The effect of foundation flexibility on the dynamic response of a rigid block.

摘要

This research investigates the overturning behavior of rigid-body type structures, not anchored to their foundation, and subject to earthquake ground excitation. In particular the effect of the foundation flexibility on this behavior is studied. Examples of structures which exhibit this rigid-body type response include water tanks, petroleum-cracking towers, stone pillars, electric power transformers, free-stand machinery and industrial equipment. Research on this general problem was initiated by Housner in 1963 wherein he assumed the foundation to be rigid. Subsequent work has studied various aspects of this highly nonlinear system, however the effect of the foundation flexibility has not been properly studied in particular its effect on the overturning potential of the structure.; This research herein develops the full nonlinear equations of motion for a rigid block interacting with a modified Winkler foundation. The modified Winkler foundation includes an effective mass contribution from the foundation and the stiffness, mass, and damping properties are directly related to the material properties of the typical elastic half space model. Preliminary studies verify the full nonlinear equations of motion when a rigid block sits on two-spring-dashpot foundation, and highlights the importance of foundation flexibility on rigid body overturning.; With the improved mathematical model, the overturning behavior of a rigid block on the modified Winkler foundation is studied. In particular, the effect of foundation flexibility is evaluated on the dynamic behavior of a rigid block subjected to ground excitation. A parameter study is conducted separately for two types of earthquake ground motions: pulse-type (near-source) and random-type earthquake ground motion. For pulse type motion, an overturning spectra is generated numerically in the plane of the two parameters characterizing the pulse-type ground motions, i.e., a frequency and an amplitude. For filtered white-noise type ground motion, a probabilistic study is conducted. 695 artificial ground motions are generated with each considered as a realization of the same stochastic process. The probability of overturning is computed by performing time history analysis using the entire family of simulated earthquake ground motions. For both types of input ground motion, it is shown that the prediction of the potential for overturning can be drastically in error if the flexibility of the foundation is not properly accounted for.