刚性环梁支撑圆形基坑支护结构变形解析解

将圆形基坑支护结构视为弹性圆柱壳，利用广义Delta函数和Heaviside函数，基于圆柱薄壳轴对称弯曲变形的控制方程，利用Laplace变换及其逆变换，得到了具有任意数目刚性环梁支撑的圆形深基坑支护结构变形的解析解．在此基础上，以某一圆形基坑工程为背景，分析了基坑底部混凝土底板、支护结构底部边界条件、基坑开挖深度以及支护结构的几何和物理参数等对支护结构变形和内力分布的影响，结果表明：随着基坑半径和挖掘深度的增大，支护结构的位移和内力增大，但随着支护结构厚度的增加，径向位移减小，而内力增加．同时，随着支护结构弹性模量的增加，基坑位移减小，但内力几乎没有变化，这些结果为圆形基坑支护结构设计提供了理论依据和指导．

Analytical Solution for Deformation of Circular Foundation Pit Support Structure Supported by Rigid Ring Beam

The circular foundation pit support structure is regarded as an elastic cylindrical shell. Using the generalized Delta function and Heaviside function, based on the governing equation of the axisymmetric bending deformation of the cylindrical thin shell and using the Laplace transform and its inverse transform, the analytical solution of deformation of the circular deep foundation pit supporting structure with any number of rigid ring beams is obtained. On this basis, taking a circular foundation pit as the background, the influences of the bottom concrete floor of the foundation pit, the bottom boundary conditions of the support structure, the excavation depth of the foundation pit, and the geometric and physical parameters of the support structure on the deformation and internal force distribution of the support structure are analyzed. The results show that with the increase of the excavation depth and the radius of the foundation pit, the displacement and the internal forces of the supporting structure increase. With the increase of the thickness of the supporting structure, the radial displacement decreases, while the internal forces increase. At the same time, with the increase of the elastic modulus of the support structure, the displacement of the foundation pit decreases, while the internal forces hardly change. These results provide theoretical basis and guidance for the design of the circular foundation pit support structure.