Finite element analysis of the dynamic response of a free-standing cylindrical column: a statistical approach

This paper presents a modeling approach for predicting the shake-table response of a rocking and sliding column. A three-dimensional finite element (FE) model was developed and validated statistically against experimental results, which involved testing the column under a set of 115 bidirectional ground motions. The free-standing body had a circular cross-section and was allowed to slide and rock in all directions. Both the rocking body and the shake table were modeled using elastic elements. The contact surface was simulated using Coulomb friction for the tangential behavior and stiff contact for the normal direction. Friction was the main energy dissipation mechanism. Rocking is characterized as a chaotic and unpredictable problem, with experiments being non-repeatable. Therefore, this study employs a statistical approach to validate the numerical results. This is achieved by using the cumulative distribution function (CDF) for the main response quantity (i.e., maximum displacement at the top of the column) instead of comparing the numerical and experimental results one by one for each test (deterministic comparison). It was proved that the model performs poorly in the deterministic validation but demonstrates satisfying agreement with the experimental results when validated statistically. Important modeling parameters, such as the solution time step and the value of the integrated numerical damping, were elucidated through an extensive sensitivity analysis, employing non-linear time-history analyses. It was shown that a small change of the value of these parameters leads to a different individual rocking oscillation but only marginally influences the statistical response.