Design of slopes and analysis of existing slopes subjected to seismic shaking are carried out routinely using approximations of plane strain and substitution of a quasi-static load for the seismic excitation. A three-dimensional ͑3D͒ analysis of slopes is carried out, based on the kinematic theorem of limit analysis. A rotational failure mechanism is used with the failure surface in the shape of a curvilinear cone sector passing through the slope toe, typical of steep slopes. A quasi-static approach is used to develop stability charts allowing assessment of the factor of safety of slopes without the need for an iterative procedure. The charts are of practical importance in cases of excavation slopes and whenever a slope is physically constrained, preventing a plane failure.

Design of slopes and analysis of existing slopes are carried out routinely using approximations of plane strain and substitution of quasi-static load for the seismic excitation. A three-dimensional analysis of slopes is used here, based on the kinematic theorem of limit analysis. A 3D rotational mechanism with a failure surface passing through the slope toe was developed, applicable to steep slopes. A quasi-static approach is used and an example of charts for the assessment of the factor of safety for slopes with predefined width of the failure mechanism is shown. Critical acceleration is also calculated for 3D slopes, and a sliding block analysis is carried out to develop a solution for displacements of slopes subjected to seismic excitation.