Response of unbounded soil in scaled boundary finite element method. - Wolf, John P. (Earthquake engineering & structural dynamics.)
The scaled boundary finite element method is a powerful semi analytical computational procedure to calculate the dynamic stiffness of the unbounded soil at the structure soil interface. This permits the analysis of dynamic soil structure interaction using the substructure method. The response in the neighbouring soil can also be determined analytically. The method is extended to calculate numerically the response throughout the unbounded soil including their field. The three dimensional vector wave equation of elasto dynamics is addressed. The radiation condition at infinity is satisfied exactly. By solving an eigenvalue problem, the high frequency limit of the dynamic stiffness is constructed to be positive definite. However, a direct determination using impedances is also possible. Solving two first order ordinary differential equations numerically sequentially, leading to the displacements in the unbounded soil. A generalization to viscoelastic material using the correspondence principle is straightforward. Alternatively, the displacements can also be calculated analytically in the far field. Good agreement of displacements along the free surface and below a prism foundation embedded in a half space with the results of the boundary element method is observed.