考虑水平摩阻效应的交通荷载下路面沉降分析
|
摘要
为分析计算高速公路水泥混凝土路面承载结构在交通荷载作用下的沉降,将路面结构视为黏弹性地基梁.在Kelvin地基梁模型的基础上,考虑路面结构与路基土界面摩阻效应的影响,进而分析交通荷载下黏弹性地基有限长梁的瞬态问题,通过三角级数展开法和Laplace-Fourier积分变换以及逆变换得到黏弹性地基梁在半正弦波荷载作用下的位移解析解.并研究分析了路基路面摩阻效应、荷载移动速度、路面结构刚度、路基竖向反力系数、路基阻尼等因素对路面沉降的影响.分析结果表明:路面沉降随车辆移动速度的增大而减小,随路基黏滞阻力系数及路基刚度的增大而减小,随路面结构刚度及结构层高度的增大而减小,与此同时增大路面结构刚度还可减小路面的波动.
To analyze the settlement of bearing structure of the cement concrete pavement of highway under traf-fic loads, pavement structure was regarded as a viscoelastic foundation beam. The interfacial friction effect between the foundation beam and soil below was introduced into the Kelvin foundation beam model. Based on the Kelvin model and taking the interfacial friction forces into consideration, an analytical solution of settlement for the vis-coelastic foundation beam under traffic load was proposed by using trigonometric series, Laplace-Fourier transform and inverse transformation. Influence parameter study was presented to quantify the effects of various factors, such as the interfacial friction of subgrade and pavement, velocity of moving load, pavement structure stiffness, the coeffi-cient of vertical soil reaction and viscous damping of subgrade. The results show that the settlement of pavement in-creases with the decrease of moving load speed,deformation decreases with the increase of viscous damping or subgrade stiffness, and deformation decreases with the increase of pavement stiffness or height of pavement structure.Meanwhile, the wave phenomenon of pavement decreases with the increase of the pavement structure stiffness.
To analyze the settlement of bearing structure of the cement concrete pavement of highway under traf-fic loads, pavement structure was regarded as a viscoelastic foundation beam. The interfacial friction effect between the foundation beam and soil below was introduced into the Kelvin foundation beam model. Based on the Kelvin model and taking the interfacial friction forces into consideration, an analytical solution of settlement for the vis-coelastic foundation beam under traffic load was proposed by using trigonometric series, Laplace-Fourier transform and inverse transformation. Influence parameter study was presented to quantify the effects of various factors, such as the interfacial friction of subgrade and pavement, velocity of moving load, pavement structure stiffness, the coeffi-cient of vertical soil reaction and viscous damping of subgrade. The results show that the settlement of pavement in-creases with the decrease of moving load speed,deformation decreases with the increase of viscous damping or subgrade stiffness, and deformation decreases with the increase of pavement stiffness or height of pavement structure.Meanwhile, the wave phenomenon of pavement decreases with the increase of the pavement structure stiffness.
引文
[1]杨成永，寇鼎涛，程霖，等.对称荷载作用下弹性地基梁的傅里叶级数解[J].湖南大学学报（自然科学版），2018,45(3):136—141.YANG C Y,KOU D T,CHENG L,et al. Fourier series solution for elastic foundation beams under symmetric loads[J]. Journal of Hunan University(Natural Sciences),2018,45(3):136—141.(In Chinese)
[2]庄妍，王孟，王康宇.移动荷载作用下结构弹塑性安定分析方法及其应用研究[J].湖南大学学报（自然科学版），2018,45(7):93—102.ZHUANG Y,WANG M,WANG K Y. Study on shakedown analysis method of elastic-plastic structures under moving loads structures and its application[J]. Journal of Hunan University(Natural Sciences),2018,45(7):93—102.(In Chinese)
[3] KENNY J T. Steady-state vibration of beam on elastic foundation for moving load[J]. Journal of Applied Mechanics,1954,21:359—364.
[4] FRYBA L. Vibration of solids and structures under moving loads[M]. London:Thomas Telford,1999:124—126.
[5] BEN-HAIM Y,FRYBA L,YOSHIKAWA N. Robust reliability of dynamically loaded beam on an uncertain foundation[C]//Kumar B,Topping,BHV. Computing Developments in Civil and Structural Engineering. 7th International Conference on Civil and Structural Engineering. Oxford:Civil Computer Press,1999:71—75.
[6] YAU J D,FRYBA L. A quasi-vehicle/bridge interaction model for high speed railways[J]. Journal of Mechanics,2014,31(2):217—225.
[7] YAU J D,FRYBA L. Interaction dynamics of a high-speed train moving on multi-span railway bridges with support settlements[C]//Sas P,Moens D,Denayer H. Proceedings of International Conference on Noise and Vibration Engineering(ISMA2014)and International Conference on Uncertainty in Structural Dynamics(USD2014);International Conference on Noise and Vibration Engineering(ISMA). Leuven:Katholieke University of Lauven,2014:955—963.
[8] SUN L. A closed-form solution of beam on viscoelastic subgrade subjected to moving loads[J]. Computers and Structures,2002,80(1):1—8.
[9] KIM S M. Vibration and stability of axial loaded beams on elastic foundation under moving harmonic loads[J]. Engineering Structures,2004,26:95—105.
[10] DIMITROVOVA Z. Critical velocity of a uniformly moving load on a beam supported by a finite depth foundation[J]. Journal of Sound and Vibration,2016,366:325—342.
[11]黄晓明，邓学钧.文克勒地基上板在动荷载下的挠度计算方法[J].东南大学学报，1989,19(6):55—60.HUANG X M,DENG X J. Calculation method of plate on winkler foundation under transient load[J]. Journal of Southeast University,1989,19(6):55—60.(In Chinese)
[12]孙璐，邓学钧.匀速运动的线源荷载激励下无限长梁动力分析[J]．应用数学和力学，1998,19(4):341—347.SUN L,DENG X J. Dynamic analysis to infinite beam under a moving line load with uniform velocity[J]. Applied Mathematics and Mechanics,1998,19(4):341—347.(In Chinese)
[13]郑小平，王尚文，陈百屏.弹性地基无限长梁动力问题的一般解[J].应用数学和力学，1991,12(7):593—597.ZHENG X P,WANG S W,CHEN B P. General solution for dynamical problem of infinite beam on an elastic foundation[J]. Applied Mathematics and Mechanics,1991,12(7):593—597.(In Chinese)
[14]张选兵，罗先启，葛修润，等.双参数弹性地基上板承受冲击荷载的动力响应的解析解[J].岩石力学与工程学报，2001,20(6):846—850.ZHANG X B,LUO X Q,GE X R,et al. Analytical solution on dynamic response of rectangular plate with free edges on two parameters elastic foundation under impact load[J]. Chinese Journal of Rock Mechanics and Engineering,2001,20(6):846—850.(In Chinese)
[15]蒋建群，周华飞，张土乔.移动荷载下黏弹性地基上无限大板的稳态响应[J].中国公路学报，2006,19(1):6—11.JIANG J Q,ZHOU H F,ZHANG T Q. Steady state response of infinite plate on visco-elastic foundation subjected to moving load[J].China Journal of Highway and Transport,2006,19(1):6—11.(In Chinese)
[16]颜可珍，夏唐代.双参数地基矩形板在运动荷载下的动力响应分析[J].哈尔滨工业大学学报，2006,38(6):972—974,1011—1012.YAN K Z,XIA T D. Dynamic response of rectangular plate on twoparameter foundation to moving load[J]. Journal of Harbin Institute of Technology University,2006,38(6):972—974,1011—1012.(In Chinese)
[17]颜可珍，吴建良，夏唐代，等.运动荷载作用下Vlazov地基上梁的动力分析[J].湖南大学学报（自然科学版），2007,34(12):11—14.YAN K Z,WU J L,XIA T D,et al. Dynamic analysis of beam subjected to moving load on Vlazov subgrade[J]. Journal of Hunan University(Natural Sciences),2007,34(12):11—14.(In Chinese)
[18]谈至明.具有水平摩阻力的弹性地基上梁的解[J].力学与实践，1997,19(3):33—35.TAN Z M. Solution of beams on elastic foundation with horizontal friction resistance[J]. Mechanics in Engineering,1997,19(3):33—35.(In Chinese)
[19]赵明华，张玲，马缤辉，等．考虑水平摩阻力的弹性地基梁非线性分析[J].岩土工程学报，2009,42(7):106—112.ZHAO M H,ZHANG L,MA B H,et al. Nonlinear analysis of beams on elastic foundation with consideration of horizontal resistance[J].China Civil Engineering Journal,2009,42(7):106—112.(In Chinese)
[20]ZHANG L,ZHAO M H,ZOU X W,et al. Analysis of geocell-reinforced mattress with consideration of horizontal-vertical coupling[J]. Computers and Geotechnics,2010,37(6):748—756.
[21]赵明华，张玲，刘敦平.考虑摩阻效应的弹性地基梁幂级数解[J].铁道学报，2010,32(6):72—77.ZHAO M H,ZHANG L,LIU D P. Power-series analytic solutions for the finite beam on elastic foundation with consideration of Interface Resistance[J]. Journal of the China Railway Society,2010,32(6):72—77.(In Chinese)
[22]邓学钧.车辆-地面结构系统动力学研究[J].东南大学学报（自然科学版），2002,32(3):474—479.DENG X J. Study on dynamics of vehicle-ground pavement structure system[J]. Journal of Southeast University(Natural Science Edition),2002,32(3):474—479.(In Chinese)
[23]董泽蛟，谭忆秋.沥青路面动力响应研究[M].北京：科学出版社，2015:17—20.DONG Z J,TAN Y Q. Study on dynamic response of asphalt pavement[M]. Beijing:Sceience Press,2015:17—20.(In Chinese)
[24]张颖，交通荷载下高速公路低路堤沉降研究[D].上海:上海交通大学船舶海洋与建筑工程学院，2013:20—22.ZHANG Y. Study on traffic-load-induced settlement of highway low embankment[D]. Shanghai:School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,2013:20—22.(In Chinese)
[25]周华飞，蒋建群，张土乔.移动荷载下Kelvin地基上无限长梁的稳态响应[J].浙江大学学报（工学版），2004,38(10):1328—1333.ZHOU H F,JIANG J Q,ZHANG T Q. Steady-state response of infinite beam on Kelvin foundation under moving loads[J]. Journal of Zhejiang University(Engineering Science),2004,38(10):1328—1333.(In Chinese)
[2]庄妍，王孟，王康宇.移动荷载作用下结构弹塑性安定分析方法及其应用研究[J].湖南大学学报（自然科学版），2018,45(7):93—102.ZHUANG Y,WANG M,WANG K Y. Study on shakedown analysis method of elastic-plastic structures under moving loads structures and its application[J]. Journal of Hunan University(Natural Sciences),2018,45(7):93—102.(In Chinese)
[3] KENNY J T. Steady-state vibration of beam on elastic foundation for moving load[J]. Journal of Applied Mechanics,1954,21:359—364.
[4] FRYBA L. Vibration of solids and structures under moving loads[M]. London:Thomas Telford,1999:124—126.
[5] BEN-HAIM Y,FRYBA L,YOSHIKAWA N. Robust reliability of dynamically loaded beam on an uncertain foundation[C]//Kumar B,Topping,BHV. Computing Developments in Civil and Structural Engineering. 7th International Conference on Civil and Structural Engineering. Oxford:Civil Computer Press,1999:71—75.
[6] YAU J D,FRYBA L. A quasi-vehicle/bridge interaction model for high speed railways[J]. Journal of Mechanics,2014,31(2):217—225.
[7] YAU J D,FRYBA L. Interaction dynamics of a high-speed train moving on multi-span railway bridges with support settlements[C]//Sas P,Moens D,Denayer H. Proceedings of International Conference on Noise and Vibration Engineering(ISMA2014)and International Conference on Uncertainty in Structural Dynamics(USD2014);International Conference on Noise and Vibration Engineering(ISMA). Leuven:Katholieke University of Lauven,2014:955—963.
[8] SUN L. A closed-form solution of beam on viscoelastic subgrade subjected to moving loads[J]. Computers and Structures,2002,80(1):1—8.
[9] KIM S M. Vibration and stability of axial loaded beams on elastic foundation under moving harmonic loads[J]. Engineering Structures,2004,26:95—105.
[10] DIMITROVOVA Z. Critical velocity of a uniformly moving load on a beam supported by a finite depth foundation[J]. Journal of Sound and Vibration,2016,366:325—342.
[11]黄晓明，邓学钧.文克勒地基上板在动荷载下的挠度计算方法[J].东南大学学报，1989,19(6):55—60.HUANG X M,DENG X J. Calculation method of plate on winkler foundation under transient load[J]. Journal of Southeast University,1989,19(6):55—60.(In Chinese)
[12]孙璐，邓学钧.匀速运动的线源荷载激励下无限长梁动力分析[J]．应用数学和力学，1998,19(4):341—347.SUN L,DENG X J. Dynamic analysis to infinite beam under a moving line load with uniform velocity[J]. Applied Mathematics and Mechanics,1998,19(4):341—347.(In Chinese)
[13]郑小平，王尚文，陈百屏.弹性地基无限长梁动力问题的一般解[J].应用数学和力学，1991,12(7):593—597.ZHENG X P,WANG S W,CHEN B P. General solution for dynamical problem of infinite beam on an elastic foundation[J]. Applied Mathematics and Mechanics,1991,12(7):593—597.(In Chinese)
[14]张选兵，罗先启，葛修润，等.双参数弹性地基上板承受冲击荷载的动力响应的解析解[J].岩石力学与工程学报，2001,20(6):846—850.ZHANG X B,LUO X Q,GE X R,et al. Analytical solution on dynamic response of rectangular plate with free edges on two parameters elastic foundation under impact load[J]. Chinese Journal of Rock Mechanics and Engineering,2001,20(6):846—850.(In Chinese)
[15]蒋建群，周华飞，张土乔.移动荷载下黏弹性地基上无限大板的稳态响应[J].中国公路学报，2006,19(1):6—11.JIANG J Q,ZHOU H F,ZHANG T Q. Steady state response of infinite plate on visco-elastic foundation subjected to moving load[J].China Journal of Highway and Transport,2006,19(1):6—11.(In Chinese)
[16]颜可珍，夏唐代.双参数地基矩形板在运动荷载下的动力响应分析[J].哈尔滨工业大学学报，2006,38(6):972—974,1011—1012.YAN K Z,XIA T D. Dynamic response of rectangular plate on twoparameter foundation to moving load[J]. Journal of Harbin Institute of Technology University,2006,38(6):972—974,1011—1012.(In Chinese)
[17]颜可珍，吴建良，夏唐代，等.运动荷载作用下Vlazov地基上梁的动力分析[J].湖南大学学报（自然科学版），2007,34(12):11—14.YAN K Z,WU J L,XIA T D,et al. Dynamic analysis of beam subjected to moving load on Vlazov subgrade[J]. Journal of Hunan University(Natural Sciences),2007,34(12):11—14.(In Chinese)
[18]谈至明.具有水平摩阻力的弹性地基上梁的解[J].力学与实践，1997,19(3):33—35.TAN Z M. Solution of beams on elastic foundation with horizontal friction resistance[J]. Mechanics in Engineering,1997,19(3):33—35.(In Chinese)
[19]赵明华，张玲，马缤辉，等．考虑水平摩阻力的弹性地基梁非线性分析[J].岩土工程学报，2009,42(7):106—112.ZHAO M H,ZHANG L,MA B H,et al. Nonlinear analysis of beams on elastic foundation with consideration of horizontal resistance[J].China Civil Engineering Journal,2009,42(7):106—112.(In Chinese)
[20]ZHANG L,ZHAO M H,ZOU X W,et al. Analysis of geocell-reinforced mattress with consideration of horizontal-vertical coupling[J]. Computers and Geotechnics,2010,37(6):748—756.
[21]赵明华，张玲，刘敦平.考虑摩阻效应的弹性地基梁幂级数解[J].铁道学报，2010,32(6):72—77.ZHAO M H,ZHANG L,LIU D P. Power-series analytic solutions for the finite beam on elastic foundation with consideration of Interface Resistance[J]. Journal of the China Railway Society,2010,32(6):72—77.(In Chinese)
[22]邓学钧.车辆-地面结构系统动力学研究[J].东南大学学报（自然科学版），2002,32(3):474—479.DENG X J. Study on dynamics of vehicle-ground pavement structure system[J]. Journal of Southeast University(Natural Science Edition),2002,32(3):474—479.(In Chinese)
[23]董泽蛟，谭忆秋.沥青路面动力响应研究[M].北京：科学出版社，2015:17—20.DONG Z J,TAN Y Q. Study on dynamic response of asphalt pavement[M]. Beijing:Sceience Press,2015:17—20.(In Chinese)
[24]张颖，交通荷载下高速公路低路堤沉降研究[D].上海:上海交通大学船舶海洋与建筑工程学院，2013:20—22.ZHANG Y. Study on traffic-load-induced settlement of highway low embankment[D]. Shanghai:School of Naval Architecture,Ocean and Civil Engineering,Shanghai Jiao Tong University,2013:20—22.(In Chinese)
[25]周华飞，蒋建群，张土乔.移动荷载下Kelvin地基上无限长梁的稳态响应[J].浙江大学学报（工学版），2004,38(10):1328—1333.ZHOU H F,JIANG J Q,ZHANG T Q. Steady-state response of infinite beam on Kelvin foundation under moving loads[J]. Journal of Zhejiang University(Engineering Science),2004,38(10):1328—1333.(In Chinese)
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |