基于Copula理论的盾构隧道管片拼装
质量评价研究
陈思思
摘 要
随着城市化进程的不断推进，越来越多的城市开始大规模开发城市地下空间、地铁及地下综合管廊等典型城市地下基础设施建设与运营，盾构法隧道施工是地铁隧道与综合管廊建设的主要施工技术之一，管片拼装是盾构法工序的重要一步。作为盾构隧道主要支护结构的管片衬砌，管片错台、破损与开裂等管片拼装质量问题未及时解决可能出现隧道防水隐患。根据《盾构法隧道施工与验收规范GB：50446-2017》第9.3.5条，衬砌环椭圆度不得超过±5‰。现有盾构隧道椭圆度的检验参数指标为管片环的横径（Horizontal diameter，HD）与竖径（Vertical diameter，VD），以此作为盾构隧道管片拼装质量评价指标，并开展量化分析。
盾构隧道管片拼装质量呈现出一定的不确定性特征，而诸多质量不确定性因素的研究目前大多仍还是理论阐述与定性分析，不确定性因素的概率耦合效应尚无法定量表达，预制管片隧道整体的拼装质量控制决策还缺乏量化评价指标支撑。因此，利用有限的监测数据实现盾构管片拼装质量的评估，构建更加精准的管片拼装质量评价模型，对盾构隧道的施工质量评价与管控，意义尤为突出。
本文通过引入能表征多元随机变量间概率关联的Copula函数，研究盾构隧道管片拼装质量不确定性因素之间的空间分布特征及其概率分布率，实现管片拼装质量不确定性因素概率耦合效应的定量分析，并结合可靠性分析理论对盾构隧道管片拼装质量进行评估，为拼装质量控制的提供决策辅助。本文的主要研究工作如下：
（1）通过对某超大直径双线盾构隧道工程的调研，结构化搜集了该隧道左右线盾构出洞（始发）段各自前100环的管片环横径（HD）与竖径（VD）的施工人工测量记录，按左线与右线的端头加固区（有预埋件）、无加固区（负环未拆除）及无加固区（负环已拆除）分为6组，整理形成本文研究工作的实测数据样本组，为研究建立了具有工程指导意义的研究背景。
（2）建立了基于Copula理论的盾构隧道横断面椭圆度的参数二维分布模型，针对两项常用拼装质量检测指标，即：HD与VD检测数据，首先，对可分别拟合这两项指标的边缘分布函数即正态分布、威布尔分布、指数分布、伽马分布、贝塔分布，采用AIC与BIC准则，以及 
、Kolmogorov–Smirnov（K-S）和Anderson–Darling（A-D）等检验方法，分别识别出最优的边缘分布函数。其次，依次采用了Guassian、t、Plackett、FGM、AMH、Frank、No.9、Gumbel-Barnett、No.10、No.13、No.16、No.17等12种常用的Copula函数，描述HD与VD的负相关性，并采用AIC、BIC准则从常用Copula函数中识别出拟合HD与VD相关结构（correlation structure）最优的Copula函数，在此基础上，研究了Copula函数的选取对随机变量模拟、联合概率密度函数、条件累积分布函数的影响。最后以某超大直径盾构隧道试掘进段为工程背景，并以实测的6组管片HD、VD数据样本组为例验证了Copula理论方法的有效性。
（3）基于最优的Copula函数采用Kc法、Genest法、条件分布法三种方式做蒙特卡罗模拟实现了HD与VD的随机模拟对比，得出这三种模拟方法均能较好的模拟出原始监测数据的分布特征，其中Genest法与条件分布法模拟结果一致，且较Kc法效果较优的结论。
利用本文构建的二元离散相依模型，能够较为敏感的捕捉到盾构隧道管片拼装质量的变化规律，为盾构隧道管片拼装质量可靠度分析提供了更有力的支撑。
关键词：盾构隧道管片；拼装质量；Copula理论；可靠性分析
Abstract
With the continuous advancement of urbanization, more and more cities have begun to develop large-scale underground infrastructure construction and operation of urban underground space, subways and underground integrated pipe corridors. Shield tunnel construction is one of the main construction techniques for the construction of subway tunnels and integrated pipe corridors. Segment assembly is an important step in the shield process. As the lining of the main support structure of the shield tunnel, the problem of segment assembly quality such as segment misalignment, damage and cracking has not been solved in time, and there may be hidden dangers of tunnel waterproofing. According to Article 9.3.5 of the "Code for Construction and Acceptance of Shield Tunnelling Method (GB: 50446-2017)", the ellipticity of the lining ring is required to be no more than ±5‰. The test parameters of the existing shield tunnel ellipticity are the horizontal diameter (HD) and the vertical diameter (VD) of the segment ring, used as a quality evaluation index for the shield tunnel segment assembly and quantitative analysis.
The quality of shield tunnel segment assembly presents certain uncertainties, and most of the research on quality uncertainty factors are still theoretical and qualitative analysis, and the probability coupling of uncertainty factors. The effect can’t be quantitatively expressed, and the overall quality control decision of the prefabricated segment tunnel is still lacking quantitative evaluation index support. Moreover, the research on the quality control of such shield tunnel construction is insufficient. As the diameter of the shield tunnel increases, the problem will become more and more prominent. Therefore, the use of limited monitoring data to achieve the assessment of the quality of shield segment assembly, the significance is particularly prominent .to build a more accurate segment assembly quality evaluation model, the construction quality evaluation and control of shield tunnels.
This paper introduces the Copula function which can characterize the probability correlation between multivariate random variables, and studies the spatial distribution characteristics and probability distribution rate of the assembly quality uncertainty factors of shield tunnel segments, and realizes the probability coupling of the uncertainty of segment assembly quality. The quantitative analysis of the effect, combined with the reliability analysis theory, evaluates the assembly quality of the shield tunnel segment and provides decision-making assistance for the assembly quality control.The main research work of this paper is as follows:
(1) Through the investigation of a super-large diameter double-line shield tunnel project, the horizontal and vertical diameter (HD) and vertical diameter of the segment ring of each of the first 100 rings of the left and right lines of the tunnel are collected. (VD) construction manual measurement records, according to the left and right line end reinforcement area (with embedded parts), no reinforcement area (negative ring not removed) and no reinforcement area (negative ring has been removed) are divided into 6 groups, finishing the research work The measured data sample group has established a research background with engineering guiding significance for the research.
(2) The two-dimensional distribution model of the cross-section ellipticity of shield tunnel based on Copula theory is established. For the two common assembly quality inspection indicators, namely: HD and VD detection data, firstly, the edge distribution functions, ie Normal, Weibull, Exponential, Gamma and Beta distribution function, which can fit the two indexes respectively, are identified by AIC and BIC criteria and Kolmogorov–Smirnov (KS) and Anderson–Darling (AD) test methods to identify the optimal edge distribution function. Secondly, 12 commonly used Copula functions such as Guassian, t, Plackett, FGM, AMH, Frank, No.9, Gumbel-Barnett, No.10, No.13, No.16, No.17 are used in sequence to describe HD. The negative correlation with VD, and the Copula function which fits the optimal correlation structure between HD and VD is identified from the commonly used Copula function by AIC and BIC. On this basis, the selection of Copula function is studied. The effects of variable simulation, joint probability density function, and conditional cumulative distribution function. Finally, the test section of a super-large diameter shield tunnel is taken as the engineering background, and the effectiveness of Copula theory is verified by taking the measured HD and VD data samples of 6 sets of segments.
(3) Based on the optimal Copula function, Monte Carlo simulation is performed by Kc method, Genest method and conditional distribution method to realize the random simulation comparison between HD and VD. It is concluded that the three simulation methods can well simulate the distribution characteristics of the original monitoring data, and the Genest method is consistent with the conditional distribution method and the results are better than the Kc method.
By using the two-dimensional discrete correlation model constructed in this paper, the variation law of the assembly quality of shield tunnels can be sensitively captured, which provides more powerful support for the analysis of the quality reliability of shield tunnel subway tunnel assembly.
Key words：Shield tunnel segment; Assembly quality; Copula theory; Reliability analysis
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