Comparison between the seismic response of 2D and 3D models of rigid blocks

A three-dimensional model of rigid body with a rectangular base, able to rock around a side or a vertex of the base, is used to evaluate the seismic response of rigid blocks lying on a horizontal support. Eccentricity of the center of mass with respect to the geometrical center of the body is also considered. Three Italian registered earthquakes, with different spectral characteristics, are used to excite the body. The analyses are mainly conducted to highlight the differences between the seismic response of 2D and 3D models of rigid blocks, with the aim to understand if, in some cases, the use of the 3D model of rigid block is required to obtain results in favor of safety. In fact, the outcomes show that, in some ranges of the geometrical and mechanical parameters that characterize the excitation and the body, a bi-dimensional model, that does not consider the 3D rocking motions on a vertex of the base, is not in favor of safety. It is found, in particular, that the overturning of the three-dimensional block can take place for amplitudes of excitation smaller than those able to overturn a corresponding two-dimensional block.