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