,the system of partial differential equations was solved by Fourier integral transform,and dislocation density function was introduced to characterize fracture mechanics. The residue theorem was used to calculate complex integrals and singular integral equations were obtained. Lobatto-Chebyshev quadrature formula was applied to solve singular integral equations. Finally,the analytical expressions and numerical solutions of displacement,stress and stress intensity factors at any point of the road were obtained. Based on the engineering example,the main factors affecting the crack reflection of the base course were analyzed. The calculation results show that: under the action of vehicle load,shear failure is the main form of crack propagation,and the elasticity of semi-rigid base is the main factor affecting crack reflection. The research results can provide theoretical reference for the design and construction of semi-rigid base asphalt pavement.
引文
[1]YU B,LU Q,YANG J. Evaluation of anti-reflective cracking measures by laboratory test[J]. International Journal of Pavement Engineering,2013,14(6):553-560.
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[3]HORNICEK L,RAKOWSKI Z. Mechanical stabilization of intermediate granular layers in pavement structures-laboratory study[J]. Procedia Engineering,2017,189:174-180.
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[8]徐华,杨绿峰,佘振平.半刚性基层沥青路面反射裂缝扩展过程分析的Williams单元[J].工程力学,2013,30(6):247-253.XU Hua, YANG Lvfeng, SHE Zhenping. Williams element for reflective crack propagation in asphalt pavement on semi-rigid base course[J]. Engineering Mechanics,2013,30(6):247-253.
[9]王雪莲,黄晓明,卞国剑. LSPM对防治半刚性基层沥青路面反射裂缝机理分析[J].公路交通科技,2016,33(7):12-18.WANG Xuelian,HUANG Xiaoming,BIAN Guojian. Analysis on mechanism of using LSPM for preventing reflective cracks in asphalt prevent with semi-rigid base[J]. Journal of Highway and Transportation Research and Development,2016,33(7):12-18.
[10]郑大为,焉妮,郝连学.基于FLAC3D数值模拟的基层水泥含量对反射裂缝影响研究[J].硅酸盐通报,2017,36(4):1371-1376.ZHENG Dawei,YAN Ni,HAO Lianxue. Effect of cement content on reflection crack based on FLAC3D numerical simulation[J]. Bulletin of the Chinese Ceramic Society,2017,36(4):1371-1376.
[11]元松,李雪莲.交通荷载下半刚性基层沥青路面反射裂缝疲劳断裂分析[J].中外公路,2008,28(4):59-63.YUAN Song,LI Xuelian. Fatigue fracture analysis of reflective crack of semi-rigid base asphalt pavement under traffic load[J]. Journal of China&Foreign Highway,2008,28(4):59-63.
[12]李永东.断裂力学理论与应用[M].北京:科学出版社,2000:145-153.LI Yongdong. Theory Fracture Mechanics[M]. Beijing:Science Press,2000:145-153.
[13]ZHAO H Q. Fracture and Fatigue Analysis of Functionally Graded and Homogeneous Materials Using Singular Integral Equation Approach[D]. Baltimore:Johns Hopkins University,1998:79-83.
[2]GONZALEZ-TORRE I,CALZADA-PEREZ M A,VEGA-ZAMANILLO A,et al. Evaluation of reflective cracking in pavements using a new procedure that combine loads with different frequencies[J]. Construction and Building Materials,2015,75:368-374.
[3]HORNICEK L,RAKOWSKI Z. Mechanical stabilization of intermediate granular layers in pavement structures-laboratory study[J]. Procedia Engineering,2017,189:174-180.
[4] CHEN D,HONG F,ZHOU F. Premature cracking from cementtreated base and treatment to mitigate its effect[J]. Journal of Performance of Constructed Facilities,2011,25(2):113-120.
[5]武贤慧,张登良,李德超.沥青路面反射裂缝足尺试验[J].长安大学学报(自然科学版),2003,23(6):4-6.WU Xianhui,ZHANG Dengliang, LI Dechao. Full-scale test of asphalt pavement reflection cracking[J]. Journal of Chang'an University:Natural Science Edition,2003,23(6):4-6.
[6] ZHANG J,DAI L,ZHENG J,et al. Reflective crack propagation and control in asphalt pavement widening[J]. Journal of Testing and Evaluation,2016,44(2):838-846.
[7]赵复笑,余天庆,金生吉.沥青路面反射裂缝机理及夹层结构应力分析[J].沈阳建筑大学学报(自然科学版),2010,26(2):296-300.ZHAO Fuxiao,YU Tianqing,JIN Shengji. Experimental study on deformati of multi-level retaining[J]. Journal of Shenyang Jianzhu University:Natural Science,2010,26(2):296-300.
[8]徐华,杨绿峰,佘振平.半刚性基层沥青路面反射裂缝扩展过程分析的Williams单元[J].工程力学,2013,30(6):247-253.XU Hua, YANG Lvfeng, SHE Zhenping. Williams element for reflective crack propagation in asphalt pavement on semi-rigid base course[J]. Engineering Mechanics,2013,30(6):247-253.
[9]王雪莲,黄晓明,卞国剑. LSPM对防治半刚性基层沥青路面反射裂缝机理分析[J].公路交通科技,2016,33(7):12-18.WANG Xuelian,HUANG Xiaoming,BIAN Guojian. Analysis on mechanism of using LSPM for preventing reflective cracks in asphalt prevent with semi-rigid base[J]. Journal of Highway and Transportation Research and Development,2016,33(7):12-18.
[10]郑大为,焉妮,郝连学.基于FLAC3D数值模拟的基层水泥含量对反射裂缝影响研究[J].硅酸盐通报,2017,36(4):1371-1376.ZHENG Dawei,YAN Ni,HAO Lianxue. Effect of cement content on reflection crack based on FLAC3D numerical simulation[J]. Bulletin of the Chinese Ceramic Society,2017,36(4):1371-1376.
[11]元松,李雪莲.交通荷载下半刚性基层沥青路面反射裂缝疲劳断裂分析[J].中外公路,2008,28(4):59-63.YUAN Song,LI Xuelian. Fatigue fracture analysis of reflective crack of semi-rigid base asphalt pavement under traffic load[J]. Journal of China&Foreign Highway,2008,28(4):59-63.
[12]李永东.断裂力学理论与应用[M].北京:科学出版社,2000:145-153.LI Yongdong. Theory Fracture Mechanics[M]. Beijing:Science Press,2000:145-153.
[13]ZHAO H Q. Fracture and Fatigue Analysis of Functionally Graded and Homogeneous Materials Using Singular Integral Equation Approach[D]. Baltimore:Johns Hopkins University,1998:79-83.