Keywords: hybrid, shaking, soil-structure interaction, earthquake, identification.

The aim of the paper is to propose an effective algorithm for a hybrid shaking table test that can simulate soil-structure interaction without using a physical soil box. In the hybrid shaking table testing algorithm, the soil-structure interaction (SSI) effects are taken into account by actively controlling the input table motion. The adjusted table motion is calculated in real-time from the input earthquake ground motion, the impedance function of the foundation that represents the flexible ground and the measured response of the test structure. With the help of this algorithm only the structural part of the whole soil-structure system needs to be tested on the shaking table.

The hybrid testing scheme can be applied to solve the dynamic SSI problem economically and efficiently [1]. To investigate SSI reliably through a laboratory shaking table test, the structure model needs to be set in a large size soil box that is mounted on the shaking table. The table motion will be transmitted to the structure through the soil. The soil box must be designed in such a way as to satisfy any radiation boundary conditions. If a scale model is used, the soil particles also need to be scaled down and manufactured, which is not an easy task. The formation of the soil foundation requires a special apparatus. The heavy weight of the soil box will be a great burden to the actuator. All these difficulties motivated the development of an alternative testing method, i.e., the hybrid shaking table test.

In order to develop this hybrid test method a simple analytical model is employed in which the soil region is represented by springs and dampers. Because of functional limitations of the laboratory shaking table, the model is simplified further to one without the rocking motion. In this very simple model the stiffness and damping coefficients of the massless foundation are assumed to be constants independent of the excitation frequency. The SSI effects can be delivered to the structure only through the spring and damper. Thus the coupled soil-structure interaction system can be decomposed into two subsystems: the structure model mounted on the shaking table (superstructure) and massless foundation on the soil ground (substructure). The superstructure will be subjected to the shaking table test, and the substructure will be represented by a numerical model. The governing equations are also separated into two parts accordingly.

Each set of separated equations contains variables dependent on the information provided from the other set of equations. Therefore, the two separated sets of equations are inter-connected and should be solved recursively. Two algorithms of simple feedback and predictive feedback are developed and the results are compared through simulation studies. To examine the efficacy of the feedback algorithms, simulation studies are carried out with a sample two-story shear building founded on soft ground. The predictive feedback algorithm renders much better results than the simple feedback algorithm. Of the time integration methods that are used in the algorithm, the Wilson- method performed the best.

To examine the proposed hybrid shaking table test scheme, a laboratory experiment is carried out with a two-story shear building model. Accelerometers are placed at each floor and LabVIEW is used for the data acquisition and control of the motion. Before performing the hybrid shaking table test, structural parameters of the model shear building are first estimated through the application of a system identification method. To identify mass and stiffness synchronously, a frequency-domain system identification method are applied [2]. The computed natural frequencies using the identified parameters are compared with those directly identified from measured accelerations. The closeness of the natural frequencies could indicate the correctness of the identified structural parameters.

Before evaluating the SSI effects on the response of the shear building, the predictive feedback algorithm is examined under the fixed base condition. For this study, a modified El-Centro earthquake excitation with a reduction in the amplitude is applied. The computed frequency response function matches very well in both frequency and amplitude with the one identified from the measured acceleration data. To investigate the SSI effects, the predictive feedback algorithm is also applied and the computed accelerations are compared with the measured ones. The favourable comparison of acceleration time histories demonstrates the efficacy of the proposed hybrid shaking test method.

Because of functional limitations of the available laboratory shaking table, the rocking motion is not considered in the present study. In the future, a more rigorous examination of the present method is required. Further refinement in the soil model and feedback algorithm should be considered.

1

S.K. Lee, "Shaking table testing method based on the substructure method considering dynamic soil-structure interaction (1) - superstructure with foundation on half-space", paper No. SE04-088, July 6-9, Smart Structures Technologies and Earthquake Engineering, 2004.

2

S.M. Lee, "Synchronous estimation of mass and stiffness parameters using measured modal data", Ph.D. thesis, Dept. of Civil Eng., Dong-A University, 2005.

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