Mechanism and bounding of earthquake energy input to building structure on surface ground subjected to engineering bedrock motion

• Mechanism of earthquake energy input to soil–structure interaction systems is clarified.
• The input energy to a swaying–rocking model under white input is constant regardless of soil property.
• The proposed upper bound of energy is a reasonable bound of the actual one for all soil types.
• The proposed theory can be used for models with uncertain soil stiffness and damping.
• Extension of the theory to a general input at engineering bedrock can be made.

The mechanism of earthquake energy input to building structures is clarified by considering the surface ground amplification and soil–structure interaction. The earthquake input energies to superstructures, soil–foundation systems and total swaying–rocking system are obtained by taking the corresponding appropriate free bodies into account and defining the energy transfer functions. It has been made clear that, when the ground surface motion is white, the input energy to the swaying–rocking model is constant regardless of the soil property (input energy constant property). The upper bound of earthquake input energy to the swaying–rocking model is derived for the model including the surface ground amplification by taking full advantage of the above-mentioned input energy constant property and introducing the envelope function for the transfer function of the surface ground amplification. Extension of the theory to a general earthquake ground motion model at the engineering bedrock is also made by taking full advantage of the above-mentioned input energy constant property.