基于桩径大小的圆形均布荷载垂直附加应力解析解

龚道平; 王泗; 方强

doi:10.20265/j.cnki.issn.1007-2993.2024-0181

基于桩径大小的圆形均布荷载垂直附加应力解析解

doi: 10.20265/j.cnki.issn.1007-2993.2024-0181

湖南省交通规划勘察设计院有限公司，湖南长沙　410200

基金项目: 湖南省交通运输厅科技进步与创新计划资助项目（202120）

详细信息

作者简介:
龚道平，男，1969年生，大学本科，研究员级高级工程师，主要从事岩土工程勘察与设计。E-mail：hncdigdp@163.com

中图分类号: TU470
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- 文章访问数: 20
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- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2024-04-29
- 修回日期: 2024-07-15
- 录用日期: 2024-08-29
- 刊出日期: 2025-06-09

Analytical solution for vertical additional stress under circular uniformly distributed loads based on pile diameter

Hunan Provincial Communications Planning, Survey and Design Institude, Changsha 410200, Hunan, China

摘要

摘要: 圆形均布荷载下地基垂直附加应力计算是沉降计算的基础。现行《建筑地基基础设计规范》沿用Geddes应力解计算附加应力，视桩端阻力、桩侧阻力为集中力作用在桩轴线上，未考虑桩径大小，因此存在一定误差。现行《建筑桩基技术规范》在Geddes应力解的基础上，计算端阻力作用时，考虑桩径大小，得到了沿桩身轴线下附加应力的解析表达式，但未提供桩轴线以外附加应力的解析表达式；同时桩侧阻力仍假设作用在桩轴线上，亦未考虑桩径大小的影响，同样存在一定误差。针对上述方法中的不足，本文以圆形面积均布荷载为基础，考虑桩径大小，通过积分运算，推导出了桩轴线以外任意点垂直附加应力的Mindlin解析式和桩侧阻力作用下附加应力的Mindlin解析式。利用这些解析式，在软件平台上编制计算程序，可计算桩基荷载作用下，半无限空间弹性体中任意点的垂直附加应力。对比计算表明，本文所提出的解析表达式精度可靠，可应用于实际工程的计算，并对圆形均布荷载作用下附加应力计算的研究有一定的借鉴意义。
- 圆形均布荷载 /
- 附加应力 /
- 桩径影响 /
- 解析解
Abstract: The calculation of vertical additional stress on the foundation under uniformly distributed circular loads is fundamental for settlement calculation. The Code for Design of Builiding Foundation continues to use the Geddes stress solution to calculate additional stresses, considering pile end resistance and pile side resistance are concentrated forces acting on the pile axis, yet neglecting the pile diameter’s influence. Therefore, there is a certain degree of error. The Technical Code for Building Pile Foundations considers the size of pile diameter when calculating the effect of end resistance, and an analytical expression for the additional stress along the axis of the pile has been obtained, but no analytical expression was provided for the additional stress outside the pile axis, as well as ignoring the size of the pile diameter. Addressing the shortcomings of the above methods, based on the uniformly distributed load of the circular area, considering the size of pile diameter, the Mindlin analytical formula for the vertical additional stress at any point outside the pile axis and under the side resistance was derived by integral operation. By using these analytical formulas to develop calculation programs, it is convenient to calculate vertical additional stress at any point in an elastic body in a semi-infinite space. Comparative calculations show that the method proposed has reliable accuracy. The method can be applied to practical engineering and has certain reference significance for further research on the calculation of additional stress under uniformly distributed circular loads.
- circular uniformly distributed loads /
- additional stress /
- influence of pile diameter /
- analytical solution

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图 1 圆形均匀荷载桩端附加应力计算示意图

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图 2 圆形均匀荷载桩端外附加应力计算示意图

下载: 全尺寸图片幻灯片

图 3 考虑桩径的桩侧均匀阻力作用下附加应力计算示意图

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图 4 线性增加桩侧摩阻力作用下附加应力计算示意图

下载: 全尺寸图片幻灯片

表 1 附加应力影响系数计算对比表

承台底面以下深度/m	附加应力影响系数
	n		0.00	0.02	0.04	0.06	0.08	0.10	0.12	0.16	0.20	0.30	0.40	0.50	0.60	0.80	1.00	1.20
	m	系数	0.00	0.02	0.04	0.06	0.08	0.10	0.12	0.16	0.20	0.30	0.40	0.50	0.60	0.80	1.00	1.20
39.60	1.8	I_pi	0.386	0.386	0.384	0.382	0.378	0.374	0.369	0.356	0.340	0.293	0.244	0.198	0.159	0.104	0.070	0.050
		I_pi′	0.386	0.386	0.385	0.383	0.380	0.376	0.371	0.358	0.344	0.298	0.248	0.202	0.162	0.106	0.071	0.051
		I_si	0.253	0.253	0.253	0.252	0.250	0.249	0.246	0.241	0.235	0.215	0.192	0.168	0.145	0.107	0.078	0.057
		I_si′	0.253	0.253	0.252	0.251	0.250	0.248	0.246	0.241	0.235	0.215	0.192	0.168	0.145	0.107	0.078	0.057
44.00	2.0	I_pi	0.259	0.259	0.259	0.258	0.256	0.254	0.252	0.246	0.239	0.218	0.192	0.166	0.142	0.101	0.072	0.053
		I_pi′	0.259	0.259	0.259	0.258	0.257	0.255	0.253	0.248	0.241	0.220	0.195	0.168	0.144	0.103	0.073	0.053
		I_si	0.186	0.186	0.186	0.186	0.185	0.184	0.183	0.180	0.177	0.167	0.154	0.139	0.125	0.098	0.075	0.057
		I_si′	0.186	0.186	0.186	0.185	0.185	0.184	0.183	0.180	0.177	0.166	0.153	0.139	0.125	0.098	0.075	0.057

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参考文献(10)

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