匀质地下管线沉降的傅里叶级数解

发布时间：2018-06-10 10:18

本文选题：隧道工程 + 地下管线　；参考：《中国铁道科学》2017年02期

【摘要】：采用傅里叶级数方法求解地铁盾构隧道开挖引起邻近匀质地下管线沉降较大的问题。假设管线轴向伸长只发生在沉降槽附近并在此范围内是一常量,合理降低控制微分方程的非线性程度,使之能够采用级数法求解。按照土层沉降曲线符合Peck曲线推导管线沉降的傅里叶级数系数的显式表达式,得到管线沉降和内力的计算方法。根据文献[11]的数据,采用基于傅里叶级数的计算方法计算管线随土层沉降的级数解,并与文献[11]中的近似解方法的求解结果对比,验证级数解的正确性。结果表明:在土层沉降曲线为Peck曲线的情况下,管线沉降曲线也符合Peck曲线;近似解与级数解非常接近,两者能够良好地相互印证;级数解的求解过程表明,基于傅里叶级数的求解方法不需要事先假定管线沉降曲线的形式,并且可以处理不同的荷载类型,如集中荷载、局部而非全长范围的土层抗力等;可以通过增加级数的项数达到要求的计算精度。
[Abstract]:Fourier series method is used to solve the problem of large settlement of adjacent homogeneous underground pipeline caused by excavation of shield tunnel. Assuming that the axial elongation of the pipeline only occurs near the settlement trough and is a constant in this range, the nonlinear degree of the governing differential equation is reduced reasonably, and the series method is used to solve the problem. According to the Peck curve, the explicit expression of Fourier series coefficient of pipeline settlement is derived, and the calculation method of pipeline settlement and internal force is obtained. According to the data of reference [11], the series solution of pipeline settlement with soil layer is calculated by using the method of Fourier series, and the result is compared with the approximate solution method in reference [11] to verify the correctness of the series solution. The results show that when the settlement curve of soil layer is Peck curve, the pipeline settlement curve also accords with Peck curve, the approximate solution is very close to the series solution, and the two solutions can be confirmed each other well. The method based on Fourier series does not need to presuppose the form of pipeline settlement curve, and it can deal with different load types, such as concentrated load, local but not full-length soil resistance and so on. The required accuracy can be achieved by increasing the number of terms of the series.
【作者单位】：北京交通大学土木建筑工程学院;北京城市快轨建设管理有限公司;
【基金】：国家自然科学基金资助项目(51278044,51478032)
【分类号】：U455.43;TU990.3

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