LAUSR

Abstract The highly nonlinear differential equations describing the complex rocking-sliding instability of a freely standing on the ground multi-rigid block assembly under horizontal ground motion are analytically derived using an energy variational approach. A major step for deriving these equations is the evaluation of the displacements (horizontally and vertically) of the gravity centers of all rigid blocks of the assembly, after rocking initiation of the lower block and separation of all blocks to each other. This is conveniently achieved by combining the corresponding displacements of the same assembly without sliding (based on previous author's analyses) with the additional displacements due to slidings between consecutive blocks except the lower one with the ground. The increase of the magnitude of sliding along the height of the assembly (from bottom to the top) implies respective increase in the loss of energy. Thus, the beneficial effect of sliding on the minimum amplitude ground acceleration (leading to overturning) becomes more pronounced as the number of rigid blocks of the assembly increases. It was shown qualitatively and quantitatively that a very small sliding in a two-rigid block assembly may provoke a significant increase of the minimum amplitude ground acceleration (stabilizing considerably the assembly). It was also proved via a qualitative analysis that the number of configuration patterns to be examined can be substantially reduced which confines considerably the computational effort. Moreover, some new findings for the rocking-sliding response for one- rigid block systems are also presented contributing to the rocking-sliding analysis of multi-rigid block assemblies.