Bulletin of Earthquake Engineering

, Volume 17, Issue 3, pp 1285–1330 | Cite as

Empirical drift-fragility functions and loss estimation for infills in reinforced concrete frames under seismic loading

  • Carlo Del Gaudio
  • Maria Teresa De RisiEmail author
  • Paolo Ricci
  • Gerardo Mario Verderame
Original Research


Earthquakes that have occurred in the last twenty years in the Mediterranean area have had significant economic and social impacts. Most of the economic losses of reinforced concrete (RC) frames was due to nonstructural component damage, particularly masonry infills and partitions. Therefore, the seismic behaviour of masonry infills should be reliably characterized. The main goals of this study for a more reliable loss estimation for infilled RC frames are: (i) the analysis of the inter-story drift ratio (IDR) capacity at given damage states (DSs) with the aim to define drift-based fragility functions and (ii) analyse direct losses due to infill damage following seismic events. First, a database of experimental tests performed on 1-bay, 1-story scaled RC frames infilled with clay bricks or concrete blocks is collected. Drift-based fragility curves are obtained, which depend on the infill brick materials and properties. Then, the drift capacity threshold at each DS is correlated to the in-plane response of the infill panel to directly quantify the relationship that exists among them. The influence of openings on drift capacities is also evaluated. Then, seismic losses related to infills are computed, providing expected monetary losses depending on the infill typology. The required reparation activities and their costs are also listed. The bearing of each activity and cost at each DS is explicitly evaluated. Additionally, loss functions that directly depend on IDR demand are provided, thus fusing together the damage analysis and loss analysis. Finally, a simplified formulation for loss functions is proposed for a simple, practice-oriented loss calculation.


RC buildings Masonry infills Brick typology Experimental data Damage states Fragility curves Loss functions 



This work was developed under the support of ReLUIS-DPC 2014-2018 “PR2. Strutture in cemento armato-WP6. Capacità sismica di tamponature ed interventi di rafforzamento”, funded by the Italian Department of Civil Protection (DPC), and AXA Research Fund Post-Doctoral Grant “Advanced nonlinear modelling and performance assessment of masonry infills in RC buildings under seismic loads: the way forward to design or retrofitting strategies and reduction of losses”. These financial supports are gratefully acknowledged.


  1. Akhound F, Vasconcelos G, Lourenço PB, Palha CAOF, Silva LC (2015) In-plane and out-of plane experimental characterization of RC masonry infilled frames. In: M2D-6th international conference on mechanics and materials in design, pp 427–440Google Scholar
  2. Alwashali H, Torihata Y, Jin K, Maeda M (2018) Experimental observations on the in-plane behaviour of masonry wall infilled RC frames; focusing on deformation limits and backbone curve. Bull Earthq Eng 16(3):1373–1397CrossRefGoogle Scholar
  3. Angel RD, Abrams DP, Shapiro D, Uzarski J, Webster M (1994) Behavior of reinforced concrete frames with masonry infills. University of Illinois Engineering Experiment Station. College of Engineering. University of Illinois at Urbana-ChampaignGoogle Scholar
  4. ASCE (2013) ASCE/SEI 41-13. Seismic evaluation and retrofit of existing buildings. American Society of Civil Engineers, RestonGoogle Scholar
  5. Baggio C, Bernardini A, Colozza R, Coppari S, Corazza L, Della Bella M, Di Pasquale G, Dolce M, Goretti A, Martinelli A, Orsini G, Papa F, Zuccaro G (2007) Field manual for post-earthquake damage and safety assessment and short term countermeasures. Translation from Italian: Goretti A, Rota M, JRC Scientific and Technical Reports, EUR 22868 EN-2007Google Scholar
  6. Baran M, Sevil T (2010) Analytical and experimental studies on infilled RC frames. Int J Phys Sci 5(13):1981–1998Google Scholar
  7. Bergami AV, Nuti C (2015) Experimental tests and global modeling of masonry infilled frames. Earthq Struct 9(2):281–303CrossRefGoogle Scholar
  8. Bertoldi SH, Decanini LD, Gavarini C (1993) Telai tamponati soggetti ad azioni sismiche, un modello semplificato: confronto sperimentale e numerico. Atti del 6 Convegno Nazionale L’ingegneria sismica in Italia, pp 815–824Google Scholar
  9. B.U.R.A. (Official Journal of Regione Abruzzo) (n. 10—08/03/2017—ordinary), Price List of Public Works in Abruzzi Region, Italy (in Italian) Google Scholar
  10. B.U.R.A. (Official Journal of Regione Abruzzo) (n. 10—28/10/2009—extraordinary), Updating of the regional price list for reconstruction after the April 6, 2009 earthquake (in Italian) Google Scholar
  11. Calvi GM, Bolognini D (2001) Seismic response of reinforced concrete frames infilled with weakly reinforced masonry panels. J Earthq Eng 5(02):153–185Google Scholar
  12. Cardone D, Perrone G (2015) Developing fragility curves and loss functions for masonry infill walls. Earthq Struct 9(1):257–279CrossRefGoogle Scholar
  13. Cavaleri L, Di Trapani F (2014) Cyclic response of masonry infilled RC frames: experimental results and simplified modeling. Soil Dyn Earthq Eng 65:224–242CrossRefGoogle Scholar
  14. CEN (2005) Eurocode 8: design of structures for earthquake resistance-part 1: general rules, seismic actions and rules for buildings. European Committee for Standardization, BrusselsGoogle Scholar
  15. Centeno J, Ventura CE, Foo S (2008) Shake table testing of gravity load designed reinforced concrete frames with unreinforced masonry infill walls. In: The 14th world conference on earthquake engineering, BeijingGoogle Scholar
  16. Chiou TC, Hwang SJ (2015) Tests on cyclic behavior of reinforced concrete frames with brick infill. Earthq Eng Struct Dyn 44(12):1939–1958CrossRefGoogle Scholar
  17. Chiozzi A, Miranda E (2017) Fragility functions for masonry infill walls with in-plane loading. Earthq Eng Struct Dyn 46(15):2831–2850CrossRefGoogle Scholar
  18. Chrysostomou CZ, Asteris PG (2012) On the in-plane properties and capacities of infilled frames. Eng Struct 41:385–402CrossRefGoogle Scholar
  19. Colangelo F (2005) Pseudo-dynamic seismic response of reinforced concrete frames infilled with non-structural brick masonry. Earthq Eng Struct Dyn 2005(34):1219–1241CrossRefGoogle Scholar
  20. Colangelo F (2013) Drift-sensitive non-structural damage to masonry-infilled reinforced concrete frames designed to Eurocode 8. Bull Earthq Eng 11(6):2151–2176CrossRefGoogle Scholar
  21. Crisafulli FJ (1997) Seismic behaviour of reinforced concrete structures with masonry infills. PhD Thesis, University of CanterburyGoogle Scholar
  22. De Risi MT, Del Gaudio C, Ricci P, Verderame GM (2017). Simplified numerical modelling for hollow clay-masonry infills in RC frames under in-plane seismic loads. In: ANIDIS 2017, PistoiaGoogle Scholar
  23. De Risi MT, Del Gaudio C, Ricci P, Verderame GM (2018) In-plane behaviour and damage assessment of masonry infills with hollow clay bricks in RC frames. Eng Struct 168:257–275CrossRefGoogle Scholar
  24. Decreto Ministeriale del (2008) Approvazione delle nuove norme tecniche per le costruzioni. G.U. n. 29 del 4/2/2008 (in Italian) Google Scholar
  25. Del Gaudio C, Ricci P, Verderame GM, Manfredi G (2016a) Observed and predicted earthquake damage scenarios: the case study of Pettino (L’Aquila) after the 6th April 2009 event. Bull Earthq Eng 14(10):2643–2678CrossRefGoogle Scholar
  26. Del Gaudio C, De Martino G, Di Ludovico M, Manfredi G, Prota A, Ricci P, Verderame GM (2016b) Empirical fragility curves from damage data on RC buildings after the 2009 L’Aquila earthquake. Bull Earthq Eng.
  27. Del Gaudio C, De Risi MT, Ricci P, Verderame GM (2017) Fragility functions for clay masonry infills in RC buildings under in-plane seismic actions. In: ANIDIS 2017, PistoiaGoogle Scholar
  28. Dolce M, Goretti A (2015) Building damage assessment after the 2009 Abruzzi earthquake. Bull Earthq Eng 13(8):2241–2264CrossRefGoogle Scholar
  29. Dolšek M, Fajfar P (2008) The effect of masonry infills on the seismic response of a four-storey reinforced concrete frame—a deterministic assessment. Eng Struct 30(7):1991–2001CrossRefGoogle Scholar
  30. FEMA P-58, ATC—Applied Technology Council (2012b), FEMA P-58 Next-generation Seismic Performance Assessment for Buildings, vol 2—Implementation Guide, Federal Emergency Management Agency, Washington, DCGoogle Scholar
  31. Frumento S, Magenes G, Morandi P, Calvi GM (2009). Interpretation of experimental shear tests on clay brick masonry walls and evaluation of q-factors for seismic design. Research Report EUCENTRE 2009/02, IUSS Press, Pavia, ISBN: 978-88-6198-034-1Google Scholar
  32. Gazić G, Sigmund V (2016) Cyclic testing of single-span weak frames with masonry infill. Građevinar 68(08):617–633Google Scholar
  33. Grünthal G., (1998). Cahiers du Centre Européen de Géodynamique et de Séismologie: vol 15—European macroseismic scale 1998. European Center for Geodynamics and Seismology, LuxembourgGoogle Scholar
  34. Guidi G, da-Porto F, Dalla-Benetta M, Verlato N, Modena C (2013) Comportamento sperimentale nel piano e fuori piano di tamponamenti in muratura armata e rinforzata. Dipartimento di Ingegneria Civile, Edile e Ambientale, PadovaGoogle Scholar
  35. Haider S (1995) In-plane cyclic response of reinforced concrete frames with unreinforced masonry infills. PhD Thesis, Rice UniversityGoogle Scholar
  36. Hak S, Morandi P, Magenes G, Sullivan TJ (2012) Damage control for clay masonry infills in the design of RC frame structures. J Earthq Eng 16(sup1):1–35CrossRefGoogle Scholar
  37. Kakaletsis D (2009) Masonry infills with window openings and influence on reinforced concrete frame constructions. WIT Trans Built Environ 104:445–455CrossRefGoogle Scholar
  38. Kakaletsis D, Karayannis C (2007) Experimental investigation of infilled R/C frames with eccentric openings. Struct Eng Mech 26(3):231–250CrossRefGoogle Scholar
  39. Kakaletsis DJ, Karayannis CG (2008) Influence of masonry strength and openings on infilled R/C frames under cyclic loading. J Earthq Eng 12(2):197–221CrossRefGoogle Scholar
  40. Kakaletsis DJ, Karayannis CG (2009) Experimental investigation of infilled reinforced concrete frames with openings. ACI Struct J 106(2):132Google Scholar
  41. Khoshnoud HR, Marsono K (2016) Experimental study of masonry infill reinforced concrete frames with and without corner openings. Struct Eng Mech 57(4):641–656CrossRefGoogle Scholar
  42. Kyriakides MA, Billington SL (2008) Seismic retrofit of masonry-infilled non-ductile reinforced concrete frames using sprayable ductile fiber-reinforced cementitious composites. In: The 14th world conference on earthquake Engineering, BeijingGoogle Scholar
  43. Lowes L, Li J (2011) Background document FEMA P-58/BD/3.8. 6: fragility functions for reinforced concrete moment frames. Federal Emergency Management Agency, Washington, DCGoogle Scholar
  44. Mansouri A, Marefat MS, Khanmohammadi M (2014) Experimental evaluation of seismic performance of low-shear strength masonry infills with openings in reinforced concrete frames with deficient seismic details. Struct Design Tall Spec Build 23(15):1190–1210CrossRefGoogle Scholar
  45. Mehrabi AB, Benson Shing P, Schuller MP, Noland JL (1996) Experimental evaluation of masonry-infilled RC frames. J Struct Eng 122(3):228–237. CrossRefGoogle Scholar
  46. Misir IS, Ozcelik O, Girgin SC, Yucel U (2016) The behavior of infill walls in RC frames under combined bidirectional loading. J Earthq Eng 20(4):559–586CrossRefGoogle Scholar
  47. Morandi P, Hak S, Magenes G (2014). In-plane experimental response of strong masonry infills. In: 9th international masonry conference 2014, GuimaraesGoogle Scholar
  48. Pereira MFP, Pereira MF, Ferreira JE, Lourenço PB (2011) Behavior of masonry infill panels in RC frames subjected to in plane and out of plane loads. In: 7th international conference on analytical models and new concepts in concrete and masonry structuresGoogle Scholar
  49. Petry S, Beyer K (2014) Influence of boundary conditions and size effect on the drift capacity of URM walls. Eng Struct 2014(65):76–88CrossRefGoogle Scholar
  50. Ricci P, De Risi MT, Verderame GM, Manfredi G (2013) Influence of infill distribution and design typology on seismic performance of low-and mid-rise RC buildings. Bull Earthq Eng 11(5):1585–1616CrossRefGoogle Scholar
  51. Ricci P, De Risi MT, Verderame GM, Manfredi G (2016) Procedures for calibration of linear models for damage limitation in design of masonry-infilled RC frames. Earthq Eng Struct Dyn 45(8):1315–1335CrossRefGoogle Scholar
  52. Ricci P, Di Domenico M, Verderame GM (2017) Experimental assessment of the out-of-plane seismic response of URM infill walls. In: ANIDIS 2017, PistoiaGoogle Scholar
  53. Ross SM (2003) Peirce’s criterion for the elimination of suspect experimental data. J Eng Technol 20(2):38–41Google Scholar
  54. Saneinejad A, Hobbs B (1995) Inelastic design of infilled frames. J Struct Eng 121(4):634–650CrossRefGoogle Scholar
  55. Sassun K, Sullivan TJ, Morandi P, Cardone D (2016) Characterising the in-plane seismic performance of infill masonry. Bull N Z Soc Earthq Eng 49(1):100–117Google Scholar
  56. Schwarz S, Hanaor A, Yankelevsky DZ (2015) Experimental response of reinforced concrete frames with AAC masonry infill walls to in-plane cyclic loading. In Structures, vol 3, pp 306–319Google Scholar
  57. Sigmund V, Penava D (2012) Experimental study of masonry infilled R/C frames with opening. In: Proceedings of the 15WCEE, LisbonGoogle Scholar
  58. Stafford Smith B (1962) Lateral stiffness of infilled frames. ASCE J Struct Div 88(ST6):183–199Google Scholar
  59. Stavridis A (2009) Analytical and experimental study of seismic performance of reinforced concrete frames infilled with masonry walls. University of California, San DiegoGoogle Scholar
  60. Suzuki T, Choi H, Sanada Y, Nakano Y, Matsukawa K, Paul D, Gulkan P, Binici B (2017) Experimental evaluation of the in-plane behaviour of masonry wall infilled RC frames. Bull Earthq Eng 15(10):4245–4267CrossRefGoogle Scholar
  61. Turgay T, Durmus MC, Binici B, Ozcebe G (2014) Evaluation of the predictive models for stiffness, strength, and deformation capacity of RC Frames with masonry infill walls. ASCE J Struct Eng 140(10):06014003CrossRefGoogle Scholar
  62. Velázquez-Dimas J, Quiñonez-Esquivel B, Castorena-González J, Reyes-Salazar A, González-Cuevas J, López-López D (2012) In-plane behaviour of confined masonry walls with holes retrofitted with GFRP and subjected to lateral cyclic loading. In: Proceedings of the 15th Word Conference of Earthquake Engineering, Lisbon, PortugalGoogle Scholar
  63. Verderame G.M., Ricci P., Del Gaudio C. & De Risi M.T. (2016), Experimental tests on masonry infilled gravity- and seismic-load designed RC frames, Brick and Block Masonry: Trends, Innovations and Challenges - Proceedings of the 16th International Brick and Block Masonry Conference, IBMAC 2016, pp. 1349-1358Google Scholar
  64. Waly (2010) Experimental and analytical work on the seismic performance of different types of masonry infilled reinforced concrete frames under cyclic loading, thesis, School of Natural and Applied Sciences of Dokuz Eylül UniversityGoogle Scholar
  65. Zarnic R, Tomazevic M (1984) The behaviour of masonry infilled reinforced concrete frames subjected to cyclic lateral loading. In: Proceedings of the 8th world conference on earthquake engineering, San Francisco, Prentice-HallGoogle Scholar
  66. Zhai C, Kong J, Wang X, Chen Z (2016) Experimental and finite element analytical investigation of seismic behavior of full-scale masonry infilled RC frames. J Earthquake Eng 20(7):1171–1198CrossRefGoogle Scholar
  67. Zovkic J, Sigmund V, Guljas I (2013) Cyclic testing of a single bay reinforced concrete frames with various types of masonry infill. Earthq Eng Struct Dyn 42:1131–1149CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Structures for Engineering and Architecture (DIST)University of Naples Federico IINaplesItaly

Personalised recommendations