基于随机介质理论和Peck公式的矩形顶管地表沉降改进计算方法

沈青松; 陈烨; 叶盛华; 吉乔伟; 王强

doi:10.20265/j.cnki.issn.1007-2993.2024-0214

基于随机介质理论和Peck公式的矩形顶管地表沉降改进计算方法

doi: 10.20265/j.cnki.issn.1007-2993.2024-0214

沈青松^{1, 2,},
陈烨^{1, 2},
叶盛华^{1, 2},
吉乔伟^{1, 2},
王强^{1, 2}

1.
中国电建华东勘测设计研究院有限公司，浙江杭州　311100
2.
浙江省华东生态环境工程研究院，浙江杭州　310000

详细信息

作者简介:
沈青松，男，1996年生，博士，工程师，主要研究方向为市政管线及地下工程。E-mail：shen_qs1@hdec.com

中图分类号: TU992
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- 文章访问数: 15
- HTML全文浏览量: 4
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-17
- 修回日期: 2024-09-26
- 录用日期: 2025-01-02
- 刊出日期: 2025-08-08

Improved calculation method for settlement of rectangular pipe jacking based on random medium theory and Peck formula

Shen Qingsong^{1, 2
,},
Chen Ye^{1, 2},
Ye Shenghua^{1, 2},
Ji Qiaowei^{1, 2},
Wang Qiang^{1, 2}

1.
PowerChina Huadong Engineering Corporation Limited, Hangzhou 311100, Zhejiang, China
2.
Huadong Eco-Environmental Engineering Research Institute of Zhejiang Province, Hangzhou 310000, Zhejiang, China

摘要

摘要: 顶管施工引起的地表沉降计算是顶管工程设计中的关键环节。常用的peck公式是在总结大量圆形顶管的基础上得到的，在矩形顶管的应用中存在一定误差。圆形和矩形顶管都适用的随机介质理论只给出了积分公式，没有最终的积分计算结果，导致计算过程复杂，难以在工程设计中推广应用。本研究对随机介质理论中的被积函数进行改进处理，提出更为简单的近似函数，并推导得到最终积分结果，从而大幅简化计算过程。改进方法计算结果与工程实测沉降值（除个别测点外）的相对误差在5%左右，表明改进方法具有一定的准确度。利用该方法分析研究了各种因素对地表沉降的影响，为后续工程设计提供参考依据。
- 矩形顶管 /
- 沉降 /
- 随机介质理论 /
- Peck公式
Abstract: The calculation of the settlement caused by pipe jacking has always been a critical aspect in the design of pipe jacking engineering. The commonly used Peck formula was summarized on the basis of a large number of circular pipe jacking, and there are some errors in the application of rectangular pipe jacking. The random medium theory, which is suitable for both circular and rectangular pipe jacked, only gives the integral formula without the final integral calculation result, which leads to the complex calculation process and is difficult to be applied in engineering design. This study improves the integrand function in the random medium theory, proposes a simpler approximation function, and derives the final integration result, which greatly simplifies the calculation process. The relative error between the calculated result of the improved method and the measured settlement value (except for some measuring points) is approximately 5%, which indicates that the improved method demonstrates reasonable accuracy. The improved method was used to analyze the influence of various factors on the surface settlement, which provides a reference for future engineering design.
- rectangular pipe jacking /
- settlement /
- random medium theory /
- Peck formula

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图 1 被积原函数与改进函数

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图 2 沉降计算示意图

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图 3 工程实测沉降值与改进计算结果

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图 4 不同顶管宽度、高度对应的沉降

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图 5 不同顶管埋深和土体系数对应的沉降

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图 6 不同偏移位置和土体损失量对应的沉降

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表 1 矩形顶管开挖区域坐标计算

区域	坐标位置	坐标	计算公式	区域	坐标位置	坐标	计算公式
顶管区域	左上	(ξ₁,η₁)	$ \begin{gathered} {\xi _1} = - a \\ {\xi _2} = a \\ {\eta _1} = H - b \\ {\eta _2} = H + b \\ \end{gathered} $	超挖区域	左上	(ξ′₁,η′₁)	$ \begin{gathered} \xi {'_1} = - a - \Delta {a_1} \\ \xi {'_2} = a + \Delta {a_2} \\ \eta {'_1} = H - b - \Delta {b_1} \\ \eta {'_2} = H + b + \Delta {b_2} \\ \end{gathered} $
	右上	(ξ₂,η₁)			右上	(ξ′₂,η′₁)
	左下	(ξ₁,η₂)			左下	(ξ′₁,η′₂)
	右下	(ξ₂,η₂)			右下	(ξ′₂,η′₂)

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表 2 顶管四周超挖量

偏移位置	四周超挖量	土体损失量	四周超挖量
上偏	Δa₁=Δa₂=0.05 m; Δb₁=0 m; Δb₂=0.1 m	0.60	Δa₁=Δa₂=Δb₁=Δb₂=0.03 m
下偏	Δa₁=Δa₂=0.05 m; Δb₁=0.1 m; Δb₂=0 m	0.80	Δa₁=Δa₂=Δb₁=Δb₂=0.04 m
居中	Δa₁=Δa₂=Δb₁=Δb₂=0.05 m	1.01	Δa₁=Δa₂=Δb₁=Δb₂=0.05 m
左偏	Δa₁=0 m;Δa₂=0.1 m; Δb₁=Δb₂=0.05 m	1.21	Δa₁=Δa₂=Δb₁=Δb₂=0.06 m
右偏	Δa₁=0.1 m;Δa₂=0 m; Δb₁=Δb₂=0.05 m	1.42	Δa₁=Δa₂=Δb₁=Δb₂=0.07 m

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