This paper reports some results from a study of toppling as a truly three-dimensional (3D) problem using physical models and 3D Discontinuous Deformation Analysis (DDA). A series of physical models consisting of blocks corresponding to different combinations of variables was built to study the effects of these variables. The same models, as well as ones modified by adding lateral confinement, were analyzed using 3D DDA. The physical modeling and 3D DDA results show that the tendency for toppling becomes greater if the blocks are taller for the same base width, if the friction angle of all joints is larger, if the base inclination is larger, and if there is no lateral confinement. For the cases studied, 3D DDA results agree well with the physical modeling results not only in terms of the effective failure mode but also in terms of the displacement histories of the blocks in the model.


A jointed rock slope is susceptible to failure by toppling if the joints dip steeply into the slope. For toppling to be kinematically feasible, it is usually assumed that the strike of the steeply dipping joint set is roughly the same as that of the slope face. Therefore, the problem can be reduced to a twodimensional (2D) one that can be analyzed by considering a section perpendicular to the slope face. Existing kinematic tests for toppling usually allow for some deviation from the condition that the strike of the joint set is the same as that of the slope face (same-strike condition). For example, the kinematic test for toppling using stereographic projections in Goodman (1989) implies that for toppling to be kinematically feasible, the strike of the joint set must not differ from the strike of the slope face by more than 30 degrees.

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