The motivation for this project developed from testing of a full scale building isolated with triple friction pendulum bearings on the E-defense shake table in Japan. The test demonstrated experimentally that the vertical component of ground motion can amplify both the base shear and the story acceleration in the isolated building. Vertical shaking introduced high-frequency variation in the axial force of the bearings, and, consequently, a high-frequency component in the bearing lateral force, which excited higher structural modes in the building. Since vertical bridges are flexible in the vertical direction because of long spans, similar effects may be observed in bridges.
The objectives of this study are to develop a physical understanding of the amplification of responses and develop a simplified method to predict amplification of base shear in three-dimensional (3D) shaking relative to two-dimensional (2D) shaking, for bridges isolated with spherical sliding bearings. A series of ground motions with a wide range of vertical shaking intensity were applied to 3D models of bridges isolated with triple pendulum bearings (TPBs), both excluding the vertical component (2D motion) and including the vertical component (3D motion). This enabled the comparison of the bridge response under 2D and 3D shaking such that the direct effect of vertical shaking could be investigated. The selected ground motions were fit to target spectra in the horizontal and vertical directions, and divided into three groups based on vertical peak ground acceleration (PGAV). Multi-span concrete box girder bridges were selected for this study, as they are a prominent bridge type in California, and are suitable for seismic isolation. Models were developed for a 3-span, 45-ft wide, multi-column Base Model bridge; various superstructure and isolation-system parameter variations were implemented to evaluate the effect of these variations on the amplification of base shear. Response histories were compared for a representative motion from each ground-motion group under 2D and 3D shaking. Modal and spectral analyses were conducted to understand dynamic properties and behavior of the bridge under vertical motion. Based on simplified theory, a method to estimate the amplification of base shear due to vertical shaking was developed. The accuracy of the simplified method was assessed through a base shear normalized error metric, and different amplification factors were considered.
Response history analysis showed significant amplification of base shear under 3D motion implying that exclusion of vertical component could lead to under estimation of demand shear forces on bridge piers. Deck acceleration spectral response at different locations revealed that a transverse-vertical modal coupling response was present in the Base Model bridge, which led to amplification of deck accelerations in addition to base shear due to excitation of the superstructure transverse mode. The simplified method predicted that in addition to the peak vertical ground acceleration base shear amplification depended on the isolation-system period (radius of curvature) and friction coefficient. The error in the simplified method was approximately constant across the range of isolation-system parameters. Variations in the bridge superstructure or substructure modeling parameters had only a minor effect on the base shear since the deck acts as a single mass sliding on isolators; therefore, the simplified method can be applied to a range of bridge models. The simplified method includes an amplification factor that indirectly represents the dynamic amplification of vertical acceleration from the ground to the isolation system. An amplification factor of 1.0 was found to be sufficiently conservative to estimate the base shear due to 3D shaking. The lack of apparent dynamic amplification could mean that the peak vertical acceleration is out-of-phase with the base shear. The simplified method is more likely to be unconservative for high-intensity vertical ground motions due to the complexities associated with uplift and pounding. Further investigation is recommended to determine the threshold shaking intensity limit for the simplified method.
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