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Journal of ZheJiang University (Engineering Science)  2019, Vol. 53 Issue (11): 2175-2184    DOI: 10.3785/j.issn.1008-973X.2019.11.016
Civil Engineering, Municipal Engineering     
Probabilistic degradation model for tunnel lining flexural capacity
Xing-bo HAN1,2(),Yong-xu XIA1,*(),Yong-dong WANG1,Fei YE1
1. School of Highway, Chang’an University, Xi’an 710064, China
2. School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2552, Australia
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Abstract  

A reliability analysis framework with the consideration of the time influence and the uncertainties of the parameters was established. A time-variant flexural capacity model was obtained by considering the reduction of the cross-sectional area of the steel bar and the decrease of the bond strength of the steel-concrete caused by environmental erosion. A time-variant probabilistic model was established with the consideration of the uncertainties of the parameters. Accuracy and computational efficiency of the theoretical approach were investigated by using Monte-Carlo simulation (MCS) method. The distribution of the flexural capacity was also discussed through the analysis of the simulation results. The load model of the reliability analysis was established using the finite element analysis with the load reverse and stress release method. The joint committee (JC) method was used to form the degradation reliability analysis framework of the lining flexural capacity calculation. The influence of the chloride erosion on the lining time-variant and probabilistic flexural capacity was investigated by an engineering case. Results show that mean value and standard deviation of the flexural capacity both decrease with the increase of the time. The simulation data has a better agreement with the lognormal distribution than with the normal distribution when both normal and lognormal distributed variables exist. The reliability of the lining subjected to negative bending moment is higher than that of the positive bending moment.



Key wordstunnel lining      flexural capacity      reliability degradation model      finite element method-Monte-Carlo simulation      statistics characteristics     
Received: 02 July 2018      Published: 21 November 2019
CLC:  U 451  
Corresponding Authors: Yong-xu XIA     E-mail: Xingbo.han@chd.edu.cn;yongxuxia@126.com
Cite this article:

Xing-bo HAN,Yong-xu XIA,Yong-dong WANG,Fei YE. Probabilistic degradation model for tunnel lining flexural capacity. Journal of ZheJiang University (Engineering Science), 2019, 53(11): 2175-2184.

URL:

http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2019.11.016     OR     http://www.zjujournals.com/eng/Y2019/V53/I11/2175


隧道衬砌抗弯承载能力概率劣化模型

提出同时考虑时间效应与参数不确定性的隧道衬砌可靠度分析框架. 考虑衬砌受环境侵蚀引起的钢筋截面面积减少以及钢筋-混凝土黏结力下降,得到其抗弯承载能力时变模型. 考虑模型中参数不确定性,建立时变概率模型. 采用蒙特卡洛模拟(MCS)方法对理论模型的准确性以及计算效率进行验证. 分析模拟结果,对抗弯承载能力的分布进行讨论. 通过有限元分析,使用反转应力荷载释放法得到可靠度分析的荷载模型. 采用当量正态化(JC)法,构建隧道衬砌抗弯承载能力劣化可靠度分析框架. 通过算例对地下水氯离子侵蚀下衬砌抗弯承载能力的时变概率特征进行研究. 结果表明,随时间增长抗弯承载力的均值和标准差均减小;当初始计算变量同时存在正态变量与对数正态变量时,抗弯承载力计算结果更服从对数正态分布;衬砌负弯矩区域可靠度远高于正弯矩区域.


关键词: 隧道衬砌,  抗弯承载能力,  可靠度劣化模型,  有限元-蒙特卡洛模拟,  统计特征 
Fig.1 Schematic diagram of flexural capacity calculation
Fig.2 Schematic diagram of detailed information of test beams
编号 fcd/MPa fsd/MPa η/% Pm/kN Ps/kN
Φ12 Φ18 上缘 下缘
1 34.55 359.6 366.7 1.14 4.10 172 168.7
2 34.55 359.6 366.7 1.07 12.90 139 102.9
3 34.55 359.6 366.7 0.85 6.10 144 149.3
Tab.1 Model parameters and comparison between experimental and theoretical results
Fig.3 Flow chart of lining degradation reliability calculation
Fig.4 Bar distribution of lining section
参数 分布类型 均值 变异系数 备注
fcd/MPa 对数正态 18.4 0.12 JCSS(2012)
As/mm2 对数正态 1 900 0.05 JCSS(2012)
Es/MPa 正态 200 0.15 JCSS(2012)
a′s/mm 正态 65 0.10 JCSS(2012)
h/mm 正态 500 0.05 JCSS(2012)
d/mm 正态 22 0.05 JCSS(2012)
Jin/(μA·cm?2 正态 0 0.10 假定
Jout/(μA·cm?2 正态 0.5 0.10 文献[4]
Tab.2 Calculation parameters of degraded flexural capacity
Fig.5 Time-variant flexural capacity statistical parameters
Fig.6 Frequency histogram and probability curve of flexural capacity (positive moment)
Fig.7 Frequency histogram and probability curve of flexural capacity (negative moment)
Fig.8 Flexural capacity statistical characteristics (positive moment)
Fig.9 Flexural capacity statistical characteristics (negative moment)
Fig.10 Calculation result of lining force
Fig.11 Three-dimension surface of lining reliability index of flexural capacity with time and angle
Fig.12 Reliability index and failure probability at 160 degree
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