Rocking behaviour of multi-block columns subjected to pulse-type ground motion accelerations

Ancient columns, made with a variety of materials such as marble, granite, stone or masonry are an important part of the<br/>European cultural heritage. In particular columns of ancient temples in Greece and Sicily which support only the architrave are<br/>characterized by small axial load values. This feature together with the slenderness typical of these structural members clearly<br/>highlights as the evaluation of the rocking behaviour is a key aspect of their safety assessment and maintenance. It has to be noted<br/>that the rocking response of rectangular cross-sectional columns modelled as monolithic rigid elements, has been widely investigated<br/>since the first theoretical study carried out by Housner (1963). However, the assumption of monolithic member, although being<br/>widely used and accepted for practical engineering applications, is not valid for more complex systems such as multi-block columns<br/>made of stacked stone blocks, with or without mortar beds. In these cases, in fact, a correct analysis of the system should consider<br/>rocking and sliding phenomena between the individual blocks of the structure. Due to the high non-linearity of the problem, the<br/>evaluation of the dynamic behaviour of multi-block columns has been mostly studied in the literature using a numerical approach<br/>such as the Discrete Element Method (DEM). This paper presents an introductory study about a proposed analytical-numerical<br/>approach for analysing the rocking behaviour of multi-block columns subjected to a sine-pulse type ground motion. Based on the<br/>approach proposed by Spanos (2001) for a system made of two rigid blocks, the Eulero-Lagrange method to obtain the motion<br/>equations of the system is discussed and numerical applications are performed with case studies reported in the literature and with a<br/>real acceleration record. The rocking response of single block and multi-block columns is compared and considerations are made<br/>about the overturning conditions and on the effect of forcing function’s frequency.<br/>.