北京城市副中心站综合交通枢纽深大基坑两级反压土支护数值分析

张绪虎; 徐明; 宋二祥; 王永成; 孙俊岭

doi:10.6052/j.issn.1000-4750.2024.04.0297

北京城市副中心站综合交通枢纽深大基坑两级反压土支护数值分析

张绪虎^1,,
徐明^1, ,,
宋二祥^1,,
王永成^2,,
孙俊岭^2,

1.
清华大学土木工程系，北京 100084
2.
中国铁路设计集团有限公司，天津 300142

基金项目: 国家自然科学基金项目(51978382)

详细信息

作者简介:
张绪虎(1998−)，男，湖北人，硕士生，主要从事基坑支护理论与数值模拟研究(E-mail: xh-zhang20@mails.tsinghua.edu.cn)

宋二祥(1957−)，男，河北人，教授，博士，博导，主要从事岩土力学及工程领域的教学及科研工作(E-mail: songex@tsinghua.edu.cn)

王永成(1974−)，男，河北人，高工，硕士，主要从事岩土及结构工程的设计及研究工作(E-mail: wangyongcheng01@crdc.com)

孙俊岭(1971−)，男，河北人，正高工，学士，主要从事岩土及结构工程的设计及研究工作(E-mail: sunjunling@crdc.com)

通讯作者:
徐　明(1974−)，男，湖北人，副教授，博士，博导，主要从事岩土力学试验研究及理论分析(E-mail: mingxu@mail.tsinghua.edu.cn)

中图分类号: TU470
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出版历程
- 收稿日期: 2024-04-22
- 修回日期: 2024-10-06
- 网络出版日期: 2024-11-06

NUMERICAL ANALYSIS FOR TWO-STAGE EARTH BERM SUPPORT OF A DEEP EXCAVATION IN BEIJING SUB-CENTRAL STATION

1.
Department of Civil Engineering, Tsinghua University, Beijing 100084, China
2.
China Railway Design Corporation, Tianjin 300142, China

摘要

摘要:
在大型深基坑工程中，反压土支护由于经济性好、施工方便而得到了越来越多的应用，但是现有基坑规范并未给出设计方法。亚洲最大的地下综合交通枢纽北京城市副中心站V区基坑采用两级反压土支护，开挖深度达34.4 m，变形控制要求严格。通过三维数值模拟研究其支护效果，建立包含19个计算阶段的有限元模型，并基于相关试验结果确定了适用于北京地区土层的HSs模型参数。有限元预测结果表明该支护体系能够满足工程要求，反压土支护效果明显。同时，对比分析了小应变模型与常用的摩尔-库伦模型的计算结果，发现即便人为提高摩尔-库伦模型刚度，由于其单一模量的特点，仍无法得到合理的变形预测，深基坑变形计算中必须考虑土体小应变刚度特性，但是摩尔-库伦模型对支挡结构内力的计算结果与小应变模型比较接近。
- 深基坑 /
- 反压土 /
- 有限元分析 /
- 小应变刚度 /
- 本构模型
Abstract:
In large-scale deep excavation, earth berm support has been widely used due to economy and convenient construction, but the existing standards do not give a design method. The V-area excavation of Beijing Sub-Central Station, the largest underground comprehensive transportation hub in Asia, is supported by two-stage earth berm, with an excavation depth of 34.4 m and strict deformation requirements. The support effect was studied through three-dimensional numerical simulation, a finite element model containing 19 calculation stages was established, and the HSs model parameters suitable for the soil layer in Beijing were determined based on relevant test results. The finite element prediction results show that the support system can meet the engineering requirements, and the supporting effect of the earth berm is significant. At the same time, the calculation results of the small strain model and the commonly used Mohr-Coulomb model was compared, the results of which show even if the stiffness of the Mohr-Coulomb model is artificially increased, reasonable deformation prediction cannot be obtained due to its single modulus parameter, as a result, the small strain stiffness of soil must be considered in the deformation calculation of deep excavation, but the Mohr-Coulomb model is close to the small strain model in the calculation of the internal force of the supporting structure.
- deep excavation /
- earth berm /
- finite element analysis /
- small strain stiffness /
- constitutive model

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图 1 基坑分区

Figure 1. Excavation division

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图 2 反压土支护典型剖面

Figure 2. Typical cross-section of earth berm support

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图 3 典型支护布置

Figure 3. Typical support arrangement

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图 4 整体有限元模型

Figure 4. The overall finite element model

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图 5 数值模型计算阶段划分

Figure 5. Numerical model calculation phasing

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图 6 数值模型详图

Figure 6. Numerical model detailing

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图 7 挡土墙侧移

Figure 7. Horizontal displacement of retaining wall

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图 8 挡土墙后地表沉降

Figure 8. Settlement for ground surface behind retaining wall

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图 9 基坑附近土体剪应变

Figure 9. Shear strain of soil near excavation

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图 10 B3层反压土开槽引起的水平变形

Figure 10. Horizontal deformation by grooving of berm in B3

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图 11 B2层反压土开槽引起的水平变形

Figure 11. Horizontal deformation by grooving of berm in B2

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图 12 HSs与MC模型的坑底回弹对比

Figure 12. Comparison of excavation rebound between HSs model and MC models

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图 13 HSs与MC模型的挡土墙侧移对比

Figure 13. Comparison of horizontal displacement of retaining wall between HSs model and MC models

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图 14 HSs与MC模型的挡土墙后地表沉降对比

Figure 14. Comparison of settlement for ground surface behind retaining wall between HSs model and MC models

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图 15 HSs与MC模型的挡土墙弯矩对比

Figure 15. Comparison of bending moments of retaining wall between HSs model and MC models

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表 1 支护结构尺寸

Table 1 Sizes of supporting structures

支护结构	尺寸
地连墙	厚度1 m
排桩	直径1.2 m、间距1.4 m
立柱	直径1 m、间距10 m
工程桩	直径2 m、间距10 m
B3层顶板	厚度0.6 m
B3层底板	厚度1.5 m
B3层侧墙	厚度1.9 m
B2层顶板	厚度0.3 m
B2层边跨底板	厚度2.7 m
B2层侧墙	厚度2 m
斜撑	截面0.8 m×0.8 m、间距4.5 m

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表 2 HSs模型参数取值

Table 2 Parameters for HSs model

参数	取值
$c'$	砂土：考虑湿砂取小值3 kPa 粉土与粉质粘土：根据地勘报告测孔压CU试验取值
$\varphi '$	砂土：根据地勘报告休止角取值粉土与粉质粘土：根据地勘报告测孔压CU试验取值
${R_{\text{f}}}$	0.9
${\nu _{{\text{ur}}}}$	0.2
$K_{\text{0}}^{{\text{nc}}}$	$1-\sin \varphi '$
$\psi$	$\psi = \varphi '-{30^ \circ }$ ，若 $\varphi ' < {30^ \circ }$ ，则取 $\psi = {0^ \circ }$
${p^{{\text{ref}}}}$	100 kPa
$E_{{\text{oed}}}^{{\text{ref}}}$	地勘报告给出了 ${E_{{\text{s1-2}}}}$ ，考虑取土扰动取 $E_{{\text{oed}}}^{{\text{ref}}} = {E_{{\text{s1-2}}}}$
$E_{50}^{{\text{ref}}}$	砂土： $E_{50}^{{\text{ref}}} = {E_{{\text{s1-2}}}}$ 粉土： $E_{50}^{{\text{ref}}} = 2{E_{{\text{s1-2}}}}$ 粉质黏土： $E_{50}^{{\text{ref}}} = {E_{{\text{s1-2}}}}$
$E_{{\text{ur}}}^{{\text{ref}}}$	砂土： $E_{{\text{ur}}}^{{\text{ref}}} = 4{E_{{\text{s1-2}}}}$ 粉土： $E_{{\text{ur}}}^{{\text{ref}}} = 6{E_{{\text{s1-2}}}}$ 粉质黏土： $E_{{\text{ur}}}^{{\text{ref}}} = 5{E_{{\text{s1-2}}}}$
$m$	砂土：0.5 粉土：0.6 粉质黏土：0.8
$G_{\text{0}}^{{\text{ref}}}$	根据剪切波波速用公式 $G_{\text{0}}^{} = \rho V_{\text{s}}^{\text{2}}$ 计算 $G_{\text{0}}^{}$ ，再根据应力水平换算成 $G_{\text{0}}^{{\text{ref}}}$
${\gamma _{{\text{0}}{\text{.7}}}}$	砂土：4×10⁻⁴ 粉土：3.5×10⁻⁴ 粉质黏土：3×10⁻⁴

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表 3 各土层HSs模型参数取值

Table 3 Parameters of each soil layer for HSs model

土层编号	土性	厚度/m	$\gamma$ /(kN/m³)	$c'$ /kPa	$\varphi '$ /(°)	m	γ_0.7	$E_{{\text{oed}}}^{{\text{ref}}}$ /MPa	$E_{50}^{{\text{ref}}}$ /MPa	$E_{{\text{ur}}}^{{\text{ref}}}$ /MPa	$G_{\text{0}}^{{\text{ref}}}$ /MPa
①	素填土	1.5	19.0	15.0	23.0	0.8	3.0×10⁻⁴	7.7	7.7	38.4	106.8
②	黏质粉土-砂质粉土	6.0	19.4	10.0	30.0	0.6	3.5×10⁻⁴	9.2	18.5	55.4	120.4
③	细砂-中砂	6.0	19.5	3.0	32.0	0.5	4.0×10⁻⁴	30.0	30.0	120.0	143.5
④	细砂-中砂	5.9	20.0	3.0	32.0	0.5	4.0×10⁻⁴	32.5	32.5	130.0	157.9
⑤	细砂-中砂	10.1	20.5	3.0	32.0	0.5	4.0×10⁻⁴	35.0	35.0	140.0	200.9
⑥₁	重粉质黏土-粉质黏土	2.3	19.4	20.0	22.5	0.8	3.0×10⁻⁴	14.6	14.6	72.9	239.2
⑥	细砂-中砂	3.7	20.1	3.0	34.0	0.5	4.0×10⁻⁴	37.5	37.5	150.0	256.8
⑦	粉质黏土-重粉质黏土	4.0	19.8	19.6	23.5	0.8	3.0×10⁻⁴	18.2	18.2	91.2	263.4
⑦₁	黏质粉土-砂质粉土	5.0	20.6	8.0	35.5	0.6	3.5×10⁻⁴	29.4	58.8	176.3	264.5
⑧	细砂-中砂	6.0	20.3	3.0	35.0	0.5	4.0×10⁻⁴	40.0	40.0	160.0	277.3
⑨₁	粉质黏土-重粉质黏土	4.0	19.9	14.0	24.0	0.8	3.0×10⁻⁴	20.8	20.8	104.2	232.3
⑨	细砂-中砂	2.0	20.3	3.0	36.0	0.5	4.0×10⁻⁴	42.5	42.5	170.0	217.0
⑩	粉质黏土-重粉质黏土	4.0	20.1	15.2	24.0	0.8	3.0×10⁻⁴	23.6	23.6	118.0	169.2
⑪	细砂-中砂	13.0	20.5	3.0	36.0	0.5	4.0×10⁻⁴	45.0	45.0	180.0	245.8
⑫₁	重粉质黏土-粉质黏土	2.0	19.9	14.2	24.0	0.8	3.0×10⁻⁴	24.0	24.0	120.2	179.3
⑫	细砂-中砂	9.0	20.5	3.0	36.0	0.5	4.0×10⁻⁴	47.5	47.5	190.0	266.4
⑬	粉质黏土-重粉质黏土	4.0	20.3	13.7	24.0	0.8	3.0×10⁻⁴	28.8	28.8	143.9	217.9
⑬₁	细砂-中砂	5.0	20.5	3.0	38.0	0.5	4.0×10⁻⁴	50.0	50.0	200.0	239.6
⑭	粉质黏土-重粉质黏土	4.0	20.1	15.0	24.0	0.8	3.0×10⁻⁴	30.4	30.4	152.2	217.6
⑭₁	中砂-细砂	2.5	20.5	3.0	38.0	0.5	4.0×10⁻⁴	52.5	52.5	210.0	271.9

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参考文献(31)

[1]	金亚兵, 周志雄. 挡土墙(桩)前堆载反压或预留土体分析与计算[J]. 岩土力学, 1999, 20(3): 56 − 60. doi: 10.3969/j.issn.1000-7598.1999.03.011 JIN Yabing, ZHOU Zhixiong. Analysis and calculation method of surcharge reaction and remaining soils near retaining wall [J]. Rock and Soil Mechanics, 1999, 20(3): 56 − 60. (in Chinese) doi: 10.3969/j.issn.1000-7598.1999.03.011
[2]	郑刚, 陈红庆, 雷扬, 等. 基坑开挖反压土作用机制及其简化分析方法研究[J]. 岩土力学, 2007, 28(6): 1161 − 1166. doi: 10.3969/j.issn.1000-7598.2007.06.018 ZHENG Gang, CHEN Hongqing, LEI Yang, et al. A study of mechanism of earth berm and simplified analysis method for excavation [J]. Rock and Soil Mechanics, 2007, 28(6): 1161 − 1166. (in Chinese) doi: 10.3969/j.issn.1000-7598.2007.06.018
[3]	DALY M P, POWRIE W. Undrained analysis of earth berms as temporary supports for embedded retaining walls [J]. Proceedings of the Institution of Civil Engineers - Geotechnical Engineering, 2001, 149(4): 237 − 248. doi: 10.1680/geng.2001.149.4.237
[4]	刘畅, 孙盼盼, 赵露伟, 等. 基坑开挖反压土截面特性对基坑性状影响的有限元分析[J]. 地下空间与工程学报, 2017, 13(3): 788 − 795. LIU Chang, SUN Panpan, ZHAO Luwei, et al. Finite element analysis of earth berm excavation pit traits affect section properties [J]. Chinese Journal of Underground Space and Engineering, 2017, 13(3): 788 − 795. (in Chinese)
[5]	张绪虎, 徐明, 宋二祥, 等. 不排水条件下反压土支护悬臂挡墙的稳定分析[J]. 工程力学, doi: 10.6052/j.issn.1000-4750.2023.06.0415. ZHANG Xuhu, XU Ming, SONG Erxiang, et al. Stability analysis of cantilever retaining wall supported by earth berm under undrained conditions [J]. Engineering Mechanics, doi: 10.6052/j.issn.1000-4750.2023.06.0415. (in Chinese)
[6]	祁凌飞, 曲新钢, 周山君, 等. 富水砂层深基坑悬挂式止水帷幕降水方案优化研究[J]. 工程力学, 2023, 40(增刊): 213 − 218. doi: 10.6052/j.issn.1000-4750.2022.06.S025 QI Lingfei, QU Xingang, ZHOU Shanjun, et al. Dewatering design optimization for deep excavation with suspended impervious curtain in water-sandy layer [J]. Engineering Mechanics, 2023, 40(Suppl): 213 − 218. (in Chinese) doi: 10.6052/j.issn.1000-4750.2022.06.S025
[7]	ZHANG M J, SONG E X, CHEN Z Y. Ground movement analysis of soil nailing construction by three-dimensional (3-D) finite element modeling (FEM) [J]. Computers and Geotechnics, 1999, 25(4): 191 − 204. doi: 10.1016/S0266-352X(99)00025-7
[8]	ZDRAVKOVIC L, POTTS D M, ST JOHN H D. Modelling of a 3D excavation in finite element analysis [J]. Géotechnique, 2005, 55(7): 497 − 513.
[9]	王海波, 徐明, 宋二祥. 考虑土体小应变特性的一种实用本构模型[J]. 工程力学, 2011, 28(6): 60 − 65. WANG Haibo, XU Ming, SONG Erxiang. A practical constitutive model of soil considering the behavior at small strains [J]. Engineering Mechanics, 2011, 28(6): 60 − 65. (in Chinese)
[10]	王海波, 徐明, 宋二祥. 基于硬化土模型的小应变本构模型研究[J]. 岩土力学, 2011, 32(1): 39 − 43, 136. doi: 10.3969/j.issn.1000-7598.2011.01.007 WANG Haibo, XU Ming, SONG Erxiang. A small strain constitutive model based on hardening soil model [J]. Rock and Soil Mechanics, 2011, 32(1): 39 − 43, 136. (in Chinese) doi: 10.3969/j.issn.1000-7598.2011.01.007
[11]	JARDINE R J, POTTS D M, FOURIE A B, et al. Studies of the influence of non-linear stress-strain characteristics in soil-structure interaction [J]. Géotechnique, 1986, 36(3): 377 − 396.
[12]	邹文浩, 徐明. 考虑土体小应变刚度特征时隔断结构保护效果的三维数值分析[J]. 岩土工程学报, 2013, 35(增刊1): 203 − 209. ZOU Wenhao, XU Ming. 3D numerical analysis of mitigation effect of separation pile and diaphragm wall considering small strain stiffness of soils [J]. Chinese Journal of Geotechnical Engineering, 2013, 35(Suppl 1): 203 − 209. (in Chinese)
[13]	宋二祥, 邱玥. 基坑复合土钉支护的有限元分析[J]. 岩土力学, 2001, 22(3): 241 − 244, 253. SONG Erxiang, QIU Yue. Finite element analysis of composite soil nailing for excavation support [J]. Rock and Soil Mechanics, 2001, 22(3): 241 − 244, 253. (in Chinese)
[14]	刘国彬, 侯学渊. 软土的卸荷模量[J]. 岩土工程学报, 1996, 18(6): 18 − 23. LIU Guobin, HOU Xueyuan. Unloading modulus of the Shanghai soft clay [J]. Chinese Journal of Geotechnical Engineering, 1996, 18(6): 18 − 23. (in Chinese)
[15]	宋广, 宋二祥. 基坑开挖数值模拟中土体本构模型的选取[J]. 工程力学, 2014, 31(5): 86 − 94. doi: 10.6052/j.issn.1000-4750.2012.08.0583 SONG Guang, SONG Erxiang. Selection of soil constitutive models for numerical simulation of foundation pit excavation [J]. Engineering Mechanics, 2014, 31(5): 86 − 94. (in Chinese) doi: 10.6052/j.issn.1000-4750.2012.08.0583
[16]	BENZ T. Small-strain stiffness of soils and its numerical consequences [D]. Stuttgart: Universität Stuttgart, 2007.
[17]	王卫东, 王浩然, 徐中华. 上海地区基坑开挖数值分析中土体HS-Small模型参数的研究[J]. 岩土力学, 2013, 34(6): 1766 − 1774. WANG Weidong, WANG Haoran, XU Zhonghua. Study of parameters of HS-Small model used in numerical analysis of excavations in Shanghai area [J]. Rock and Soil Mechanics, 2013, 34(6): 1766 − 1774. (in Chinese)
[18]	HUYNH Q T, LAI V Q, BOONYATEE T, et al. Verification of soil parameters of hardening soil model with small-strain stiffness for deep excavations in medium dense sand in Ho Chi Minh City, Vietnam [J]. Innovative Infrastructure Solutions, 2022, 7(1): 15. doi: 10.1007/s41062-021-00621-x
[19]	李连祥, 刘嘉典, 李克金, 等. 济南典型地层HSS参数选取及适用性研究[J]. 岩土力学, 2019, 40(10): 4021 − 4029. LI Lianxiang, LIU Jiadian, LI Kejin, et al. Study of parameters selection and applicability of HSS model in typical stratum of Jinan [J]. Rock and Soil Mechanics, 2019, 40(10): 4021 − 4029. (in Chinese)
[20]	BU F, YU W R, CHEN L, et al. Investigation of three-dimensional deformation mechanisms of box culvert due to adjacent deep basement excavation in clays [J]. Geomechanics and Engineering, 2022, 30(6): 565 − 577.
[21]	LIU G G, GENG P, WANG T Q, et al. Seismic vulnerability of shield tunnels in interbedded soil deposits: Case study of submarine tunnel in Shantou Bay [J]. Ocean Engineering, 2023, 286: 115500. doi: 10.1016/j.oceaneng.2023.115500
[22]	BOLTON M D. The strength and dilatancy of sands [J]. Géotechnique, 1986, 36(1): 65 − 78.
[23]	罗敏敏, 陈赟, 周江. 小应变土体硬化模型参数取值研究现状与展望[J]. 工业建筑, 2021, 51(4): 172 − 180. LUO Minmin, CHEN Yun, ZHOU Jiang. Research status and prospect of parameter selection for the HS-small model [J]. Industrial Construction, 2021, 51(4): 172 − 180. (in Chinese)
[24]	王浩然. 上海软土地区深基坑变形与环境影响预测方法研究[D]. 上海: 同济大学, 2012. WANG Haoran. Prediction of deformation and response of adjacent environment of deep excavation in Shanghai soft deposit[D]. Shanghai: Tongji University, 2012. (in Chinese)
[25]	李亚玲, 张彬, 苏海峰, 等. Hardening-Soil模型中参数选取试验研究[J]. 工程地质学报, 2012, 20(增刊): 164 − 169. LI Yaling, ZHANG Bin, SU Haifeng, et al. Parameter selection based on test with Hardening-Soil model [J]. Journal of Engineering Geology, 2012, 20(Suppl 1): 164 − 169. (in Chinese)
[26]	周恩平. 考虑小应变的硬化土本构模型在基坑变形分析中的应用[D]. 哈尔滨: 哈尔滨工业大学, 2010. ZHOU Enping. Application of hardening soil model with small-strain in deformation analysis for foundation pit [D]. Harbin: Harbin Institute of Technology, 2010.
[27]	顾晓强, 吴瑞拓, 梁发云, 等. 上海土体小应变硬化模型整套参数取值方法及工程验证[J]. 岩土力学, 2021, 42(3): 833 − 845. GU Xiaoqiang, WU Ruituo, LIANG Fayun, et al. On HSS model parameters for Shanghai soils with engineering verification [J]. Rock and Soil Mechanics, 2021, 42(3): 833 − 845. (in Chinese)
[28]	张绪虎. 基于深度学习反分析的反压土支护基坑变形预测及设计[D]. 北京: 清华大学, 2023. ZHANG Xuhu. Deformation prediction and design of excavation supported by earth berm based on deep learning inverse analysis [D]. Beijing: Tsinghua University, 2023. (in Chinese)
[29]	彭俊国, 朱彦鹏. 刚性挡土墙粘性填土被动土压力简化计算[J]. 工程力学, 2022, 39(5): 204 − 209, 223. doi: 10.6052/j.issn.1000-4750.2021.03.0183 PENG Junguo, ZHU Yanpeng. Simplified method for calculating the passive earth pressure of cohesive backfill against rigid retaining walls [J]. Engineering Mechanics, 2022, 39(5): 204 − 209, 223. (in Chinese) doi: 10.6052/j.issn.1000-4750.2021.03.0183
[30]	吕桂阳, 和西良, 梁汝鸣, 等. 超固结黏土中不排水柱孔扩张弹塑性解及应用[J]. 工程力学, 2024, 41(1): 160 − 170. doi: 10.6052/j.issn.1000-4750.2022.03.0228 LYU Guiyang, HE Xiliang, LIANG Ruming, et al. Elastoplastic solution and application of undrained cylindrical cavity expansion in overconsolidated clay [J]. Engineering Mechanics, 2024, 41(1): 160 − 170. (in Chinese) doi: 10.6052/j.issn.1000-4750.2022.03.0228
[31]	李淑, 张顶立, 房倩, 等. 北京地铁车站深基坑地表变形特性研究[J]. 岩石力学与工程学报, 2012, 31(1): 189 − 198. LI Shu, ZHANG Dingli, FANG Qian, et al. Research on characteristics of ground surface deformation during deep excavation in Beijing subway [J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(1): 189 − 198. (in Chinese)

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