浅埋管幕法隧道竖向应力计算模型与工程应用

黄明; 陈骏宁; 赖丰文; 路德春; 肖雄; 李洪江

doi:10.19818/j.cnki.1671-1637.2026.273

浅埋管幕法隧道竖向应力计算模型与工程应用

doi: 10.19818/j.cnki.1671-1637.2026.273

黄明^1,,
陈骏宁¹,
赖丰文¹,
路德春^{2, 3, ,},
肖雄⁴,
李洪江⁵

1.
福州大学土木工程学院，福建福州 350108
2.
厦门大学建筑与土木工程学院，福建厦门 361005
3.
北京工业大学岩土与地下工程研究所，北京 100124
4.
厦门特区建投建筑材料有限公司，福建厦门 361000
5.
东南大学岩土工程研究所，江苏南京 210096

基金项目:

国家自然科学基金青年科学基金项目 52438005

国家自然科学基金青年科学基金项目 52378392

国家自然科学基金青年科学基金项目 52408356

国家级青年人才项目 00389335

详细信息

作者简介:
黄明(1983-)，男，江西瑞金人，教授，博士生导师，工学博士，E-mail: huangming05@fzu.edu.cn

通讯作者:
路德春(1977-)，男，黑龙江绥化人，教授，博士生导师，工学博士，E-mail: dechun@bjut.edu.cn

中图分类号: U452
计量
- 文章访问数: 52
- HTML全文浏览量: 40
- PDF下载量: 16
- 被引次数: 0
出版历程
- 收稿日期: 2026-01-13
- 录用日期: 2026-03-20
- 修回日期: 2026-03-11
- 刊出日期: 2026-07-28

Calculation model for vertical stress of shallowly buried pipe-roofing tunnels and its engineering application

1.
College of Civil Engineering, Fuzhou University, Fuzhou 350108, Fujian, China
2.
School of Architecture and Civil Engineering, Xiamen University, Xiamen 361005, Fujian, China
3.
Institute of Geotechnical and Underground Engineering, Beijing University of Technology, Beijing 100124, China
4.
Xiamen Special Zone Construction Investment Materials Co., Ltd., Xiamen 361000, Fujian, China
5.
Institute of Geotechnical Engineering, Southeast University, Nanjing 210096, Jiangsu, China

Funds:

National Natural Science Foundation of China for Youth Science Foundation 52438005

National Natural Science Foundation of China for Youth Science Foundation 52378392

National Natural Science Foundation of China for Youth Science Foundation 52408356

National Youth Talent Project 00389335

More Information

Corresponding author: LU De-chun, professor, PhD, E-mail: dechun@bjut.edu.cn

Article Text (Baidu Translation)

摘要

摘要: 传统水平微分单元法表征土拱效应时，忽略了单元层间剪切力对竖向应力传递的贡献，从而导致计算结果偏于保守。鉴于此，首先将管幕法隧道简化为活动门(Trapdoor)模型，采用有限元极限分析(FELA)方法，系统探究了不同深宽比及土体内摩擦角条件下浅埋活动门滑裂角的变化规律；据此，基于大主应力轨迹线，建立了拱形微分单元竖向应力计算模型，推导了浅埋活动门竖向应力解；进一步阐明了土体内摩擦角、剪胀角及地面超载对活动门归一化竖向应力的影响规律；最后将所提模型应用于某管幕法隧道工程，探究其工程适用性。研究结果表明：所提模型计算结果与既有解、FELA解及室内模型试验结果吻合良好；相较于经典Terzaghi理论及规范方法，归一化竖向应力分别降低30.7%与45.3%，碳排放量分别减少9.1%与16.6%。
- 隧道工程 /
- 管幕法隧道 /
- 拱形微分单元法 /
- 竖向应力 /
- 土拱效应
Abstract: The traditional horizontal differential element method used to characterize the soil arching effect neglects the contribution of inter-layer shear forces to vertical stress transfer, leading to conservative calculation results. In view of this, the pipe-roofing tunnel was first simplified into a "trapdoor" model. A finite element limit analysis (FELA) method was adopted to systematically investigate the variation of the slip angle of the shallow trapdoor under different depth-to-width ratios and soil internal friction angles. Accordingly, based on the trajectory of the major principal stress, a vertical stress calculation model of an arched differential element was established, and the vertical stress solution for the shallow trapdoor was derived. Furthermore, the influences of soil internal friction angle, dilation angle, and surface surcharge on the normalized vertical stress of the trapdoor were clarified. Finally, the proposed model was applied to a pipe-roofing tunnel project to explore its engineering applicability. Research results indicate that the calculation results of the proposed model show good agreement with existing solutions, FELA solutions, and laboratory model test results; compared with the classical Terzaghi theory and code methods, the proposed model reduces the normalized vertical stress by 30.7% and 45.3%, respectively, and it reduces carbon emissions by 9.1% and 16.6%, respectively.
- tunnel engineering /
- pipe-roofing tunnel /
- arched differential element method /
- vertical stress /
- soil arching effect

HTML全文

图 1 问题定义及数值模型

Figure 1. Problem definition and numerical model

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图 2 大主应力偏转矢量图

Figure 2. Vector diagram of major principal stress rotation

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图 3 滑裂角和内摩擦角拟合结果

Figure 3. Fitting result of slip surface angle and internal friction angle

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图 4 活动门竖向应力计算模型

Figure 4. Vertical stress calculation model of the trapdoors

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图 5 D点应力状态

Figure 5. Stress state at point D

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图 6 拱形微分单元受力平衡

Figure 6. Force balance of arched differential elements

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图 7 不同深宽比下归一化竖向应力计算结果对比

Figure 7. Comparison chart of normalized vertical stress calculation results under different aspect ratios

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图 8 不同理论下归一化竖向应力计算结果对比

Figure 8. Comparison of normalized vertical stress calculation results by different theories

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图 9 竖向应力分布计算结果对比

Figure 9. Comparison of the calculation results of vertical stress distribution

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图 10 不同深宽比下内摩擦角对归一化竖向应力的影响规律

Figure 10. Influence law of internal friction angle on normalized vertical stress under different depth-to-width ratios

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图 11 不同深宽比下归一化剪胀角对归一化竖向应力的影响规律

Figure 11. Influence law of normalized dilatancy angle on normalized vertical stress under different depth-to-width ratios

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图 12 不同深宽比下归一化地面超载对归一化竖向应力的影响规律

Figure 12. Influence law of normalized ground surcharge on normalized vertical stress under different depth-to-width ratios

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图 13 深圳某管幕法隧道

Figure 13. Pipe-roofing tunnel in Shenzhen

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图 14 土压力盒布置

Figure 14. Layout of the earth pressure box

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图 15 竖向应力分布计算结果对比

Figure 15. Comparison of calculation results of vertical stress distribution

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图 16 归一化竖向应力随深度变化对比

Figure 16. Comparison of normalized vertical stress varying with depth

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图 17 管幕挠度计算模型

Figure 17. Calculation model of pipe roof deflection

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图 18 工程造价及碳排放量对比

Figure 18. Comparison of engineering cost and carbon emissions

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表 1 不同深宽比及内摩擦角的活动门上方滑裂角的变化

Table 1. Variation of slip surface angle above the trapdoors under different depth-to-width ratios and internal friction angles

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表 2 不同深宽比及内摩擦角的活动门上方滑裂角的大小

Table 2. Slip surface angle above the trapdoors under different depth-to-width ratios and internal friction angles

φ/(°)	H/B	α/(°)	φ/(°)	H/B	α/(°)
15	0.5	15.20	30	1.5	31.38
15	1.0	15.74	30	2.0	30.60
15	1.5	15.96	35	0.5	35.56
15	2.0	16.16	35	1.0	36.39
20	0.5	20.90	35	1.5	33.58
20	1.0	20.82	35	2.0	33.33
20	1.5	21.48	40	0.5	39.19
20	2.0	20.91	40	1.0	41.09
25	0.5	26.16	40	1.5	39.49
25	1.0	26.30	40	2.0	39.32
25	1.5	25.34	45	0.5	45.90
25	2.0	25.72	45	1.0	45.54
30	0.5	30.48	45	1.5	43.62
30	1.0	30.61	45	2.0	43.88

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表 3 现场地质情况

Table 3. The on-site geological conditions

参数	土体
参数	中砂	粗砂	花岗岩
层顶深度	0	8.1	9.7
黏聚力c/kPa	0	0	27.5
内摩擦角φ/(°)	33.0	26.0	25.5
土体重度γ/(kN·m^-3)	19.2	19.8	18.3
弹性模量E/MPa	30	42	205

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