Combination rule for critical structural response in soft soil

This work studies the problem of combining the seismic effects on structures caused by the simultaneous action of two horizontal orthogonal components of ground motion. In accordance with the random vibrations theory, several analytical expressions were developed to combine the two horizontal orthogonal seismic effects in order to estimate the elastic bi-directional peak response. The main hypothesis made in the development of these expressions was that the Fourier amplitude spectrum for the two orthogonal components of ground motion could be represented by a Dirac's delta. This hypothesis is supported by the observed characteristics of ground motions of earthquakes recorded in soft soils. Through the fully bi-directional elastic “step-by-step” analysis of different structural models, the accuracy of the proposed method was verified, in contrast with different combination rules. The exposed procedure explicitly considers the angle of the earthquake incidence and the type of response in terms of the direction of its components (orthogonal or collinear).