A simplified model for coupled horizontal and rocking vibrations of embedded foundations

For a foundation–soil system undergoing coupled horizontal and rocking motions, a simplified mass–spring–dashpot model is proposed to simulate unbounded soil. Through three equivalent criteria, a group of equivalent models are established for the foundation–soil system. An optimal equivalent model is then determined to represent the best simplified model. The method proposed to develop the optimal equivalent model may be more efficient than lengthy optimization techniques used by most existing models. The dynamic responses of the foundation–soil system using the optimal equivalent model are compared with those obtained by the half-space theory and by the existing lumped-parameter models. A validation of the proposed model in time domain is also provided. Since the coupling of horizontal and rocking motions is adequately considered, the optimal equivalent model is found to have more accurate results than most existing models. It is also found that the rotational responses of embedded foundations subjected to a harmonic rocking moment may be significantly underestimated without considering the coupling behavior. This proposed method may be effectively applied to practical engineering problems.

► A simple model is proposed to simulate the dynamic behavior of soil.
► The proposed model is validated with theoretical solutions and existing models.
► The proposed model may be applied to practical foundation vibration analysis.