Design implications of the vertical pseudo-static coefficient in slope analysis

Most design manuals and codes recommend a simple pseudo-static (PS) approach for analysis of slope stability under seismic conditions. Exceptions to this recommendation include problems involving liquefaction, and exceptionally large earthquakes. These extreme situations are not considered in the present work. Most codes neglect the vertical component of the PS force. The rational basis for this practice has not been properly established in the professional literature, and the main purpose of the present work is to check the validity of this assumption. The analysis is based on the realization that the direction (up or down), of the vertical PS force of a future earthquake cannot be predicted, so the designer must consider the direction leading to a minimum safety factor. It is shown that under most conditions the vertical PS force has significant effect on slope stability, and neglecting this force leads to over estimation of safety factors. An analytical solution of the PS stability problem in cohesionless material shows that in this case the critical conditions are realized when the vertical PS force acts opposite to the direction of gravity. In such materials the errors introduced by neglecting the vertical pseudo-static forces may be considered acceptable. A strength reduction numerical procedure was used to solve PS stability problems in a frictional-cohesive material. These solutions show that for steep slopes the critical vertical PS force acts in the direction of gravity, but for small slope inclinations the critical direction of this force is upwards. The errors in safety factors introduced by the common practice of neglecting vertical PS forces are proportional to the absolute value of the ratio between vertical and horizontal pseudo-static coefficients. These errors are relatively small for intermediate slope inclinations, but they become unacceptable for very steep and very gentle slopes.