Fourier Series Solution for Deformation of Buried Jointed Pipelines

DOI：

 作者 单位 程霖1?覮，杨成永1，李延川2，马文辉1 （1.北京交通大学 土木建筑工程学院，北京 100044；2.北京城建设计发展集团股份有限公司，北京 100037）

地铁隧道开挖将引起地下管线产生附加变形，造成管线的破坏.将带接头地下管线视为弹性地基梁，引入“相当荷载”改进匀质管线变形的控制微分方程，使之能够考虑接头处的刚度折减.采用傅里叶级数解法求解控制微分方程，得到未知傅里叶级数系数的表达式，进而得到关于管线接头相对转角的线性方程组.假定地层变形符合Peck曲线，将基于傅里叶级数法得到的计算结果与数值模拟方法进行对比，验证了方法的正确性.计算结果表明，在地层位移荷载作用下，管线产生变形，管线接头处产生明显转动.地层沉降对距隧道开挖中线3i（i为沉降槽宽度系数）以外的管线影响较小，该区域内接头相对转角远小于容许值，在计算时可不作考虑，以减少未知量的数目.当某个管线接头位于隧道开挖中心的正上方时，该接头处将产生最大的相对转角，因此在缺少管线接头位置资料的情况下，可假定某个管线接头与隧道开挖中线重合，以得到接头相对转角的保守计算值.

The excavation of subway tunnel will induce the extra deformation or even damage of pipelines that lies above. The jointed pipeline was regarded as a beam on elastic foundation. By introducing the equivalent loads to consider the reduction of rigidity at joints， the governing differential equation for the deformation of jointed pipeline was established. Fourier series method was used to solve the governing differential equation. Expressions of the unknown coefficients of Fourier series were derived， and then a set of linear equations for determining relative joint rotations was obtained. Meanwhile， assuming that the soil settlement fits a Peck curve， the settlement of pipeline was computed and compared with that obtained from numerical simulation， which verifies the correctness of the Fourier series method. Results show that， with the loading of soil displacement， the pipeline deforms and rotates largely around its joints. The settlement of soil has small influence on pipe segments beyond 3i (where i is the width of settlement trough)， where joints can be ignored to reduce unknowns because relative joint rotations are far less than the tolerant value. When a joint is located above the excavation center， the soil subsidence can induce the maximum relative rotation at this joint. Therefore， if the locations of joints are unknown， one joint can be set right above the tunnel centerline in order to assure a conservative result.