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Damage Assessment of Reinforced Concrete Structures Using Fractal Analysis of Residual Crack Patterns

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Abstract

Currently, assessing the performance and safety of reinforced concrete structures relies on routine-based visual inspection (VI). Cracks width measurements are commonly used as a convenient indicator of damage; however other factors, such as distribution and pattern of the cracks should be considered equally important in measuring the extent of damage present in the structure. As a result, condition assessed by VI is subjective in nature and depends on the experience, knowledge, expertise, and judgment of the inspector carrying out the assessment. A new approach based on the fractal analysis of residual crack patterns is proposed in this paper to assess the structural integrity of reinforced concrete elements. A new damage index is presented to quantitatively perform a damage classification. The methodology is validated through experimental studies on two large-scale reinforced concrete shear walls subjected to a displacement controlled reversed cyclic loading. Damage grades are also identified based on width of cracks and proposed damage index (DI). The results demonstrate a more accurate estimation of damage grades using DI. Furthermore, it is demonstrated that the DI can estimate the relative stiffness loss of the specimens with acceptable accuracy.

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Abbreviations

DG:

Damage grade

FD:

Fractal dimension

DI:

Damage index

HD:

High definition

IAEA:

International atomic energy agency

LS:

Load step

NDE:

Non-destructive evaluation

RC:

Reinforced concrete

RT :

Transition box size

RO :

Object box size

RS :

Structure box size

RD :

Discretization size

RCSW:

Reinforced concrete shear wall

RSL:

Relative stiffness loss

SHM:

Structural health monitoring

SW:

Shear wall

VI:

Visual inspection

References

  1. IAEA (2002) Guidebook on non-destructive testing of concrete structures. International Atomic Energy Agency, Vienna

    Google Scholar 

  2. Farhidzadeh A, Salamone S, Luna B, Whittaker A (2013) Acoustic emission monitoring of a reinforced concrete shear wall by b-value based outlier analysis. J Struct Health Monit Int J 12(1):3–13. doi:10.1177/1475921712461162

    Article  Google Scholar 

  3. RAIU (2010) Malahide viaduct collapse on the Dublin to Belfast line, on the 21st August 2009. Railway Accident Investigation Unit, Dublin

    Google Scholar 

  4. Comerio M, Elwood K, Berkowitz R et al (2011) The M 6.3 Christchurch, New Zealand, Earthquake of February 22, 2011. EERI special earthquake report. Earthquake Engineering Research Institute (EERI), Oakland

    Google Scholar 

  5. DBH (2011) Christchurch CBD Buildings 22 February 2011 aftershock stage 1 expert panel report. New Zealand Department of Building and Housing, Wellington

    Google Scholar 

  6. NBIS (1996) Code of federal regulations, No. 23CFR650. National Bridge Inspection Standards, Washington, DC

    Google Scholar 

  7. FHWA (1995) Recording and coding guide for the structure inventory and appraisal of the nation’s bridges. Report No. FHWA-PD-96-001. Federal Highway Administration, Washington, D.C

    Google Scholar 

  8. ATC-43 (1998) FEMA 306. Evaluation of earthquake damaged concrete and masonry wall buildings. The Applied Technology Council, Redwood City

    Google Scholar 

  9. Chen Z, Hutchinson TC (2010) Image-based framework for concrete surface crack monitoring and quantification. Adv Civ Eng 2010:1–18. doi:10.1155/2010/215295

    MATH  Google Scholar 

  10. Sohn H-G, Lim Y-M, Yun K-H, Kim G-H (2005) Monitoring crack changes in concrete structures. Comput-Aided Civ Inf 20(1):52–61

    Article  Google Scholar 

  11. Farhidzadeh A, Salamone S, Singla S (2013) A probabilistic approach for damage identification and crack mode classification in reinforced concrete structures. J Intel Mat Syst Str. doi:10.1177/1045389X13484101

    Google Scholar 

  12. Farhidzadeh A, Dehghan Niri E, Salamone S, Luna B, Whittaker A (2012) Monitoring crack propagation in reinforced concrete shear walls by acoustic emission. ASCE J Struct Eng. doi:10.1061/(ASCE)ST.1943-541X.0000781, First published on 01 December 2012

    Google Scholar 

  13. ATC (1998) FEMA 308. Repair of earthquake damaged concrete and masonry wall buildings. The Applied Technology Council, Redwood City

    Google Scholar 

  14. Issa MA, Issa MA, Islam MS, Chudnovsky A (2003) Fractal dimension - a measure of fracture roughness and toughness of concrete. Eng Fract Mech 70:125–137

    Article  Google Scholar 

  15. Jahanshahi MR, Masri SF (2012) Adaptive vision-based crack detection using 3D scene reconstruction for condition assessment of structures. Autom Constr 22:567–576. doi:10.1016/j.autcon.2011.11.018

    Article  Google Scholar 

  16. Carpinteri A, Chiaia B, Nemati KM (1997) Complex fracture energy dissipation in concrete under different loading conditions. Mech Mater 26(2):93–108

    Article  Google Scholar 

  17. Carpinteri A, Yang GP (1996) Fractal dimension evolution of microcrack net in disordered materials. Theor Appl Fract Mec 25(1):73–81

    Article  Google Scholar 

  18. Lee YH, Carr JR, Barr DJ, Haas CJ (1990) The fractal dimension as a measure of the roughness of rock discontinuity profiles. Int J Rock Mech Min 27(6):453–464

    Article  Google Scholar 

  19. Kulatilake PHSW, Fiedler R, Panda BB (1997) Box fractal dimension as a measure of statistical homogeneity of jointed rock masses. Eng Geol 48(3–4):217–229

    Article  Google Scholar 

  20. Carpinteri A, Lacidogna G, Niccolini G (2009) Fractal analysis of damage detected in concrete structural elements under loading. Chaos Soliton Fract 42(4):2047–2056

    Article  MATH  Google Scholar 

  21. Carpinteri A, Corrado M, Lacidogna G (2012) Three different approaches for damage domain characterization in disordered materials: Fractal energy density, b-value statistics, renormalization group theory. Mech Mater 53:15–28

    Article  Google Scholar 

  22. Chiaia B, van Mier JGM, Vervuurt A (1998) Crack growth mechanisms in four different concretes: microscopic observations and fractal analysis. Cem Concr Res 28(1):103–114

    Article  Google Scholar 

  23. Saouma VE, Barton CC (1994) Fractals, fractures, and size effects in concrete. J Eng Mech-ASCE 120(4):835–854

    Article  Google Scholar 

  24. Peng J, Wu Z, Zhao G (1997) Fractal analysis of fracture in concrete. Theor Appl Fract Mec 27(997):135–140

    Article  Google Scholar 

  25. Carpinteri A, Cornetti P (2011) Size effects on concrete tensile fracture properties: an interpretation of the fractal approach based on the aggregate grading. J Mech Behav Mater 13(3–4):233–246

    Google Scholar 

  26. Sun H-Q, Ding J, Guo J, Fu DL (2011) Fractal research on cracks of reinforced concrete beams with different aggregates sizes. Adv Mat Res 250–253:1818–1822

    Article  Google Scholar 

  27. Cao M, Ren Q, Asce M, Qiao P (2006) Nondestructive assessment of reinforced concrete structures based on fractal damage characteristic factors. J Eng Mech-ASCE 132(9):924–931

    Article  Google Scholar 

  28. Mandelbrot BB (1982) The fractal geometry of nature. W. H. Freeman, New York

    MATH  Google Scholar 

  29. Dubuc B, Quiniou JF, Roques-Carmes C, Tricot C, Zucker SW (1989) Evaluating the fractal dimension of profiles. Phys Rev A 39:

  30. Taylor CC, Taylor SJ (1991) Estimating the dimension of a fractal. J Roy Stat Soc B Met 53(2):353–364

    MATH  Google Scholar 

  31. Esteller R, Vachtsevanos G, Echauz J, Litt B (2001) A comparison of waveform fractal dimension algorithms. IEEE T Circuits-I 48(2):177–183

    Article  Google Scholar 

  32. Theiler J (1990) Estimating fractal dimension. J Opt Soc Am A 7(6):1055–1073

    Article  MathSciNet  Google Scholar 

  33. Moustafa A, Salamone S (2012) Fractal dimension-based Lamb wave tomography algorithm for damage detection in plate-like structures. J Intel Mat Syst Str 23(11):1269–1276

    Article  Google Scholar 

  34. Raghavendra BS, Narayana Dutt D (2010) Computing fractal dimension of signals using multiresolution box-counting method. Int J Inf Math Sci 6(1):50–65

    Google Scholar 

  35. Shoupeng S, Peiwen Q (2007) A fractal-dimension-based signal-processing technique and its use for nondestructive testing. Russ J Nondestruct 43(4):270–280

    Article  Google Scholar 

  36. Hadjileontiadis LJ, Douka E (2007) Crack detection in plates using fractal dimension. Eng Struct 29(7):1612–1625

    Article  Google Scholar 

  37. Long QY, Suqin L, Lung CW (1991) Studies on the fractal dimension of a fracture surface formed by slow stable crack propagation. J Phys D Appl Phys 24:602–607

    Article  Google Scholar 

  38. Mandelbrot BB (1985) Self-affine fractals and fractal dimension. Phys Scr 32(4):257

    Article  MathSciNet  MATH  Google Scholar 

  39. ACI Committee 318 (2008) Building code requirements for structural concrete and commentary (ACI 318-08). American Concrete Institute (ACI), Farmington Hills. ISBN 9780870312649

    Google Scholar 

  40. Farhidzadeh A, Salamone S, Dehghan-Niri E, Luna B, Whittaker AS (2012) Damage assessment of reinforced concrete shear walls by acoustic emission. NDE/NDT for Highways and Bridges: Structural Materials Technology (SMT), NY, pp 74–81

    Google Scholar 

  41. Farhidzadeh A, Salamone S (2012) Introducing sifted b-value analysis and a new crack classification for monitoring reinforced concrete shear walls by acoustic emission. 54th Acoustic Emission Working Group Meeting, Princeton, NJ, USA (Student paper award), pp 55–57

  42. Rocks JF (2012) Large scale testing of low aspect ratio reinforced concrete walls. M.Sc. Thesis, University at Buffalo, NY

  43. Adobe Photoshop Element, version 9, adobe company, Copyright © 2010 Adobe Systems Incorporated. http://www.adobe.com

  44. Autodesk AutoCAD Civil 3D, student version 2011, Copyright © 2012 Autodesk, Inc. http://students.autodesk.com/

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Acknowledgments

The authors acknowledge National Science Foundation (NSF) for providing the financial support under Grant No. CMMI-0829978. The experiments presented herein could not have been completed without contributions from the staff of the Structural Engineering and Earthquake Simulation Laboratory (SEESL) of the State University of New York at Buffalo. The financial support and work of the SEESL staff are gratefully acknowledged. The authors also acknowledge the advice and help provided by the technical staff at the NEES Equipment Site at the University at Buffalo.

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Correspondence to S. Salamone.

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Farhidzadeh, A., Dehghan-Niri, E., Moustafa, A. et al. Damage Assessment of Reinforced Concrete Structures Using Fractal Analysis of Residual Crack Patterns. Exp Mech 53, 1607–1619 (2013). https://doi.org/10.1007/s11340-013-9769-7

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