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带接头管线变形计算的传递矩阵法
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作者单位:

1.北京交通大学土木建筑工程学院;2.北京市轨道交通建设管理有限公司;3.北京市市政工程设计研究总院有限公司

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基金项目:

国家自然科学基金项目(面上项目,重点项目,重大项目)


Transfer Matrix Method for Calculating Deformation of Jointed Pipeline
Author:
Affiliation:

1.School of Civil Engineering,Beijing Jiaotong University;2.Beijing Metro Construction Administration Corporation Ltd;3.Beijing General Municipal Engineering Design &4.Research Institute Co., Ltd

Fund Project:

National Natural Science Foundation of China

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    摘要:

    地铁隧道开挖引起邻近地下管线产生附加变形,甚至造成管线破坏。将带接头地下管线视为弹性地基梁,根据管线接头传递弯矩的性能,将接头简化为“自由铰”与“弹簧铰”。基于Winkler地基模型列出管线变形的控制微分方程,采用传递矩阵法求解,推导了管节场矩阵和管线接头点矩阵,得到关于微分方程未知边值的线性方程组。将本文方法计算结果与有限元法、经验方法和实测数据进行对比,验证了传递矩阵法的正确性。对管线变形的影响因素进行了参数分析,结果表明,对于接头变形,隧道中线与接头位置重合为最不利工况。在土质地层中,自由铰相对转角基本不受地基系数影响,因而自由铰管线易产生较大的相对转角。管节长度为1.6i时,接头相对转角出现峰值。接头相对转角的极限值为1.1Smax/i,在缺少设计资料情况下,该值可作为接头相对转角的保守估计值。

    Abstract:

    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 elastic foundation. According to the performance of pipeline joints transferring bending moment, the joints were simplified as “free hinge” and “spring hinge”. Based on Winkler’s foundation model, a governing differential equation for the pipeline deformation was given and solved by transfer matrix method. The field matrix for pipeline sections and the point matrix for pipeline joints were derived, and the linear equations about unknown boundary values of the differential equation were obtained. Comparing calculation results of this paper with finite element method, empirical method and measured data, the correctness of the transfer matrix method was verified. Parametric analysis of factors influencing pipeline deformation was carried out. Results show that, the worst situation for joint deformation is when tunnel centerline is right below the joint. The relative rotation angle of free hinge is hardly affected by foundation coefficient in the soil stratum. Therefore, the pipeline with 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 1.6i. The limit of the relative rotation angle is 1.1Smax/i. This limit can be used as a conservative estimate of the relative rotation angle in the case of shortage of design data.

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  • 收稿日期: 2020-07-16
  • 最后修改日期: 2020-08-25
  • 录用日期: 2020-09-16
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