基于边界配点法浅埋隧道开挖引起 周围土体变形的分析

对于浅埋隧道施工引起土层位移的解析解，其边界条件的数学处理上比较困难，因此实际工程的应用中受到限制。为解决这一缺陷，基于弹性力学的Airy应力函数，将半无限平面内土体的应力及位移分布转化为解析函数。然后，采用边界配点的方法，控制地表处的应力边界条件( = 0， = 0)及隧道周边土体的位移边界条件( ， )。最后，采用最小二乘法，确定土体应力及位移函数的各项系数，求得浅埋隧道在周边土体产生径向位移的作用下，地表及深层土体位移的半数值半解析解。算例分析表明，该方法可以考虑任意荷载及位移作用的边界条件，能够充分发挥解析法和数值法两者的优点，且计算结果与实测结果较吻合，在预测地表及深层土层位移中具有一定的实用价值，可为进一步采取工程措施控制地层变形提供理论依据。

Response analysis of soil deformation induced by shallow tunnel excavation base on boundary collocation method

Due to its difficulty in mathematical method for boundary conditions, analytical method for soil deformation induced by shield tunneling subject to certain restrictions in the practical engineering. In order to solve this problem, Airy function in elastic mechanics is introduced to put stress and displacement distribution into analytic function in the infinite half plane. And the boundary collocation method is adopted to determine stress boundary conditions in the ground surface ( = 0， = 0) and displacement boundary conditions around tunnel ( ， ). Stress and displacement function’s coefficients can be obtained by the least square method. And the semi-numerical and semi-analytical solution could be deduced by putting the coefficients into the corresponding functions. As shown by calculation for a project case, this method can consider any boundary condition for stress and displacement, and make full use of advantages for both numerical method and analytical method. The results are consistent with the observations. So there are practical values in predicting surface settlement and deep soil deformation, so as to provide a theoretical basis for controlling soil deformation.