用子结构法将上部结构向边界凝聚，得上部结构的控制方程．筏板的控制方程由薄板理论和虚位移原理得到．利用层状粘弹性饱和土表面作用垂直载荷的基本解和筏板与地基的变形协调条件，可以得到筏板和地基相互作用的控制方程．对上述控制方程进行Laplace变换，得到变换域内的控制方程．求解上述变换域内的方程并进行相应的逆变换，则可求解出共同作用问题．

By using substructure method, the superstructure can be condensed to the interface of the superstructure and the raft, and the governing equation of the superstructure is obtainable. The governing equations of the raft are obtained based on the thin plate theory and the virtual work principle. By employing the elementary solution of the vertical force applied on the surface of the layered viscoelastic saturated soil and the compatibility conditions between the raft and the layered soil, the governing equation of the interaction between soil and raft is established. Laplace transform is applied to the obtained governing equations and the governing equations in transformed domain are gotten. Solving the governing equations in transformed domain and applying the corresponding inverse transform, the proposed interaction problem can be solved.