Frequency-domain analysis of earthquake input energy to structure–pile systems

A new frequency-domain method is developed for evaluating the earthquake input energy to a structure–pile system or a super-structure alone subjected to a horizontal ground motion at an outcropping engineering bedrock surface. An efficient continuum model consisting of a dynamic Winkler-type soil element and a pile is used to express the dynamic behavior of the structure–pile system with an acceptable accuracy. It is shown that the formulation of the earthquake input energy in the frequency domain is essential for including the frequency-dependent vibration property of the surface ground in terms of the wave propagation theory and the frequency-dependent property of the dynamic Winkler-type soil element around the pile. It is also demonstrated that (1) the present formulation is effective for various input levels and various ground properties and (2) the energy input mechanism or energy flow in the building structure–pile system can be well described by the newly introduced energy transfer function (F-function). A new concept, called input energy densities at various underground levels, is introduced to disclose the energy input mechanism and energy flow in the building structure–pile system.