基于UH模型的盾构隧道非线性地基反力确定方法

梁发云; 魏圣明; 陈可; 袁强; 闫静雅; 顾晓强

doi:10.11779/CJGE20230919

基于UH模型的盾构隧道非线性地基反力确定方法 English Version

1.
同济大学地下建筑与工程系, 上海 200092
2.
上海申通地铁集团有限公司, 上海 200070

基金项目:

上海市优秀技术带头人计划项目 21XD1430900

详细信息

作者简介:
梁发云(1976—)，男，博士，教授，主要从事土力学与基础工程的教学科研工作。E-mail: fyliang@tongji.edu.cn

中图分类号: TU473
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出版历程
- 收稿日期: 2023-09-17
- 网络出版日期: 2024-06-12
- 刊出日期: 2025-01-31

Method for determining nonlinear foundation reaction of shield tunnels based on the UH model

1.
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
2.
Shanghai Shentong Metro Group, Shanghai 200070, China

摘要

摘要: 为合理反映堆载作用下盾构隧道地基系数的非线性特征，基于UH模型（统一硬化模型）和MSD方法（mobilizable strength design）提出了一种确定隧道非线性地基反力的方法；并以隧道中心处的土体应力-应变曲线描述全土域的力学行为，提出了预测盾构隧道地基反力的实用简化方法；基于上海第④、⑤₁层土的UH模型统计参数，将隧道地基反力拟合为双曲线函数形式，进一步将由此获得的初始刚度及极限强度与本构模型参数进行拟合，提出上海地铁盾构隧道的地基反力函数表达式；通过对上海软土盾构隧道堆载工况的多因素分析，验证了该公式对隧道大变形预测问题的实用性。计算结果表明，堆载工况下隧道收敛变形对地基反力曲线的初始刚度要比其极限强度更为敏感，而隧道地基初始刚度主要与土体κ/λ、围压大小等因素相关。
- 地基反力曲线 /
- UH模型 /
- MSD方法 /
- 堆载 /
- 地铁隧道
Abstract: To accurately capture its nonlinear characteristics under surcharge, an approach for the subgrade reaction of shield tunnels is implemented on the basis of the soil strength design method (MSD method) and the unified hardening model (UH model). The practical simplified version is proposed by conducting the description of the mechanical properties of the entire soil zone with constitutive curves of soils at the height of tunnel center. Furthermore, using the statistically derived UH constitutive parameters for soil layers ④ and ⑤₁ in Shanghai, the subgrade reactions for both soil layers are predicted and fitted by using the hyperbolic curve function. After the secondary fitting process is conducted to obtain the initial stiffness and the ultimate strength in relation to the parameters of the constitutive model, the functions for subgrade reactions of shield tunnels in Shanghai are established. Eventually, the multifactorial evaluation of shield tunnels in Shanghai under surcharge conditions is performed, confirming the capacity of the developed formulas for predicting the large deformation of tunnels under surcharge. The convergence deformation of the tunnels under surcharge is more sensitive to the initial stiffness of subgrade reactions, governed by various soil parameters such as κ/λ and confining pressure, than to its ultimate strength.
- subgrade reaction curve /
- UH model /
- MSD method /
- surcharge /
- metro tunnel

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图 1 隧道圆形变形模式

Figure 1. Two deformation modes of circular tunnels

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图 2 隧道圆形变形模式地基反力计算曲线

Figure 2. Flow chart for calculating subgrade reaction of tunnels under uniformed deformation mode

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图 3 上海黏土不排水三轴试验及模型预测结果

Figure 3. Comparison between model predictions and results of undrained triaxial tests for Shanghai soft clay

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图 4 隧道MSD简化方法在隧道圆形变形模式中的精度

Figure 4. Precisions of simplified MSD method

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图 5 上海第④、⑤₁层土侧限压缩试验

Figure 5. Confined compression tests on soil layers ④ and ⑤₁ in Shanghai

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图 6 上海第④、⑤₁层土侧限固结及回弹系数统计图

Figure 6. Statistical chart of the confined compression index or swell index of soil layers ④ and ⑤₁ in Shanghai

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图 7 上海第④、⑤₁层土摩擦角统计图

Figure 7. Statistical chart of effective friction angles of soil layers ④ and ⑤₁ in Shanghai

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图 8 上海第④、⑤₁层土地基反力随M变化曲线

Figure 8. Variation of subgrade reaction with M for soil layers ④ and ⑤₁ in Shanghai

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图 9 上海第④、⑤₁层土地基反力随OCR变化曲线

Figure 9. Variation of subgrade reaction with OCR for soil layers ④ and ⑤₁ in Shanghai

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图 10 上海第④、⑤₁层土地基反力随κ/λ变化曲线

Figure 10. Variation of subgrade reaction with κ/λ for soil layers ④ and ⑤₁ in Shanghai

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图 11 上海第④、⑤₁层土地基反力随埋深变化曲线

Figure 11. Variation of subgrade reaction with depth for soil layers ④ and ⑤₁ in Shanghai

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图 12 土体弹簧模量与地基反力初始刚度关系

Figure 12. Relationship between elastic modulus of soil and initial stiffness of subgrade reaction

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图 13 κ/λ=0.2时地基极限强度拟合图

Figure 13. Fitting and error distribution of ultimate strength of subgrade while κ/λ=0.2

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图 14 κ/λ=0.15时地基极限强度拟合图

Figure 14. Fitting and error distribution of ultimate strength of subgrade while κ/λ=0.15

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图 15 MSD法和拟合公式的地基反力对比图

Figure 15. Comparison of subgrade reactions by MSD and fitting formulas

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图 16 隧道结构荷载计算法简图

Figure 16. Schematic diagram of computational model

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图 17 隧道在第④层土不同埋深条件下的变形

Figure 17. Tunnel deformations under different h for soil layer ④

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图 18 隧道在第④层土不同κ/λ下的变形

Figure 18. Tunnel deformations under different κ/λ for soil layer ④

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图 19 隧道在第④层土不同M下的变形

Figure 19. Tunnel deformations under different M for soil layer ④

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图 20 第④层土隧道不同堆载情况下的变形

Figure 20. Tunnel deformations under different surcharges for soil layer ④

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表 1 上海软黏土三轴试验方案

Table 1 Triaxial test schemes for Shanghai soft clay

土样编号	取土地点	深度/m	固结压力/kPa	剪切方式
1	四川北路	20~20.5	102.2	不排水拉伸
2	四川北路	20~20.5	109.4	不排水压缩
3	徐家汇	38~38.5	217.5	不排水拉伸
4	徐家汇	38~38.5	219.5	不排水压缩
5	张江	41~41.5	219.0	不排水压缩
6	张江	41~41.5	226.7	不排水拉伸

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表 2 上海黏土各场地UH模型参数

Table 2 Parameters of UH models for Shanghai soft clay under exploration

取样点	埋深/ m	$\lambda$	$\kappa$	${e_0}$	$M$	OCR
四川北路	20	0.107	0.016	0.990	1.32	3.0
徐家汇	38	0.065	0.010	0.860	1.33	2.8
张江	41	0.040	0.006	0.691	1.19	3.5

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表 3 验证MSD简化方法精度的试验方案

Table 3 Verification schemes for precision of simplified MSD method

验证分组	$\lambda$	${\kappa \mathord{\left/ {\vphantom {\kappa \lambda }} \right. } \lambda }$	${e_0}$	$\nu$	$M$	OCR
1	0.09	0.20	1.2	0.3	1.2	1
2	0.09	0.20	1.2	0.3	1.2	2
3	0.12	0.20	1.2	0.3	1.2	2
4	0.09	0.10	1.2	0.3	1.2	2

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表 4 上海第④，⑤₁层土隧道MSD数值试验表

Table 4 Schemes for obtaining subgrade reaction of tunnel of soil layers ④ and ⑤₁ based on MSD method

土层标号	试验标号	埋深/ m	$\lambda$	$\kappa /\lambda$	${e_0}$	$\nu$	M	OCR
④	1	15	0.177	0.15	1.118	0.35	1.2	1
	2	15	0.177	0.20	1.118	0.35	1.2	1
	3	15	0.177	0.25	1.118	0.35	1.2	1
	4	10	0.177	0.20	1.118	0.35	1.2	1
	5	20	0.177	0.20	1.118	0.35	1.2	1
	6	15	0.177	0.20	1.118	0.35	1.2	2
	7	15	0.177	0.20	1.118	0.35	1.2	4
	8	15	0.177	0.20	1.118	0.35	1.1	1
	9	15	0.177	0.20	1.118	0.35	1.3	1
⑤₁	10	25	0.136	0.10	0.959	0.35	1.3	1
	11	25	0.136	0.15	0.959	0.35	1.3	1
	12	25	0.136	0.20	0.959	0.35	1.3	1
	13	20	0.136	0.15	0.959	0.35	1.3	1
	14	30	0.136	0.15	0.959	0.35	1.3	1
	15	25	0.136	0.15	0.959	0.35	1.3	2
	16	25	0.136	0.15	0.959	0.35	1.3	4
	17	25	0.136	0.15	0.959	0.35	1.2	1
	18	25	0.136	0.15	0.959	0.35	1.4	1

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表 5 上海第④、⑤₁层土隧道地基反力曲线拟合数据表

Table 5 Summary of fitting parameters for soil layers ④ and ⑤₁ in Shanghai

试验标号	第④层土		试验标号	第⑤₁层土
试验标号	${\zeta _{r,0}}$ / (kPa·m^-1)	${p_{r,\lim }}$ /kPa	试验标号	${\zeta _{r,0}}$ / (kPa·m^-1)	${p_{r,\lim }}$ / kPa
1	5045.23	86.17	10	13979.34	160.16
2	3791.89	88.70	11	9743.96	159.74
3	3012.78	92.35	12	7420.14	162.45
4	2578.48	54.49	13	7945.51	127.38
5	4966.76	120.31	14	11503.00	190.71
6	3678.72	106.62	15	9342.75	188.87
7	3570.91	136.48	16	8946.58	238.69
8	3742.71	81.55	17	9572.67	149.07
9	3828.29	95.81	18	9884.26	170.24

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