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Transfer Matrix Method for Calculating Deformation of Jointed Pipeline

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    Excavation of subway tunnels often causes additional deformation or even damage of adjacent underground pipelines. The jointed pipeline can be regarded as a beam on an elastic foundation. The joints were simplified as "free hinge" and "spring hinge". Based on Winkler's foundation model,a governing differential equation for calculating the pipeline deformation was given and solved by the transfer matrix method. The field matrix for pipeline sections and the point matrix for pipeline joints were derived,and the linear equations for unknown boundary values of the differential equation were obtained. Case calculation and centrifugal model test were conducted and in-situ data were collected. Through comparing the calculation results of this paper with these of finite element method,as well as with in-situ data and test results,the correctness of the calculation model and the transfer matrix method was verified. Parametric analysis of the factors influencing pipeline deformation was carried out. The results show that the worst situation for joint deformation is that the tunnel centerline is right below the joint. The relative rotation angle of the free hinge is hardly affected by the foundation coefficient in the soil stratum. Therefore,the pipeline with a free hinge is easy to have a large relative rotation angle. The peak value of the relative rotation angle appears when the length of the pipeline segment is times of the width coefficient of the settlement trough. The limit of the normalized relative rotation angle is 1.1. This limit can be used as a conservative estimate of the normalized relative rotation angle in the case of a shortage of design data.

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  • Online: September 28,2021
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