Skip to main content
Log in

Crack width-based fragility curves for repairability of substandard beam-column joints

  • Original Article
  • Published:
Bulletin of Earthquake Engineering Aims and scope Submit manuscript

Abstract

Post-earthquake observations have outlined the poor seismic performance of substandard reinforced concrete (RC) beam-column joints in existing buildings. They often exhibit significant cracking even under moderate intensity earthquakes, compromising the seismic performance of the entire building. This makes the quantification of their residual capacity and the definition of reliable repairability thresholds critical. Different approaches are available in the literature to establish the repairability of RC joints. However, a simple crack width-based criterion is required for practitioners during in-situ inspections. This study deals with the definition of crack width-based fragility curves relying on numerical analyses. Those are carried out by using the validated finite element (FE) models, being capable of reproducing the initiation and development of cracks in RC joints. To this end, the uncertainties in material properties, influencing the seismic performance of structural components, are accounted for different joints. In particular, experimentally validated FE models are evolved to stochastic level by generating random variables of material properties with the stratified sampling scheme. Fragility curves representing a certain level of probability of exceeding the defined crack width at the joint back, joint core, and beam-to-joint interface are developed. An application of the proposed methodology for in-situ inspections is also presented, and the results of in-situ measurements of residual crack width from real buildings damaged by recent earthquakes are used for the validation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.

References

  • ACI 318 (2019) Building code requirements for structural concrete and commentary (aci 318m-11), USA: American Concrete Institute

  • Akyüz S, Uyan M (1992) A study on the concrete steel bars used in Turkey [In Turkish]. Tech J Turkish Chamber Civ Eng 35:497–508

    Google Scholar 

  • ATENA (2017) Software for nonlinear analysis of reinforced concrete structures, Cervenka Consulting, http://www.cervenka.cz/

  • ATENA Program Documentation, Part 1 (2014) Atena theory manual, Cervenka Consulting, http://www.cervenka.cz/

  • ATENA Program Documentation, Part 8. (2015) User’s manuel for ATENA-GID interface

  • ATENA Program Documentation Part 4-9 (2016) ATENA Science – GiD Strengthening of concrete structures, Step by step guide for modelling strengthening with ATENA and GiD, http://www.cervenka.cz/

  • Bal İE, Crowley H, Pinho R, Gülay FG (2008) Detailed assessment of structural characteristics of Turkish RC building stock for loss assessment models. Soil Dyn Earthq Eng 28:914–932. https://doi.org/10.1016/j.soildyn.2007.10.005

    Article  Google Scholar 

  • Cardone D (2016) Fragility curves and loss functions for RC structural components with smooth rebars. Earthq Struct 10:1181–1212

    Article  Google Scholar 

  • CEN (2004) Design of structures for earthquake resistance - Part 1: General rules, seismic actions and rules for buildings. EN1998–1. Brussels, Belgium: Comité Européen de Normalisation (CEN)

  • CEN (2002) Basis of structural design. EN1990. Brussels, Belgium: Comité Européen de Normalisation (CEN)

  • Chen G, Baker G (2003) Influence of bond slip on crack spacing in numerical modeling of reinforced concrete. J Struct Eng 129:1514–1521. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:11(1514)

    Article  Google Scholar 

  • Cuevas A, Pampanin S (2017) Post-seismic capacity of damaged and repaired reinforced concrete plastic hinges extracted from a real building. In: New Zealand Society for Earthquake Engineering Conference, Wellington, New Zelland, pp. 12

  • Del Vecchio C, Di Ludovico M, Balsamo A et al (2014a) Experimental investigation of exterior RC beam-column joints retrofitted with FRP systems. ASCE J Compos Constr 18:1–13

    Google Scholar 

  • Del Vecchio C, Di Ludovico M, Balsamo A et al (2014b) Experimental investigation of exterior RC beam-column joints retrofitted with FRP systems. J Compos Constr 18:04014002. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000459

    Article  Google Scholar 

  • Del Vecchio C, Di Ludovico M, Balsamo A, Prota A (2018) Seismic retrofit of real beam-column joints using fiber-reinforced cement composites. J Struct Eng 144:04018026. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001999

    Article  Google Scholar 

  • Del Vecchio C, Di Ludovico M, Prota A, Manfredi G (2016) Modelling beam-column joints and FRP strengthening in the seismic performance assessment of RC existing frames. Compos Struct 142:107–116. https://doi.org/10.1016/j.compstruct.2016.01.077

    Article  Google Scholar 

  • Duran B, Tunaboyu O, Avşar Ö (2017) Determination of elasticity modulus of low strength concrete and its effect on the risk assessment results by DSVB. J Fac Eng Archit Gazi Univ 32:253–264

    Google Scholar 

  • Engindeniz M (2008) Repair and strengthening of pre-1970 reinforced concrete corner beam-column joints using CFRP composites. Ph.D. Thesis, Georgia Institute of Technology, Georgia, USA.

  • ESM 98 (1998) European Macroseismic Scale (EMS)

  • European Commission & Joint Research Centre (2007) Field Manual for post-earthquake damage and safety assessment and short-term countermeasures (AeDES), Institute for the Protection and Security of the Citizen, Joint Research Centre, European Commission

  • Faleschini F, Gonzalez-Libreros J, Zanini MA et al (2019) Repair of severely-damaged RC exterior beam-column joints with FRP and FRCM composites. Compos Struct 207:352–363. https://doi.org/10.1016/j.compstruct.2018.09.059

    Article  Google Scholar 

  • FEMA 306 (1998) Evaluation of earthquake damaged concrete and masonry wall buildings: basic procedures manual (FEMA 306), Federal Emergency Management Agency, USA

  • FEMA P58 (2018) Seismic performance assessment of buildings (FEMA P58), Federal Emergency Management Agency, USA

  • Fib (2010) Model code for concrete structures. Fédération Internationale du Béton (fib), Berlin: Ernst, Wilhelm & Sohn

  • Fib Bulletin No. 22 (2003) Monitoring and safety evaluation of existing concrete structures. Fédération Internationale du Béton (fib), Lausanne, Switzerland

  • Fib Bulletin No. 25 (2003) Displacement-based seismic design of reinforced concrete buildings. State-of-art report. Fédération Internationale du Béton (fib). Lausanne, Switzerland

  • Haach VG, Debs LHDCE, A, Khalil El Debs M, (2008) Evaluation of the influence of the column axial load on the behavior of monotonically loaded R/C exterior beam–column joints through numerical simulations. Eng Struct 30:965–975. https://doi.org/10.1016/j.engstruct.2007.06.005

    Article  Google Scholar 

  • Hassan WM (2011) Analytical and experimental assessment of seismic vulnerability of beam-column joints without transverse reinforcement in concrete buildings. PhD Thesis, University of California, Berkeley, USA

  • HAZUS MR4 (2003) Multi-hazard loss estimation methodology. Earthquake Model (HAZUS MH. MR4) Technical Manual. Department of Homeland Security, Emergency Preparedness and Response Directorate, FEMA

  • Hordijk DA (1991) Local approach to fatigue of concrete. Ph.D. Thesis, Delft University of Technology, Netherlands

  • Hotelling H (1936) Relations between two sets of variates. Biometrika 28:321–377. https://doi.org/10.2307/2333955

    Article  Google Scholar 

  • JBDPA (2001) Guideline for post-earthquake damage evaluation and rehabilitation, The Japan Building Disaster Prevention Association (JBDPA), Japan

  • Joint Committee on Structural Safety (2000) Probabilistic model code, Part 3: Material properties. https://www.jcss-lc.org/

  • Kalogeropoulos GI, Tsonos A-DG, Konstandinidis D, Tsetines S (2016) Pre-earthquake and post-earthquake retrofitting of poorly detailed exterior RC beam-to-column joints. Eng Struct 109:1–15. https://doi.org/10.1016/j.engstruct.2015.11.009

    Article  Google Scholar 

  • Kollegger J, Mehlhorn G (1988) Experimentelle und analytische untersuchungen zur aufstellung eines materialmodels für gerissene stahlbetonscheiben (in German), Nr.6 Forschungsbericht, Massivbau, Gesamthochschule Kassel

  • Kolmar W (1986) Beschreibung der kraftübertragung über risse in nichtlinearen finite- element-berechnungen von stahlbetontragwerken (in German). Dissertation, T.H. Darmstadt

  • Kulkarni SA, Li B, Yip WK (2008) Finite element analysis of precast hybrid-steel concrete connections under cyclic loading. J Constr Steel Res 64:190–201. https://doi.org/10.1016/j.jcsr.2007.05.002

    Article  Google Scholar 

  • Marder K, Elwood KJ, Motter CJ, Clifton GC (2020) Post-earthquake assessment of moderately damaged reinforced concrete plastic hinges. Earthq Spectra 36:299–321. https://doi.org/10.1177/8755293019878192

    Article  Google Scholar 

  • Marder K, Sarrafzadeh M, Elwood K (2018) Effectiveness of repair via epoxy injection of earthquake damaged reinforced concrete beam elements. In: 17th U.S.-Japan-New Zealand Workshop on the Improvement of Structural Engineering and Resilience, pp. 8

  • Mencik J (2016) Latin hypercube sampling, Concise reliability for engineers, IntechOpen, DOI: https://doi.org/10.5772/62370. Available from: https://www.intechopen.com/books/concise-reliability-for-engineers/latin-hypercube-sampling

  • MIT (2018) Aggiornamento delle, Norme tecniche per le costruzioni, (in Italian). Supplemento ordinario n. 8 alla Gazzetta uiciale del 20–2–2018. Rome, Italy

  • Najafgholipour MA, Dehghan SM, Dooshabi A, Niroomandi A (2017) Finite element analysis of reinforced concrete beam-column connections with governing joint shear failure mode. Latin Am J Solids Struct 14:1200–1225. https://doi.org/10.1590/1679-78253682

    Article  Google Scholar 

  • Novák D, Vořechovský M, Rusina R (2015) FReET v.1.5 – program documentation. User´s and Theory Guides. http://www.freet.cz. Brno/Červenka Consulting, Czech Republic

  • Pagni CA, Lowes LN (2006) Fragility functions for older reinforced concrete beam-column joints. Earthq Spectra 22:215–238. https://doi.org/10.1193/1.2163365

    Article  Google Scholar 

  • Pantelides CP, Hansen J, Nadauld JD, Reaveley LD (2002) Assessment of reinforced concrete building exterior joints with substandard details. Technical Report PEER 2002–18, Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA

  • Pohoryles DA, Melo J, Rossetto T et al (2018) Experimental comparison of novel CFRP retrofit schemes for realistic full-scale RC beam–column joints. J Compos Constr 22:18. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000865

    Article  Google Scholar 

  • Priestley MJN (1997) Displacement-based seismic assessment of reinforced concrete buildings. J Earthquake Eng 1:157–192. https://doi.org/10.1080/13632469708962365

    Article  Google Scholar 

  • Pukl R, Sajdlova T, Routil L et al. (2016) Case study ‒ Nonlinear reliability analysis of a concrete bridge. In: Maintenance, monitoring, safety, risk and resilience of bridges and bridge networks: proceedings of the 8th international conference on bridge maintenance, safety and management (IABMAS2016)

  • Rankine W (1857) On the stability of loose earth. Philos Trans R Soc Lond. https://doi.org/10.1098/rstl.1857.0003

    Article  Google Scholar 

  • Rimkus A, Cervenka V, Gribniak V, Cervenka J (2020) Uncertainty of the smeared crack model applied to RC beams. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2020.107088

    Article  Google Scholar 

  • Samad AA, Noorwirdawati A, Mohamad N et al (2017) Shear strengthening and shear Repair of 2-Span continuous RC beams with CFRP strips. J Compos Constr 21:04016099. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000756

    Article  Google Scholar 

  • Shayanfar J, Hemmati A, Bengar HA (2019) A simplified numerical model to simulate RC beam–column joints collapse. Bull Earthquake Eng 17:803–844. https://doi.org/10.1007/s10518-018-0472-z

    Article  Google Scholar 

  • TBEC (2018) Turkish Building Earthquake Code, Specification for structures to be built in disaster areas. Ministry of Public Works and Settlement Government of Republic of Turkey, Turkey

    Google Scholar 

  • TEC (1975) Turkish Earthquake Code, Specification for structures to be built in disaster areas. Turkey: Turkish Goverment Ministry of Reconstruction and Resettlement

  • Van Mier JGM (1986) Multiaxial strain-softening of concrete, Part I: fracture. Materials and Structures, RILEM 19

  • Vecchio FJ, Collins MP (1986) Modified compression-field theory for reinforced concrete beams subjected to shear. ACI J 83:219–231

    Google Scholar 

  • Yurdakul Ö, Avşar Ö (2016) Strengthening of substandard reinforced concrete beam-column joints by external post-tension rods. Eng Struct 107:9–22. https://doi.org/10.1016/j.engstruct.2015.11.004

    Article  Google Scholar 

  • Yurdakul O, Avsar O (2015) Structural repairing of damaged reinforced concrete beam-column assemblies with CFRPs. Struct Eng Mech 54:521–543. https://doi.org/10.12989/sem.2015.54.3.521

    Article  Google Scholar 

  • Yurdakul Ö, Balaban E, Artagan SS, Routil L (2021a) Stochastic assessment of bond-slip behavior of plain round bars in low strength concrete. Eng Struct 229:111658. https://doi.org/10.1016/j.engstruct.2020.111658

    Article  Google Scholar 

  • Yurdakul O, Del Vecchio C, Di Ludovico M et al. (2019a) Sensitivity of cyclic response of substandard beam-column joints to material properties. In: Computational methods in structural dynamics and earthquake engineering (COMPDYN 2019), Crete, Greece

  • Yurdakul Ö, Del Vecchio C, Di Ludovico M, Avsar Ö (2020a) Numerical simulation of substandard beam-column joints with different failure mechanisms. Struct Concr. https://doi.org/10.1002/suco.201900003

    Article  Google Scholar 

  • Yurdakul Ö, Del Vecchio C, Ludovico MD, Avsar O (2018a) Comparison of refined numerical modeling for substandard beam-column joints. In: 16th European Conference on Earthquake Enginering (16ECEE), Thessaloniki, Greece

  • Yurdakul Ö, Duran B, Tunaboyu O, Avşar Ö (2021b) Field reconnaissance on seismic performance of RC buildings after the January 24, 2020 Elazığ-Sivrice earthquake. Nat Hazards 105:859–887. https://doi.org/10.1007/s11069-020-04340-x

    Article  Google Scholar 

  • Yurdakul Ö, Tunaboyu O, Avşar Ö (2018b) Retrofit of non-seismically designed beam-column joints by post-tensioned superelastic shape memory alloy bars. Bull Earthq Eng 16:5279–5307. https://doi.org/10.1007/s10518-018-0323-y

    Article  Google Scholar 

  • Yurdakul Ö, Tunaboyu O, Routil L, Avşar Ö (2019b) Stochastic-based nonlinear numerical modeling of shear critical RC beam repaired with bonded CFRP sheets. J Compos Constr 23:04019042. https://doi.org/10.1061/(ASCE)CC.1943-5614.0000966

    Article  Google Scholar 

  • Yurdakul Ö, Tunaboyu O, Routil L, Avşar Ö (2020b) Parameter sensitivity of CFRP retrofitted substandard joints by stochastic computational mechanics. Compos Struct 238:112003. https://doi.org/10.1016/j.compstruct.2020.112003

    Article  Google Scholar 

Download references

Acknowledgements

This study has been accomplished with the support of the Educational and Research Centre in Transport, Faculty of Transport Engineering, University of Pardubice.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Özgür Yurdakul.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yurdakul, Ö., Del Vecchio, C., Di Ludovico, M. et al. Crack width-based fragility curves for repairability of substandard beam-column joints. Bull Earthquake Eng 19, 6081–6111 (2021). https://doi.org/10.1007/s10518-021-01218-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-021-01218-6

Keywords

Navigation