A limit equilibrium method to compute both dynamic bearing capacity and earthquake-induced settlements of foundations on soils using a log spiral potential failure surface is presented in this paper. The method is limited to soil materials that conform to the Mohr-Coulomb criterion. Time-varying inertia forces can be applied directly to the building. The procedure is capable of estimating vertical displacements and foundation tilting by integrating the differential equation developed from equilibrium of acting and resisting moments. The reliability of the method is assessed by comparing calculated and observed permanent movements of foundations for the September 1985 Earthquake in the soft ground area of Mexico City. The position of the failure surface is obtained by a minimization process at every time increment during the shaking. Results show that when an earthquake occurs the potential failure surface, obtained from static load, moves upwards and its length shortens as the seismic accelerations increase, reducing the bearing capacity and thus increasing its seismic risk. In this paper, the influence of earthquake acceleration on the time-varying positions of the potential failure is shown graphically.