Abstract
A novel automated image processing-based methodology is proposed for quantification of stiffness degradation in non-ductile reinforced concrete moment frames after a seismic event. A database of 264 surface crack patterns from quasi-static experiments on 61 non-ductile beam-column subassemblies at various damage levels is used for development and verification of the methodology. The reference databank includes a wide range of structural and geometric parameters. Multifractal dimensions of the images of non-ductile beam-column joints are considered as the mathematical complexity indices of the surface crack patterns. Five predictive equations are developed for estimating the updated stiffness of damaged non-ductile reinforced concrete moment frames following an earthquake. The equations are obtained using symbolic regression method and their input parameters vary based on the accessibility of the characteristic parameters of the beam-column joint. The effectiveness of the proposed empirical equations is shown for a sample specimen at a variety of damage levels. Results reveal that the multifractal dimensions of the surface crack maps are highly correlated with the stiffness loss in the non-ductile reinforced concrete beam-column joints. The stiffness based damage index obtained by the proposed predictive equations can be used for post-earthquake system identification, stability assessment, or subsequent seismic analysis of the damaged structure.
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References
AASHTO (2019) Caltrans bridge element inspection manual. American Association of State Highway and Transportation Officials, USA
Abuzeid AT, Ghallab A, Al Tuhami AY (2021) Behavior of closing knee joints using L-shaped coupler instead of bending bars. ACI Struct J 118:153–166
ACI-201 (2008) Guide for conducting a visual inspection of concrete in service. American Concrete Institute, USA
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. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000566
Adibi M, Shafaei J, Aliakbari F (2020) Experimental evaluation of external beam-column joints reinforced by deformed and plain bar. Earthq Struct 18:113–127. https://doi.org/10.12989/eas.2020.18.1.113
Alire DA (2002) Seismic evaluation of existing unconfined reinforced concrete beam-column joints. MS Thesis, Department of Civil and Environmental Engineering, University of Washington
Alzate YFV (2013) Probabilistic static and dynamic structural analysis of reinforced concrete buildings. Methodological aspects and applications to the damage assessment. Ph.D. Thesis, Universidad Politecnica de Cataluna Superior Technical School of Roads, Channels and ports Engineers (ETSECCPB), Barcelona, Spain
Anderson M, Lehman D, Stanton J (2008) A cyclic shear stress–strain model for joints without transverse reinforcement. Eng Struct 30:941–954. https://doi.org/10.1016/j.engstruct.2007.02.005
Asjodi AH, Daeizadeh MJ, Hamidia M, Dolatshahi KM (2021) Arc Length method for extracting crack pattern characteristics. Struct Control Heal Monit 28:1–14. https://doi.org/10.1002/stc.2653
ATC-20 (2005) Post-earthquake safety evaluation of buildings, USA: Applied Technology Council
ATC-43 (1998) Evaluation of earthquake damaged concrete and masonry wall buildings, USA: Applied Technology Council
Athanasiou A, Ebrahimkhanlou A, Zaborac J, Hrynyk T, Salamone S (2020) A machine learning approach based on multifractal features for crack assessment of reinforced concrete shells. Comput Civ Infrastruct Eng 35:565–578. https://doi.org/10.1111/mice.12509
Banon H, Veneziano D (1982) Seismic safety of reinforced concrete members and structures. Earthq Eng Struct Dyn 10:179–193. https://doi.org/10.1002/eqe.4290100202
Beres A, White RN, Gergely P (1992) Seismic behavior of reinforced concrete frame structures with nonductile details.Technical Report NCEER-92-0024, National Center fot Earthquake Engineering Research (NCEER), Cornell University, New York, USA
Beydokhti EZ, Shariatmadar H (2016) Strengthening and rehabilitation of exterior RC beam–column joints using carbon-FRP jacketing. Mater Struct 49:5067–5083. https://doi.org/10.1617/s11527-016-0844-2
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. https://doi.org/10.1007/s10518-020-00964-3
Cao M, Ren Q, Qiao P (2006) Nondestructive assessment of reinforced concrete structures based on fractal damage characteristic factors. J Eng Mech 132:924–931. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:9(924)
Cao VV, Ronagh HR, Ashraf M, Baji H (2014) A new damage index for reinforced concrete structures. Earthq Struct 6:581–609. https://doi.org/10.12989/eas.2014.6.6.581
Carrillo J (2015) Damage index based on stiffness degradation of low-rise RC walls. Earthq Eng Struct Dyn 44:831–848. https://doi.org/10.1002/eqe.2488
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. https://doi.org/10.14359/51700919
Castiglioni CA, Pucinotti R (2009) Failure criteria and cumulative damage models for steel components under cyclic loading. J Constr Steel Res 65:751–765. https://doi.org/10.1016/j.jcsr.2008.12.007
Cha Y, Choi W, Büyüköztürk O (2017) Deep learning-based crack damage detection using convolutional neural networks. Comput Civ Infrastruct Eng 32:361–378. https://doi.org/10.1111/mice.12263
Clyde C, Pantelides CP, Reaveley LD (2000) Performance-based evaluation of exterior reinforced concrete building joints for seismic excitation. Technical Report PEER 2000-05, Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA
Comartin CD (1995) The Hyogoken Nambu earthquake, Great Hanshin earthquake disaster, January 17, 1995. Preliminary Reconnaissance Report, Earthquake Engineering Research Institute (EERI), Oakland, CA
De Melo RHC, Conci A (2013) How succolarity could be used as another fractal measure in image analysis. Telecommun Syst 52:1643–1655. https://doi.org/10.1007/s11235-011-9657-3
Dogan G, Arslan MH, Baykan OK (2020) Determination of damage levels of RC columns with a smart system oriented method. Bull Earthq Eng 18:1432–1445. https://doi.org/10.1007/s10518-020-00826-y
Dolatshahi KM, Beyer K (2019) Stiffness and strength estimation of damaged unreinforced masonry walls using crack pattern. J Earthq Eng 00:1–20. https://doi.org/10.1080/13632469.2019.1693446
Dong Y-R, Xu Z-D, Zeng K, Cheng Y, Xu C (2018) Seismic behavior and cross-scale refinement model of damage evolution for RC shear walls. Eng Struct 167:13–25. https://doi.org/10.1016/j.engstruct.2018.03.096
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. https://doi.org/10.1177/1475921715624502
Ebrahimkhanlou A, Athanasiou A, Hrynyk TD et al (2019) Fractal and multifractal analysis of crack patterns in prestressed concrete girders. J Bridge Eng 24:4019059. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001427
Ebrahimkhanlou A, Farhidzadeh A, Salamone S (2015) Multifractal analysis of two-dimensional images for damage assessment of reinforced concrete structures. Sensors Smart Struct Technol Civil, Mech Aerosp Syst 2015 9435: 94351A. https://doi.org/10.1117/12.2084052
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. https://doi.org/10.1016/j.conbuildmat.2015.12.018
Farhidzadeh A, Dehghan-Niri E, Moustafa A, Salamone S, Whittaker A (2013) Damage assessment of reinforced concrete structures using fractal analysis of residual crack patterns. Exp Mech 53:1607–1619. https://doi.org/10.1007/s11340-013-9769-7
Günay SM, Mosalam KM (2010) Structural engineering reconnaissance of the April 6, 2009, Abruzzo, Italy, Earthquake, and Lessons Learned. Technical Report PEER 2010-105, Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA
Guo Z, Zhang Y, Lu J, Fan J (2016) Stiffness degradation-based damage model for RC members and structures using fiber-beam elements. Earthq Eng Eng Vib 15:697–714. https://doi.org/10.1007/s11803-016-0359-4
Hadjileontiadis LJ, Douka E (2007) Crack detection in plates using fractal dimension. Eng Struct 29:1612–1625. https://doi.org/10.1016/j.engstruct.2006.09.016
Hakuto S (1995) Retrofitting of reinforced concrete Moment Resisting Frames. Ph.D. Thesis, University of Canterbury, New Zealand
Hall JF, Holmes WT, Somers P (1994) Northridge earthquake, January 17, 1994. Preliminary Reconnaissance Report, Earthquake Engineering Research Institute (EERI), Oakland, CA
Hamidia M, Filiatrault A, Aref A (2014a) Simplified Seismic Sidesway Collapse Capacity-Based Evaluation and Design of Frame Buildings with Linear Viscous Dampers. J Earthquake Eng 18(4):528–552. https://doi.org/10.1080/13632469.2013.876948
Hamidia M, Filiatrault A, Aref A (2014b) Simplified seismic sidesway collapse analysis of frame buildings. Earthquake Eng Struct Dyn 43(3):429–448. https://doi.org/10.1002/eqe.2353
Hamidia M, Filiatrault A, Aref A (2015) Seismic Collapse Capacity-Based Evaluation and Design of Frame Buildings with Viscous Dampers Using Pushover Analysis. J Struct Eng 141(6):04014153. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001114
Hamidia M, Ganjizadeh A, Dolatshahi KM (2022c) Peak drift ratio estimation for RC moment frames using multifractal dimensions of surface crack patterns. Eng Struct 255:113893. https://doi.org/10.1016/j.engstruct.2022.113893
Hamidia M, Shokrollahi N, Nasrolahi M (2021) Soil-structure interaction effects on the seismic collapse capacity of steel moment-resisting frame buildings. Structures 32:1331–1345. https://doi.org/10.1016/j.istruc.2021.03.068
Hamidia M, Shokrollahi N, Rasti Ardakani R (2022a) The collapse margin ratio of steel frames considering the vertical component of earthquake ground motions. J Constr Steel Res 188:107054. https://doi.org/10.1016/j.jcsr.2021.107054
Hamidia M, Vafaei A, Dolatshahi KM (2022b) Seismic displacement ratios for soil-pile-structure systems allowed to uplift. Soil Dyn Earthquake Eng 155:107171. https://doi.org/10.1016/j.soildyn.2022.107171
Hamidia M, Ganjizadeh A (2022) Post-earthquake damage evaluation of non-ductile RC moment frames using surface crack patterns. Struct Control Heal Monit. https://doi.org/10.1002/stc.3024
Harte D (2001) Multifractals: theory and applications. Chapman and Hall/CRC
Hertanto E (2005) Seismic assessment of pre-1970s reinforced concrete structures. MS Thesis, University of Canterbury
Hurmet K, Fatih A (2020) The seismic behaviour of RC exterior shear walls used for strengthening of intact and damaged frames. Bull Earthquake Eng 18:3683–3709. https://doi.org/10.1007/s10518-020-00839-7
Hyslip JP, Vallejo LE (1997) Fractal analysis of the roughness and size distribution of granular materials. Eng Geol 48:231–244. https://doi.org/10.1016/S0013-7952(97)00046-X
Ibrahim HHA (2011) Stud reinforcement in beam-column joints under seismic loads. Ph.D. Thesis, University Calgary, Canada
Ingham JM, Liddell D, Davidson BJ (2002) An assessment of parameters describing the response of a reinforced concrete beam. Bull N Z Soc Earthq Eng 35:1–16. https://doi.org/10.5459/bnzsee.35.1.1-16
Jemaa Y (2013) Seismic behavior of deficient exterior RC beam-column joints. Ph.D. Thesis, University of Sheffield, United Kingdom
Jeon JS, Lowes LN, DesRoches R, Brilakis I (2015) Fragility curves for non-ductile reinforced concrete frames that exhibit different component response mechanisms. Eng Struct 85:127–143. https://doi.org/10.1016/j.engstruct.2014.12.009
Jeon JS, DesRoches R, Brilakis I, Lowes LN (2012) Modeling and fragility analysis of non-ductile reinforced concrete buildings in low-to-moderate seismic zones. In: Structures Congress 2012, Chicago, United States, pp 2199–2210
Júlio ENBS, Branco FAB, Silva VD (2005) Reinforced concrete jacketing-interface influence on monotonic loading response. ACI Struct J 102:252
Kamaris GS, Vallianatou Y-M, Beskos DE (2012) Seismic damage estimation of in-plane regular steel moment resisting and x-braced frames. Bull Earthq Eng 10:1745–1766. https://doi.org/10.1007/s10518-012-9387-2
Kamaris GS, Hatzigeorgiou GD, Beskos DE (2013) A new damage index for plane steel frames exhibiting strength and stiffness degradation under seismic motion. Eng Struct 46:727–736. https://doi.org/10.1016/j.engstruct.2012.07.037
Kappos AJ (1997) Seismic damage indices for RC buildings: evaluation of concepts and procedures. Prog Struct Eng Mater 1:78–87
Lehman D, Stanton J, Anderson M, Alire D, Walker S (2004) Seismic performance of older beam-column joints. In: 13th World conference on earthquake engineering (13WCEE), Vancouver, Canada, p 1464
Li B, Wang Z, Mosalam KM, Xie H (2008) Wenchuan earthquake field reconnaissance on reinforced concrete framed buildings with and without masonry infill walls. In: The 14th World conference on earthquake engineering (14WCEE). Beijing, China
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. https://doi.org/10.1007/s00004-020-00482-4
Liu Y, Yeoh JKW (2021) Automated crack pattern recognition from images for condition assessment of concrete structures. Autom Constr 128:103765. https://doi.org/10.1016/j.autcon.2021.103765
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. https://doi.org/10.1016/j.conbuildmat.2014.06.046
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. https://doi.org/10.1016/j.jobe.2021.103177
Lopes R, Betrouni N (2009) Fractal and multifractal analysis: a review. Med Image Anal 13:634–649. https://doi.org/10.1016/j.media.2009.05.003
Madani HM, Dolatshahi KM (2020) Strength and stiffness estimation of damaged reinforced concrete shear walls using crack patterns. Struct Control Heal Monit 27:1–18. https://doi.org/10.1002/stc.2494
Mandelbrot BB (1985) Self-affine fractals and fractal dimension. Phys Scr 32:257. https://doi.org/10.1088/0031-8949/32/4/001
Mandelbrot BB (1983) The fractal geometry of nature/Revised and enlarged edition. New York, WH Free Co, 1983, 495 p. https://doi.org/10.1002/esp.3290080415
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. https://doi.org/10.1016/j.engstruct.2004.01.011
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. https://doi.org/10.1002/stc.2230
Mohebi B (2019) A new damage index for steel MRFs based on incremental dynamic analysis. J Constr Steel Res 156:137–154. https://doi.org/10.1016/j.jcsr.2019.02.005
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. https://doi.org/10.1016/j.engstruct.2019.04.018
Moore E (2021) Experimental study and retrofit of a non-ductile concrete moment frame building subjected to biaxial quasi-static seismic loading. Ph.D. Thesis, University of California, Los Angeles, USA
Ni X, Cao S, Li Y, Liang S (2019) Stiffness degradation of shear walls under cyclic loading: experimental study and modelling. Bull Earthquake Eng 17:5183–5216. https://doi.org/10.1007/s10518-019-00682-5
Oliveira Santos B, Valenca J, Julio E (2019) Automatic mapping of cracking patterns on concrete surfaces with biological stains using hyper-spectral images processing. Struct Control Heal Monit 26:e2320. https://doi.org/10.1002/stc.2320
Pantelides CP, Hansen J, Nadauld J, 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
Park S, Mosalam KM (2013) Simulation of reinforced concrete frames with nonductile beam-column joints. Earthq Spectra 29:233–257. https://doi.org/10.1193/1.4000100
Pessiki SP, Conley CH, Gergely P, White RN (1990) Seismic behavior of lightly-reinforced concrete column and beam-column joint details. Technical Report PEER 1990-0014, Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA
Plotnick RE, Gardner RH, O’Neill RV (1993) Lacunarity indices as measures of landscape texture. Landsc Ecol 8:201–211. https://doi.org/10.1038/nbt1289-1219
Qazi S, Michel L, Ferrier E (2019) Seismic behavior of RC short shear wall strengthened with externally bonded CFRP strips. Compos Struct 211:390–400. https://doi.org/10.1016/j.compstruct.2018.12.038
Rezaie A, Mauron AJP, Beyer K (2020) Sensitivity analysis of fractal dimensions of crack maps on concrete and masonry walls. Autom Constr 117:103258. https://doi.org/10.1016/j.autcon.2020.103258
Ricci P, De Luca F, Verderame GM (2011) 6th April 2009 L’Aquila earthquake, Italy: reinforced concrete building performance. Bull Earthquake Eng 9:285–305. https://doi.org/10.1007/s10518-010-9204-8
Russell DA, Hanson JD, Ott E (1980) Dimension of strange attractors. Phys Rev Lett 45:1175. https://doi.org/10.1016/j.media.2009.05.003
Sadeghi A, Kazemi H, Hashemi SV (2018) Prioritization and assessment of the existing damage indices in steel moment-resisting framed structures. J Civ Eng Struct 2:20–42
Schmidt M, Lipson H (2009) Distilling free-form natural laws from experimental data. Science 324:81–85. https://doi.org/10.1126/science.1165893
Sezen H, Elwood KJ, Whittaker AS, Mosalam K, Wallace J, Stanton J (2000) Structural engineering reconnaissance of the August 17, 1999 earthquake: Kocaeli (Izmit), Turkey. Technical Report PEER 2000-09, Pacific Earthquake Engineering Research Center (PEER), University of California, Berkeley, CA
Shafaei J, Hosseini A, Marefat MS, Ingham J, Zare H (2017) Experimental evaluation of seismically and non-seismically detailed external RC beam-column joints. J Earthq Eng 21:776–807. https://doi.org/10.1080/13632469.2016.1185052
Sharif MR, Ketabi MS (2020) An improved plastic hinge relocation technique for RC beam–column joints: experimental and numerical investigations. Bull Earthq Eng 18:4191–4225. https://doi.org/10.1007/s10518-020-00855-7
Skjaerbaek PS, Nielsen SRK, Kirkegaard PH, Cakmak AS (1996) Case study of local damage indicators for a 2-Bay, 6-Storey RC-Frame subject to earthquakes. Fracture and dynamics report 9639 No. 83, Department of Building Technology and Structural Engineering, Aalborg University, Denmark
Song Q-Y, Heidarpour A, Zhao X-L, Han L-H (2016) Performance of double-angle bolted steel I-beam to hollow square column connections under static and cyclic loadings. Int J Struct Stab Dyn 16:1450098. https://doi.org/10.1142/S0219455414500989
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. https://doi.org/10.1016/j.engstruct.2020.111347
Uang C-M, Elgamal A, Li W-S, Chou C-C (1999) Ji-Ji Taiwan earthquake of September 21, 1999: a brief reconnaissance report. Department of Structural Engineering, University of California, CA
Walker S (2001) Seismic performance of existing reinforced concrete beam-column joints. MS Thesis, Department of Civil and Environmental Engineering, University of Washington
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. https://doi.org/10.1007/s10518-020-00974-1
Werner S, Neumann I, Thienel KC, Heunecke O (2013) A fractal-based approach for the determination of concrete surfaces using laser scanning techniques: a comparison of two different measuring systems. Mater Struct 46:245–254. https://doi.org/10.1617/s11527-012-9898-y
Wong HF (2005) Shear strength and seismic performance of non-seismically designed reinforced concrete beam-column joints. Ph.D. Thesis, Hong Kong University of Science and Technology, China
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. https://doi.org/10.1016/j.jcsr.2021.106888
Yeum CM, Dyke SJ, Ramirez J (2018) Visual data classification in post-event building reconnaissance. Eng Struct 155:16–24. https://doi.org/10.1016/j.engstruct.2017.10.057
Yuen KW (2010) Selective weakening and post-tensioning for the seismic retrofit of non-ductile RC frames. Ph.D. Thesis, University of Canterbury, New Zealand
Zhang H, Zhao Y (2019) Cracking of reinforced recycled aggregate concrete beams subjected to loads and steel corrosion. Constr Build Mater 210:364–379. https://doi.org/10.1016/j.conbuildmat.2019.03.161
Zhang N (2017) Seismic performance and shear strength of reinforced concrete beam-column knee joints. Ph.D. Thesis, Hong Kong University of Science and Technology, China
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. https://doi.org/10.1016/j.autcon.2011.03.004
Asjodi AH, Dolatshahi KM, Ebrahimkhanlou A (2022) Spatial analysis of damage evolution in cyclic-loaded reinforced concrete shear walls. J Build Eng 49:104032. https://doi.org/10.1016/j.jobe.2022.104032
Mansourdehghan S, Dolatshahi KM, Asjodi AH (2022) Data-driven damage assessment of reinforced concrete shear walls using visual features of damage. J Build Eng 53:104509. https://doi.org/10.1016/j.jobe.2022.104509
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Hamidia, M., Ganjizadeh, A. Computer vision-based automated stiffness loss estimation for seismically damaged non-ductile reinforced concrete moment frames. Bull Earthquake Eng 20, 6635–6658 (2022). https://doi.org/10.1007/s10518-022-01408-w
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DOI: https://doi.org/10.1007/s10518-022-01408-w