考虑轴力的管线变形控制微分方程及其优化解  

Governing differential equations and optimal solution for deformation of jointless pipeline considering axial force

作　　者：程霖[1] 杨成永[1] 王伟 马文辉[1] CHENG Lin;YANG Chengyong;WANG Wei;MA Wenhui(School of Civil Engineering,Beijing Jiaotong University,Beijing 100044,China;No.5 Engineering Corporation Limited of CR20G,Kunming 650200,China)

机构地区：[1]北京交通大学土木建筑工程学院,北京100044 [2]中铁二十局集团第五工程有限公司,云南昆明650200

出　　处：《华中科技大学学报（自然科学版）》2021年第3期126-132,共7页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51278044,51478032)。

摘　　要：为计算地铁施工引起的既有管线附加变形,将地埋管线视为弹性地基梁,受到地层竖向和水平位移荷载作用,考虑管线变形的几何非线性,建立了管线变形的控制微分方程组.采用优化方法进行模型求解,进行了案例计算和离心模型试验.将有限元解和试验结果同优化解进行了对比,验证了优化方法的正确性.分析了地层水平位移和几何非线性对管线变形和内力的影响.结果表明:管土摩擦系数较小时,管线在开挖影响范围内全长受拉.管土摩擦系数较大时,管线在隧道开挖中线附近受压,在其余范围内受拉,在管线变形计算中应同时考虑压应变和拉应变.较大的地层沉降使管线变形呈现几何非线性,表现为管线竖向位移引起管线轴向伸长,且管线弯曲变形与轴向变形存在一定的相互影响.In order to calculate the additional deformation of existing pipeline caused by subway construction,the pipeline was regarded as an elastic foundation beam which is subjected to vertical and horizontal displacement loads of soil. Considering geometric nonlinearity of the pipeline,governing differential equations were established and solved by optimization method. Case calculation and centrifugal model test were conducted. Finite element solution and test results were compared with the optimal solution,which verifies the correctness of the optimal method. The effects of horizontal displacement of soil and geometric nonlinearity on pipeline deformation and internal forces were analyzed. Results show that,when frictional coefficient between pipeline and soil is small,only tension occurs in the pipeline.When frictional coefficient is large,the pipeline will be compressed in the middle of the settlement trough of tunnel excavation and will be extended at two sides. The compressive and tensile strain of pipeline should be considered simultaneously in the case of large frictional coefficient between pipeline and soil. Geometric nonlinearity in pipeline deformation appears at large soil subsidence,where vertical displacement of pipeline causes its axial elongation.There exists interaction between deflection and axial deformation of pipeline.

关 键 词：地埋管线 轴向变形 地层水平位移 优化解 几何非线性 

分 类 号：U455[建筑科学—桥梁与隧道工程]