Abstract
There has been ever-increasing interest over the past decade in improving understanding of the mechanisms responsible for the progressive collapse of structures. Existing design recommendations and analyses are largely limited to instantaneous (time-independent) collapse. However, recent experiments revealed that reinforced concrete (RC) structures may be susceptible to delayed collapse, prompting the consideration of time-dependent material behavior as part of progressive collapse analysis and design. A reduced-order computational model for delayed collapse behavior of RC structures is introduced here in which the potential damage zones that evolve within a structure are treated as cohesive elements. The constitutive model of the cohesive element accounts for viscoelastic deformation and time-dependent damage accumulation of the concrete and hardening plasticity of the steel reinforcement. The remaining part of the structure is treated as a viscoelastic continuum. The model is first applied to simulate a pushdown experiment on a RC frame subassemblage under displacement-controlled loading. The deformation and failure mechanisms are in good agreement with experimental observations. The model is then used to investigate the behavior of the subassemblage in a “static fatigue scenario” in which the load is monotonically increased to a prescribed level and is then held constant until ultimate structural failure resulting from the assumed time-dependent response of the concrete material. The corresponding timescale of the delayed failure is on the order of hours, a result that has important implications not only for the analysis and design of RC structures against progressive collapse but also for the safety of first responders who enter structures that may collapse within that period of time.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The computer code generated during the study is available from the corresponding author by request.
Acknowledgments
The authors deeply appreciate Dr. Bing Xue for stimulating discussion on the numerical implementation of the model in ABAQUS. They also acknowledge the University of Houston’s Hewlett Packard Enterprise Data Science Institute for providing computational and IT resources for this work.
References
ACI (American Concrete Institute). 2003. Bond and development of straight reinforcing bars in tension. ACI 408R-03. Farmington Hills, MI: ACI.
ACI (American Concrete Institute). 2008. Guide for modeling and calculating shrinkage and creep in hardened concrete. ACI 209.2R-08. Farmington Hills, MI: ACI.
Alashker, Y., H. Li, and S. El-Tawil. 2011. “Approximations in progressive collapse modeling.” J. Struct. Eng. 137 (9): 914–924. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000452.
Alnaggar, M., G. Di Luzio, and G. Cusatis. 2017. “Modeling time-dependent behavior of concrete affected by alkali silica reaction in variable environmental conditions.” Materials 10 (5): 471. https://doi.org/10.3390/ma10050471.
ASCE. 2010. Minimum design loads for buildings and other structures. ASCE/SEI 7-10. Reston, VA: ASCE.
Atkinson, B. K. 1984. “Subcritical crack growth in geological materials.” J. Geophys. Res. 89 (B6): 4077–4114. https://doi.org/10.1029/JB089iB06p04077.
Bao, Y., S. K. Kunnath, S. El-Tawil, and H. S. Lew. 2008. “Macromodel-based simulation of progressive collapse: RC frame structures.” J. Struct. Eng. 134 (7): 1079–1091. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:7(1079).
Barenblatt, G. I. 1959. “The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks.” J. Appl. Math. Mech. 23 (3): 622–636. https://doi.org/10.1016/0021-8928(59)90157-1.
Bažant, Z. P., and L. Cedolin. 1991. Stability of structures: Elastic, inelastic, fracture and damage theories. New York: Oxford University Press.
Bažant, Z. P., and M. Jirásek. 2018. Creep and hygrothermal effects in concrete structures. Dordrecht, Netherlands: Springer.
Bažant, Z. P., and J.-L. Le. 2017. Probabilistic mechanics of quasibrittle structures: Strength, lifetime, and size effect. Cambridge, UK: Cambridge University Press.
Bažant, Z. P., J.-L. Le, and M. Z. Bažant. 2009. “Scaling of strength and lifetime distributions of quasibrittle structures based on atomistic fracture mechanics.” Proc. Natl. Acad. Sci. 106 (28): 11484–11489. https://doi.org/10.1073/pnas.0904797106.
Bažant, Z. P., J.-L. Le, F. R. Greening, and D. B. Benson. 2008. “What did and did not cause collapse of WTC twin towers in New York.” J. Eng. Mech. 134 (10): 892–906. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:10(892).
Bažant, Z. P., and W. P. Murphy. 1995. “Creep and shrinkage prediction model for analysis and design of concrete structures: Model B3.” Mater. Struct. 28 (6): 357–365. https://doi.org/10.1007/BF02473152.
Bažant, Z. P., and J. Planas. 1998. Fracture and size effect in concrete and other quasibrittle materials. London: CRC Press.
Bažant, Z. P., and S. Prasannan. 1989. “Solidification theory for concrete creep. I: Formulation.” J. Eng. Mech. 115 (8): 1691–1703. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:8(1691).
Bažant, Z. P., and P. C. Prat. 1988. “Effect of temperature and humidity on fracture energy of concrete.” ACI Mater. J. 85 (4): 262–271.
Bažant, Z. P., and M. Verdue. 2007. “Mechanics of progressive collapse: Learning from world trade center and building demolitions.” J. Eng. Mech. 133 (3): 308–319. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:3(308).
Bažant, Z. P., and Y. Xi. 1995. “Continuous retardation spectrum for solidification theory of concrete creep.” J. Eng. Mech. 121 (2): 281–288. https://doi.org/10.1061/(ASCE)0733-9399(1995)121:2(281).
Bažant, Z. P., Q. Yu, and G.-H. Li. 2012. “Excessive long-time deflections of collapsed pre-stressed box girders. II: Numerical analysis and lessons learned.” J. Struct. Eng. 138 (6): 687–696. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000375.
Boumakisa, I., G. Di Luzio, M. Marcon, J. Vorel, and R. Wan-Wendner. 2018. “Discrete element framework for modeling tertiary creep of concrete in tension and compression.” Eng. Fract. Mech. 200 (Sep): 263–282. https://doi.org/10.1016/j.engfracmech.2018.07.006.
BSI (British Standard Institute). 2006. Actions on structures. 1–7: General actions—Accidental actions. BS EN 1991-1-7. London: BSI.
Carpinteri, A., S. Valente, F. P. Zhou, G. Ferrara, and G. Melchiorri. 1997. “Tensile and flexural creep rupture tests on partially-damaged concrete specimens.” Mater. Struct. 30 (5): 269–276. https://doi.org/10.1007/BF02486351.
Di Luzio, G. 2009. “Numerical model for time-dependent fracturing of concrete.” J. Eng. Mech. 135 (7): 632–640. https://doi.org/10.1061/(ASCE)0733-9399(2009)135:7(632).
DoD (Department of Defense). 2009. Design of buildings to resist progressive collapse. UFC-4-023-03. Washington, DC: DoD.
Dugdale, D. S. 1960. “Yielding of steel sheets containing slits.” J. Mech. Phys. Solids 8 (2): 100–104. https://doi.org/10.1016/0022-5096(60)90013-2.
Evans, A. G. 1972. “A method for evaluating the time-dependent failure characteristics of brittle materials and its application to polycrystalline alumina.” J. Mater. Sci. 7 (10): 1146–1173. https://doi.org/10.1007/BF00550196.
Evans, A. G., and Y. Fu. 1984. “The mechanical behavior of alumina.” In Fracture in ceramic materials, 56–88. Park Ridge, NJ: Noyes Publications.
Gardner, N. J., and M. J. Lockman. 2001. “Design provisions for drying shrinkage and creep of normal strength concrete.” ACI Mater. J. 98 (2): 159–167. https://doi.org/10.14359/10199.
Grierson, D. E., L. Xu, and Y. Liu. 2005. “Progressive-failure analysis of buildings subjected to abnormal loading.” Comput.-Aided Civ. Infrastruct. Eng. 20 (3): 155–171. https://doi.org/10.1111/j.1467-8667.2005.00384.x.
GSA (General Services Administration). 2003. Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. Washington, DC: GSA.
Hedegaard, B. D., C. E. W. French, and C. K. Shield. 2017. “Time-dependent monitoring and modeling of I-35W St. Anthony Falls bridge. II: Finite element modeling.” J. Bridge Eng. 22 (7): 04017026. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001054.
Helmy, H., H. Salem, and S. Mourad. 2012. “Progressive collapse assessment of framed reinforced concrete structures according to UFC guidelines for alternative path method.” Eng. Struct. 42 (Sep): 127–141. https://doi.org/10.1016/j.engstruct.2012.03.058.
Husak, A. D., and E. M. Krokosky. 1971. “Static fatigue of hydrated cement concrete.” ACI J. Proc. 68 (4): 263–271. https://doi.org/10.14359/11327.
ICC (International Code Council). 2009. International building code. Washington, DC: ICC.
Kachanov, L. 1986. Introduction to continuum damage mechanics: Mechanics of elastic stability, 10. Dordrecht, Netherlands: Springer.
Kachanov, M. 1994. “On the concept of damage in creep and in the brittle-elastic range.” Int. J. Damage Mech. 3 (4): 329–337. https://doi.org/10.1177/105678959400300402.
Kaewkulchai, G., and E. B. Williamson. 2004. “Beam element formulation and solution procedure for dynamic progressive collapse analysis.” Comp. Struct. 82 (7–8): 639–651. https://doi.org/10.1016/j.compstruc.2003.12.001.
Khandelwal, K., and S. El-Tawil. 2008. “Pushdown resistance as a measure of robustness in progressive collapse analysis.” Eng. Struct. 33 (9): 2653–2661. https://doi.org/10.1016/j.engstruct.2011.05.013.
Kunnath, S. K., Y. Bao, and S. El-Tawil. 2018. “Advances in computational simulation of gravity-induced disproportionate collapse of RC frame buildings.” J. Struct. Eng. 144 (2): 03117003. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001938.
Le, J.-L., and B. Xue. 2014. “Probabilistic analysis of reinforced concrete frame structures against progressive collapse.” Eng. Struct. 76 (Oct): 313–323. https://doi.org/10.1016/j.engstruct.2014.07.016.
Lemaitre, J., and R. Desmorat. 2005. Engineering damage mechanics: Ductile, creep, fatigue and brittle failures. Berlin: Springer.
Lew, H. S., Y. Bao, F. Sadek, and J. A. Main. 2011. An experimental and computational study of reinforced concrete assemblies under a column removal scenario. https://doi.org/10.6028/NIST.TN.1720.
Lowes, L. N., and A. Altoontash. 2003. “Modeling reinforced concrete beam-column joints subjected to cyclic loading.” J. Struct. Eng. 129 (12): 1686–1697. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:12(1686).
Masoero, E., F. K. Wittel, H. J. Herrmann, and B. M. Chiaia. 2010. “Progressive collapse mechanisms of brittle and ductile framed structures.” J. Eng. Mech. 136 (8): 987–995. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000143.
Pesce, C. P., L. Casetta, and F. M. dos Santos. 2012. “Equation of motion governing the dynamics of vertically collapsing buildings.” J. Eng. Mech. 138 (12): 1420–1431. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000453.
Rabotnov, Y. N. 1969. Creep problems in structural members. Amsterdam, Netherlands: North-Holland.
Rüsch, H. 1960. “Research toward a general flexural theory for structural concrete.” J. Am. Concr. Inst. 57 (1): 1–28.
Sadek, F., J. M. Main, H. S. Lew, and Y. Bao. 2011. “Testing and analysis of steel and concrete beam-column assemblies under a column removal scenario.” J. Struct. Eng. 137 (9): 881–892. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000422.
Sasani, M., and S. Sagiroglu. 2008. “Progressive collapse resistance of hotel San Diego.” J. Struct. Eng. 134 (3): 478–488. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:3(478).
Sezen, H., and J. P. Moehle. 2003. “Bond-slip behavior of reinforced concrete members.” In Proc., fib-Symp. (CEB-FIP): Concrete Structures in Seismic Regions. Lausanne, Switzerland: International Federation for Structural Concrete.
Thouless, M. D., C. H. Hsueh, and A. G. Evans. 1983. “A damage model of creep crack growth in polycrystals.” Acta Metall. 31 (10): 1675–1687. https://doi.org/10.1016/0001-6160(83)90166-9.
Xiao, Y., S. Kunnath, F. W. Li, Y. B. Zhao, H. S. Lew, and Y. Bao. 2015. “Collapse test of a 3-story half-scale RC frame building.” ACI Struct. J. 112 (4): 429–438. https://doi.org/10.14359/51687746.
Xue, B., and J.-L. Le. 2016a. “Simplified energy-based analysis of collapse risk of reinforced concrete buildings.” Struct. Saf. 63 (Nov): 47–58. https://doi.org/10.1016/j.strusafe.2016.07.003.
Xue, B., and J.-L. Le. 2016b. “Stochastic computational model for progressive collapse of reinforced concrete buildings.” J. Struct. Eng. 142 (7): 04016031. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001485.
Zhou, F. P. 1992. “Time-dependent crack growth and fracture in concrete.” Ph.D. thesis, Dept. of Building Technology, Lund Institute of Technology.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 10 • October 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Mar 20, 2020
Accepted: May 13, 2020
Published online: Jul 23, 2020
Published in print: Oct 1, 2020
Discussion open until: Dec 23, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.