Seismic settlements of shallow foundations: a sliding block approach

Allowing the seismic bearing capacity of shallow foundations to be momentarily exceeded during extreme earthquake events can function as a mechanism of natural seismic isolation that is beneficial for the superstructure. However, this effect comes at the price of accumulating foundation settlements, which also need to be accounted for in the performance-based design process. Although the seismic bearing capacity of footings can be estimated with reasonable accuracy, there is still no widely approved methodology to calculate the associated seismic settlements. This paper attempts to address this issue through an extension of Newmark’s sliding block analysis, where the footing is modeled as a rigid block on a horizontal surface, with the block-base friction being a function of the critical seismic acceleration to trigger bearing capacity failure. When the block is subjected to an earthquake excitation and the frictional resistance is exceeded, an accumulating vertical displacement is also calculated, proportional to the amount of horizontal sliding. In the case of symmetric motions, this occurs twice per cycle and vertical settlements accumulate even when the residual horizontal displacement is zero. For quick applications, a semi-analytical factor is derived, correlating the settlements predicted by the proposed model to the residual horizontal displacements of a conventional rigid block sliding on an inclined plane, under the same input motion and with the same critical acceleration. This factor can be used in combination with well-established empirical relations for seismic displacements of slopes and retaining walls, thus extending their applicability to cover the response of shallow foundations.