桩顶固定时单桩侧向变形与受力的积分方程解法
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摘要
基于Muki&Sternberg的虚拟桩方法,将水平荷载作用下桩-土相互作用问题分解为弹性半空间地基土和虚拟桩的叠加。通过求解由第二类Fredholm积分方程与桩顶转角固定的转角方程联立的方程组所得到桩顶固定时的桩身弯矩,可以得到桩顶固定时桩身的水平位移和桩身的转角,采用Fortran语言编写程序进行求解。与现有计算结果的比较验证了本文计算方法的正确性。进行了广泛的桩土弹性模量比、桩间距和桩长细比参数分析,为桩顶固定时单桩的的设计和分析提供了参考。
According to the fictitious pile method presented by Muki and Sternberg,the problem of laterally loaded pile-to-soil interaction is decomposed into a foundation soil mass characterized by the elastic property and the fictitious pile. Based on the fictitious pile bending moment in the fixed-head pile determined by solving an equation set of the Fredholm integral equation of the second kind and the slope equation for a fixed-head rotation of the pile,the horizontal displacement and slope distributions are obtained. The solution is then computed by using the Fortran program. The accuracy of the present approach is validated by the comparisons with the existing solutions. Extensive parametric studies with regard to the pile-soil stiffness ratio,pile spacing and the pile slenderness ratio are presented graphically for the design and analysis for fixed-head piles.
According to the fictitious pile method presented by Muki and Sternberg,the problem of laterally loaded pile-to-soil interaction is decomposed into a foundation soil mass characterized by the elastic property and the fictitious pile. Based on the fictitious pile bending moment in the fixed-head pile determined by solving an equation set of the Fredholm integral equation of the second kind and the slope equation for a fixed-head rotation of the pile,the horizontal displacement and slope distributions are obtained. The solution is then computed by using the Fortran program. The accuracy of the present approach is validated by the comparisons with the existing solutions. Extensive parametric studies with regard to the pile-soil stiffness ratio,pile spacing and the pile slenderness ratio are presented graphically for the design and analysis for fixed-head piles.
引文
[1] Poulos H G. Behavior of laterally loaded piles:I-Single piles[J]. Journal Soil Mechanics and Foundations Division,1971,97(5):711-731.
[2]梁发云,陈海兵,陈胜立.横向荷载下群桩相互作用的积分方程解法及参数分析[J].岩土工程学报,2012,34(5):849-854.Liang Fayun,Chen Haibing,Chen Shengli. Integral equation method and parametric analysis for interaction of laterally loaded pile groups[J]. Chinese Journal of Geotechnical Engineering,2012,34(5):849-854.(in Chinese)
[3] Chen S L,Chen L Z. Note on the interaction factor for two laterally loaded piles[J]. Journal of Geotechnical and Geoenvironmental Engineering,2008,134(11):1685-1680.
[4] Muki R,Sternberg E. Elastostatic load-transfer to a half-space from a partially embedded axially loaded rod[J]. International Journal of Solids and Structures,1970,6:69-90.
[5] Pak R Y S. On the flexure of a partially embedded bar under lateral loads[J]. Journal of Applied Mechanics Division,ASME,1989,56:263-269.
[6] Cao M. Laterally loaded piles in multi-layered soils[J]. Lowland Technology International,2017,19(2):87-98.
[7] Muki R,Sternberg E. On the diffusion of an axial load from an infinite cylindrical bar embedded in an elastic medium[J]. International Journal of Solids and Structures,1969,5:587-605.
[8]曹明.水平荷载作用下单桩的虚拟桩解法及参数[J].土木建筑与环境工程,2017,39(3):115-121.Cao Ming. Fictitious pile approach and parametric analysis of laterally loaded piles[J]. Journal of Civil,Architecture and Environmental Engineering,2017,39(3):115-121.(in Chinese)
[9] Hetenyi M. Beams on elastic foundations[M]. Ann Arbor:University of Michigan Press,1946.
[10] Poulos H G,Davis E H. Pile foundation analysis and design[M]. New York:John Wiley,1980.
[2]梁发云,陈海兵,陈胜立.横向荷载下群桩相互作用的积分方程解法及参数分析[J].岩土工程学报,2012,34(5):849-854.Liang Fayun,Chen Haibing,Chen Shengli. Integral equation method and parametric analysis for interaction of laterally loaded pile groups[J]. Chinese Journal of Geotechnical Engineering,2012,34(5):849-854.(in Chinese)
[3] Chen S L,Chen L Z. Note on the interaction factor for two laterally loaded piles[J]. Journal of Geotechnical and Geoenvironmental Engineering,2008,134(11):1685-1680.
[4] Muki R,Sternberg E. Elastostatic load-transfer to a half-space from a partially embedded axially loaded rod[J]. International Journal of Solids and Structures,1970,6:69-90.
[5] Pak R Y S. On the flexure of a partially embedded bar under lateral loads[J]. Journal of Applied Mechanics Division,ASME,1989,56:263-269.
[6] Cao M. Laterally loaded piles in multi-layered soils[J]. Lowland Technology International,2017,19(2):87-98.
[7] Muki R,Sternberg E. On the diffusion of an axial load from an infinite cylindrical bar embedded in an elastic medium[J]. International Journal of Solids and Structures,1969,5:587-605.
[8]曹明.水平荷载作用下单桩的虚拟桩解法及参数[J].土木建筑与环境工程,2017,39(3):115-121.Cao Ming. Fictitious pile approach and parametric analysis of laterally loaded piles[J]. Journal of Civil,Architecture and Environmental Engineering,2017,39(3):115-121.(in Chinese)
[9] Hetenyi M. Beams on elastic foundations[M]. Ann Arbor:University of Michigan Press,1946.
[10] Poulos H G,Davis E H. Pile foundation analysis and design[M]. New York:John Wiley,1980.