A simple mechanical model to analyse the rocking and sliding response of rigid blocks to earthquakes

Bilotti, Giancarlo ; Giliberti, Leonardo

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 2, pp. 241-252

Résumé

In order to study the effects of earthquakes on tombstones and monumental columns in recent years the dynamical analysis of rigid blocks subjected to ground accelerations has interested many researchers. Mainly, the rocking motion has been investigated and many numerical difficulties have been pointed out in such analysis [1-2-3-4]. Some computational advantages can be obtained by modelling the bonding between two blocks or between block and foundation by means of an elastic layer of Winkler's springs not reacting in traction [5]. Nevertheless, many experimental observations show that the sliding phenomena can be relevant so that an analisys that only takes into account the rocking can be inadequate for technical purposes. Recently, some mechanical models with elasto-plastic horizontal springs have been proposed in [6-7-8] which take into account such displacements. Essentially, the sliding phenomenum is related to a friction idea. In this sense the aim of the present paper is to analyse the dynamical problem of a rigid block unilaterally constrained with friction against a Winkler's foundation; the analysis is carried out as a plane problem in the context of the linearized theory. Regarding the friction forces, we assume that they are related to the horizontal velocity of the block base through an analytical relationship, which regularizes the classical Coulomb's law. In this way we obtain a very simple mechanical model, which allows us to develop a comprehensive analysis of the block motion, including both rocking and sliding without too much analytical troubles. In particular in this paper we will present the first numerical results which we obtained referring to a rigid block subjected to horizontal seismic loads. They show both the effectiveness of the mechanical model and the efficiency of the algorithm solution proposed, which utilizes a semi-implicit integration method of the dynamical equations.