匀质地下管线大变形的控制微分方程及其近似解  

Governing Differential Equation and Approximate Solution for Large Deformation of Jointless Underground Pipeline

作　　者：杨成永[1] 张彦斌[1] 张伦政[1] 

机构地区：[1]北京交通大学土木建筑工程学院,北京100044

出　　处：《中国铁道科学》2014年第1期42-46,共5页China Railway Science

基　　金：国家自然科学基金资助项目(51278044)

摘　　要：从杆件变形的空间曲线运动方程出发,引入物性方程,建立管线大变形的控制微分方程。忽略管线截面形状的改变并假设管线的轴向变形在沉降槽范围内为一常量,从而得到简化的控制微分方程。在假定土层和管线的沉降均符合正态分布曲线条件下,给出简化控制微分方程的近似解法,并推导出管线轴力和一维度规的计算公式。实例计算和对比分析结果表明:在管线和土层的沉降较小时,大变形解与小变形解基本相等,轴力的影响可以忽略;但当管线和土层的沉降较大时,轴力的影响变得明显;轴力增加了管线抵抗竖向变形的能力,因此管线沉降、弯矩和剪力的大变形解均比小变形解要小;随着沉降的增加,管线轴力和一维度规呈非线性地增大,小变形解的计算误差也迅速增大。说明本文方法能够更合理地描述管线与土层的共同作用。Based on the kinetic equation of a spatial elastica of member deformation and by introducing constitutive equation,the governing differential equation for the large deformation of underground pipeline was established.Regardless of the change in the section shape of pipeline and assuming the axial deformation of the pipe a constant within the settlement trough,the governing differential equation was simplified.Under the assumption that the settlement of soil layer and pipeline accords with normal distribution curve,an approximate solution to the simplified governing differential equation was proposed,and the formulae to compute the axial force and one-dimensional gauge of the pipeline were derived.Example calculations and comparative analyses show that,when the settlement of soil layer and pipeline is smaller,the solution by large deformation formula is almost the same with that by small deformation formula.The influence of axial force can be neglected.However,when the settlement of soil layer and pipeline is larger,the influence of axial force becomes prominent.The axial force strengthens the ability of the pipeline against vertical deformation.Therefore,the solutions to the settlement,bending moment and shear force of pipeline by large deformation formula are all smaller than those by small deformation formula.As the settlement increases,both the axial force and one-dimensional gauge of the pipeline increase nonlinearly,while the calculation error of small deformation formula goes up rapidly.It indicates that the suggested method can more rationally describe the interactions between pipeline and soil layer.

关 键 词：地下管线 地层沉降 大变形力学方法 控制微分方程 管线轴力 

分 类 号：U451[建筑科学—桥梁与隧道工程]