下穿工程中轨道大变形沉降的级数解法

依托某段下穿铁路工程，基于文克尔弹性地基梁模型，考虑梁土间的摩阻力，将路基沉降作为非线性边界条件，建立轨道大变形沉降的控制微分方程，并采用傅里叶级数法进行求解；建立数值模型得到数值解，并与级数解、余弦函数解进行对比分析。结果表明:级数解与数值解所得的轨道沉降曲线的相关系数（大于99.00 %）更高，且最大轨道沉降差值仅为数值解轨道最大沉降的0.62 %和0.84 %，级数解法精度更高，在轨道沉降无法直接测量的情况下，利用理论计算所得轨道沉降曲线可很好地反映和预测轨道的沉降情况，从而保证铁路正常运营。

A Series Solution for Large Deformation Settlement of Track in Underpass Engineering

In relation to a certain section of the underpassing railway project, based on the Winkel elastic foundation beam model, considering the friction resistance between the beam and soil, and taking the subgrade settlement as the nonlinear boundary condition, the control differential equation for the large deformation settlement of the track is established, and the Fourier series method is used to solve. The numerical model is established to obtain the numerical solution, which is compared with the series solution and the cosine function solution. The results show that the correlation coefficient (greater than 99.00 %) of the track settlement curve obtained by the series solution and the numerical solution is higher, and the maximum track settlement difference is only 0.62 % and 0.84 % of the maximum track settlement of the numerical solution, and the accuracy of the series solution is better. When the track settlement cannot be directly measured, the track settlement curve obtained by theoretical calculation can well reflect and predict the track settlement, so as to ensure the normal operation of the railway.