Fourier amplitudes of the foundation motion connected with soil-structure interaction

The main objective of this study is to understand the phenomena connected with the interaction and to give directions for improvement of the design of the earthquake resistant structures. Fourier amplitudes (amplitudes versus frequencies) of the foundation motion connected with the soil-structure interaction and differential motions of the foundation-structure contact due to the wave passage are considered. We expect that the motion of the flexible foundation will be larger than the existing solutions for the motion of the rigid foundation. As the foundation becomes stiffer, the Fourier amplitudes (transfer functions) on the building-foundation contact will decay and will approach the solution for the case of rigid foundation. The wave propagation approach in solving the problem is taken into account. The wave equation will be solved numerically in the domain consisting of the soil, foundation, and superstructure using the explicit Lax-Wendroff numerical scheme. Because in the real world, the problem is defined in infinite domain in the soil, we will incorporate an artificial boundary in the truncated domain which corresponds with the Sommerfeld radiation boundary condition at infinity. The velocities and the displacements at the points of the stress-free boundaries will be updated in each time step using the vacuum formalism approach. The stresses, the velocities, and the displacements at the points of soil-foundation and foundation-building contacts will be computed from the continuity of stresses and the continuity of displacements at those points. In present time the soil-structure interaction is underestimated as a factor in the codes and the standards for design of earthquake resistant structures.