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Traditional methods for calculations of active loads on retaining structures provide dependable forces, but these methods do not indicate reliably the location of the resultant load on the walls. The Coulomb method does not address the load distribution because it utilizes equilibrium of forces, whereas the Rankine stress distribution provides linear increase of the load with depth. Past experimental studies indicate intricate distributions dependent on the mode of displacement of the wall before reaching the limit state. The discrete element method was used to simulate soil-retaining structure interaction, and force chains characteristic of arching were identified. Arching appears to be the primary cause affecting the load distribution. A differential slice technique was used to mimic the load distributions seen in physical experiments. The outcome indicates that rotation modes of wall movement are associated with uneven mobilization of strength on the surface separating the moving backfill from the soil at rest. Calculations show that the location of the centroid of the active load distribution behind a translating wall is approximately 0.40 of the wall height above the base, but for a wall rotating about its top point, the location of the resultant is at approximately 0:55H. In the third case, rotation about the base, the location of the calculated centroid of the stress distribution on the wall is slightly below one-third of the wall height.

Seismic excitation is among the many possible factors contributing to slope failures. Typical design of slopes and analyses of existing slopes are carried out assuming plane strain mechanisms of deformation, and replacing the seismic loading with a uniformly distributed static force. A three-dimensional (3D) analysis of slopes is described in this paper, based on the kinematic theorem of limit analysis. Critical acceleration is calculated for 3D slope failures, and an analysis of a rotating block is executed to develop a solution for displacements of slopes subjected to seismic shaking. The emphasis is more on applying the displacement analysis to a 3D collapse pattern, and less on the choice of ground motion records suitable for the 3D failure analysis of slopes. The analysis is applicable to slopes for which the geometry of the failure pattern is physically confined, as for instance, in the case of excavations. A 3D failure pattern is then expected, and the results of calculations are given for a reasonable range of the width-to-slope-height ratios. The method is illustrated with practical examples.

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