Skip to main content

Advertisement

SpringerLink
Log in

Post-earthquake damage assessment for RC columns using crack image complexity measures

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

Abstract

The seismic peak interstory drift ratio (IDR) of RC columns following an earthquake is measured in this paper through surface crack image analysis. The succolarity, lacunarity and fractal dimensions of the crack patterns for damaged RC columns are considered as the quantitative representatives of the complexity and irregularity of the crack images. An extensive databank of 445 crack maps from cyclic experiments on 110 rectangular reinforced concrete column specimens with double-curvature deformation mode is collected and utilized for the development and validation of the proposed procedure. The research databank covers a broad series of structural and geometric characteristics. Eight predictive closed-form equations are derived aiming at estimating the experienced peak IDR experienced by the RC columns during a seismic event using the accessible structural data from the damaged column. Results reveal that succolarity dimension is a strong vision-based indicator of damage in RC columns. Finally, the methodology is demonstrated through a practical application for a real damaged column in 2017, M 7.3, Kermanshah earthquake.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  • Abiyev R, Kilic KI (2009) An efficient fractal measure for image texture recognition. In: 2009 Fifth international conference on soft computing, computing with words and perceptions in system analysis, decision and control. IEEE, pp 1–4

  • Adhikari RS, Moselhi O, Bagchi A (2014) Image-based retrieval of concrete crack properties for bridge inspection. Autom Constr 39:180–194

    Article  Google Scholar 

  • Adhikari RS, Moselhi O, Bagchi A, Rahmatian A (2016) Tracking of defects in reinforced concrete bridges using digital images. J Comput Civ Eng 30:4016004

    Article  Google Scholar 

  • Afzali M, Hamidia M, Safi M (2023) Data-driven strength-based seismic damage index measurement for RC columns using crack image-derived parameters. Measurement 218:113155

    Article  Google Scholar 

  • Allain C, Cloitre M (1991) Characterizing the lacunarity of random and deterministic fractal sets. Phys Rev A 44:3552

    Article  Google Scholar 

  • Amarloo N, Emami AR (2019) A 3-dimensional perspective for inter-storey drift, ductility and damage distributions in plan-irregular RC buildings considering seismic orientation effect. Bull Earthq Eng 17:3447–3474

    Article  Google Scholar 

  • Anagnostopoulos SA, Moretti M, Panoutsopoulou M, et al (2004) Post earthquake damage and usability assessment of buildings: further development and applications. Final Rep

  • Asjodi AH, Daeizadeh MJ, Hamidia M, Dolatshahi KM (2021) Arc length method for extracting crack pattern characteristics. Struct Control Heal Monit 28:e2653

    Google Scholar 

  • Asjodi AH, Dolatshahi KM (2022a) Peak drift ratio estimation for unreinforced masonry walls using visual features of damage. Bull Earthq Eng

  • Asjodi AH, Dolatshahi KM, Burton HV (2023) Three-dimensional fragility surface for reinforced concrete shear walls using image-based damage features. Earthq Eng Struct Dyn 52:2533–2553. https://doi.org/10.1002/eqe.3832

    Article  Google Scholar 

  • ATC (2005) ATC-20, Post-earthquake safety evaluation of buildings. Applied Technology Council, USA

  • Athanasiou A, Ebrahimkhanlou A, Zaborac J et al (2020) A machine learning approach based on multifractal features for crack assessment of reinforced concrete shells. Comput Civ Infrastruct Eng 35:565–578

    Article  Google Scholar 

  • Ayad A, Bakkali S (2019) Fractal assessment of the disturbances of phosphate series using lacunarity and succolarity analysis on geoelectrical images (Sidi Chennane, Morocco). Complexity 2019

  • Azuma Y, Zenriku O (1977) Examination of AF2 series experimental results. J Struct Constr Eng 25:1499–1500

    Google Scholar 

  • Azuma Y, Zenriku O, Otsuka S, Serikawa E (1976) Loading history effects on the failure modes of RC columns. J Struct Constr Eng 25:1419–1422

    Google Scholar 

  • Baggio C, Bernardini A, Colozza R, 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 (AeDES). EUR Eur Commission Joint Res Centre 22868:89

    Google Scholar 

  • Bett BJ, Jirsa JO, Klingner RE (1985) Behavior of strengthened and repaired reinforced concrete columns under cyclic deformations. Phil M. Ferguson Structural Engineering Laboratory, University of Texas

  • Bisch P, Erlicher S, Huguet M, Ruocci G (2021) Cracking in shear walls in seismic situation: experimental results and analytical predictions. Bull Earthq Eng 19:1569–1604

    Article  Google Scholar 

  • Cao M, Ren Q, Qiao P (2006) Nondestructive assessment of reinforced concrete structures based on fractal damage characteristic factors. J Eng Mech ASCE 132:924–931

    Article  Google Scholar 

  • Carrillo J, Dominguez D, Prado N (2017) Seismic damage index based on fractal dimension of cracking on thin reinforced concrete walls. ACI Struct J 114:1649–1658

    Article  Google Scholar 

  • Cha Y, Choi W, Büyüköztürk O (2017) Deep learning-based crack damage detection using convolutional neural networks. Comput Civ Infrastruct Eng 32:361–378

    Article  Google Scholar 

  • Cojocaru JIR, Popescu D, Nicolae IE (2013) Texture classification based on succolarity. In: 2013 21st telecommunications forum telfor (TELFOR). IEEE, pp 498–501

  • de Melo RHC (2007) Using fractal characteristics such as fractal dimension, lacunarity and succolarity to characterize texture patterns on images, M. Sc. Thesis, UFF

  • de Melo RHC, Conci A (2008) Succolarity: defining a method to calculate this fractal measure. In: 2008 15th International Conference on Systems, Signals and Image Processing. IEEE, pp 291–294

  • de Melo RHC, Conci A (2013) How succolarity could be used as another fractal measure in image analysis. Telecommun Syst 52:1643–1655

    Article  Google Scholar 

  • Del Gaudio C, De Risi MT, Ricci P, Verderame GM (2019) Empirical drift-fragility functions and loss estimation for infills in reinforced concrete frames under seismic loading. Bull Earthq Eng 17:1285–1330

    Article  Google Scholar 

  • Dogan G, Arslan MH, Baykan OK (2020) Determination of damage levels of RC columns with a smart system oriented method. Bull Earthq Eng 18:3223–3245

    Article  Google Scholar 

  • Dolatshahi KM, Beyer K (2022) Stiffness and strength estimation of damaged unreinforced masonry walls using crack pattern. J Earthq Eng 26:837–856

    Article  Google Scholar 

  • Dubčáková R (2011) Eureqa: software review

  • Ebrahimkhanlou A, Farhidzadeh A, Salamone S (2016) Multifractal analysis of crack patterns in reinforced concrete shear walls. Struct Heal Monit 15:81–92

    Article  Google Scholar 

  • Ebrahimkhanlou A, Athanasiou A, Hrynyk TD et al (2019) Fractal and multifractal analysis of crack patterns in prestressed concrete girders. J Bridg Eng 24:4019059

    Article  Google Scholar 

  • Ebrahimkhanlou A, Farhidzadeh A, Salamone S (2015) Multifractal analysis of two-dimensional images for damage assessment of reinforced concrete structures. In: Sensors and smart structures technologies for civil, mechanical, and aerospace systems 2015. SPIE, pp 408–415

  • Elghazouli AY, Kumar M, Stafford PJ (2014) Prediction and optimisation of seismic drift demands incorporating ground motion frequency content. Bull Earthq Eng 12:255–276

    Article  Google Scholar 

  • Farhan AH, Dawson AR, Thom NH (2016) Characterization of rubberized cement bound aggregate mixtures using indirect tensile testing and fractal analysis. Constr Build Mater 105:94–102

    Article  Google Scholar 

  • Farhidzadeh A, Dehghan-Niri E, Moustafa A et al (2013) Damage assessment of reinforced concrete structures using fractal analysis of residual crack patterns. Exp Mech 53:1607–1619

    Article  Google Scholar 

  • FEMA (2018) Seismic Performance Assessment of Buildings - Methodology, Fema P-58, Washington, DC

  • Fukada Y (1976) Experimental investigation of damage in RC columns with various longitudinal rebar arrangements. J Struct Constr Eng 25:1413–1414

    Google Scholar 

  • Gaetani d’Aragona M, Polese M, Cosenza E, Prota A (2019) Simplified assessment of maximum interstory drift for RC buildings with irregular infills distribution along the height. Bull Earthq Eng 17:707–736

    Article  Google Scholar 

  • Gefen Y, Meir Y, Mandelbrot BB, Aharony A (1983) Geometric implementation of hypercubic lattices with noninteger dimensionality by use of low lacunarity fractal lattices. Phys Rev Lett 50:145

    Article  Google Scholar 

  • Grünthal G (1998) European macroseismic scale 1998. European Seismological Commission (ESC)

  • GrzybowskiBlachowicz JT (2020) Estimation of spatial distribution and symmetry of textile materials using lacunarity. Commun Dev Assem Text Prod 1:180–185

    Google Scholar 

  • Hamidia M, Ganjizadeh A (2022a) Post-earthquake damage evaluation of non-ductile RC moment frames using surface crack patterns. Struct Control Heal Monit 29(10):e3024

    Google Scholar 

  • Hamidia M, Ganjizadeh A (2022b) Computer vision-based automated stiffness loss estimation for seismically damaged non-ductile reinforced concrete moment frames. Bull Earthq Eng 20(12):6635–6658

    Article  Google Scholar 

  • Hamidia M, Ganjizadeh A, Dolatshahi KM (2022a) Peak drift ratio estimation for RC moment frames using multifractal dimensions of surface crack patterns. Eng Struct 255:113893

    Article  Google Scholar 

  • Hamidia M, Mansourdehghan S, Asjodi AH, Dolatshahi KM (2022c) Machine learning-based seismic damage assessment of non-ductile RC beam-column joints using visual damage indices of surface crack patterns. Structures 45:2038–2050

    Article  Google Scholar 

  • Hamidia M, Mansourdehghan S, Asjodi A, Dolatshahi K (2022d) Machine learning-aided scenario-based seismic drift measurement for RC moment frames using visual features of surface damage. Measurement 205:112195 (Elsevier)

    Article  Google Scholar 

  • Hamidia M, Afzali M, Jamshidian S, Safi M (2023) Post-earthquake stiffness loss estimation for reinforced concrete columns using fractal analysis of crack patterns. Struct Concr 24(3):3933–3951

    Article  Google Scholar 

  • Harte D (2001) Multifractals: theory and applications. Chapman and Hall/CRC, Boca Raton

    Book  Google Scholar 

  • Hassan SS, Choudhury PP, Daya Sagar BS et al (2015) Quantitative description of genomic evolution of olfactory receptors. Asian-Eur J Math 8:1550043

    Article  Google Scholar 

  • HAZUS (2019) M.-H.L.E.M. FEMA, Earthquake Model HAZUS® MH MR4 Technical Manual, National Institute of Building Sciences, Washington, DC.

  • Henkhaus KW (2010) Axial failure of vulnerable reinforced concrete columns damaged by shear reversals

  • Hyslip JP, Vallejo LE (1997) Fractal analysis of the roughness and size distribution of granular materials. Eng Geol 48:231–244

    Article  Google Scholar 

  • Kilic KI, Abiyev RH (2011) Exploiting the synergy between fractal dimension and lacunarity for improved texture recognition. Signal Process 91:2332–2344

    Article  Google Scholar 

  • Kucukgoncu H, Altun F (2020) The seismic behaviour of RC exterior shear walls used for strengthening of intact and damaged frames. Bull Earthq Eng 18:3683–3709

    Article  Google Scholar 

  • Lattanzi D, Miller GR, Eberhard MO, Haraldsson OS (2016) Bridge column maximum drift estimation via computer vision. J Comput Civ Eng 30:4015051

    Article  Google Scholar 

  • Lim E, Hwang S-J, Cheng C-H, Lin P-Y (2016) Cyclic tests of reinforced concrete coupling beam with intermediate span-depth ratio. ACI Struct J 113

  • Lin B, Yang ZR (1986) A suggested lacunarity expression for Sierpinski carpets. J Phys A Math Gen 19:L49

    Article  Google Scholar 

  • Lionar ML, Ediz Ö (2020) Measuring visual complexity of Sedad Eldem’s SSK complex and its historical context: a comparative analysis using fractal dimensions. Nexus Netw J 22:701–715

    Article  Google Scholar 

  • Liu Y, Yeoh JKW (2021) Automated crack pattern recognition from images for condition assessment of concrete structures. Autom Constr 128:103765

    Article  Google Scholar 

  • Liu T, Zhang X, Li Z, Chen Z (2014) Research on the homogeneity of asphalt pavement quality using X-ray computed tomography (CT) and fractal theory. Constr Build Mater 68:587–598

    Article  Google Scholar 

  • Liu Y, Dai K, Li D et al (2021) Structural performance assessment of concrete components based on fractal information of cracks. J Build Eng 43:103177

    Article  Google Scholar 

  • Lynn AC, Moehle JP, Mahin SA, Holmes WT (1996) Seismic evaluation of existing reinforced concrete building columns. Earthq Spectra 12:715–739

    Article  Google Scholar 

  • Madani HM, Dolatshahi KM (2020) Strength and stiffness estimation of damaged reinforced concrete shear walls using crack patterns. Struct Control Heal Monit 27:e2494

    Google Scholar 

  • Mandelbrot B (1967) How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science (80-) 156:636–638

    Article  Google Scholar 

  • Mandelbrot BB (1983) The fractal geometry of Nature WH Freeman and Company. N Y 8:406

    Google Scholar 

  • Mansour MY, Dicleli M, Lee J-Y, Zhang J (2004) Predicting the shear strength of reinforced concrete beams using artificial neural networks. Eng Struct 26:781–799

    Article  Google Scholar 

  • Modarres C, Astorga N, Droguett EL, Meruane V (2018) Convolutional neural networks for automated damage recognition and damage type identification. Struct Control Heal Monit 25:e2230

    Article  Google Scholar 

  • Momeni H, Dolatshahi KM (2019) Predictive equations for drift ratio and damage assessment of RC shear walls using surface crack patterns. Eng Struct 190:410–421

    Article  Google Scholar 

  • N’Diaye M, Degeratu C, Bouler J-M, Chappard D (2013) Biomaterial porosity determined by fractal dimensions, succolarity and lacunarity on microcomputed tomographic images. Mater Sci Eng C 33:2025–2030

    Article  Google Scholar 

  • Ni X, Cao S, Li Y, Liang S (2019) Stiffness degradation of shear walls under cyclic loading: experimental study and modelling. Bull Earthq Eng 17:5183–5216

    Article  Google Scholar 

  • Omor S, Takahashi T, Ishii K, Watanabe S (1974) Failure mode of reinforced concrete columns with various ties configurations. J Struct Constr Eng 20:1313–1314

    Google Scholar 

  • Osamu C, Kondo N, Yanagishita K, Fukuzawa R (1974) Fracture mechanism identification for RC columns with large height-to-width ratios. J Struct Constr Eng 20:1311–1312

    Google Scholar 

  • Paal SG, Jeon J-S, Brilakis I, DesRoches R (2015) Automated damage index estimation of reinforced concrete columns for post-earthquake evaluations. J Struct Eng 141:4014228

    Article  Google Scholar 

  • Palanci M, Kayhan AH, Demir A (2018) A statistical assessment on global drift ratio demands of mid-rise RC buildings using code-compatible real ground motion records. Bull Earthq Eng 16:5453–5488

    Article  Google Scholar 

  • Plotnick RE, Gardner RH, O’Neill RV (1993) Lacunarity indices as measures of landscape texture. Landsc Ecol 8:201–211

    Article  Google Scholar 

  • Rezaie A, Mauron AJP, Beyer K (2020) Sensitivity analysis of fractal dimensions of crack maps on concrete and masonry walls. Autom Constr 117:103258

    Article  Google Scholar 

  • Rezvani Sharif M, Ketabi MS (2020) An improved plastic hinge relocation technique for RC beam–column joints: experimental and numerical investigations. Bull Earthq Eng 18:4191–4225

    Article  Google Scholar 

  • Russell DA, Hanson JD, Ott E (1980) Dimension of strange attractors. Phys Rev Lett 45:1175

    Article  Google Scholar 

  • Schmidt M, Lipson H (2009) Distilling free-form natural laws from experimental data. Science 324:81–85

    Article  Google Scholar 

  • Sony S, Dunphy K, Sadhu A, Capretz M (2021) A systematic review of convolutional neural network-based structural condition assessment techniques. Eng Struct 226:111347

    Article  Google Scholar 

  • Tran CTN (2010) Experimental and analytical studies on the seismic behavior of reinforced concrete columns with light transverse reinforcement. Nanyang Technol Univ

  • Vanin F, Zaganelli D, Penna A, Beyer K (2017) Estimates for the stiffness, strength and drift capacity of stone masonry walls based on 123 quasi-static cyclic tests reported in the literature. Bull Earthq Eng 15:5435–5479

    Article  Google Scholar 

  • Vehel JL (1989) Using fractal and morphological criteria for automatic classification of lung diseases. In: Visual communications and image processing IV. SPIE, pp 903–912

  • Voss RF (1991) Random fractals: characterization and measurement. Scaling phenomena in disordered systems. Springer, New York, pp 1–11

    Google Scholar 

  • Vu NS (2017) Experimental and analytical investigations on seismic behavior of corroded reinforced concrete members

  • Wang JH (2021) Cyclic behaviors of reinforced concrete beam-column joints with debonded reinforcements and beam failure: experiment and analysis. Bull Earthq Eng 19:101–133

    Article  Google Scholar 

  • Xia Y, Cai J, Perfect E et al (2019) Fractal dimension, lacunarity and succolarity analyses on CT images of reservoir rocks for permeability prediction. J Hydrol 579:124198

    Article  Google Scholar 

  • Yamamoto K, Munemura M (1974) Experiments on RC short columns with varying axial force. J Struct Constr Eng 20:1309–1310

    Google Scholar 

  • Yazdanpanah O, Dolatshahi KM, Moammer O (2021) Earthquake-induced economic loss estimation of eccentrically braced frames through roof acceleration-based nonmodel approach. J Constr Steel Res 187:106888

    Article  Google Scholar 

  • Yeum CM, Dyke SJ, Ramirez J (2018) Visual data classification in post-event building reconnaissance. Eng Struct 155:16–24

    Article  Google Scholar 

  • Zhang H, Zhao Y (2019) Cracking of reinforced recycled aggregate concrete beams subjected to loads and steel corrosion. Constr Build Mater 210:364–379

    Article  Google Scholar 

  • Zhao P, Luo M, Li D et al (2021) Fractal characterization and petrophysical analysis of 3D dynamic digital rocks of sandstone. Petrophysics SPWLA J Eval Reserv Descr 62:500–515

    Google Scholar 

  • Zhu Z, German S, Brilakis I (2011) Visual retrieval of concrete crack properties for automated post-earthquake structural safety evaluation. Autom Constr 20:874–883

    Article  Google Scholar 

  • Zhu D, Tang A, Wan C et al (2021) Investigation on the flexural toughness evaluation method and surface cracks fractal characteristics of polypropylene fiber reinforced cement-based composites. J Build Eng 43:103045

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge Amirhossein Ganjizadeh and Samira Azhari for reading the manuscript and making comments.

Author information

Authors and Affiliations

  1. Faculty of Civil, Water and Environmental Engineering, Shahid Beheshti University, Tehran, Iran

    Sara Jamshidian & Mohammadjavad Hamidia

Authors
  1. Sara Jamshidian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammadjavad Hamidia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammadjavad Hamidia.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

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

Appendix A

Appendix A

See Table 4.

Table 4 RC column specimens of the database
Full size table

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jamshidian, S., Hamidia, M. Post-earthquake damage assessment for RC columns using crack image complexity measures. Bull Earthquake Eng 21, 6029–6063 (2023). https://doi.org/10.1007/s10518-023-01745-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10518-023-01745-4

Keywords

Search

Navigation