桩顶柔性约束下管桩水平瞬态振动特性研究
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摘要
基于Pasternak地基模型,在忽略桩芯土作用的基础上,对桩顶柔性约束条件下层状地基中管桩水平瞬态动力响应进行了理论研究。采用两阶段等效线性模型描述了桩顶弯矩和转角的关系;通过传递矩阵法建立了任意桩段与桩顶状态变量关系;并结合Laplace变换及数值逆变换,求得了层状地基中管桩水平瞬态动力响应的时域解答。结果表明:随着桩顶约束(转动刚度K)的增大,管桩水平抗力增强,桩顶位移减小而弯矩增大,桩身反弯点处弯矩和剪力均减小;桩顶最大位移比χ和约束度λ在高、低K区域均有一数值不变段;中间柔性约束区段,则随着K的增大,χ逐渐减小,而λ逐渐增大,且增幅大于χ的减小幅度。
Based on two-parameter Pasternak model, the horizontal transient dynamic response of pipe pile in layered soils with partial head fixity is theoretically investigated without considering inner soil. The relation between the moment and rotation of the pile head is assumed to be two-stage equivalent linear model. By applying the matrix transfer method, the relationship of the state variables between the arbitrary pile segment and pile top is established, and then the time domain solution of pile top under horizontal transient loading is derived through Laplace transformation and its numerical inversion. The results show that the increase of rotational stiffness K improves the horizontal resistance of the pipe pile, and leads to a larger displacement, but a smaller bending moment at the pile top. The maximum bending moment and shear force of the pile decrease for a larger rotational stiffness K. Both the maximum displacement ratio χ and constraint degree λ remain invariant in the high and low ranges of the rotational stiffness K, corresponding to the approximately fixed and free conditions. When the pile head is partial fixed, the maximum displacement ratio χ decreases with the increase of the rotational stiffness K, while the constraint degree λ increases rapidly with a larger range of variation.
Based on two-parameter Pasternak model, the horizontal transient dynamic response of pipe pile in layered soils with partial head fixity is theoretically investigated without considering inner soil. The relation between the moment and rotation of the pile head is assumed to be two-stage equivalent linear model. By applying the matrix transfer method, the relationship of the state variables between the arbitrary pile segment and pile top is established, and then the time domain solution of pile top under horizontal transient loading is derived through Laplace transformation and its numerical inversion. The results show that the increase of rotational stiffness K improves the horizontal resistance of the pipe pile, and leads to a larger displacement, but a smaller bending moment at the pile top. The maximum bending moment and shear force of the pile decrease for a larger rotational stiffness K. Both the maximum displacement ratio χ and constraint degree λ remain invariant in the high and low ranges of the rotational stiffness K, corresponding to the approximately fixed and free conditions. When the pile head is partial fixed, the maximum displacement ratio χ decreases with the increase of the rotational stiffness K, while the constraint degree λ increases rapidly with a larger range of variation.
引文
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[5]刘华瑄,刘东甲,卢志堂,等.桩基三维弹性波动方程变步长交错网格有限差分数值计算[J].岩土工程学报,2014,36(9):1754-1760.(LIU Huaxuan,LIU Dongjia,LU Zhitang,et al.Numerical calculation of three-dimensional elastic wave equation of piles staggered grid finite difference using mathod with variable step lengths[J].Chinese journal of geotechnical engineering,2014,36(9):1754-1760(in Chinese)).
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[7]PASTERNAK P L.Fundamentals of a new method of analyzing structures on an elastic foundation by means of two foundation constants[M].Moscow:Gosudarstvennoe Izdatelstro Liberaturi Po Stroitelstvui Arkhitekture,1954.
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[9]张治国,徐晨,宫剑飞.考虑桩侧土体三维效应和地基剪切变形的隧道开挖对邻近桩基影响分析[J].岩土工程学报,2016,38(5):846-856.(ZHANG Zhiguo,XU Chen,GONG Jianfei.Influence of tunneling on deflection of adjacent piles considering shearing deformation of foundation and 3D effects of lateral soils beside piles[J].Chinese journal of geotechnical engineering,2016,38(5):846-856(in Chinese)).
[10]CATAL H H.Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment,axial and shear force[J].Engineering structures,2006,28(14):1911-1918.
[11]MOKWA R L,DUNCAN J M.Rotational restraint of pile caps during lateral loading[J].Journal of geotechnical and geoenvironmental engineering,ASCE,2003,129(9):829-837.
[12]PRAKASH S,SHARMA H D.Pile foundations in engineering practice[M].Hoboken,New Jersey:John Wiley&Sons,1990.
[13]SADEK M,SHAHROUR I.Influence of the head and tip connection on the seismic performance of micropiles[J].Soil dynamics and earthquake engineering,2006,26(5):461-468.
[14]孔令刚,姜丽红,陈仁朋,等.考虑桩头约束的水平受荷单桩响应分析[J].应用力学学报,2014,31(3):393-399.(KONG Linggang,JIANG Lihong,CHEN Renpeng,et al.Response of single pile with partial pile head fixity subjected to lateral loading[J].Chinese journal of applied mechanics,2014,31(3):393-399(in Chinese)).
[15]姜丽红,孔令刚,蔺港,等.不同桩头约束下水平受荷单桩简化计算方法[J].工程力学,2014,31(11):63-69.(JIANG Lihong,KONG Linggang,LIN Gang,et al.Simplified method of laterally loaded single piles with partial pile hesd fixity[J].Engineering mechanics,2014,31(11):63-69(in Chinese)).
[16]ZHENG C,LIU H,DING X,et al.Horizontal vibration of a large-diameter pipe pile in viscoelastic soil[J].Mathematical problems in engineering,2013(4):1-13.
[17]ZHENG C,LIU H,DING X.Lateral dynamic response of a pipe pile in saturated soil layer[J].International journal for numerical and analytical methods in geomechanics,2016,40(2):159-184.
[18]栾鲁宝,丁选明,刘汉龙,等.考虑竖向荷载影响的大直径管桩水平振动响应解析解[J].岩土工程学报,2016,38(10):1859-1868.(LUAN Lubao,DING Xuanming,LIU Hanlong,et al.Analytical solution of lateral dynamic response of a large diameter pipe pile considering influence of axial load[J].Chinese journal of geotechnical engineering,2016,38(10):1859-1868(in Chinese)).
[19]ROSA M A D,MAURIZI M J.The influence of concentrated masses and pasternak soil on the free vibrations of euler beams-exact solution[J].Journal of sound&vibration,1998,212(4):573-581.
[20]TANAHASHI H.Formulas for an infinitely long Bernoulli-Euler beam on the Pasternak model[J].Soils and foundation,2004,44(5):109-118.
[21]KISHI N,CHEN W F,GOTO Y,et al.Applicability of three-parameter power model to structural analysis of flexibly jointed frames[J].Mechanics computing,1991,20(3):238-242.
[22]尚微.饱和土中管桩水平瞬态动力特性研究[D].太原:太原理工大学,2018.(SHANG Wei.Horizontal transient dynamic response of pipe pile in saturated soil[D].Taiyuan:Taiyuan University of Technology,2018(in Chinese)).
[23]MATLOCK H,REESE L C.Foundation analysis of offshore pile supported structures[C]//Proceedings of the 5th International Conference of Soil Mechanics and Foundation Engineering.Paris,France:Dunod,1961.
[24]CRUMP K S.Numerical inversion of Laplace transforms using a Fourier series approximation[J].Journal of the ACM,1976,23(1):89-96.
[25]常林越.水平荷载作用下桥墩及桩基的静力与动力响应分析[D].杭州:浙江大学,2010.(CHANG Linyue.Static and dynamic response analysis of pier and pile foundation under lateral loading[D].Hangzhou:Zhengjiang University,2010(in Chinese)).
[26]TANAHASHI H.Two-dimensional analysis of ground surface displacements using Pasternak model[J].Journal of structural&construction engineering,2000,65(530):85-91.
[27]TANAHASHI H.Formulas for an infinitely long Bernoulli-Euler beam on the Pasternak model[J].Journal of the Japanese geotechnical society,2008,44(5):109-118.
[28]栾茂田,孔德森,杨庆,等.层状土中单桩竖向简谐动力响应的简化解析方法[J].岩土力学,2005,26(3):375-380.(LUANMaotian,KONG Desen,YANG Qing,et al.Simplified analytic method of vertical harmonic response of single pile embedded in layered soils[J].Rock and soil mechanics,2005,26(3):375-380(in Chinese)).
[2]刘东甲,王建国.均匀土中有限长桩瞬态横向动力响应[J].工程力学,2003,20(6):160-165.(LIU Dongjia,WANG Jianguo.Transient lateral response of a finite pile in homogeneous soil[J].Engineering mechanics,2003,20(6):160-165(in Chinese)).
[3]刘东甲,王建国.瞬态横向振动桩的Winkler参数[J].岩土力学,2003,24(6):922-926.(LIU Dongjia,WANG Jianguo.Winkler parameters k and c for transient lateral vibrating piles[J].Rock and soil mechanics,2003,24(6):922-926(in Chinese)).
[4]李正印,柯宅邦,刘东甲,等.低应变反射波法判别PHC管桩接头质量的研究[J].岩土工程学报,2011,33(增刊2):209-212.(LIZhengyin,KE Zhaibang,LIU Dongjia,et al.Tests on PHC pipe pile joint quality by low-strain reflected wave method[J].Chinese journal of geotechnical engineering,2011,33(S2):209-212(in Chinese)).
[5]刘华瑄,刘东甲,卢志堂,等.桩基三维弹性波动方程变步长交错网格有限差分数值计算[J].岩土工程学报,2014,36(9):1754-1760.(LIU Huaxuan,LIU Dongjia,LU Zhitang,et al.Numerical calculation of three-dimensional elastic wave equation of piles staggered grid finite difference using mathod with variable step lengths[J].Chinese journal of geotechnical engineering,2014,36(9):1754-1760(in Chinese)).
[6]CHANG X M,LIU D J,GAO F,et al.A study on lateral transient vibration of large diameter piles considering pile-soil interaction[J].Soil dynamics and earthquake engineering,2016,90:211-220.
[7]PASTERNAK P L.Fundamentals of a new method of analyzing structures on an elastic foundation by means of two foundation constants[M].Moscow:Gosudarstvennoe Izdatelstro Liberaturi Po Stroitelstvui Arkhitekture,1954.
[8]梁发云,李彦初,黄茂松.基于Pasternak双参数地基模型水平桩简化分析方法[J].岩土工程学报,2013,35(增刊1):300-304.(LIANG Fayun,LI Yanchu,HUANG Maosong.Simplified method for laterally loaded piles based on Pasternak double-parameter spring model for foundations[J].Chinese journal of geotechnical engineering,2013,35(S1):300-304(in Chinese)).
[9]张治国,徐晨,宫剑飞.考虑桩侧土体三维效应和地基剪切变形的隧道开挖对邻近桩基影响分析[J].岩土工程学报,2016,38(5):846-856.(ZHANG Zhiguo,XU Chen,GONG Jianfei.Influence of tunneling on deflection of adjacent piles considering shearing deformation of foundation and 3D effects of lateral soils beside piles[J].Chinese journal of geotechnical engineering,2016,38(5):846-856(in Chinese)).
[10]CATAL H H.Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment,axial and shear force[J].Engineering structures,2006,28(14):1911-1918.
[11]MOKWA R L,DUNCAN J M.Rotational restraint of pile caps during lateral loading[J].Journal of geotechnical and geoenvironmental engineering,ASCE,2003,129(9):829-837.
[12]PRAKASH S,SHARMA H D.Pile foundations in engineering practice[M].Hoboken,New Jersey:John Wiley&Sons,1990.
[13]SADEK M,SHAHROUR I.Influence of the head and tip connection on the seismic performance of micropiles[J].Soil dynamics and earthquake engineering,2006,26(5):461-468.
[14]孔令刚,姜丽红,陈仁朋,等.考虑桩头约束的水平受荷单桩响应分析[J].应用力学学报,2014,31(3):393-399.(KONG Linggang,JIANG Lihong,CHEN Renpeng,et al.Response of single pile with partial pile head fixity subjected to lateral loading[J].Chinese journal of applied mechanics,2014,31(3):393-399(in Chinese)).
[15]姜丽红,孔令刚,蔺港,等.不同桩头约束下水平受荷单桩简化计算方法[J].工程力学,2014,31(11):63-69.(JIANG Lihong,KONG Linggang,LIN Gang,et al.Simplified method of laterally loaded single piles with partial pile hesd fixity[J].Engineering mechanics,2014,31(11):63-69(in Chinese)).
[16]ZHENG C,LIU H,DING X,et al.Horizontal vibration of a large-diameter pipe pile in viscoelastic soil[J].Mathematical problems in engineering,2013(4):1-13.
[17]ZHENG C,LIU H,DING X.Lateral dynamic response of a pipe pile in saturated soil layer[J].International journal for numerical and analytical methods in geomechanics,2016,40(2):159-184.
[18]栾鲁宝,丁选明,刘汉龙,等.考虑竖向荷载影响的大直径管桩水平振动响应解析解[J].岩土工程学报,2016,38(10):1859-1868.(LUAN Lubao,DING Xuanming,LIU Hanlong,et al.Analytical solution of lateral dynamic response of a large diameter pipe pile considering influence of axial load[J].Chinese journal of geotechnical engineering,2016,38(10):1859-1868(in Chinese)).
[19]ROSA M A D,MAURIZI M J.The influence of concentrated masses and pasternak soil on the free vibrations of euler beams-exact solution[J].Journal of sound&vibration,1998,212(4):573-581.
[20]TANAHASHI H.Formulas for an infinitely long Bernoulli-Euler beam on the Pasternak model[J].Soils and foundation,2004,44(5):109-118.
[21]KISHI N,CHEN W F,GOTO Y,et al.Applicability of three-parameter power model to structural analysis of flexibly jointed frames[J].Mechanics computing,1991,20(3):238-242.
[22]尚微.饱和土中管桩水平瞬态动力特性研究[D].太原:太原理工大学,2018.(SHANG Wei.Horizontal transient dynamic response of pipe pile in saturated soil[D].Taiyuan:Taiyuan University of Technology,2018(in Chinese)).
[23]MATLOCK H,REESE L C.Foundation analysis of offshore pile supported structures[C]//Proceedings of the 5th International Conference of Soil Mechanics and Foundation Engineering.Paris,France:Dunod,1961.
[24]CRUMP K S.Numerical inversion of Laplace transforms using a Fourier series approximation[J].Journal of the ACM,1976,23(1):89-96.
[25]常林越.水平荷载作用下桥墩及桩基的静力与动力响应分析[D].杭州:浙江大学,2010.(CHANG Linyue.Static and dynamic response analysis of pier and pile foundation under lateral loading[D].Hangzhou:Zhengjiang University,2010(in Chinese)).
[26]TANAHASHI H.Two-dimensional analysis of ground surface displacements using Pasternak model[J].Journal of structural&construction engineering,2000,65(530):85-91.
[27]TANAHASHI H.Formulas for an infinitely long Bernoulli-Euler beam on the Pasternak model[J].Journal of the Japanese geotechnical society,2008,44(5):109-118.
[28]栾茂田,孔德森,杨庆,等.层状土中单桩竖向简谐动力响应的简化解析方法[J].岩土力学,2005,26(3):375-380.(LUANMaotian,KONG Desen,YANG Qing,et al.Simplified analytic method of vertical harmonic response of single pile embedded in layered soils[J].Rock and soil mechanics,2005,26(3):375-380(in Chinese)).