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The relevance of energy damping in unreinforced masonry rocking mechanisms. Experimental and analytic investigations

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Abstract

Existing unreinforced masonry buildings frequently suffer out-of-plane local collapse mechanisms when undergoing earthquake ground motion. The energy damping that occurs during the motion, due to impacts of a wall against the foundation or against other walls, is a relevant parameter on the response. An experimental investigation has been carried out to estimate the dissipation of kinetic energy that takes place during free oscillations. Restraint conditions allow for two-sided rocking (wall resting on a foundation) and one-sided rocking (wall resting on a foundation adjacent to transverse walls). Five specimens have been tested, modelling walls acted out-of-plane (façades). When one-sided rocking is under consideration, different depths of the contact surface between façade and transverse walls are considered. In the case of two-sided rocking, the experimental coefficient of restitution is slightly lower than the analytic coefficient. In the case of one-sided rocking, an analytic formulation is proposed and this is compared against experimental data. Although the coefficient of restitution of one-sided rocking is less than half that of two-sided rocking, it is not equal to zero. Thus, it cannot induce a sudden stop of the motion. Hence, nonlinear time history analyses performed under this assumption may prove unsafe. Moreover, a comparison has been carried out between overturning maps, induced by twenty natural accelerograms, computed for the analytic coefficient of restitution and those computed for the experimental coefficient of restitution. The increased energy dissipation reduces the frequency of overturning and causes a more regular behaviour.

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References

  • Ageno A, Sinopoli A (1991) Indagine teorica e sperimentale sul problema dell’urto tra blocchi rigidi. 5 Convegno Nazionale “L’Ingegneria Sismica in Italia”, Palermo, 29 Settembre–2 Ottobre 1991

  • Al Shawa O, Benedetti S, Bellisario M, de Felice G, Mauro A, Paolacci F, Ranieri N, Roselli I, Sorrentino L (2009) Prove sperimentali su tavola vibrante di pareti murarie sollecitate fuori dal piano. ReLUIS final deliverable, Annex PF-1.2-UR09_15

  • Aslam M, Godden WG, Scalise T (1980) Earthquake rocking response of rigid bodies. J Struct Div-ASCE 106: 377–392

    Google Scholar 

  • Augenti N, Parisi F (2009) Experimental data analysis on mechanical parameters of tuff masonry. Workshop on design for rehabilitation of masonry structures, Wondermasonry, Lacco Ameno, 8–10 October 2009

  • Bernardini, A, Mattone R, Modena C, Pasero G, Pavano M, Pistone G, Roccati R, Zaupa F (1984) Determinazione delle capacità portanti per carichi verticali e laterali di pannelli murari in tufo.2 Convegno ASSIRCCO, Ferrara, 30 maggio–2 giugno 1984

  • Binda L, Mirabella Roberti G, Tiraboschi C (1996) Problemi di misura dei parametri meccanici della muratura e dei suoi componenti. La meccanica delle murature tra teoria e progetto, Messina, 18–20 settembre 1996

  • D’Ayala D, Speranza E (2003) Definition of collapse mechanisms and seismic vulnerability of historic masonry buildings. Earthq Spectra 19: 479–509. doi:10.1193/1.1599896

    Article  Google Scholar 

  • Decanini LD, Gavarini C, Mollaioli F (2000) Some remarks on the Umbria-Marche earthquakes of 1997. Eur Earthq Eng 14: 18–48

    Google Scholar 

  • Decanini L, De Sortis A, Goretti A, Langenbach R, Mollaioli F, Rasulo A (2004) Performance of masonry buildings during the 2002 Molise, Italy, Earthquake. Earthq Spectra 20: S191–S220. doi:10.1193/1.1765106

    Article  Google Scholar 

  • Decanini LD, Masiani R, Al Shawa O, Benedetti S, Sorrentino L (2009) Prove sperimentali di dondolamento libero di pareti murarie. Rapporto conclusivo. ReLUIS 3rd year report, Annex 1.2-UR15-4

  • De Lorenzis L, DeJong M, Ochsendorf J (2007) Failure of masonry arches under impulse base motion. Earthq Eng Struct Dyn 36: 2119–2136. doi:10.1002/eqe.719

    Article  Google Scholar 

  • Doherty KT, Griffith MC, Lam NTK, Wilson JL (2002) Displacement-based seismic analysis for out-of-plane bending of unreinforced masonry walls. Earthq Eng Struct Dyn 31: 833–850. doi:10.1002/eqe.126

    Article  Google Scholar 

  • Goretti A, De Matteis U, Liberatore D (2007) Analisi sismica delle mura storiche di Camerino. 12 Convegno nazionale “L’ingegneria sismica in Italia”, Pisa, 10–15 Giugno 2007

  • Griffith MC, Magenes G, Melis G, Picchi L (2003) Evaluation of out-of-plane stability of unreinforced masonry walls subjected to seismic excitation. J Earthq Eng 7: 141–169. doi:10.1142/S1363246903000997

    Article  Google Scholar 

  • Griffith MC, Lam NTK, Wilson JL, Doherty KT (2004) Experimental investigation of URM walls in flexure. J Struct Eng-ASCE 130: 423–432. doi:10.1061/(ASCE)0733-9445(2004)130:3(423)

    Article  Google Scholar 

  • Hogan SJ (1992) On the notion of a rigid block, tethered at one corner, under harmonic forcing. Proc R Soc Lon Ser-A 439: 35–45

    Article  Google Scholar 

  • Housner GW (1963) The behavior of inverted pendulum structures during earthquakes. Bull Seismol Soc Am 53: 403–417

    Google Scholar 

  • Lagomarsino S, Resemini S (2009) The assessment of damage limitation state in the seismic analysis of monumental buildings. Earthq Spectra 25: 323–346. doi:10.1193/1.3110242

    Article  Google Scholar 

  • Lam NTK, Wilson JL, Hutchinson GL (1995) The seismic resistance of unreinforced masonry cantilever walls in low seismicity areas. Bull New Zealand Natl Soc Earthq Eng 28: 179–195

    Google Scholar 

  • Lam NTK, Griffith MC, Wilson JL, Doherty KT (2003) Time–history analysis of URM walls in out-of-plane flexure. Eng Struct 25: 743–754. doi:10.1016/S0141-0296(02)00218-3

    Article  Google Scholar 

  • Liberatore D, Spera G, D’Alessandro G, Nigro D (2002) Rocking of slender blocks subjected to seismic motion of the base. 12 European conference on earthquake engineering, London, 9–13 September 2002

  • Liberatore D, Spera G (2001a) Response of slender blocks subjected to seismic motion of the base: description of the experimental investigation. 5 international symposium on computer methods in structural masonry, Rome, 18–21 April 2001

  • Liberatore D, Spera G (2001b) Response of slender blocks subjected to seismic motion of the base: experimental results and initial numerical analyses. 5 international symposium on computer methods in structural masonry, Rome, 18–21 April 2001

  • Liberatore D, Spera G (2003) Analisi strutturale e intervento di consolidamento. In: Scalora G (eds) I tessuti urbani di Ortigia. Un metodo per il progetto di conservazione. Ente Scuola Edile Siracusana, Siracusa, pp 89–115

    Google Scholar 

  • Lipscombe PR, Pellegrino S (1993) Free rocking of prismatic blocks. J Eng Mech 119: 1387–1410. doi:10.1061/(ASCE)0733-9399(1993)1197(1387)

    Article  Google Scholar 

  • Peña F, Prieto F, Lourenço PB, Campos-Costa A, Lemos JV (2007) On the dynamics of rocking motion of single rigid-block structures. Earthq Eng Struct Dyn 36: 2383–2399. doi:10.1002/eqe.739

    Article  Google Scholar 

  • Plaut RH, Fielder WT, Virgin LN (1996) Fractal behavior of an asymmetric rigid block overturning due to harmonic motion of a tilted foundation. Chaos Soliton Fract 7: 177–196

    Article  Google Scholar 

  • Priestley MJN, Evison RJ, Carr AJ (1978) Seismic response of structures free to rock on their foundations. Bull New Zealand Natl Soc Earthq Eng 11: 141–150

    Google Scholar 

  • Rankine WJM (1863) A manual of civil engineering, 2nd edn. Griffin Bohn, London

    Google Scholar 

  • Shenton HW III (1996) Criteria for initiation of slide, rock, and slide-rock rigid-body modes. J Eng Mech 122: 690–693. doi:10.1061/(ASCE)0733-9399(1996)122:7(690)

    Article  Google Scholar 

  • Sorrentino L, Masiani R, Decanini LD (2006a) Overturning of rocking rigid bodies under transient ground motions. Struct Eng Mech 22: 293–310

    Google Scholar 

  • Sorrentino L, Mollaioli F, Masiani R (2006b) Overturning maps of a rocking rigid body under scaled strong ground motions. 1 European conference on earthquake engineering and seismology, Geneva, 3–8 September 2006

  • Sorrentino L, Kunnath S, Monti G, Scalora G (2008a) Seismically induced one-sided rocking response of unreinforced masonry façades. Eng Struct 30: 2140–2153. doi:10.1016/j.engstruct.2007.02.021

    Article  Google Scholar 

  • Sorrentino L, Masiani R, Griffith MC (2008b) The vertical spanning strip wall as a coupled rocking rigid body assembly. Struct Eng Mech 29: 433–453

    Google Scholar 

  • Sorrentino L, Masiani R, Benedetti S (2008c) Experimental estimation of energy damping during free rocking of unreinforced masonry walls. First Results. 2008 Seismic engineering international conference commemorating the 1908 Messina and Reggio Calabria earthquake, Reggio Calabria, 8–11 July 2008

  • Spanos PD, Roussis PC, Politis NPA (2001) Dynamic analysis of stacked rigid blocks. Soil Dyn Earthq Eng 21: 559–578. doi:10.1016/S0267-7261(01)00038-0

    Article  Google Scholar 

  • Tobriner S, Comerio M, Green M (1997) Reconnaissance report on the Umbria-Marche Italy earthquake of 1997. EERI Newsl 31

  • Yim CS, Chopra AK, Penzien J (1980) Rocking response of rigid blocks to earthquakes. Earthq Eng Struct Dyn 8: 565–587

    Article  Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “La Sapienza”, via Antonio Gramsci 53, 00197, Rome, Italy

    Luigi Sorrentino, Omar AlShawa & Luis D. Decanini

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  1. Luigi Sorrentino
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  2. Omar AlShawa
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  3. Luis D. Decanini
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Correspondence to Luigi Sorrentino.

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Sorrentino, L., AlShawa, O. & Decanini, L.D. The relevance of energy damping in unreinforced masonry rocking mechanisms. Experimental and analytic investigations. Bull Earthquake Eng 9, 1617–1642 (2011). https://doi.org/10.1007/s10518-011-9291-1

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