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.