Please wait a minute...
浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (2): 264-274    DOI: 10.3785/j.issn.1008-973X.2020.02.007
Civil and Transportation Engineering     
Influence of soft clay structure on pit excavation and adjacent tunnels
Can WANG1,2,3(),Dao-sheng LING1,2,3,Heng-yu WANG2,3,*()
1. Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China
2. MOE Key Laboratory of Soft Soils and Geoenvironmental Engineering, Zhejiang University, Hangzhou 310058, China
3. School of Civil Engineering and Architecture, Zhejiang University Ningbo Institute of Technology, Ningbo 315100, China
Download: HTML     PDF(1629KB) HTML
Export: BibTeX | EndNote (RIS)      

Abstract  

One-dimensional compression test and triaxial test were conducted based on the undisturbed silty clay of Ningbo and artificial structural soils, in order to analyze the influence of soil structure on deformation of retaining wall, ground settlement and displacement and bending moment of adjacent tunnels during pit excavation. The artificial structural soils were made by adding salt and cement of different mass fractions in the remolded soil. The relationship between mass fraction of cement and soil structure was verified and established through compressibility indexes, shear strength indexes and yield stress. The Plaxis2D was used to analyze the influence of soil structure on horizontal displacement of retaining walls, settlement of ground surface and adjacent tunnels. Results show that when the mass fraction is 2%, the compressibility indexes, shear strength indexes and structural yield stress are basically the same as that of the undisturbed soil. As the structure of the soil decreases, namely the degree of disturbance increases, the displacements of the retaining walls, ground surface and adjacent tunnels increase rapidly. The tunnel is most sensitive to the degree of disturbance, and its displacement growth trend is the most obvious. When the disturbance degree reaches 39%, the tunnel displacement exceeds the allowable value. When the tunnel is closer to the pit, the displacements of retaining wall and ground surface decrease due to the the constraint effect of the tunnel, while the tunnel displacement and bending moment increase accordingly.

Key words： artificial structured soil      disturbance degree      laboratory test      pit excavation      tunnel     
Received: 31 December 2018      Published: 10 March 2020
CLC:  TU 411  
Corresponding Authors: Heng-yu WANG     E-mail: sprinkling@zju.edu.cn;wanghengyu@vip.163.com
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Can WANG
Dao-sheng LING
Heng-yu WANG
Cite this article:

Can WANG,Dao-sheng LING,Heng-yu WANG. Influence of soft clay structure on pit excavation and adjacent tunnels. Journal of ZheJiang University (Engineering Science), 2020, 54(2): 264-274.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.02.007     OR     http://www.zjujournals.com/eng/Y2020/V54/I2/264


软土结构性对基坑开挖及邻近地铁隧道的影响

为了研究软土地基结构性改变对基坑开挖围护墙变形、地表沉降及其邻近地铁隧道位移和弯矩的影响，针对宁波粉质黏土，采用在重塑土中掺入盐粒和不同质量分数水泥的方式制备人工结构性土，开展一维压缩试验和三轴试验研究原状土与人工结构性土的工程特性，分别通过压缩性指标、抗剪强度指标和结构屈服应力验证和建立水泥质量分数与土体结构性之间的联系；采用Plaxis2D，分析土体结构性改变对基坑开挖过程中围护墙水平位移、地表沉降及其邻近地铁隧道的影响. 研究结果表明，当水泥质量分数为2%时，其压缩性指标、抗剪强度指标和结构屈服应力与原状土基本一致；随着土体结构性降低，扰动度增加，围护墙水平位移、地表沉降和隧道位移急剧增大，其中隧道对于土体扰动度最为敏感，位移增长趋势最为明显，当扰动度为39%时，隧道位移会超过规范允许值；当隧道距离基坑较近时，由于隧道的约束作用，围护墙水平位移和地表沉降较小，但是隧道位移和弯矩会相应增大.


关键词： 人工结构性土,  扰动度,  室内试验,  基坑开挖,  隧道 
土样 Gs w/% γ/（kN?m?3） ρd /（g?cm?3） wL/% wP/%
粉质黏土 2.73 39 17.5 1.29 36 20
Tab.1 Basic physical properties of Ningbo silty clay
Fig.1 Consolidation apparatus and triaxial apparatus for test
Fig.2 Compression curves of one-dimensional compression test
土样 α1-2/MPa?1 Es1?2/MPa Cc
原状土 0.833 2.487 0.278
wc=2.0% 0.837 2.466 0.279
wc=1.5% 0.893 2.286 0.298
wc=1.0% 1.006 2.004 0.335
wc=0.5% 1.065 1.854 0.355
重塑土 1.095 1.744 0.365
Tab.2 Compressibility indexes of different structural soils
Fig.3 Fitting curves of compressibility indexes and cement mass fraciton
Fig.4 Stress-strain curves of different structural soils
Fig.5 Relationship between effective shear strength indexes and cement mass fraction
土样 结构屈服应力/kPa SD/%
原状土 132 ?
wc=2.0% 127 4
wc=1.5% 108 18
wc=1.0% 80 40
wc=0.5% 50 62
重塑土 23 83
Tab.3 Disturbance degree of different structural soils
Fig.6 Fitting curve of disturbance and cement mass fraction
参数 取值
$E_{\rm{oed}}^{\rm{ref}} $ $E_{\rm{oed}}^{\rm{ref}} $=0.9~1.1Es1-2[31]
$E_{\rm{50}}^{\rm{ref}} $ $E_{\rm{50}}^{\rm{ref}}=1.2E_{\rm{oed}}^{\rm{ref}} $[31]
$E_{\rm{ur}}^{\rm{ref}} $ $E_{\rm{ur}}^{\rm{ref}} $=6.7~8.4 $E_{\rm{50}}^{\rm{ref}} $[32]
ψ 对于黏性土，一般取0[30]
m 黏性土一般取0.5~1.0[28]，取0.8[33]
μur 0.2[30]
pref 100 kPa[30]
Rf 0.9[34-35]
K0 1?sin $\varphi '$[36]
$G_{\rm{0}}^{\rm{ref}} $ $G_{\rm{0}}^{\rm{ref}} $=3.5~5.0 $E_{\rm{ur}}^{\rm{ref}} $[29]
Tab.4 Partial parameters of HSS model
土样 $c'$ /kPa $\varphi '$ /（°） $E_{\rm{oed}}^{\rm{ref}}$ /kPa $E_{\rm{50}}^{\rm{ref}}$ /kPa $E_{\rm{ur}}^{\rm{ref}}$ /kPa K0 $G_{\rm{0}}^{\rm{ref}}$ /kPa γ0.7 /10?4 Rinter
原状土 16.2 22.42 2 487 2 984 20 891 0.619 83 563 7.1 0.7
wc=2.0% 16.8 23.18 2 466 2 959 20 714 0.607 82 858 7.4 0.7
wc=1.5% 11.8 22.32 2 286 2 743 19 202 0.620 76 810 7.2 0.7
wc=1.0% 7.1 24.10 2 004 2 405 16 833 0.591 67 334 8.1 0.7
wc=0.5% 4.5 25.90 1 854 2 225 15 574 0.563 62 294 9.0 0.7
重塑土 3.9 26.02 1 744 2 093 14 650 0.562 58 598 9.5 0.7
Tab.5 Main parameters of different structural soils
围护结构 单元类型 EA /（107 kN?m?1） EI /（105 kN·m2?m?1） ω /（kN·m?1·m?1） μ Lspa /m
隧道 板单元 1.4 1.43 8.0 0.10 ?
围护墙 板单元 2.0 16.70 8.0 0.15 ?
钢筋混凝土支撑 梁单元 0.6 3.00 ? 0.15 4
钢支撑 梁单元 0.2 0.90 ? 0.20 3
Tab.6 Paramaters of envelope structure and tunnel
Fig.7 Model sketch of pit excavation adjacent to tunnel
工况 地基土类型
1 原状土
2 人工结构性土1（wc=2.0%，SD=4%）
3 人工结构性土2（wc=1.5%，SD=18%）
4 人工结构性土3（wc=1.0%，SD=40%）
5 人工结构性土4（wc=0.5%，SD=62%）
6 重塑土（SD=83%）
Tab.7 Calculation conditions based on different structural soft clay foundation
Fig.8 Soil displacement field after excavation
Fig.9 Curves of horizontal displacement of retaining wall after excavation in different structural soils
Fig.10 Curves of surface settlement after excavation in different structural soils
Fig.11 Curves of tunnel absolute displacement after each excavation in different structural soils
Fig.12 Curves of maximun bending moment of tunnels after each excavation in different structural soils
内容 控制值
围护墙水平位移 0.14% he
地表沉降 0.10% he
隧道位移 20 mm
Tab.8 Control standard of deformation
Fig.13 Curve of influence of disturbance degree on displacement
Fig.14 Curve of influence of disturbance degree on maximun bending moment of tunnels
[1]   BURFORD D Heave of tunnels beneath the Shell Centre, London, 1959-1986[J]. Geotechnique, 1988, 38 (1): 135- 137
doi: 10.1680/geot.1988.38.1.135
[2]   MARTA D Tunnel complex unloaded by a deep excavation[J]. Computers and Geotechnics, 2001, 28 (6): 469- 493
[3]   黄茂松, 王卫东, 郑刚 软土地下工程与深基坑研究进展[J]. 土木工程学报, 2012, (6): 146- 161
HUANG Mao-song, WANG Wei-dong, ZHENG Gang A review of recent advances in the underground engineering and deep excavations in soft soils[J]. China Civil Engineering Journal, 2012, (6): 146- 161
[4]   张治国, 张孟喜, 王卫东 基坑开挖对临近地铁隧道影响的两阶段分析方法[J]. 岩土力学, 2011, 32 (7): 2085- 2092
ZHANG Zhi-guo, ZHANG Meng-xi, WANG Wei-dong Two-stage method for analyzing effects on adjacent metro tunnels due to foundation pit excavation[J]. Rock and Soil Mechanics, 2011, 32 (7): 2085- 2092
doi: 10.3969/j.issn.1000-7598.2011.07.028
[5]   杨雨冰, 周彪, 谢雄耀 邻近基坑施工作用下盾构隧道横向变形及开裂特性研究[J]. 岩石力学与工程学报, 2016, 35 (Suppl.2): 4082- 4093
YANG Yu-bing, ZHOU Biao, XIE Xiong-yao Study on transverse deformation and cracking property of shield-driven tunnel induced by adjacent excavation[J]. Chinese Journal of Rock Mechanics and Engineering, 2016, 35 (Suppl.2): 4082- 4093
[6]   郑刚, 崔涛, 姜晓婷 砂土层中盾构隧道局部破坏引发连续破坏的机理研究[J]. 岩土工程学报, 2015, 37 (9): 1556- 1571
ZHENG Gang, CUI Tao, JIANG Xiao-ting Mechanism of progressive collapse induced by partial failure of shield tunnels in sandy soil[J]. Chinese Journal of Geotechnical Engineering, 2015, 37 (9): 1556- 1571
doi: 10.11779/CJGE201509002
[7]   LIMITEDP M Sealing sorenberg success[J]. Tunnels and Tunnelling International, 2001, 11: 5
[8]   徐长节, 孙凤明, 陈金友, 等 基坑相邻地铁隧道变形与应力控制措施[J]. 土木建筑与环境工程, 2013, (Suppl.1): 75- 80
XU Chang-jie, SUN Feng-ming, CHEN Jin-you, et al Analysis on the deformation and stress control measures of metro tunnel near a foundation pit[J]. Journal of Civil, Architectural and Environmental Engineering, 2013, (Suppl.1): 75- 80
[9]   ZHENG G, WEI S W Numerical analyses of influence of overlying pit excavation on existing tunnels[J]. Journal of Central South University of Technology, 2008, 15 (Suppl.2): 69- 75
[10]   HUANG H, HUANG X, ZHANG D Centrifuge modelling of deep excavation over existing tunnels[J]. Geotechnical Engineering, 2015, 167 (1): 3- 18
[11]   SHI J W. Investigation of three-dimensional tunnel responses due to basement excavation [D]. HongKong: The Hong Kong University of Science and Technology, 2015.
[12]   蒋明镜, 沈珠江 结构性黏土试样人工制备方法研究[J]. 水利学报, 1997, (1): 56- 61
JIANG Ming-jing, SHEN Zhu-jiang A method of artificial preparation of structured clay samples[J]. Journal of Hydraulic Engineering, 1997, (1): 56- 61
doi: 10.3321/j.issn:0559-9350.1997.01.009
[13]   刘恩龙. 岩土结构块破损机理与二元介质模型研究[D]. 北京: 清华大学, 2005.
LIU En-long. Study on damage mechanism and binary medium model of geotechnical structure blocks [D]. Beijing: Tinghua University, 2005.
[14]   刘恩龙, 沈珠江 人工制备结构性土力学特性试验研究[J]. 岩土力学, 2007, 28 (4): 679- 683
LIU En-long, SHEN Zhu-jiang Experimental study on mechanical properties of artificially structured soils[J]. Rock and Soil Mechanics, 2007, 28 (4): 679- 683
doi: 10.3969/j.issn.1000-7598.2007.04.009
[15]   胡琦, 许四法, 陈仁朋, 等 深基坑开挖土体扰动及其对邻近地铁隧道的影响分析[J]. 岩土工程学报, 2013, 35 (Suppl.2): 537- 541
HU Qi, XU Si-fa, CHEN Ren-peng, et al Influence of soil disturbance on metro tunnel in soft clay due to excavation of deep foundation pit[J]. Chinese Journal of Geotechnical Engineering, 2013, 35 (Suppl.2): 537- 541
[16]   雷华阳, 仇王维, 丁小冬, 等 人工结构性土的次固结特性研究[J]. 天津大学学报, 2015, (11): 995- 1000
LEI Hua-yang, QIU Wang-wei, DING Xiao-dong, et al Characteristics of secondary consolidation considering the structure of artificial soil[J]. Journal of Tianjin University: Science and Technology, 2015, (11): 995- 1000
[17]   陈仁朋, 王诚杰, 鲁立, 等. 开挖对地铁盾构隧道影响及控制措施[C] // 全国结构工程学术会议. 长沙: [s.n.], 2017: 1-13.
CHEN Ren-peng, WANG Cheng-jie, LU Li, et al. Influence of excavation on exist metro shield tunnel and control measures [C]// National Conference on Structural Engineering. Changsha: [s.n.], 2017: 1-13.
[18]   HUANG X, SCHWEIGER H F, HUANG H Influence of deep excavations on nearby existing tunnels[J]. International Journal of Geomechanics, 2013, 13 (2): 170- 180
doi: 10.1061/(ASCE)GM.1943-5622.0000188
[19]   BENZ T. Small strain stiffness of soils and its numerical consequences [D]. Stuttgart: University of Stuttgart, 2006.
[20]   陈仁朋, 叶跃鸿, 王诚杰, 等 大型地下通道开挖对下卧地铁隧道上浮影响[J]. 浙江大学学报: 工学版, 2017, 51 (7): 1269- 1277
CHEN Ren-peng, YE Yue-hong, WANG Chen-jie, et al Influence of open-cut tunneling on uplift behavior of underlying metro tunnel[J]. Journal of Zhejiang University: Engineering Science, 2017, 51 (7): 1269- 1277
[21]   中华人民共和国建设部. 土工试验方法标准: GBT50123-1999 [S]. 北京: 中国标准出版社, 1999: 16-19.
[22]   黄星迪. 饱和结构性土的结构性强弱的室内试验确定研究[D]. 杭州: 浙江工业大学, 2015.
HUANG Xing-di. The laboratory testresearch of saturation structured soil on the structural strength [D]. Hangzhou: Zhejiang University of Technology, 2015.
[23]   张彤炜, 徐海波, 邓永锋 结构性软黏土损伤变量与扰动度的相关性研究[J]. 岩土力学, 2015, 36 (4): 958- 964
ZHANG Tong-wei, XU Hai-bo, DENG Yong-feng A study of the correlation between the damage variable anddisturbance degree of structural soft clay[J]. Rock and Soil Mechanics, 2015, 36 (4): 958- 964
[24]   HVORSLEVM J. Subsurface exploration and sampling of soils for civil engineering purposes [M]// Waterways experiment station. Vicksburg: [s.n.], 1949: 22-100.
[25]   LADD C C The strength of 'undisturbed' clay determined from undrained tests[J]. ASTM STP, 1963, 85: 361- 365
[26]   RAYMONDG P, TOWNSEND D L, LOJKASEK M J The effect of sampling on the undrained soil properties of a leda soil[J]. Canadian Geotechnical Journal, 1900, 8 (8): 546- 557
[27]   NAGARAJ T S Analysis and assessment of sampling disturbance of soft sensitive clays[J]. Géotechnique, 2003, 53 (7): 679- 683
doi: 10.1680/geot.2003.53.7.679
[28]   徐永福 土体受施工扰动影响程度的定量化识别[J]. 大坝观测与土工测试, 2000, 24 (2): 8- 10
XU Yong-fu Quantitative determination of disturbance degree of soils influenced by construction[J]. Dam Observation and Soil Testing, 2000, 24 (2): 8- 10
[29]   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 Wei-dong, WANG Hao-ran, XU Zhong-hua 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
[30]   BRINKGREVE R B J, BROERE W. Plaxis material models manual [M]. Netherlands: [s.n.], 2006.
[31]   王卫东, 王浩然, 徐中华 基坑开挖数值分析中土体硬化模型参数的试验研究[J]. 岩土力学, 2012, 33 (8): 2283- 2290
WANG Wei-dong, WANG Hao-ran, XU Zhong-hua Experimental study of parameters of hardening soil model for numerical analysis of excavations of foundation pits[J]. Rock and Soil Mechanics, 2012, 33 (8): 2283- 2290
doi: 10.3969/j.issn.1000-7598.2012.08.008
[32]   梁发云, 贾亚杰, 丁钰津, 等 上海地区软土HSS模型参数的试验研究[J]. 岩土工程学报, 2017, 39 (2): 269- 278
LIANG Fa-yun, JIA Ya-jie, DING Yu-jin, et al Experimental study on parameters of HSS model for soft soils in Shanghai[J]. Chinese Journal of Geotechnical Engineering, 2017, 39 (2): 269- 278
doi: 10.11779/CJGE201702010
[33]   徐中华, 王建华, 王卫东 主体地下结构与支护结构相结合的复杂深基坑分析[J]. 岩土工程学报, 2006, 28: 1355- 1359
XU Zhong-hua, WANG Jian-hua, WANG Wei-dong Analysis of a complicated deep excavations supported by substructures[J]. Chinese Journal of Geotechnical Engineering, 2006, 28: 1355- 1359
doi: 10.3321/j.issn:1000-4548.2006.z1.010
[34]   MEDINA D G Z. Semi-empirical method for designing excavation support systems based on deformation control [D]. Lexington: University of Kentucky, 2007.
[35]   SCHWEIGER H F. Design of deep excavations with FEM-influence of constitutive model and comparison of EC7 design approaches [C]// Proceedings of the 2010 Earth Retention Conference, ASCE. Washington: ASCE, 2010.
[36]   GAO D Z, WEI D D, HU Z X Geotechnical properties of Shanghai soils and engineering applications[J]. Marine Geotechnology and Near-shore/Offshore Structures, 1986, 923: 161- 177
[37]   ZHENG G, DU Y M, CHENG X S, et al Characteristics and prediction methods for tunnel deformations induced by excavations[J]. Geomechanics and Engineering, 2017, 12 (3): 361- 397
doi: 10.12989/gae.2017.12.3.361
[38]   王卫东, 徐中华 预估深基坑开挖对周边建筑物影响的简化分析方法[J]. 岩土工程学报, 2010, (Suppl.1): 32- 38
WANG Wei-dong, XU Zhong-hua Simplified analysis method for evaluating excavation-induced damage of adjacent buildings[J]. Chinese Journal of Geotechnical Engineering, 2010, (Suppl.1): 32- 38
[39]   上海市市政工程管理局. 上海市地铁基坑工程施工规程: SZ-08-2000 [S]. 北京: 人民交通出版社, 2000: 3.
[40]   刘庭金 地铁盾构隧道弯矩和变形控制值研究[J]. 隧道建设, 2010, (Suppl.1): 109- 112
LIU Ting-jin Study on control values of bending moment and deformation of shield-bored metro tunnels[J]. Tunnel Construction, 2010, (Suppl.1): 109- 112
[1] You-cai WAN,Lei ZHANG,Ming LI,Bin LIU,Yuan-gui MEI. Maximum dynamic equivalent leakage area while high-speed train passing through tunnels[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(4): 695-703.
[2] Guo-shou ZHAO,Rui WU,Bang-xiang CHE,Lin-lin CAO,Da-zhuan WU. Blade cavitation control by obstacles in axial-flow pump[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(4): 742-749.
[3] Yi-zhe MAO,Guo-fang GONG,Xing-hai ZHOU,Fei WANG. Identification of TBM surrounding rock based on Markov process and deep neural network[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(3): 448-454.
[4] Yun-liang CUI,Zhi-yuan LI,Gang WEI,Jiang CHEN,Lian-ying ZHOU. Pre-protection effect of underground comprehensive pipe gallery over proposed tunnel[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(2): 330-337.
[5] Hong-wei YING,Kang CHNEG,Jian-lin YU,Ri-qing XU,Zhi-jian QIU,Xiao-bo ZHAN,Jian-she QIN,Chun-hui LOU. Prediction of shield tunnel displacement due to adjacent basement excavation considering continuous deformation of ground[J]. Journal of ZheJiang University (Engineering Science), 2021, 55(2): 318-329.
[6] Guo-hui SHEN,Yu-nan BAO,Yong GUO,Gang SONG,Yi-wen WANG. Along-line wind loads and distribution patterns of transmission lines[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(9): 1658-1665.
[7] Qi WANG,Kun XIE,Yan MA,Qun CONG. Detection of DNS tunnels based on log statistics feature[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(9): 1753-1760.
[8] Fei WANG,Guo-fang GONG,Li-wen DUAN,Yong-feng QIN. XGBoost based intelligent determination system design of tunnel boring machine operation parameters[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(4): 633-641.
[9] Wei-ming HUANG,Jin-chang WANG,Ri-qing XU,Zhong-xuan YANG,Rong-qiao XU. Structural analysis of shield tunnel lining using theory of curved beam resting on elastic foundation[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(4): 787-795.
[10] Zi-xin ZHANG,Jia-qi ZHANG,Xin HUANG,Qian-wei ZHUANG. Experimental study on prediction of long-term durability of sealing gasket of shield tunnel[J]. Journal of ZheJiang University (Engineering Science), 2020, 54(1): 118-125.
[11] Hao-su LIU,Jun-qing LEI. Identification of three-component coefficients of double deck truss girder for long-span bridge[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(6): 1092-1100.
[12] Shao-heng HE,Tang-dai XIA,Lian-xiang LI,Bing-qi YU,Ze-yong LIU. Influence of groundwater seepage on deformation of foundation pits with suspended impervious curtains[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(4): 713-723.
[13] Yu-xi CHEN,Guo-fang GONG,Zhuo SHI,Hua-yong YANG. Coordinated control of gripper and thrust system for TBM based on construction data[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(2): 250-257.
[14] Yan-chao TIAN,Fei HE,Xiao ZHANG. Adaptive design of shield radius for open type hard rock TBM[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(12): 2280-2288.
[15] Xing-bo HAN,Yong-xu XIA,Yong-dong WANG,Fei YE. Probabilistic degradation model for tunnel lining flexural capacity[J]. Journal of ZheJiang University (Engineering Science), 2019, 53(11): 2175-2184.