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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (12): 2593-2603    DOI: 10.3785/j.issn.1008-973X.2025.12.014
    
Deformation analysis and parameter determination of hardening soil model with small strain of an ultra-deep subway excavation in Tianjin
Zhongjie ZHANG1,2(),Hechen ZHOU3(),Xiaoqiang GU3,4,*(),Jiahe CHEN1,Hang WU1
1. Shanghai Urban Construction Design and Research Institute (Group) Co. Ltd, Shanghai 200125, China
2. School of Civil Engineering, Tianjin University, Tianjin 300072, China
3. Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
4. School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, Hangzhou 310018, China
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Abstract  

There exists the issue of overreliance on the empirical multiplicative relationship between the modulus parameters of the hardening soil model with small strain (HSS) and the compression modulus Es1-2, as well as the neglect of the confining pressure dependence of the shear modulus reduction parameter γ0.7, in the context of Tianjin soft soil area. The ultra-deep subway excavation of Xiawafang Station on Tianjin Metro Line 8 was taken as a case study. The Xiawafang station was currently the deepest metro station in soft soil areas in China, with an excavation depth of 38.3 m. By utilizing extensive laboratory and field test data, particularly the small-strain shear modulus G0 obtained from in-situ wave velocity tests, a statistical relationship between G0, the initial void ratio, and confining pressure was established. The variation of γ0.7 with soil depth was considered and a statistical relationship between the tangent modulus for primary oedometer loading $ E_{{\text{oed}}}^{{\text{ref}}} $ and Es1-2 was established. As a result, the HSS parameters applicable to soils in the Tianjin area were finally determined. A detailed three-dimensional finite element model of the Xiawafang Station excavation was established using PLAXIS 3D, and the results of lateral displacement of the retaining wall and surface settlement outside the pit were compared with the field measured data. The results demonstrate that the proposed HSS parameter determination is reasonable, with calculated excavation deformations closely matching measured values. These findings can provide an engineering reference for the design of deep excavations and the selection of geotechnical soil parameters in the Tianjin soft soil area.

Key words： ultra-deep subway excavation      deformation analysis      finite element simulation      hardening soil model with small strain      small strain shear modulus      parameter determination     
Received: 19 November 2024      Published: 25 November 2025
CLC:  TU 473  
Fund:  国家自然科学基金资助项目（52178344）.
Corresponding Authors: Xiaoqiang GU     E-mail: zhangzhongjie@sucdri.com;zhouhechen@tongji.edu.cn;guxiaoqiang@tongji.edu.cn
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Zhongjie ZHANG
Hechen ZHOU
Xiaoqiang GU
Jiahe CHEN
Hang WU
Cite this article:

Zhongjie ZHANG,Hechen ZHOU,Xiaoqiang GU,Jiahe CHEN,Hang WU. Deformation analysis and parameter determination of hardening soil model with small strain of an ultra-deep subway excavation in Tianjin. Journal of ZheJiang University (Engineering Science), 2025, 59(12): 2593-2603.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.12.014     OR     https://www.zjujournals.com/eng/Y2025/V59/I12/2593


天津某超深地铁基坑变形分析与小应变硬化参数取值

天津地区小应变硬化（HSS）模型模量参数多依赖与压缩模量Es1-2的经验倍数关系，且忽略剪切模量衰减参数γ0.7随围压变化的影响. 为此，以天津地铁8号线下瓦房站超深基坑（当前国内软土地区最深地铁车站，挖深为38.3 m）为研究背景，依托大量室内和现场试验数据，特别是通过现场原位波速试验测得土体小应变剪切模量G0，建立G0与初始孔隙比和围压的统计关系，考虑γ0.7随土层深度的变化，并统计标准固结试验的参考切线模量$ E_{{\text{oed}}}^{{\text{ref}}} $与Es1-2的经验关系，最终确定了适用于天津地区土体的HSS模型参数. 使用PLAXIS 3D建立下瓦房站基坑开挖的精细化三维有限元模型，将基坑围护墙变形及坑外地表沉降的计算结果与现场实测数据进行对比验证. 结果表明，提出的HSS参数取值合理可靠，基坑变形计算值与实测结果较吻合，研究结果可为天津软土地区深基坑设计及岩土工程参数的选取提供参考.


关键词： 超深地铁基坑,  变形分析,  有限元模拟,  小应变硬化模型,  小应变剪切模量,  参数取值 
Fig.1 Schematic diagram of subway excavation
Fig.2 Section view of subway excavation
Fig.3 Plan of support strut
土层e0γ/(kN·m?3)c'/kPaφ'/(°)Es1-2/MPa
①2填土0.95118.822.617.34.1
④1粉质黏土0.76119.522.617.36.0
⑥3砂质粉土0.72819.68.036.810.9
⑥4粉质黏土0.82619.219.921.85.5
⑦粉质黏土0.72619.816.324.15.4
⑧1粉质黏土0.72719.821.423.45.3
⑧2砂质粉土0.47121.214.534.312.4
⑨1粉质黏土0.74619.617.327.95.7
⑨2粉砂0.62420.215.234.116.4
⑩1粉质黏土0.60720.433.822.66.5
?1粉质黏土0.61620.315.830.46.8
?2粉砂0.60620.312.634.117.0
?3粉质黏土0.68420.040.823.96.8
?4粉砂0.63120.116.836.113.6
?5粉质黏土0.71019.835.526.36.7
?1粉质黏土0.61220.343.418.37.2
?1粉质黏土0.61220.445.413.97.6
?2粉砂0.69319.614.433.013.2
?3粉质黏土0.64720.127.316.37.2
?1粉质黏土0.68620.044.020.77.4
?2粉砂0.68219.614.433.014.7
Tab.1 Physical and mechanical parameters of soils
Fig.4 Relation curve between $ E_{{\text{oed}}}^{{\text{ref}}} $ and Es1-2
Fig.5 Relation curve between G0 and e0、σ3 determined by field wave velocity test
深度/mG/G0
γ = 5×10?6γ = 1×10?5γ = 5×10?5γ = 1×10?4γ = 5×10?4γ = 1×10?3γ = 5×10?3γ = 1×10?2
0~100.994 360.988 830.947 080.900 610.657 720.498 830.176 720.098 81
10~200.994 720.989 520.950 200.906 090.671 600.515 200.189 050.107 48
20~300.995 530.991 110.957 470.919 170.706 180.556 140.223 610.133 55
30~400.995 700.991 430.958 950.921 690.710 530.558 130.212 260.120 62
40~500.995 860.991 780.960 490.924 590.719 770.571 450.229 150.135 33
50~600.996 040.992 120.961 960.927 130.724 890.575 050.226 630.131 77
60~700.995 790.991 620.959 800.923 370.717 160.567 780.222 350.127 91
70~900.996 290.992 620.964 460.931 980.742 250.597 940.244 430.147 53
>900.996 450.992 830.965 840.934 330.747 290.604 240.255 320.154 29
Tab.2 Statistics of shear modulus degradation with shear strain under different depths for silty clays in Tianjin area[28]
深度/mγ0.7/10?4深度/mγ0.7/10?4
0~103.8250~605.29
10~204.1060~705.12
20~304.9570~905.71
30~404.89>906.09
40~505.24——
Tab.3 Statistical average value of γ0.7 with different depths
Fig.6 Schematic diagram of excavation retaining structure
结构单元尺寸E/GPa
地连墙1.40、1.50 m厚31.5
混凝土板撑首道0.80 m厚，其余0.40 m厚30.0
混凝土梁支撑1.3 m×1.1 m与1.2 m×1.0 m30.0
钢支撑?800 mm (t=20 mm)206.0
钻孔灌注桩?2.5 m30.0
Tab.4 Structural element parameters
土层$\Delta{d} $/mψ/(°)K0$ E_{{\text{oed}}}^{{\text{ref}}} $/MPa$ E_{{\text{50}}}^{{\text{ref}}} $/MPa$ E_{{\text{ur}}}^{{\text{ref}}} $/MPa$ G_{\text{0}}^{{\text{ref}}} $/MPaγ0.7/10?4mRf
①2填土2.5000.653.573.5721.4087.483.820.8720.9
④1粉质黏土3.5000.655.225.2231.3293.323.820.8720.9
⑥3砂质粉土3.036.80.609.489.4856.90117.583.820.9170.9
⑥4粉质黏土5.6200.664.794.7928.7191.124.100.8720.9
⑦粉质黏土1.5000.574.704.7028.1994.604.100.8720.9
⑧1粉质黏土2.8500.564.614.6127.6794.564.100.8720.9
⑧2砂质粉土1.584.30.5010.7910.7964.73133.414.100.9170.9
⑨1粉质黏土6.5200.534.964.9629.7593.864.950.8720.9
⑨2粉砂2.654.10.4813.4513.4580.69126.274.950.9970.9
⑩1粉质黏土1.7500.535.665.6633.9399.644.890.8720.9
?1粉质黏土9.0000.525.925.9235.5099.224.890.8720.9
?2粉砂2.454.10.4413.9413.9483.64127.355.240.9970.9
?3粉质黏土4.3000.525.925.9235.5096.255.240.8720.9
?4粉砂2.206.10.4311.1511.1566.91125.865.240.9970.9
?5粉质黏土2.9000.505.835.8334.9795.215.290.8720.9
?1粉质黏土7.9000.536.266.2637.5899.405.290.8720.9
?1粉质黏土12.3500.526.616.6139.6799.405.120.8720.9
?2粉砂6.203.00.4310.8210.8264.94122.495.710.9970.9
?3粉质黏土2.7000.566.266.2637.5897.815.710.8720.9
?1粉质黏土4.1500.556.446.4438.6396.175.710.8720.9
?2粉砂24.353.00.4412.0512.0572.32123.065.710.9970.9
Tab.5 Parameters of HSS model and soil layer thickness
计算步骤工况
1计算初始地应力场，K0过程
2重置位移，激活地连墙，坑底抗拔桩，激活坑表超载
3开挖?0.40 m，激活东端头井第1道钢支撑，
钢支撑施加预应力407.4 kN
4-Phase I开挖?4.20 m，激活顶板（第1道砼板撑）
5覆土回填，取消东端头井第1道钢支撑
6-Phase II开挖?9.00 m，激活第2道砼板撑
7开挖?10.90 m，激活东端头井第2道钢支撑，
施加预应力545.0 kN
8-Phase III开挖?14.30 m，激活第3道砼板撑以及中庭混凝土支撑
9开挖?16.90 m，激活东端头井第3道钢支撑
（预应力827.5 kN），西端头井第1道钢支撑
（预应力1 068.7 kN）
10-Phase IV开挖?20.60 m，激活第4道砼板撑，
取消西端头井第1道钢支撑
11开挖?22.60 m，激活东端头井第4道钢支撑
（预应力1 415.0 kN），西端头井第2道钢支撑
（预应力1 138.6 kN）
12-Phase V开挖?27.70 m，激活第5道砼板撑，
取消西端头井第2道钢支撑
13开挖?33.50 m，激活最底部混凝土支撑
14-Phase VI开挖至坑底（最深?38.30 m）
Tab.6 Steps for simulating excavation process
Fig.7 Excavation measuring point distribution
开挖阶段$\delta_{\mathrm{hm,M}} $/mm$\delta_{\mathrm{hm,C}} $
本研究方法常规方法
Phase I13.610.314.6
Phase II17.610.915.2
Phase III23.515.823.5
Phase IV28.425.839.7
Phase V38.938.560.7
Phase VI39.746.676.7
Tab.7 Maximum lateral displacement of wall in different excavation stages
Fig.8 Comparison of calculated and measured lateral displacement of retaining wall
Fig.9 Comparison of calculated and measured values of surface settlement behind excavation
测点H/mδhm/mmδvm/mm(δhm/H)/%(δvm/H)/%
J536.6539.523.60.110.64
J836.6525.923.30.070.64
J1536.6539.523.40.110.64
J1836.6539.523.50.110.64
J1238.0023.323.60.060.62
Tab.8 Maximum lateral movement of retaining wall and maximum surface settlement of excavation at final excavation depth (measured value)
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