带接头管线变形计算的传递矩阵法

Transfer Matrix Method for Calculating Deformation of Jointed Pipeline

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,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.收集了现场实测数据并进行案例计算和离心模型试验,将本文方法计算结果与有限元法、实测数据和试验结果进行对比,验证了计算模型和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.管节长度为沉降槽宽度系数的1.6倍时,接头相对转角出现峰值.接头归一化相对转角的极限值为1.1,在缺少设计资料情况下,该值可作为接头归一化相对转角的保守估计值.

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.