简便积分方程法分析桩

云天铨

简便积分方程法分析桩

云天铨

武汉华中工学院

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出版历程
- 收稿日期: 1980-02-29
- 刊出日期: 1981-06-15

Pile Analysis by Simple Integral Equation Methods

Yun Tian-quan

Department of Mechanics, Huazhong Institute of Technology, Wuhan

摘要

摘要: 本文用两种方法来分析桩受垂直载荷作用问题.一种是:将由Mindlin集中力组成的轴对称载荷沿弹性半空间z轴的[0,L]内分布,并迭加Boussinesq的解;另一种是:除上述诸虚载荷外,还将Mindlin的垂直集中力沿z轴的[0,L]内分布.前者使边界条件为: 的桩受垂直载荷问题归结为一个Fredholm第一种积分方程;后者使边界条件(其中1,3式同)(0.1)式中的2为:0≤z≤L,U(e,z)=a-e,(e→a);W(a,z)=常数(0.2)的桩受垂直载荷问题归结为两个联立的Fredholm第一种方程式.对刚性桩而言,前者适于容许桩和其侧面附着的土有相对滑动情况;后者适于无相对滑动情形.这两种方法较现有的虚载荷分布于桩表面的诸法具有下列优点:1.所得的积分方程不是二维、奇异的;而是一维、非奇异的.2.能考虑初应力的影响.第一种方法还无须预先假定沉陷函数W;在可压缩桩中容易考虑三维应力的影响的好处.本文还给出Fredholm第一种积分方程近似解误差估计的一个定理,以及两种方法用DJS—21机计算单桩沉陷的结果.

Abstract: Two simple integral equation methods are proposed for the aaalysis of vertical loaded pile.One of them is; let the aaisymmetrical loads formed by Mindlin's horizontal point forces be distributed along the azis z in [0,L] of the elastic half-space,and composed with the Boussinesq's point force.The other is; in addition to the above fictitious loads,the Mindlin's vertical forces are distributed along the azis z in [0,L].The former reduces the problem of a vertical loaded pile embedded in a half-space with the following boundary conditions.

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参考文献(5)

[1]	Banerjee,P.K.,Integral equation method for analysis of piece-wise non-homogeneous three-dimensional elastic solids of arbitrary shape,Int,J.Mech.Sc s.,18(1976),293.
[2]	Butterfield,R.and Banerjee P,K The elastic analysis of compressible piles and pile groups,Geotechnique,21,(1971),43.
[3]	Poulos,H,G.,Load-settlement predictions for piles and piers,Proc.ASCE SM.9,(1972),879.
[4]	Mattes,N.S.,The influence of radial displacement compatibility on pile settlements,Geotechnique,19(1969),157.
[5]	Muki,R.and Sternberg,E,Elastostatic load-transfer to a half-space from a partially embedded axially loaded rod,Int,J.Solid Structures,5(1969),587.