桩基规范桩端应力影响系数解析式商榷

Analytical Formula of Pile and Stress Influence Coefficient for File Foundation Standard

《建筑桩基技术规范》(JGJ 94—2008)考虑了桩侧应力随深度的均匀分布及三角形分布,同时考虑了桩径影响的桩端应力的均匀分布。桩侧应力影响系数采用了Geddes解析公式,桩端应力影响系数则采用了徐志英在《土木工程学报》1957年第4期发表的论文"以明特林(Mindlin)公式为根据的地基中垂直应力的计算公式"中的公式(33)。原徐文公式(33)疏忽了数的开方性质(z-L)21/2=|z-L|≠z-L,仅适用于桩端面以下(z>L)。在有埋置深度集中力Mindlin应力解的基础上,考虑桩径影响的桩端均布应力,重新导出了桩轴线上桩端应力影响系数一维积分的一般解。解函数对z变量在桩端处(z=L)不连续,该间断点为跳跃间断点。计算结果用一维及二维数值积分值、规范表格值进行了对比验证。

In the Technical Code for Building Pile Foundations(JGJ 94—2008),the uniform distribution and the triangular distribution of pile side stress against depth were considered,and the uniform distribution of pile end stress affected by pile diameter was also taken into account.Meanwhile,the Geddes analytical formula was used in the pile side stress influence coefficient,and the formula(33)in the paper"Calculation Formula of Vertical Stress in Foundation Based on Mindlin Formula"published by Xu Zhiying in the fourth issue of Civil Engineering Journal in 1957 was used in the pile end stress influence coefficient.However,the square root property of(z-L)21/2=|z-L|≠z-L was neglected in Xu’s formula(33),so this formula was only applicable to the case under the pile end(z>L).Therefore,the uniformly distributed stress at pile end affected by pile diameter was considered on the basis of the Mindlin stress solution of buried depth concentration force,and then the onedimensional integral analytic general solution of pile end stress influence coefficient on pile axis was derived again.The solution function is discontinuous to variable z at the pile end(z=L),and the discontinuity point is a jump discontinuity point.Moreover,the calculation results of the general solution were compared and verified by the one-dimensional and two-dimensional numerical integral values,as well as the Standard’s tabulated values.