Finite element modeling of the shake-table response of a bridge-like model comprising rocking columns

This paper presents a three-dimensional finite element model to predict the shake-table response of a rocking bridge-like specimen. The numerical model is statistically validated against experimental results, which involved testing of the system under 169 three-directional ground motions. The model comprises four cylindrical rocking columns capped with a concrete slab. The columns are connected to the slab with flexible tendons and they are allowed to uplift and wobble. The use of flexible tendons allows for large displacements of the system and negative post-uplift stiffness. This mechanism acts as a form of seismic isolation, limiting the accelerations transmitted to the superstructure. The rocking columns, the slab and the shake table are modeled using elastic elements. The tangential behavior of the contact surfaces is modeled with Coulomb friction, which is the main energy dissipation mechanism. The tendons are modeled with equivalent elastic springs. The numerical analysis accounts for the geometric non-linearity of the response. Rocking motion is sensitive to the parameters that define it and experimental tests are often non-repeatable. Hence, this study employs a statistical approach to validate the proposed numerical model. The cumulative distribution function (CDF) of the response quantity of interest (e.g., maximum displacement at the center of the slab) is employed, instead of comparing the numerical and experimental results one-by-one for each test (deterministic comparison). The deterministic validation of the model shows a moderate correlation of the experimental and the numerical results. However, the model can accurately predict the statistical response for both parameters of interest (i.e., maximum displacement and maximum rotation) of the system under 169 ground motion excitations.