Abstract

This study investigated the fractal and multifractal characteristics of crack patterns observed in prestressed concrete girders. In particular, it focused on cracks that form in the end regions of prestressed girders during the fabrication phase and attributed to prestress transfer operations (i.e., end-region cracks), and shear cracks that form due to subsequent structural (i.e., mechanical) loading. Synthetic crack patterns and experimental data collected during the fabrication and bending test of two large-scale girder specimens were used in this study. The results supported one of the key contributions of the study, which is using fractal analysis to quantify the extent of cracking that develops in prestressed concrete members. Another contribution of the study is that both fractal and multifractal analyses can be used to identify the development of different cracking mechanisms.

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Acknowledgments

The authors acknowledge the support of the Texas Department of Transportation (Grant 0-6919). Gratitude is also expressed to Dr. Hossein Yousefpour and Alessandro Musumeci, as well as the students and staff of Ferguson Structural Engineering Laboratory at the University of Texas at Austin for assisting with the acquisition of the experimental data used in this study.

References

AASHTO. 2016. AASHTO LRFD bridge design specifications, customary U.S. units: AASHTO load and resistance factor design bridge design specifications. Washington, DC: AASHTO.
ASTM. 2014. Standard test method for compressive strength of cylindrical concrete specimens. C39/C39M - 14. West Conshohocken, PA: ASTM.
Ayoub, A., and F. C. Filippou. 2010. “Finite-element model for pretensioned prestressed concrete girders.” J. Struct. Eng. 136 (4): 401–409. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000132.
Balomenos, G. P., and M. D. Pandey. 2017. “Probabilistic finite element investigation of prestressing loss in nuclear containment wall segments.” Nucl. Eng. Des. 311: 50–59. https://doi.org/10.1016/j.nucengdes.2016.11.018.
Baqersad, M., M. Mohammadafzali, B. Choubane, C. Holzschuher, A. Hamedi, and H. Ali. 2018. “Precision assessment of the Florida texture meter in hot mix asphalt.” J. Transp. Eng. Part B: Pavements 144 (2): 04018003. https://doi.org/10.1061/JPEODX.0000029.
Bonstedt, H. 2017. “How are we doing? Learning from the National Bridge Inventory.” Aspire 201: 38–39.
Briere, V., K. A. Harries, J. Kasan, and C. Hager. 2013. “Dilation behavior of seven-wire prestressing strand—The Hoyer effect.” Constr. Build. Mater. 40: 650–658. https://doi.org/10.1016/j.conbuildmat.2012.11.064.
Calvi, P. M., E. C. Bentz, and M. P. Collins. 2018. “Model for assessment of cracked reinforced concrete membrane elements subjected to shear and axial loads.” Struct. J. 115 (2): 501–509.
Cao, M., Q. Ren, and P. Qiao. 2006. “Nondestructive assessment of reinforced concrete structures based on fractal damage characteristic factors.” J. Eng. Mech. 132 (9): 924–931. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:9(924).
Carrillo, J., D. Dominguez, and N. Prado. 2017. “Seismic damage index based on fractal dimension of cracking on thin reinforced concrete walls.” Struct. J. 114 (6): 1649–1658.
Chhabra, A., and R. Jensen. 1989. “Direct determination of the f(α) singularity spectrum.” Phys. Rev. Lett. 62 (12): 1327–1330.
Chhabra, A., C. Meneveau, R. Jensen, and K. Sreenivasan. 1989. “Direct determination of the f(α) singularity spectrum and its application to fully developed turbulence.” Phys. Rev. A 40 (9): 5284–5294.
Clarke, K. C. 1986. “Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method.” Comput. Geosci. 12 (5): 713–722. https://doi.org/10.1016/0098-3004(86)90047-6.
Clauset, A., C. R. Shalizi, and M. E. J. Newman. 2009. “Power-law distributions in empirical data.” SIAM Rev. 51 (4): 661–703. https://doi.org/10.1137/070710111.
Davoudi, R., G. R. Miller, and J. N. Kutz. 2017. “Computer vision based inspection approach to predict damage state and load level for RC members.” In Proc., 11th Int. Workshop on Structural Health Monitoring, 3155–3162. Lancaster, PA: Destech Publications.
Davoudi, R., G. R. Miller, and J. N. Kutz. 2018. “Structural load estimation using machine vision and surface crack patterns for shear-critical RC beams and slabs.” J. Comput. Civ. Eng. 32 (4): 04018024. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000766.
Dorafshan, S., and M. Maguire. 2018. “Bridge inspection: Human performance, unmanned aerial systems and automation.” J. Civ. Struct. Health Monit. 8 (3): 443–476. https://doi.org/10.1007/s13349-018-0285-4.
Dorafshan, S., R. J. Thomas, and M. Maguire. 2018a. “Comparison of deep convolutional neural networks and edge detectors for image-based crack detection in concrete.” Constr. Build. Mater. 186: 1031–1045. https://doi.org/10.1016/j.conbuildmat.2018.08.011.
Dorafshan, S., R. J. Thomas, and M. Maguire. 2018b. “Fatigue crack detection using unmanned aerial systems in fracture critical inspection of steel bridges.” J. Bridge Eng. 23 (10): 04018078. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001291.
Ebrahimkhanlou, A., A. Farhidzadeh, and S. Salamone. 2015. “Multifractal analysis of two-dimensional images for damage assessment of reinforced concrete structures.” In Vol. 9435 of Proc., Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems. 94351A. Bellingham, WA: SPIE.
Ebrahimkhanlou, A., A. Farhidzadeh, and S. Salamone. 2016. “Multifractal analysis of crack patterns in reinforced concrete shear walls.” Struct. Health Monit. 15 (1): 81–92. https://doi.org/10.1177/1475921715624502.
Ebrahimkhanlou, A., and S. Salamone. 2017. “A probabilistic model for visual inspection of concrete shear walls.” In Vol. 10168 of Proc., Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems. 101680Y. Bellingham, WA: SPIE.
Falconer, K. J. 2003. Fractal geometry: Mathematical foundations and applications. West Sussex, UK: John Wiley & Sons Ltd.
Farhidzadeh, A., E. Dehghan-Niri, A. Moustafa, S. Salamone, and A. Whittaker. 2013. “Damage assessment of reinforced concrete structures using fractal analysis of residual crack patterns.” Exp. Mech. 53 (9): 1607–1619. https://doi.org/10.1007/s11340-013-9769-7.
Farhidzadeh, A., A. Ebrahimkhanlou, and S. Salamone. 2014. “A vision-based technique for damage assessment of reinforced concrete structures.” In Vol. 9064 of Proc., Health Monitoring of Structural and Biological Systems. 90642H. Bellingham, WA: SPIE.
Harte, D. 2001. Multifractals: Theory and applications. London: CRC Press.
Hoyer, E., and E. Friedrich. 1939. “Contribution towards the question of bond strength in reinforced concrete members.” Beton Eisen 38 (5): 107–110.
Jahanshahi, M. R., and S. F. Masri. 2013. “A new methodology for non-contact accurate crack width measurement through photogrammetry for automated structural safety evaluation.” Smart Mater. Struct. 22 (3): 035019. https://doi.org/10.1088/0964-1726/22/3/035019.
Jahanshahi, M. R., S. F. Masri, and G. S. Sukhatme. 2011. “Multi-image stitching and scene reconstruction for evaluating defect evolution in structures.” Struct. Health Monit. 10 (6): 643–657. https://doi.org/10.1177/1475921710395809.
Katz, A., H. Yousefpour, H. Kim, R. A. Abyaneh, J. Salazar, T. Hrynyk, and O. Bayrak. 2017. “Shear performance of pretensioned concrete I-girders employing 0.7 in. (17.8 mm) strands.” Struct. J. 114 (5): 1273–1284.
Kulicki, J. M., and D. R. Mertz. 2006. “Evolution of vehicular live load models during the interstate design era and beyond.” In Proc., 50 Years of Interstate Structures: Past, Present, and Future, Transportation Research Circular, E-C104. Washington, DC: Transportation Research Board, National Research Council.
Lantsoght, E. O. L., C. Van Der Veen, J. Walraven, and A. De Boer. 2013. “Recommendations for the shear assessment of reinforced concrete slab bridges from experiments.” Struct. Eng. Int. 23 (4): 418–426. https://doi.org/10.2749/101686613X13627347100239.
Lopes, R., and N. Betrouni. 2009. “Fractal and multifractal analysis: A review.” Med. Image Anal. 13 (4): 634–649. https://doi.org/10.1016/j.media.2009.05.003.
Mandelbrot, B. 2010. Les objets fractals forme, hasard et dimension. Paris: Flammarion.
Mangual, J., M. K. El Batanouny, P. Ziehl, and F. Matta. 2013. “Acoustic-emission-based characterization of corrosion damage in cracked concrete with prestressing strand.” Mater. J. 110 (1): 89–98.
Mehdipour, I., and K. H. Khayat. 2018. “Elucidating the role of supplementary cementitious materials on shrinkage and restrained-shrinkage cracking of flowable eco-concrete.” J. Mater. Civ. Eng. 30 (3): 04017308. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002191.
Moore, M., B. Phares, B. Graybeal, D. Rolander, and G. Washer. 2001. Reliability of visual inspection for highway bridges. Washington, DC: Federal Highway Administration.
Okumus, P., and M. Oliva. 2013. “Evaluation of crack control methods for end zone cracking in prestressed concrete bridge girders.” PCI J. 58 (2): 91–105. https://doi.org/10.15554/pcij.03012013.91.105.
Okumus, P., M. G. Oliva, and S. Becker. 2012. “Nonlinear finite element modeling of cracking at ends of pretensioned bridge girders.” Eng. Struct. 40: 267–275. https://doi.org/10.1016/j.engstruct.2012.02.033.
Paal, S. G., J.-S. Jeon, I. Brilakis, and R. DesRoches. 2015. “Automated damage index estimation of reinforced concrete columns for post-earthquake evaluations.” J. Struct. Eng. 141 (9): 04014228. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001200.
Pachepsky, Y., D. E. D. Radcliffe, and H. M. Selim. 2003. Scaling methods in soil physics. Danvers, MA: CRC Press.
Rényi, A. 1961. “On measures of information and entropy.” In Proc., Berkeley Symp. on Mathematics, Statistics and Probability, 547–561. Berkeley, CA: University of California Press.
Ronanki, V. S., D. I. Burkhalter, S. Aaleti, W. Song, and J. A. Richardson. 2017. “Experimental and analytical investigation of end zone cracking in BT-78 girders.” Eng. Struct. 151: 503–517. https://doi.org/10.1016/j.engstruct.2017.08.014.
Russell, D. A., J. D. Hanson, and E. Ott. 1980. “Dimension of strange attractors.” Phys. Rev. Lett. 45 (14): 1175–1178. https://doi.org/10.1103/PhysRevLett.45.1175.
Salazar, J. L., H. Yousefpour, R. A. Abyaneh, H. s. Kim, A. T. Katz, T. D. Hrynyk, and O. Bayrak. 2018. “End-region behavior of pretensioned I-girders employing 0.7 in. (17.8 mm) strands.” Struct. J. 115 (1): 91–102.
Sarrafi, A., and Z. Mao. 2018. “Structural operating deflection shape estimation via a hybrid computer-vision algorithm.” In Proc., Health Monitoring of Structural and Biological Systems XII. Bellingham, WA: SPIE.
Song, M., S. Yousefianmoghadam, M.-E. Mohammadi, B. Moaveni, A. Stavridis, and R. L. Wood. 2018. “An application of finite element model updating for damage assessment of a two-story reinforced concrete building and comparison with lidar.” Struct. Health Monit. 17 (5): 1129–1150. https://doi.org/10.1177/1475921717737970.
Sun, H., S. Pashoutani, and J. Zhu. 2018. “Nondestructive evaluation of concrete bridge decks with automated acoustic scanning system and ground penetrating radar.” Sensors 18 (6): 1955. https://doi.org/10.3390/s18061955.
Theiler, J. 1990. “Estimating fractal dimension.” J. Opt. Soc. Am. A 7 (6): 1055. https://doi.org/10.1364/JOSAA.7.001055.
TxDOT (Texas Dept. of Transportation). 2013. Bridge inspection manual. Austin, TX: Texas Dept. of Transportation.
TxDOT (Texas Dept. of Transportation). 2015. Bridge design manual—LRFD. Austin, TX: Texas Dept. of Transportation.
Wu, N., and S. Chase, 2010. An exploratory data analysis of national bridge inventory. Rep. UVA-2009-03. Charlottesville, VA: Univ. of Virginia Center for Transportation Studies.
Yang, Y., and S. Nagarajaiah. 2016. “Dynamic imaging: Real-time detection of local structural damage with blind separation of low-rank background and sparse innovation.” J. Struct. Eng. 142 (2): 04015144. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001334.

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Go to Journal of Bridge Engineering
Journal of Bridge Engineering
Volume 24Issue 7July 2019

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Received: Aug 7, 2018
Accepted: Jan 18, 2019
Published online: Apr 30, 2019
Published in print: Jul 1, 2019
Discussion open until: Sep 30, 2019

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Postdoctoral Fellow, Ferguson Structural Engineering Laboratory (FSEL), Dept. of Civil Architectural and Environmental Engineering, Univ. of Texas at Austin, 10100 Burnet Rd., Building 177, Austin, TX 78758 (corresponding author). ORCID: https://orcid.org/0000-0002-0740-5807. Email: [email protected]
Apostolos Athanasiou, S.M.ASCE [email protected]
Ph.D. Candidate, Ferguson Structural Engineering Laboratory (FSEL), Dept. of Civil Architectural and Environmental Engineering, Univ. of Texas at Austin, 10100 Burnet Rd., Building 177, Austin, TX 78758. Email: [email protected]
Trevor D. Hrynyk [email protected]
Assistant Professor, Ferguson Structural Engineering Laboratory (FSEL), Dept. of Civil Architectural and Environmental Engineering, Univ. of Texas at Austin, 10100 Burnet Rd., Building 177, Austin, TX 78758. Email: [email protected]
Oguzhan Bayrak, M.ASCE [email protected]
Professor, Ferguson Structural Engineering Laboratory (FSEL), Dept. of Civil Architectural and Environmental Engineering, Univ. of Texas at Austin, 10100 Burnet Rd., Building 177, Austin, TX 78758. Email: [email protected]
Salvatore Salamone, M.ASCE [email protected]
Associate Professor, Ferguson Structural Engineering Laboratory (FSEL), Dept. of Civil Architectural and Environmental Engineering, Univ. of Texas at Austin, 10100 Burnet Rd., Building 177, Austin, TX 78758. Email: [email protected]

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