Rocking motion is notoriously sensitive to the parameters that define it, with experimental tests oftentimes being non-repeatable. Therefore, validating numerical models using a deterministic approach is impossible, since the consistency of any benchmark experimental test is dubious. Three-dimensional rocking is even harder to predict than planar rocking. This paper presents a three-dimensional finite element model to predict the statistics of the rocking/sliding response of free-standing cylindrical columns. The response parameters of interest were the maximum displacement at the top of the columns and the residual displacement. Three different columns with varying slenderness and size were examined. The columns were able to slide, rock, and wobble in all directions, with this behavior being representative of building components and monumental structures. The numerical results were statistically compared to a large database of experimental tests, proving the accuracy of the proposed model. The influence of all modeling and physical parameters was elucidated, employing a large number of non-linear time-history analyses. It is shown that, when the numerical parameters are varied within a reasonable range, they do not influence the statistics of the response, even though they influence each individual oscillation. The friction coefficient between the interfaces (physical parameter) can influence the statistics of the response and should be carefully selected. Energy dissipation should be modeled explicitly, following the physics of the problem.
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