考虑主应力偏转和土拱效应的干砂盾构隧道掌子面极限支护力计算方法研究

张宇; 陶连金; 刘军; 赵旭; 郭飞; 边金

doi:10.11779/CJGE20211349

考虑主应力偏转和土拱效应的干砂盾构隧道掌子面极限支护力计算方法研究 English Version

张宇^{1, 2,},
陶连金^2, ,,
刘军¹,
赵旭²,
郭飞³,
边金⁴

1.
北京建筑大学土木与交通工程学院, 北京 102627
2.
北京工业大学城市与工程安全减灾教育部重点实验室, 北京 100124
3.
北京市政建设集团有限责任公司, 北京 100048
4.
广东海洋大学海洋工程学院, 广州湛江 524094

基金项目:

北京未来城市设计高精尖创新中心项目 UDC2019032824

国家重点研发计划项目 2017YFC0805403

国家重点研发计划项目 2019YFC1509704

国家自然科学基金项目 41877218

国家自然科学基金项目 42072308

详细信息

作者简介:
张宇(1993—)，男，博士后，主要从事地下工程施工风险方面的研究工作。E-mail：411101866@qq.com

通讯作者:
陶连金, E-mail:ljtao@bjut.edu.cn

中图分类号: U45
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出版历程
- 收稿日期: 2021-11-13
- 网络出版日期: 2023-03-15
- 刊出日期: 2023-02-28

Method for calculating limit support pressure of face of shield tunnels considering principal stress axis rotation and soil arching effects in dry sand

ZHANG Yu^{1, 2,},
TAO Lianjin^2, ,,
LIU Jun¹,
ZHAO Xu²,
GUO Fei³,
BIAN Jin⁴

1.
School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing 102627, China
2.
Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China
3.
Beijing Municipal Construction Co., Ltd., Beijing 100048, China
4.
College of Ocean Engineering, Guangdong Ocean University, Zhanjiang 524000, China

摘要

摘要: 深埋干砂盾构隧道在施工过程中存在显著的土拱效应，如何确定考虑土拱效应的隧道掌子面极限支护力至关重要。基于极限平衡法和楔形体理论，提出了一种多层抛物线承载拱模型。根据隧道不同埋深下掌子面失稳破坏的特征和土拱类别，将隧道状态划分为浅埋隧道、过渡隧道和深埋隧道。考虑多层抛物线承载拱区域主应力偏转角和侧向土压力系数的连续性，并假定抛物线承载拱为满足合理拱轴线三铰拱结构，推导了过渡区和深埋区多层抛物线承载拱荷载传递的计算公式，进而通过极限平衡法计算得到掌子面极限支护力。将本模型计算结果与已有理论模型、模型试验和数值结果进行对比，验证了本模型计算得到的掌子面极限支护力和失稳破坏区的合理性。最后，通过参数分析讨论了土体内摩擦角对隧道浅埋和深埋分界线以及极限支护力的影响。该研究成果可为深埋干砂盾构隧道极限支护力的预测提供理论依据。
- 盾构隧道 /
- 极限平衡 /
- 极限支护力 /
- 理论解析 /
- 土拱效应
Abstract: For the deep-buried shield tunnels in dry cohesionless soils, it is critical to determine the support pressure acting on the tunnel face due to the significant soil arching effects. Based on the limit equilibrium method and the wedge theory, a multi-layer parabolic bearing arch model is proposed. According to the characteristics of failure zone of the tunnel face and the category of soil arch under different buried depths, the tunnel state is divided into shallow buried tunnel, transition tunnel and deep buried tunnel, respectively. By considering the continuity of the principal stress deflection angle and lateral earth pressure coefficient in the multi-layer parabolic bearing arch and assuming the parabolic bearing arch as a three-hinged structural arch with reasonable arch axis, the load transfer expression for the multi-layer parabolic bearing arch is derived in transition zone and deep buried zone respectively, and then the limit support pressure is calculated. By comparing the proposed model with the existing model, model tests and numerical model, the rationality of the limit support pressure and failure zone of the tunnel face obtained by the proposed model is verified. Finally, the influences of the internal friction angle on the boundary between shallow and deep burials and the limit support pressure are discussed through parameter analysis. This study may provide a theoretical basis for predicting the limit support pressure acting on the tunnel face in dry sand.
- shield tunnel /
- limit equilibrium /
- limit support pressure /
- theoretical analysis /
- soil arching effect

HTML全文

图 1 干砂地层掌子面前方失稳破坏区^[12]

Figure 1. Failure zones in front of tunnel face in dry sand^[12]

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图 2 不同埋深下的力学模型

Figure 2. Mechanical model under different buried depths

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图 3 极限状态下掌子面前方破坏区

Figure 3. Failure zones in front of tunnel face under limit state

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图 4 力学模型荷载传递路径

Figure 4. Load transfer path of mechanical model

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图 5 抛物线模型

Figure 5. Parabolic model

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图 6 当C/D≥1时不同模型试验的H₃/L

Figure 6. Results of H₃/L under different model tests

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图 7 过渡隧道多层抛物线承载拱力学模型

Figure 7. Mechanical model for bearing arch in transition tunnel

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图 8 深埋隧道多层抛物线承载拱力学模型

Figure 8. Mechanical model for bearing arch in deep buried tunnel

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图 9 筒仓微分土层受力分析

Figure 9. Stress analysis of differential soil layers in silo

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图 10 楔形体模型受力情况

Figure 10. Force condition of wedge model

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图 11 参数n敏感性分析

Figure 11. Sensitivity analysis of parameter n

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图 12 数值模型

Figure 12. Numerical model

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图 13 归一化支护力与掌子面中心点水平位移关系

Relationship between ${\sigma _{\text{T}}}$ /(γD) and horizontal displacement at central point of tunnel face

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图 14 模型计算结果与数值结果的比较

Figure 14. Comparison between results obtained by proposed model and numerical ones

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图 15 归一化极限支护力计算结果比较

Comparison of ${\sigma _{\text{T}}}$ /(γD) on tunnel face

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图 16 土体内摩擦角和归一化极限支护力关系

Relationship between φ and ${\sigma _{\text{T}}}$ /(γD)

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图 17 失稳破坏区计算结果与模型试验结果^[23]对比

Figure 17. Comparison between calculated results of failure zone and model tests^[23]

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图 18 隧道状态与土体内摩擦角的关系

Figure 18. Relationship between tunnel state and φ

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图 19 不同内摩擦角下深径比与归一化极限支护力的关系

Figure 19. Relationship between C/D and ${\sigma _{\text{T}}}$ /(γD)

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表 1 干砂掌子面失稳的模型试验研究

Table 1 Model tests on stability of tunnel face in dry sand

文献	研究方法	材料	深径比C/D	筒仓高度 H₃	楔形体宽度L	H₃/L	内摩擦角φ	楔形体倾斜角β	归一化极限支护力σ_T/γD
Chambon等^[12]	离心机试验	枫丹白露砂	0.5	0.5D	0.46D	1.09	40°	73.25°	0.045/0.041
			1	0.76D	0.5D	1.52		73.22°	0.046/0.041/0.037/0.043
			2	0.84D	0.5D	1.68		74°	0.05
			4	—	—	—		—	0.051/0.064
Oblozinsky等^[17]	离心机试验	丰浦砂	2	0.59D	0.26D	2.27	32°	73.15°	0.056
			4	0.59D	0.26D	2.27		—	0.041
			6	0.59D	0.26D	2.27		—	0.085
Chen等^[7]	1g试验	长江河砂	0.5	—	—	—	37°	—	0.065
			1	—	—	—		—	0.076
			2	1.5D	0.75D	2		53°	0.072
Takano等^[18]	1g试验	丰浦砂	2	1.18D	0.5D	2.36	31.5°	69°	—
Kirsch^[19]	1g试验	石英砂	1	0.61D	0.35D	1.74	32°	68.44°	0.051/0.055/0.11/0.097
Idinger等^[20]	离心机试验	—	0.5	—	—	—	34°	—	0.038
			1	—	—	—		—	0.074
			1.5	0.67D	0.46D	1.46		68°	0.084/0.08
Lü等^[21]	1g试验	福建标准砂	0.5	0.5D	0.41D	1.22	35.7°	69.44°	0.108
			1	0.65D	0.41D	1.58		69.86°	0.116
			2	0.66D	0.41D	1.61		70.42°	0.155
汤旅军等^[22]	离心机试验	长江河砂	0.5	0.5D	0.3D	1.67	37°	71.3°	0.037
			1	0.6D	0.3D	2			0.042
			2	0.6D	0.3D	2			0.049
Sun等^[23]	1g模型试验	长江河砂	1	—	0.66D	—	31.2°	56.5°	0.073
			2	—	0.54D	—		61.5°	0.087
			3	—	0.46D	—		65.1°	0.107
			1	—	0.39D	—	35.2°	68.75°	0.094
			2	—	0.36D	—		70.1°	0.125
			3	—	0.31D	—		72.6°	0.169
			1	—	0.31D	—	40°	72.7°	0.141
			2	—	0.28D	—		74.3°	0.165
			3	—	0.25D	—		76.1°	0.200

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表 2 数值模型参数

Table 2 Parameters of numerical model

工况	E/MPa	$\gamma$ /(kN·m^-3)	K₀	$\nu$	φ/(°)	c /kPa
1	25	18	0.577	0.366	25	0
2	25	18	0.5	0.333	30	0
3	25	18	0.426	0.299	35	0
4	25	18	0.357	0.263	40	0
5	25	18	0.293	0.226	45	0

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