Bound of earthquake input energy to building structure considering shallow and deep ground uncertainties

The bound of earthquake input energy to building structures is clarified by considering shallow and deep ground uncertainties and soil-structure interaction. The ground motion amplification in the shallow and deep ground is described by a one-dimensional wave propagation theory. The constant input energy property to a swaying-rocking model with respect to the free-field ground surface input regardless of the soil property is used effectively to derive a bound. An extension of the previous theory for the engineering bedrock surface motion to a general earthquake ground motion model at the earthquake bedrock is made by taking full advantage of the above-mentioned input energy constant property. It is shown through numerical examples that a tight bound of earthquake input energy can be derived for the shallow and deep ground uncertainties.