Mahin and Espinoza 2006
In this paper, the authors discuss the bridge pier design which allows rocking. They explained a series of preliminary shake table tests of a simple inverted pendulum reinforced concrete bridge column, conducted for horizontal and vertical components of excitation. The results represented the effects of multi-directional earthquake excitation on the elastic response of bridge columns. Finally, analytical simulations of the elastic rocking response and fixed base response were compared in terms of the benefits of foundation uplift.
System Concept
Rocking behavior can limit local displacement demand and allow the design of smaller footings and members by forming isolation and by reducing displacement and force demands on a bridge.
Bridge structures on a competent soil are generally designed with rectangular spread footings and have fixed base response. This leads to inelastic behavior at or near columns during earthquakes. Although elastic behavior can dissipate input energy, it also results in residual damage to the column. On the other hand, rocking behavior of the bridge pier foundation acts as an isolation mechanism by introducing other modes of non-linearity and energy dissipation. Moreover, rocking behavior reduces damage in the column and residual displacements in the bridge after an earthquake.
Experimental Study, Results, and Discussion
To model the bridge pier uplift, simple reinforced concrete column and footing resting on neoprene was used. Two and three dimensional excitations were tested. Two recorded earthquake excitations were considered at different amplitude levels or frequency scales in order to examine the behavior of rocking for square footings. The column was expected to remain elastic after the series of test.
In the preliminary tests were performed in order to evaluate the ability of the neoprene pad to mimic soil behavior, evaluate test setup and predict rocking response.
From the experimental results, it was concluded that the periods of the columns and damage levels were different from each other. The period for the fixed base column was 0.28 s and the period for the specimen resting on neoprene pads was 0.52 s. Even though applied excitation level would have damaged a fixed base column, the test column had no damage.
Analytical Study
OpenSees was used to model the experimental setup. The Beam on Nonlinear Winkler Foundation model was used. After that, analytical and measured displacements were compared. A reasonable correlation was observed between recorded and analytical model.
Reference
Mahin, S. and Espinoza, A. (2006). “Rocking of Bridge Piers Subjected to Multi-Directional Earthquake Loading,” Journal of Technical Memorandum of Public Works Research Institute, vol. no 4009, pp. 65-71.