重载铁路路基面动应力峰值随机分布特征研究
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摘要
掌握列车移动荷载作用下路基的动应力响应特性可为路基沉降预测、状态评估提供依据。建立重载铁路车辆-轨道-路基三维动力有限元模型,并在钢轨轨面引入中国三大干线不平顺轨道谱以实现轨道不平顺的模拟。通过数值计算,分析了轨道高低不平顺对路基面动应力分布的影响,统计了4种列车轴重下路基面3个位置(钢轨下方,线路中心)处的动应力峰值沿线路纵向的分布,对路基面动应力峰值的随机分布形式进行了正态性检验,对动应力峰值的最大值进行了预测。结果表明:轨道不平顺导致路基面动应力沿路基面中心不对称,路基面动应力峰值沿线路纵向服从正态分布。随着轴重的增大,动应力峰值离散程度增大,动应力峰值分布曲线变陡。动应力峰值的预测值和现场实测值相吻合,证明了有限元模型及统计分析方法的正确性。研究结果对路基动变形及累积沉降的可靠性分析提供依据。
The dynamic stress response of subgrade under moving train loads provides information on subgrade settlement prediction and condition evaluation. In this paper, a 3 D dynamic finite element(FE) model, which considered the interaction of wagon-track-subgrade, was firstly built. And then, the vertical irregularity track spectra of China's three major lines were applied to simulate the track irregularity. Through numerical calculation, the influence of vertical track irregularity on dynamic stress at the subgrade surface was investigated. The distributions of peak dynamic stresses at three locations of subgrade surface(beneath the rails and at the track center) along the track under the passage of the trains with various axle loads were statistically acquired. The normal distributions of peak dynamic stresses on subgrade surface were verified. The maximums of peak dynamic stresses were forecasted.The results indicated that dynamic stresses on the subgrade surface were asymmetric along the center of subgrade surface, attributed by the random distribution of track irregularity. The peak dynamic stresses were found to follow the normal distribution along the track. The dispersion of peak dynamic stresses gradually increased, and the distribution curve of peak dynamic stresses became steeper with the increase of axle load. The computing peak dynamic stresses were consistent with field test data, indicating that the3 D dynamic FE model and statistical analysis method were reasonable. The research results provide the basis for the reliability analysis of the dynamic deformation and accumulated settlement of subgrade.
The dynamic stress response of subgrade under moving train loads provides information on subgrade settlement prediction and condition evaluation. In this paper, a 3 D dynamic finite element(FE) model, which considered the interaction of wagon-track-subgrade, was firstly built. And then, the vertical irregularity track spectra of China's three major lines were applied to simulate the track irregularity. Through numerical calculation, the influence of vertical track irregularity on dynamic stress at the subgrade surface was investigated. The distributions of peak dynamic stresses at three locations of subgrade surface(beneath the rails and at the track center) along the track under the passage of the trains with various axle loads were statistically acquired. The normal distributions of peak dynamic stresses on subgrade surface were verified. The maximums of peak dynamic stresses were forecasted.The results indicated that dynamic stresses on the subgrade surface were asymmetric along the center of subgrade surface, attributed by the random distribution of track irregularity. The peak dynamic stresses were found to follow the normal distribution along the track. The dispersion of peak dynamic stresses gradually increased, and the distribution curve of peak dynamic stresses became steeper with the increase of axle load. The computing peak dynamic stresses were consistent with field test data, indicating that the3 D dynamic FE model and statistical analysis method were reasonable. The research results provide the basis for the reliability analysis of the dynamic deformation and accumulated settlement of subgrade.
引文
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[15]詹永祥,蒋关鲁.无碴轨道路基基床动力特性的研究[J].岩土力学,2010,31(2):392-396.ZHAN Yong-xiang,JIANG Guan-lu.Study of dynamic characteristics of soil subgrade bed for ballastless track[J].Rock and Soil Mechanics,2010,31(2):392-396.
[16]杨琪,张友谊,刘华强,等.一种气泡轻质土路基受载-破坏模型试验[J].岩土力学,2018,39(9):1001-1009.YANG Qi,ZHANG You-yi,LIU Hua-qiang,et al.Model test study on load-failure of a foamed lightweight soil subgrade[J].Rock and Soil Mechanics,2018,39(9):1001-1009.
[17]SAYEED M A,SHAHIN M A.Three-dimensional numerical modelling of ballasted railway track foundations for high-speed trains with special reference to critical speed[J].Transportation Geotechnics,2016,6:55-65.
[18]CORREIA A G,CUNHA J.Analysis of nonlinear soil modelling in the subgrade and rail track responses under HST[J].Transportation Geotechnics,2014,1(4):147-156.
[19]TAKEMIYA H.Substructure simulation of inhomogeneous track and layered ground dynamic interaction under train passage[J].Journal of Engineering Mechanics,2005,131(7):699-711.
[20]YAO S,ALBERS B,SAVIDIS S A.Influence of different transition zones on the dynamic response of track-subgrade systems[J].Computers&Geotechnics,2013,48:21-28.
[21]翟婉明.车辆-轨道垂向系统的统一模型及其耦合动力学原理[J].铁道学报,1992,14(3):10-21.ZHAI Wan-ming.The vertical model of vehicle-track system and its coupling dynamics[J].Journal of the China Railway Society,1992,14(3):10-21.
[22]翟婉明.车辆-轨道耦合动力学[M].北京:科学出版社,2007.ZHAI Wan-ming.Vehicle-track coupled dynamics[M].Beijing:Science Press,2007.
[23]ZHU Z Y,LING X Z,CHEN S J,et al.Analysis of dynamic compressive stress induced by passing trains in permafrost subgrade along Qinghai-Tibet Railway[J].Cold Regions Science&Technology,2011,65(3):465-473.
[24]SHAN Y,SHU Y,ZHOU S.Finite-infinite element coupled analysis on the influence of material parameters on the dynamic properties of transition zones[J].Construction&Building Materials,2017,148:548-558.
[25]CHEN R P,CHEN J M,WANG H L,et al.Recent research on the track-subgrade of high-speed railways[J].Journal of Zhejiang University Science,2014,15(12):1034-1038.
[26]董亮,赵成刚,蔡德钩,等.高速铁路无砟轨道路基动力特性数值模拟和试验研究[J].土木工程学报,2008,41(10):81-86.DONG Liang,ZHAO Cheng-gang,CAI De-gou,et al.Experimental validation of a numerical model for prediction of the dynamic response of ballastless subgrade of high-speed railways[J].China Civil Engineering Journal,2008,41(10):81-86.
[27]刘扬.有砟轨道沉降的概率预测模型[D].上海:同济大学,2007.LIU Yang.Probability predicting model of ballasted track[D].Shanghai:Tongji University,2007.
[28]陈仁朋,江朋,段翔,等.高速铁路板式无砟轨道不平顺下路基动应力的概率分布特征[J].铁道学报,2016,38(9):86-91.CHEN Ren-peng,JIANG Peng,DUAN Xiang,et al.Probability distribution of dynamic stress of high-speed subgrade under slab track irregularity[J].Journal of the China Railway Society,2016,38(9):86-91.
[29]张石友,孙海建,陈艳国.高速铁路双线路基动应力的特性研究[J].振动与冲击,2016,35(17):165-170.ZHANG Shi-you.SUN Hai-jian,CHEN Yan-guo.Dynamic stress distribution of high-speed railway double-subgrade[J].Journal of Vibration and Shock,2016,35(17):165-170.
[30]刘晓敏.典型轨道谱的仿真分析研究[D].长春:吉林大学,2009.LIU Xiao-min.Research on simulation and analysis of typical track spectrum[D].Changchun:Jilin University,2009.
[31]康高亮,刘丙强,柯在田.大秦线2万t货物列车条件下线桥设备试验研究[J].中国铁道科学,2008,29(6):35-40.KANG Gao-liang,LIU Bing-qiang,KE Zai-tian.Test study on track bridge and subgrade equipment of Datong-Qinhuangdao railway under 20 000 t freight trains[J].China Railway Science,2008,29(6):35-40.
[32]王立军.重载铁路路基评估的试验研究[D].北京:中国铁道科学研究院,2005.WANG Li-jun.Test research of subgrade assessment of heavy load railway[D].Beijing:China Academy of Railway Sciences,2005.
[33]贾晋中.重载铁路路基动荷载特征[J].铁道建筑,2014(7):89-91.JIA Jin-zhong.Dynamical load characteristic of heavy haul railway subgrade[J].Railway Engineering,2014(7):89-91.
[34]薛继连.重载铁路路基状态检测与强化技术[M].北京:科学出版社,2014.XUE Ji-lian.State detection and strengthen technology of heavy haul railway subgrade[M].Beijing:Science Press,2014.
[35]苗雷强,冯怀平,岳祖润,等.大轴重条件下重载铁路路基变形特性研究[J].路基工程,2015(3):35-37.MIAO Lei-qiang,FENG Huai-ping,YUE Zu-run,et al.On deformation characteristics of heavy-haul railways subgrade under heavy axle load[J].Subgrade Engineering,2015(3):35-37.
[2]LAMAS-LOPEZ F,CUI Y J,CALON N,et al.Track-bed mechanical behaviour under the impact of train at different speeds[J].Soils&Foundations,2016,56(4):627-639.
[3]YAO H,HU Z,LU Z,et al.Analytical model to predict dynamic responses of railway subgrade due to high-speed trains considering wheel-track interaction[J].International Journal of Geomechanics,2016,16(2):737-756.
[4]KEMPFERT H,HU Y.Measured dynamic loading of railway underground[C]//Proceedings of the 11th Pan-American Conference on Soil Mechanics and Geotechnical Engineering.[S.l.]:International Society for Soil Mechanics,1999:843-847.
[5]GR?BE P J,SHAW F J,CLAYTON C R I.Deformation measurement on a heavy haul track formation[C]//International Heavy Haul Conference.[S.l.]:[s.n.],2005:287-295.
[6]詹永祥,蒋关鲁,胡安华,等.遂渝线无碴轨道桩板结构路基动力响应现场试验研究[J].岩土力学,2009,30(3):832-835.ZHAN Yong-xiang,JIANG Guan-lu,HU An-hua,et al.Study of dynamic response of pile-plank embankment of ballastless track based on field test in Suining-Chongqing High-speed Railway[J].Rock and Soil Mechanics,2009,30(3):832-835.
[7]徐鹏,蒋关鲁,任世杰,等.红层泥岩及其改良填料路基动力响应试验研究[J].岩土力学,2019,40(2):1-7.XU Peng,JIANG Guan-lu,REN Shi-jie,et al.Test study on dynamic response of subgrade with red mudstone and improved red mudstone[J].Rock and Soil Mechanics,2019,40(2):1-7.
[8]SHAER A A,DUHAMEL D,SAB K,et al.Experimental settlement and dynamic behavior of a portion of ballasted railway track under high speed trains[J].Journal of Sound&Vibration,2008,316(1):211-233.
[9]BIAN X,JIANG H,CHENG C,et al.Full-scale model testing on a ballastless high-speed railway under simulated train moving loads[J].Soil Dynamics&Earthquake Engineering,2014,66:368-384.
[10]CHEN R,ZHAO X,WANG Z,et al.Experimental study on dynamic load magnification factor for ballastless track-subgrade of high-speed railway[J].Journal of Rock Mechanics and Geotechnical Engineering,2013,5(4):306-311.
[11]TATSUYA ISHIKAWA,ETSUO SEKINE,SEIICHIMIURA.Cyclic deformation of granular material subjected to moving-wheel loads[J].Canadian Geotechnical Journal,2011,48(5):691-703.
[12]边学成,蒋红光,金皖锋,等.板式轨道-路基相互作用及荷载传递规律的物理模型试验研究[J].岩土工程学报,2012,34(8):1488-1495.BIAN Xue-cheng,JIANG Hong-guang,JIN Wan-feng,et al.Full-scale model tests on slab track-subgrade interaction and load transfer in track system[J].Chinese Journal of Geotechnical Engineering,2012,34(8):1488-1495.
[13]董云,阎宗岭.土石混填路基沉降变形特征的二维力学模型试验研究[J].岩土工程学报,2007,29(6):943-947.DONG Yun,YAN Zong-ling.2D mechanical model tests on settlement of rock-soil filled roadbed[J].Chinese Journal of Geotechnical Engineering,2007,29(6):943-947.
[14]陈爱云,郭建湖.武广客运专线软岩填筑路基的模型试验研究[J].岩土力学,2008,29(10):2882-2886.CHEN Ai-yun,GUO Jian-hu.Research on model test of soft rock roadbed in special passenger railway line of Wuhan-Guangzhou[J].Rock and Soil Mechanics,2008,29(10):2882-2886.
[15]詹永祥,蒋关鲁.无碴轨道路基基床动力特性的研究[J].岩土力学,2010,31(2):392-396.ZHAN Yong-xiang,JIANG Guan-lu.Study of dynamic characteristics of soil subgrade bed for ballastless track[J].Rock and Soil Mechanics,2010,31(2):392-396.
[16]杨琪,张友谊,刘华强,等.一种气泡轻质土路基受载-破坏模型试验[J].岩土力学,2018,39(9):1001-1009.YANG Qi,ZHANG You-yi,LIU Hua-qiang,et al.Model test study on load-failure of a foamed lightweight soil subgrade[J].Rock and Soil Mechanics,2018,39(9):1001-1009.
[17]SAYEED M A,SHAHIN M A.Three-dimensional numerical modelling of ballasted railway track foundations for high-speed trains with special reference to critical speed[J].Transportation Geotechnics,2016,6:55-65.
[18]CORREIA A G,CUNHA J.Analysis of nonlinear soil modelling in the subgrade and rail track responses under HST[J].Transportation Geotechnics,2014,1(4):147-156.
[19]TAKEMIYA H.Substructure simulation of inhomogeneous track and layered ground dynamic interaction under train passage[J].Journal of Engineering Mechanics,2005,131(7):699-711.
[20]YAO S,ALBERS B,SAVIDIS S A.Influence of different transition zones on the dynamic response of track-subgrade systems[J].Computers&Geotechnics,2013,48:21-28.
[21]翟婉明.车辆-轨道垂向系统的统一模型及其耦合动力学原理[J].铁道学报,1992,14(3):10-21.ZHAI Wan-ming.The vertical model of vehicle-track system and its coupling dynamics[J].Journal of the China Railway Society,1992,14(3):10-21.
[22]翟婉明.车辆-轨道耦合动力学[M].北京:科学出版社,2007.ZHAI Wan-ming.Vehicle-track coupled dynamics[M].Beijing:Science Press,2007.
[23]ZHU Z Y,LING X Z,CHEN S J,et al.Analysis of dynamic compressive stress induced by passing trains in permafrost subgrade along Qinghai-Tibet Railway[J].Cold Regions Science&Technology,2011,65(3):465-473.
[24]SHAN Y,SHU Y,ZHOU S.Finite-infinite element coupled analysis on the influence of material parameters on the dynamic properties of transition zones[J].Construction&Building Materials,2017,148:548-558.
[25]CHEN R P,CHEN J M,WANG H L,et al.Recent research on the track-subgrade of high-speed railways[J].Journal of Zhejiang University Science,2014,15(12):1034-1038.
[26]董亮,赵成刚,蔡德钩,等.高速铁路无砟轨道路基动力特性数值模拟和试验研究[J].土木工程学报,2008,41(10):81-86.DONG Liang,ZHAO Cheng-gang,CAI De-gou,et al.Experimental validation of a numerical model for prediction of the dynamic response of ballastless subgrade of high-speed railways[J].China Civil Engineering Journal,2008,41(10):81-86.
[27]刘扬.有砟轨道沉降的概率预测模型[D].上海:同济大学,2007.LIU Yang.Probability predicting model of ballasted track[D].Shanghai:Tongji University,2007.
[28]陈仁朋,江朋,段翔,等.高速铁路板式无砟轨道不平顺下路基动应力的概率分布特征[J].铁道学报,2016,38(9):86-91.CHEN Ren-peng,JIANG Peng,DUAN Xiang,et al.Probability distribution of dynamic stress of high-speed subgrade under slab track irregularity[J].Journal of the China Railway Society,2016,38(9):86-91.
[29]张石友,孙海建,陈艳国.高速铁路双线路基动应力的特性研究[J].振动与冲击,2016,35(17):165-170.ZHANG Shi-you.SUN Hai-jian,CHEN Yan-guo.Dynamic stress distribution of high-speed railway double-subgrade[J].Journal of Vibration and Shock,2016,35(17):165-170.
[30]刘晓敏.典型轨道谱的仿真分析研究[D].长春:吉林大学,2009.LIU Xiao-min.Research on simulation and analysis of typical track spectrum[D].Changchun:Jilin University,2009.
[31]康高亮,刘丙强,柯在田.大秦线2万t货物列车条件下线桥设备试验研究[J].中国铁道科学,2008,29(6):35-40.KANG Gao-liang,LIU Bing-qiang,KE Zai-tian.Test study on track bridge and subgrade equipment of Datong-Qinhuangdao railway under 20 000 t freight trains[J].China Railway Science,2008,29(6):35-40.
[32]王立军.重载铁路路基评估的试验研究[D].北京:中国铁道科学研究院,2005.WANG Li-jun.Test research of subgrade assessment of heavy load railway[D].Beijing:China Academy of Railway Sciences,2005.
[33]贾晋中.重载铁路路基动荷载特征[J].铁道建筑,2014(7):89-91.JIA Jin-zhong.Dynamical load characteristic of heavy haul railway subgrade[J].Railway Engineering,2014(7):89-91.
[34]薛继连.重载铁路路基状态检测与强化技术[M].北京:科学出版社,2014.XUE Ji-lian.State detection and strengthen technology of heavy haul railway subgrade[M].Beijing:Science Press,2014.
[35]苗雷强,冯怀平,岳祖润,等.大轴重条件下重载铁路路基变形特性研究[J].路基工程,2015(3):35-37.MIAO Lei-qiang,FENG Huai-ping,YUE Zu-run,et al.On deformation characteristics of heavy-haul railways subgrade under heavy axle load[J].Subgrade Engineering,2015(3):35-37.