Dynamics of rigid block structures

by P.R. Lipscombe

This dissertation investigates the dynamic behaviour of structures which consist of a small number of unbonded rigid blocks. These structures exhibit an apparently simple rocking behaviour which, however, in the past has proved difficult to analyse.

A review of available literature on rocking structures reveals that the most popular model used to describe the dynamic rocking behaviour of a single rigid block is G.W. Housner's classical theory. A study of published experimental results reveals some discrepancies with this theory.

The accuracy and limitations of the classical theory are established with the aid of experiments. A new theoretical model is developed to explain the experimental behaviour, it allows the block to lose contact with the foundation after impact. The predictions of the new 'bouncing' model match the experimental results well. For slender blocks, the model coincides with the classical theory. Any slight asymmetry significantly affects the observed response.

The concepts developed for the 'bouncing' model are extended to develop a three-dimensional model for a single block and a general model for multi-block structures.

A series of random vibration experiments, on a shaking table indicate that the rocking response of rigid structures is very difficult to predict for any one particular simulation. However, statistical interpretation of the results shows that the theory and experiments agree remarkably well. An example is given, showing how the statistical interpretation may be applied to a practical assessment of stability.

Keywords: Rigid block : Rigid body : Rocking : Structural dynamics : Earthquake response.