Bulletin of Earthquake Engineering

, Volume 15, Issue 1, pp 149–174 | Cite as

Non-linear static procedures applied to high-rise residential URM buildings

  • R. Gonzalez-Drigo
  • J. Avila-Haro
  • L. G. Pujades
  • A. H. Barbat
Original Research Paper


In this work, the vulnerability of an unreinforced masonry building, evaluated on the one hand by using the incremental dynamic analysis, and on the other hand by using nine representative non-linear static incremental procedures, is compared. For comparison reasons among the different non-linear static procedures, the obtained incremental dynamic analyses results are used as reference values. The aim of this analysis is to evaluate the applicability and reliability of the diverse non-linear static procedures for unreinforced masonry buildings, and to propose modifications oriented to improve their use in this typology of structures. For this purpose, a fully representative unreinforced masonry building of the dominating building type in the Eixample district of Barcelona, is analyzed. Furthermore, the conditional spectrum approach procedure has been applied with the aim to conveniently define the seismic demand. Regarding the definition of the fragility curves, two different methodologies were used for each non-linear static procedure and incremental dynamic analyzes. Subsequently, the corresponding damage indices as well as the damage curves were calculated and compared for the different considered peak ground acceleration values. The results of this comparison seem to confirm that the damage curves obtained by performing the NSP and by applying the Risk-UE methodology overestimate the damage corresponding to low values of the PGA and underestimate the damage for higher values of the PGA.


Unreinforced masonry Push-over Non-linear static procedures Multi stripe analysis Vulnerability 



This research has been partially funded by the government of Spain (Ministerio de Economía y Competitividad-MINECO) and by the Fondo Europeo de Desarrollo Regional (FEDER) of the European Union (UE) through projects referenced as: CGL2011-23621 and CGL2015-65913-P (MINECO/FEDER, UE).


  1. Abrahamson NA, Al Atik L (2010) Scenario spectra for design ground motions and risk calculation. In: 9th US national and 10th Canadian conference on earthquake engineering, TorontoGoogle Scholar
  2. ATC-40 (1996) Seismic evaluation and retrofit of concrete buildings. California Seismic Safety Commission, CaliforniaGoogle Scholar
  3. Baker JW (2014) Code supplement to efficient analytical fragility function using dynamic structural analysis.
  4. Baker JW (2015) Efficient analytical fragility function fitting using dynamic structural analysis. Earthq Spectra 31(1):579–599Google Scholar
  5. Barbat A (1982) Cálculo sísmico de estructuras. Editores Técnicos Asociados, BarcelonaGoogle Scholar
  6. Barbat A, Yépez F, Canas JA (1996) Damage scenarios simulation for risk assessment in urban zones. Earthq Spectra 2:371–394CrossRefGoogle Scholar
  7. Barbat A, Oller S, Vielma JC (2005) Cálculo y diseño sismorresistente de edificios: aplicación de la norma NCSE-02. In: Barbat A (ed) Monografías de Ingeniería Sísmica. Centro Internacional de Métodos Numéricos en Ingeniería, BarcelonaGoogle Scholar
  8. Barbat AH, Pujades LG, Lantada N, Moreno R (2008) Seismic damage evaluation in urban areas using the capacity spectrum method: application to Barcelona. Soil Dyn Earthq Eng 28:851–865CrossRefGoogle Scholar
  9. Barbat A, Carreño ML, Pujades L, Lantada N, Cardona OD, Marulanda MC (2010) Seismic vulnerability and risk evaluartion methods for urban areas. A review with application to a pilot area. Struct Infrastruct Eng 6:17–38CrossRefGoogle Scholar
  10. Benedetti D, Petrini V (1984) Sulla vulnerabilità sismica degli edifici in muratura: proposta di un metodo di valutazione. L’Industria della Costruzioni, RomaGoogle Scholar
  11. Bernardini A (2000) The vulnerability of buildings -evaluation on a national scale of the seismic vulnerability of ordinary buildings. CNR-GNDT, RomeGoogle Scholar
  12. Busquets J, Corominas-Ayala M (2009) Cerdà i la Barcelona del futur: realitat versus projecte, BarcelonaGoogle Scholar
  13. CID J (1998). Zonación sísmica de la ciudad de Barcelona basada en métodos de simulación numérica de efectos locales. PhD, Universitat Politècnica de Catalunya, UPCGoogle Scholar
  14. Centre De Cultura Contemporània De Barcelona (CCCB). Ordenanzas de edificación [Online]. Available:
  15. C.S.LL.PP (2008) Decreto Ministeriale del 14 gennaio 2008. Nuove norme tecniche per le costruzioni. Gazzetta Ufficiale della Repubblica Italiana 4 febbraio 2008Google Scholar
  16. D’Ayala D, Meslem A, Vamvatsikos D, Porter K, Rossetto T, Crowley H, Silva V (2014) Guidelines for analytical vulnerability assessment of low/mid-rise buildings-methodology, vulnerability global component project. Available:
  17. De Luca F, Iervolino I, Vamvatsikos D (2011) Improving the static pushover analysis in the Italian seismic code by proper piece-wise-linear fitting of capacity curves. In: ANIDIS2011 convention on seismic engineering, BariGoogle Scholar
  18. EUROCODE-8-1 (2004) Design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. Comité Européen de NormalisationGoogle Scholar
  19. Faccioli E, Cauzzi C (2006) Macroseismic intensities for seismic scenarios estimated from instrumentally based correlations. In: First European conference on earthquake engineering and seismology (a joint event of the 13th ECEE & 30th general assembly of the ESC), 2006 GenèveGoogle Scholar
  20. Fajfar P (1999) Capacity spectrum method based on inelastic demand spectra. Earthq Eng Struct Dyn 28:979–993CrossRefGoogle Scholar
  21. Fardis MN (2009) Seismic design, assessment and retrofitting of concrete buildings based on EN-Eurocode 8. Springer, New YorkCrossRefGoogle Scholar
  22. FEMA, NIBS (1999) HAZUS’99 technical manual: earthquake loss estimation methodology. Federal Emergency Management Agency and National Institute of Building Sciences (FEMA/NIBS), WashingtonGoogle Scholar
  23. FEMA-440, ATC-55 (2005) Improvement of nonlinear static seismic analysis procedures. Federal Emergency Management Agency, CaliforniaGoogle Scholar
  24. Freeman SA, Nicoletti JP, Tyrell JV (1975) Evaluation of existing buildings for seismic risk—a case study of puget sound naval shipyard. U.S. National Conference on Earthquake Engineering, Washington, Bremerton. EERI, pp 113–122Google Scholar
  25. Galasco A, Lagomarsino S, Penna A (2002) TREMURI program: seismic analyser of 3D Masonry Building. University of GenoaGoogle Scholar
  26. Gambarotta L, Lagomarsino S (1997) Computational models for the seismic response of damaging structures. In: Abrams DP, Calvi GM (eds) U.S. Italian workshop on seismic evaluation and retrofit, Columbia University, National Center for Earthquake Engineering Research, New York CityGoogle Scholar
  27. Garcia Espuche A (1990) El quadrat d’Or. Centre de la Barcelona modernista. La formació d’un espai urbà privilegiat, BarcelonaGoogle Scholar
  28. Giovinazzi S, Lagomarsino S (2002) WP04: guidelines for the implementation of the I level methodology for the vulnerability assessment of current buildings. Risk-UE report, GenoaGoogle Scholar
  29. GNDT (1994) Scheda di esposizione e vulnerabilita` e di rilevamento danni di primo livello e secondo livello (muratura e cemento armato). In: Gruppo Nazionale Per La Difesa Dai Terremoti (ed) RomaGoogle Scholar
  30. González-Drigo R, Pérez-García V, Dicapua D, Pujades L (2008) GPR survey applied to modernist buildings in Barcelona: the cultural heritage of the college of industrial engineering. J Cult Herit 9:196–202CrossRefGoogle Scholar
  31. González-Drigo R, Avila-Haro J, Barbat A, Pujades L, Vargas Y, Lagomarsino S, Cattari S (2015) Modernist URM buildings of Barcelona. Seismic vulnerability and risk assessment. Int J Archit Herit 9:214–230CrossRefGoogle Scholar
  32. Grünthal G (1998) European Macroseismic Scale 1998 (EMS-98). Cahiers du Centre Européen de Géodynamique et de Séismologie. Centre Européen de Géodynamique et de Séismologie, LuxembourgGoogle Scholar
  33. HAZUS (2012) HAZUS-MH 2.1 Technical manual. Earthquake model. In: Homeland Security & Federal Emergency Management Agency (eds) Washington, DCGoogle Scholar
  34. Irizarry J, Goula X, Susagna T (2003) Analytical formulation for the elastic acceleration-displacement response spectra adapted to Barcelona soil conditions. Institut Cartogràfic de Catalunya, BarcelonaGoogle Scholar
  35. Jalayer F, Cornel CA (2009) Alternative nonlinear demand estimation methods for probability-based seismic assessments. Earthq Eng Struct Dyn 38:951–972CrossRefGoogle Scholar
  36. Jayaram N, Lin T, Baker JW (2011) A computationally efficient ground motion selection algorithm for matching a target response spectrum mean and variance. Earthq Spectr 27:797–815CrossRefGoogle Scholar
  37. Kappos AJ (1997) Seismic damage indices for RC buildings: evaluation of concepts and procedures. Prog Struct Mat Eng 1:78–87CrossRefGoogle Scholar
  38. Keneddy RP, Cornel CA, Campbell RL, Kaplan S, Perla HF (1980) Probabilistic seismic safety study of an existing nuclear power plant. Nucl Eng Des 59:315–338CrossRefGoogle Scholar
  39. Kreslin M, Fajfar P (2012) The extended N2 method considering higher mode effects in both plan and elevation. Bull Earthq Eng 10:695–715CrossRefGoogle Scholar
  40. Lagomarsino S, Penna A (2003) Guidelines for the implementation of the II level vulnerability methodology. WP4: vulnerability assessment of current buildings. RISK-UE project: an advanced approach to earthquake risk scenarios with application to different European townsGoogle Scholar
  41. Lagomarsino S, Galasco A, Penna A (2002) Pushover and dynamic analysis of URM buildings by means of a non-linear macro-element model. International conference on earthquake loss estimation and risk reduction. RISK-UE project, BucharestGoogle Scholar
  42. Lantada N (2007) Aplicación de Técnicas GIS a Estimación de Riesgos Naturales. PhD, Universitat Politècnica de CatalunyaGoogle Scholar
  43. Lantada N, Pujades L, Barbat A (2009) Vulnerability index and capacity spectrum based methods for urban seismic risk evaluation. A comparison. Nat Hazards 51:501–524CrossRefGoogle Scholar
  44. Milutinovic ZV, Trendafiloski GS (2003) WP4: vulnerability of current buildings. RISK-UE Project handbookGoogle Scholar
  45. NIST (2011) Selecting and scaling earthquake ground motions for performing response-history analyses, NIST GCR 11-917-15. Gaithersburg, Maryland: by NEHRP Consultants Join Venture for the National Institute of Standards and TechnologyGoogle Scholar
  46. Paricio A (2001) Secrets d’un Sistema Constructiu. España, Edicions UPC, BarcelonaGoogle Scholar
  47. Pecker A (2007) Soil structure interaction structure. In: Pecker A (ed) Earthquake engineering analysis. SpringerWien, New York, pp 33–43CrossRefGoogle Scholar
  48. PEER (2011) New ground motion selection procedures and selected motions for the PEER transportation research program. Pacific Earthquake Engineering Research Center, CaliforniaGoogle Scholar
  49. Peng N, Wang SH, Jiang L, Huang RQ (2012) Seismic risk assessment of structures using multiple stripe analysis. Appl Mech Mater 226–228:897–900Google Scholar
  50. Penna A (2002) A macro-element procedure for the non-linear dynamic analysis of masonry buildings. Ph.D., Politecnico di MilanoGoogle Scholar
  51. Pérez-García V, González-Drigo R, Sala R (2012) Ground-penetrating radar resolution in cultural heritage applications. Near Surf Geophys 10:77–87Google Scholar
  52. PIET-70 (1971) Obras de Fábrica. Torroja, I.E, MadridGoogle Scholar
  53. Priestley MJN, Seible F, Calvi GM (1996) Seismic deisgn and retrofit of bridges. Wiley, New YorkCrossRefGoogle Scholar
  54. Pujades L, Barbat A, González-Drigo R, Avila-Haro J (2012) Seismic performance of a block of buildings representative of the typical construction in the eixample district in Barcelona (Spain). Bull Earthq Engs 10:331–349CrossRefGoogle Scholar
  55. Secanell R, Goula X, Susagna T, Fleta J, Roca A (1998) Analysis of seismic hazard in Catalonia (Spain) through different probabilistic approaches. In: Proceedings of the 11th European conference on earthquake engineering, Balkema, ParisGoogle Scholar
  56. Secanell R, Goula X, Susagna T, Fleta J, Roca A (2004) Seismic hazard zonation of Catalonia, Spain, integrating uncertainties. J Seismolog 8:24–40CrossRefGoogle Scholar
  57. Susagna T, Goula X (1999) Cataleg de Sismicitat. Atlas Sismic de Catalunya. In: Catalunya ICFD (ed) BarcelonaGoogle Scholar
  58. The Mathworks I (2009b) MATLAB Release 2009b MassachusettsGoogle Scholar
  59. Vamvatsikos D, Cornell CA (2002) Incremental dynamic analysis. Earthq Eng Struct Dyn 31:491–514CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • R. Gonzalez-Drigo
    • 1
  • J. Avila-Haro
    • 1
  • L. G. Pujades
    • 2
  • A. H. Barbat
    • 2
  1. 1.Department of Strength of Materials and Structural EngineeringEUETIB-UPC BarcelonaTechBarcelonaSpain
  2. 2.Department of Civil and Environmental EngineeringUPC BarcelonaTechBarcelonaSpain

Personalised recommendations