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Bulletin of Earthquake Engineering

, Volume 17, Issue 2, pp 985–1007 | Cite as

A probabilistic simplified seismic model of masonry buildings based on ambient vibrations

  • D. SpinaEmail author
  • G. Acunzo
  • N. Fiorini
  • F. Mori
  • M. Dolce
Original Research
  • 95 Downloads

Abstract

The paper presents a new simplified mathematical model for predicting the structural seismic response of buildings. The model, denominated Seismic Model from Ambient Vibrations (SMAV), is based on the experimental modal parameters identified from ambient vibration and only a few information about the geometry and the structural typology of the building. After a short review of the Multi Rigid Polygons model, recently illustrated and validated in an other paper by some of the authors, that allows to estimate the seismic participation factors of the experimental modes also for buildings characterized by complex shaped plan and structural irregularity along the height, the attention is focused on a new stochastic approach for modeling the seismic response of masonry buildings. In particular this new approach aims to take into account the non linearity occurred during a seismic event so that the nonlinear behaviour of the building is considered by reducing its modal frequencies according to the response amplitude. The reduction of the natural frequencies, extracted by Operational Modal Analysis from ambient vibrations, is computed according to specific probabilistic curves: the Frequency Shift Curves (FSCs). This curves provide the percentage reduction of the natural frequencies as a function of the maximum roof drift reached during the strong motion and they are obtained, for some specific masonry typologies, through a Monte Carlo analysis carried out using a simple mechanical model of a masonry panel with geometric and mechanical parameters that vary according to their probabilistic distributions. The seismic response of the building is then computed through a linear equivalent analysis in which an iterative algorithm updates the resonant frequencies according to the specific FSC curve. The concept of structural serviceability index (IOPS), expressing the probability of the building to remain operational, is also introduced. Finally, a comparison between the seismic response computed by the model and the experimental seismic response of the Pizzoli town hall, a masonry existing building endowed with a permanent accelerometer monitoring system, is illustrated.

Keywords

Seismic vulnerability Masonry building Frequency shift Operational modal analysis 

List of symbols

\(\varvec{f}\)

Vector of natural frequencies

\({\varvec{\Phi}}\)

Matrix of mass scaled mode shapes

\(\varvec{\xi}\)

Vector of modal damping ratios

\(k\)

Subscrit denoting that the quantity refers to the k-th mode

\(\varvec{M}\)

Mass matrix of the Multi Rigid Polygon (MRP) model

\(\varvec{D}\)

Matrix of the linear transformation from phisical to MRP degree of freedom

\(\bar{\varPsi }\)

Matrix of the mode shapes of the MRP model

\({\varvec{\Gamma}}\)

Vector of modal participation factors

T

Time

\({\mathbf{\ddot{u}}}_{g} \left( t \right)\)

Acceleration time history on the ground

\(\varvec{u}\left( t \right)\)

Vector of the dinamic displacements of the structure

\(T\)

Structural period

\(S_{\varvec{a}} \left( T \right)\)

Pseudo-acceleration response spectrum of the seismic input at \(T\)

\(S_{\varvec{d}} \left( T \right)\)

Displacement response spectrum at \(T\)

\(\delta\)

Roof drift

\(\delta_{y}\)

Yeld roof drift

\(\delta_{m}\)

Maximum roof drift

\(MIDR\)

Maximum Interstory Drift Ratio

\(\varvec{q}\)

Vector of geometrical and mechanical parameters which characterize the wall panel

\(\rho_{f} (\delta ;\, \varvec{q} )\)

Frequency Shift Curve (FSC)

\(F(\delta )\)

Force-drift relationship associated to this assumed mechanical model

References

  1. Acunzo G, Fiorini N, Mori F, Spina D (2015) VaSCO-smav: the software developed for the SMAV methodology application (in italian). In: XVI Conference of Italian national association of earthquake engineering (ANIDIS)Google Scholar
  2. Acunzo G, Fiorini N, Mori F, Spina D (2018) Modal mass estimation from ambient vibrations measurement: a method for civil buildings. Mech Syst Signal Process 98C:580–593CrossRefGoogle Scholar
  3. Bodin P, Vidale J, Walsh T, Cakir R, Celebi M (2012) Transient and long-term changes in seismic response of the natural resource building, Olympia, Washington, due to earthquake shaking. J Earthq Eng 16:607–622CrossRefGoogle Scholar
  4. Calvi GM, Pinho R, Magenes G, Bommer JJ, Restrepo-Velez LF, Crowley H (2006) Development of seismic vulnerability assessment methodologies over the past 30 years. ISET J Earthq Technol 43(3):75–104Google Scholar
  5. Celebi M (2007) On the variation of fundamental frequency (period) of an undamaged building—a continuing discussion. In: Proceedings of the conference on experimental vibration analysis for civil engineering structures (EVACES’07) Porto, Portugal, Oct 24–26, pp 317–326Google Scholar
  6. Ceravolo R, Matta E, Quattrone A, Zanotti Fragonara L (2017) Amplitude dependence of equivalent modal parameters in monitored buildings during earthquake swarms. Earthq Eng Struct Dyn.  https://doi.org/10.1002/eqe.2910 Google Scholar
  7. Clinton J (2006) The observed wander of the natural frequencies in a structure. Bull Seismol Soc Am 96:237–257CrossRefGoogle Scholar
  8. Dolce M, Masi A, Marino M, Vona M (2003) Earthquake damage scenarios of the building stock of Potenza (Southern Italy) including site effects. Bull Earthq Eng 1(1):115–140CrossRefGoogle Scholar
  9. Dolce M, Nicoletti M, De Sortis A, Marchesini S, Spina D, Talanas F (2017) Osservatorio sismico delle strutture: the Italian structural seismic monitoring network. Bull Earthq Eng 15:621–641CrossRefGoogle Scholar
  10. Dong A, Tiejun Q, Jianwen L (2013) Seismic behavior of two-story brick masonry building. Appl Mech Mater Trans Tech Publications, Switzerland 275–277:1456–1460Google Scholar
  11. Flores LE, Alcocer SM (1996) Calculated response of confined masonry structures. In: Eleventh world conference on earthquake engineeringGoogle Scholar
  12. Lagomarsino S, Cattari S (2013) Seismic vulnerability of existing buildings. In: Guéguen P (ed) Seismic vulnerability of structures. Wiley, Croydon, pp 1–62Google Scholar
  13. Lagomarsino S, Penna A, Galasco A, Cattari S (2013) TREMURI program: an equivalent frame model for nonlinear seismic analysis masonry buildings. Eng Struct 56:1787–1799CrossRefGoogle Scholar
  14. Ljung L (1987) System Identification: Theory for the user. Prentice Hall PTR, Upper Saddle River, pp 71–81Google Scholar
  15. Magenes G, Calvi GM (1997) In-plane seismic response of brick masonry walls. Earthq Eng Struct Dyn 26:1091–1112CrossRefGoogle Scholar
  16. Magenes G, Morandi P, Penna A (2008) Test results on the behaviour of masonry under static cyclic in plane lateral loads, ESECMaSE project, report RS-01/08. Department of Structural Mechanics, University of Pavia, PaviaGoogle Scholar
  17. Michel C, Guéguen P (2013) Experimental Method. In: Guéguen P (ed) Seismic vulnerability of structures. Wiley, Croydon, pp 161–212CrossRefGoogle Scholar
  18. Michel C, Guéguen P, Bard PY (2008) Dynamic parameters of structures extracted from ambient vibration measurements: an aid for the seismic vulnerability assessment of existing buildings in moderate seismic hazard regions. Soil Dyn Earthq Eng 28:593–604CrossRefGoogle Scholar
  19. Michel C, Guéguen P, El Arem S, Mazars J, Kotronis P (2010) Full-scale dynamic response of an RC building under weak seismic motions using earthquake recordings, ambient vibrations and modeling. Earthq Eng Struct Dyn 39:419–441Google Scholar
  20. Michel C, Zapico B, Lestuzzi P, Molina FJ, Weber F (2011) Quantification of fundamental frequency drop for unreinforced masonry buildings from dynamic tests. Earthq Eng Struct Dyn 40(11):1283–1296CrossRefGoogle Scholar
  21. Mori F, Spina D (2015) Vulnerability assessment of buildings based on ambient vibrations measurements. Struct Monit Maint 2(2):115–132Google Scholar
  22. Mottershead JE, Link M, Friswell MI (2011) The sensitivity method in finite element model updating: a tutorial. Mech Syst Signal Process 25(7):2275–2296CrossRefGoogle Scholar
  23. Peeters B, De Roeck G (2011) Stochastic system identification for operational modal analysis: a review. J Dyn Syst Meas Control 123:659–667CrossRefGoogle Scholar
  24. Ranieri C, Fabbrocino G (2014) Operational modal analysis of civil engineering structures: an introduction and guide for applications. Springer, BerlinCrossRefGoogle Scholar
  25. Reynders E (2012) System identification methods for (operational) modal analysis: review and comparison. Archives Comput Methods Eng 19:51–124CrossRefGoogle Scholar
  26. Shing PB, Noland JL, Klamerus E, Spaeh H (1989) Inelastic behavior of concrete masonry shear walls. J Struct Eng 115(9):2204–2225CrossRefGoogle Scholar
  27. Spina D, Lamonaca BG (1998) Strengthening assessment of building using ambient vibration tests. In: Proceeding of XI conference on earthquake engineering, Rotterdam, BalkemaGoogle Scholar
  28. Spina D, Lamonaca BG, Nicoletti M, Dolce M (2011) Structural monitoring by Italian department of civil protection and the case of 2009 Abruzzo seismic sequence. Bull Earthq Eng 9:325–346CrossRefGoogle Scholar
  29. Todorovska M (2009) Seismic interferometry of a soil structure interaction model with coupled horizontal and rocking response. Bull Seismological Soc Am 99:611–625CrossRefGoogle Scholar
  30. Tomažević M (1999) Earthquake-resistant design of masonry buildings. Imperial College Press, LondonGoogle Scholar
  31. Tomažević M, Lutman M, Petković L (1996) Seismic behavior of masonry walls: experimental simulations. J Struct Eng 122(9):1040–1047CrossRefGoogle Scholar
  32. Vasconcelos G, Lourenço PB (2009) In-plane experimental behaviour of stone masonry wall under cyclic loading. J Struct Eng 135:1269–1277CrossRefGoogle Scholar
  33. Villaverde R (2007) Methods to assess th seismic collapse capacity of building structures: state of the art. J Struct Eng 133(1):57CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Civil ProtectionRomeItaly
  2. 2.Department of Mathematics and Physics of Roma Tre (Previously, CNR-IGAG)RomeItaly
  3. 3.Department of Civil Protection External consultant (Previously, CNR-IGAG)RomeItaly
  4. 4.National Research Centre CNR-IGAGMontelibretti (Rome)Italy

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