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

Giancarlo Bilotti; Leonardo Giliberti

- Volume: 82, Issue: 2, page 241-252
- ISSN: 1120-6330

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topBilotti, Giancarlo, and Giliberti, Leonardo. "A simple mechanical model to analyse the rocking and sliding response of rigid blocks to earthquakes." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.2 (1988): 241-252. <http://eudml.org/doc/287502>.

@article{Bilotti1988,

abstract = {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.},

author = {Bilotti, Giancarlo, Giliberti, Leonardo},

journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},

keywords = {Rigid Blocks; Rocking; Sliding; Earthquakes},

language = {eng},

month = {6},

number = {2},

pages = {241-252},

publisher = {Accademia Nazionale dei Lincei},

title = {A simple mechanical model to analyse the rocking and sliding response of rigid blocks to earthquakes},

url = {http://eudml.org/doc/287502},

volume = {82},

year = {1988},

}

TY - JOUR

AU - Bilotti, Giancarlo

AU - Giliberti, Leonardo

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

JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

DA - 1988/6//

PB - Accademia Nazionale dei Lincei

VL - 82

IS - 2

SP - 241

EP - 252

AB - 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.

LA - eng

KW - Rigid Blocks; Rocking; Sliding; Earthquakes

UR - http://eudml.org/doc/287502

ER -

## References

top- HOUSUER, G.W.: «The Behaviour of Inverted Pendulum Structures During Earthquakes», Bull. Seismo. Soc. Am.53, 404-417, 1963.
- ASLAM, M., GODDEN, W.G. and SCALISE, D.T.: «Earthquake Rocking Response of Rigid Bodies», J. Struct. Div., ASCE, 106, 377-392, 1980.
- MUTO, K. et al., «3-D Non-Linear Dynamic Analysis Stacked Blocks», II Conf. on Dynamic Response of Structures, ASCE, pp. 917-930, 1981.
- GIANNINI, R.: «Analisi Dinamica dei Sistemi di Blocchi Sovrapposti», II Convegno L'Ingegneria Sismica in Italia, pp. 6.47-6.42, Rapallo1984.
- BLASI, C. and SPINELLI, P.: «Un Metodo di Calcolo Dinamico per Sistemi Formati da Blocchi Rigidi Sovrapposti», Ingegneria Sismica, Anno III, N. 1 gen. apr., 1986.
- ANGOTTI F. and TONI, P.: «Oscillazioni non Lineari di Corpi Rigidi su Semispazi Elastici Monolaterali», Congresso Nazionale AIMETA, pp. 134-143, Genova 7-8-9 ottobre 1982.
- ANDREAUS, U., D'ASDIA, P. and DI PAOLO, A.: «Sul Comportamento dei Giunti tra Conci Lapidei: un Modello di Giunto Attritivo», III Convegno Nazionale A.I.I.S., pp. 665-690, Roma, ottobre 1987.
- BLASI, C. and SPINELLI, P.: «Sul Consolidamento Antisismico di Colonne Lapidee: un Esempio», III Convegno Nazionale A.I.I.S., pp. 95-106, Roma, ottobre 1987.
- GURTIN, M.: An Introduction to Continuum Mechanics, Academic Press, 1981. Zbl0559.73001MR636255
- GLOWINSKI, R., LIONS, J.L. and TRÉMOLIERES, R.: Analyse Numérique des Inequation Variationnelles, Dunod-Paris, 1976. Zbl0358.65091
- ASCIONE, L. and BILOTTI, G.: «The Dynamical Unilateral Contact Problem with Friction of a Beam with Hetenyi's Foundation: a Finite Element Approach», «Atti dell'Accademia Nazionale dei Lincei», Rend. fis. (8), LXXXII (1988), 61-73. Zbl0705.73207MR999839

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