SOLUTION OF THE DYNAMIC RESPONSE OF RIGID FOUNDATION OF ARBITRARY SHAPE ON MULTI-LAYERED SOIL

An approach based on integral transformation, dual form of wave motion equation and precise integration method is proposed for the solution of the dynamic stiffness matrices of rigid foundation of arbitrary shape on multi-layered half-space. Firstly, to take advantage of the axisymmetric property of the load-displacement field of subdisk-element in cylindrical coordinates, the equation of Green's influence function for multi-layered half-space is formulated. Then the dual form of the uncoupled wave motion equation in the frequency-wave number domain for in-plane motion and out-of-plane motion is established. It can be solved quite accurately by the precise integration method. Finally, the contact interface between the rigid foundation and the multi-layered half-space is discretized into a number of subdisk-elements, and the matrix-equation of translational and rotational dynamic stiffnesses of the foundation is evaluated. The proposed method is efficient, accurate and computationally stable. It is well suited to the dynamic interaction analysis of rigid foundation of arbitrary shape on complex multi-layered half-space. Numerical examples clearly demonstrate the superiority of the proposed approach.