On the dynamics of rocking motion of single rigid–block structures

Abstract

This paper describes the behavior of single rigid-block structures under dynamic loading. A comprehensive experimental investigation has been carried out to study the rocking response of four blue granite stones with different geometrical characteristics under free vibration, and harmonic and random motions of the base. In total, 275 tests on a shaking table were carried out in order to address the issues of repeatability of the results and stability of the rocking motion response. Two different tools for the numerical simulations of the rocking motion of rigid blocks are considered. The first tool is analytical and overcomes the usual limitations of the traditional piecewise equations of motion through a Lagrangian formalism. The second tool is based on the discrete element method (DEM), especially effective for the numerical modeling of rigid blocks. A new methodology is proposed for finding the parameters of the DEM by using the parameters of the classical theory. An extensive comparison between numerical and experimental data has been carried out to validate and define the limitations of the analytical tools under study.