Stochastic Computational Model for Progressive Collapse of Reinforced Concrete Buildings
Publication: Journal of Structural Engineering
Volume 142, Issue 7
Abstract
A two-scale numerical model is developed to investigate the probabilistic collapse behavior of reinforced concrete (RC) buildings subjected to local structural damage. In this model, a set of coarse-scale cohesive elements is used to model the failure of potential damage zones in various RC structural members. The constitutive properties of the cohesive elements and their probability distributions are determined from detailed stochastic finite element simulations of the potential damage zones by taking into account the uncertainties in various material properties. The two-scale model is validated both experimentally and numerically for different structural subassemblages. The model is then applied to study the collapse behavior of a prototype 10-story RC building subjected to sudden column removal using both deterministic and probabilistic analysis frameworks. The deterministic calculation uses the mean material properties and the factored gravity loads according to the Unified Facilities Criteria (UFC) guidelines. The stochastic calculation considers uncertainties in both gravity loads and material properties, from which the occurrence probabilities of different collapse extents are determined. The results of the present probabilistic analysis are discussed in comparison with the existing deterministic approach, which reveals the important role of probabilistic methods in the analysis of progressive collapse.
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Acknowledgments
The authors acknowledge the Minnesota Supercomputing Institute at the University of Minnesota for providing computational resources for the numerical simulations presented in this paper.
References
ABAQUS 6.11 [Computer software]. SIMULIA, Providence, RI.
ACI (American Concrete Institute). (2003). “Bond and development of straight reinforcing bars in tension.”, Farmington Hills, MI.
ACI (American Concrete Institute). (2011). “Building code requirement for structural concrete and commentary.”, Farmington Hills, MI.
Adams, B., et al. (2011). “DAKOTA, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: Version 5.2 user’s manual.”, Sandia National Laboratories, Albuquerque, NM.
Alashker, Y., Li, H., and El-Tawil, S. (2011). “Approximations in progressive collapse modeling.” J. Struct. Eng., 914–924.
Aycardi, L. E., Mander, J. B., and Reinhorn, A. M. (1994). “Seismic resistance of reinforced concrete frame structures designed only for gravity loads: Experimental performance of subassemblages.” ACI Struct. J., 91(5), 552–563.
Bao, Y. (2008). “Macromodel-based progressive collapse simulation of reinforced concrete structures.” Ph.D. dissertation, Univ. of California, Davis, CA.
Bao, Y., and Kunnath, S. K. (2010). “Simplified progressive collapse simulation of RC frame-wall structures.” Eng. Struct., 32(10), 3153–3162.
Bao, Y., Kunnath, S. K., El-Tawil, S., and Lew, H. S. (2008). “Macromodel-based simulation of progressive collapse: RC frame structures.” J. Struct. Eng., 1079–1091.
Bažant, Z. P. (2005). Scaling of structural strength, Elsevier, London.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture, and damage theories, Oxford University Press, New York.
Bažant, Z. P., Le, J.-L., Greening, F. R., and Benson, D. B. (2008). “What did and did not cause collapse of WTC twin towers in New York.” J. Eng. Mech., 892–906.
Bažant, Z. P., and Planas, J. (1998). Fracture and size effect in concrete and other quasibrittle materials, CRC Press, Boca Raton, FL.
Bažant, Z. P., and Verdue, M. (2007). “Mechanics of progressive collapse: Learning from World Trade Center and building demolitions.” J. Eng. Mech., 308–319.
Bennett, R. M. (1988). “Formulations for probability of progressive collapse.” Struct. Saf., 5(1), 67–77.
Camacho, G. T., and Ortiz, M. (1996). “Computational modeling of impact damage in brittle materials.” Int. J. Solids Struct., 33(20–22), 2899–2938.
Cusatis, G., Bažant, Z. P., and Cedolin, L. (2003). “Confinement-shear lattice model for concrete damage in tension and compression: I. Theory.” J. Eng. Mech., 1439–1448.
Darwin, D., Idun, E. K., Zuo, J., and Tholen, M. L. (1998). “Reliability-based strength reduction factor for bond.” ACI Struct. J., 95(4), 434–443.
Der Kiureghian, A., and Ditlevsen, O. (2009). “Aleatory or epistemic? Does it matter?” Struct. Saf., 31(2), 105–112.
DoD (Department of Defense). (2009). “Design of buildings to resist progressive collapse.”, Washington, DC.
Ellingwood, B. R. (2006). “Mitigating risk from abnormal loads and progressive collapse.” J. Perform. Constr. Facil., 315–323.
Ellingwood, B. R., and Leyendecker, E. V. (1978). “Approaches for design against progressive collapse.” J. Struct. Div., 104(3), 413–423.
Ellingwood, B. R., Smilowitz, R., Dusenberry, D. O., Duthinh, D., Lew, H. S., and Carino, N. J. (2007). “Best practices for reducing the potential for progressive collapse in buildings.”, National Institute of Standards and Technology, Gaithersburg, MD.
Elstner, R. C., and Hognestad, E. (1956). “Shearing strength of reinforced concrete slabs.” ACI J. Proc., 53(2), 29–58.
El-Tawil, S., Li, H., and Kunnath, S. (2014). “Computational simulation of gravity-induced progressive collapse of steel-frame buildings: Current trends and future research needs.” J. Struct. Eng., A2513001.
Grassl, P., and Bažant, Z. P. (2009). “Random lattice-particle simulation of statistical size effect in quasi-brittle structures failing at crack initiation.” J. Eng. Mech., 85–92.
Grierson, D. E., Xu, L., and Liu, Y. (2005). “Progressive-failure analysis of buildings subjected to abnormal loading.” Comput. Aided Civ. Infrastruct. Eng., 20(3), 155–171.
Haldar, A., and Mahadevan, S. (2000). Probability, reliability, and statistical methods in engineering design, Wiley, New York.
Hawkins, N. M., Bao, A., and Yamazaki, J. (1989). “Moment transfer from concrete slabs to columns.” ACI Struct. J., 86(6), 705–716.
Helmy, H., Salem, H., and Mourad, S. (2012). “Progressive collapse assessment of framed reinforced concrete structures according to UFC guidelines for alternative path method.” Eng. Struct., 42, 127–141.
Hillerborg, A., Modeer, M., and Petersson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cem. Concr. Res., 6(6), 773–781.
Izzuddin, B. A., Vlassis, A. G., Elghazouli, A. Y., and Nethercot, N. A. (2008). “Progressive collapse of multi-storey buildings due to sudden column losses? I: Simplified assessment framework.” Eng. Struct., 30(5), 1308–1318.
Jirásek, M., and Bažant, Z. P. (2002). Inelastic analysis of structures, Wiley, New York.
Kaewkulchai, G., and Williamson, E. B. (2004). “Beam element formulation and solution procedure for dynamic progressive collapse analysis.” Comput. Struct., 82(7–8), 639–651.
Kaewkulchai, G., and Williamson, E. B. (2006). “Modeling the impact of failed members for progressive collapse analysis of frame structures.” J. Perform. Constr. Facil., 375–383.
Kanoh, Y., and Yoshizaki, S. (1979). “Strength of slab-column connections transferring shear and moment.” ACI J. Proc., 76(3), 461–478.
Khandelwal, K., and El-Tawil, S. (2008). “Pushdown resistance as a measure of robustness in progressive collapse analysis.” Eng. Struct., 33(9), 2653–2661.
Le, J. L., and Bažant, Z. P. (2011). “Why the observed motion history of World Trade Center towers is smooth.” J. Eng. Mech., 82–84.
Le, J. L., and Xue, B. (2014). “Probabilistic analysis of reinforced concrete frame structures against progressive collapse.” Eng. Struct., 76, 313–323.
Lee, J., and Fenves, G. L. (1998). “Plastic-damage model for cyclic loading of concrete structures.” J. Eng. Mech., 892–900.
Lew, H. S., Bao, Y., Sadek, F., and Main, J. A. (2011). “An experimental and computational study of reinforced concrete assemblies under a column removal scenario.”, National Institute of Standards and Technology, Gaithersburg, MD.
Lowes, L. N., and Altoontash, A. (2003). “Modeling reinforced concrete beam-column joints subjected to cyclic loading.” J. Struct. Eng., 1686–1697.
Mahadevan, S., and Raghothamachar, P. (2000). “Adaptive simulation for system reliability analysis of large structures.” Comput. Struct., 77(6), 725–734.
Masoero, E., Wittel, F. K., Herrmann, H. J., and Chiaia, B. M. (2010). “Progressive collapse mechanisms of brittle and ductile framed structures.” J. Eng. Mech., 987–995.
Moehle, J. P. (1992). “Displacement-based design of RC structures subjected to earthquakes.” Earthquake Spectra, 8(3), 403–428.
Panagiotou, M., Restrepo, J., Schoettler, M., and Kim, G. (2012). “Nonlinear cyclic truss model for reinforced concrete walls.” ACI Struc. J., 109(2), 205–214.
Park, J., and Kim, J. (2010). “Fragility analysis of steel moment frames with various seismic connections subjected to sudden loss of a column.” Eng. Struct., 32(6), 1547–1555.
Pesce, C. P., Casetta, L., and dos Santos, F. M. (2012). “Equation of motion governing the dynamics of vertically collapsing buildings.” J. Eng. Mech., 1420–1431.
Sadek, F., Main, J. M., Lew, H. S., and Bao, Y. (2011). “Testing and analysis of steel and concrete beam-column assemblies under a column removal scenario.” J. Struct. Eng., 881–892.
Sagiroglu, S., and Sasani, M. (2014). “Progressive collapse-resisting mechansims of reinforced concrete structures and effects of initial damage locations” J. Struct. Eng., 04013073.
Sasani, M., Kazemi, A., Sagiroglu, S., and Forest, S. (2011). “Progressive collapse resistance of an actual 11-story structure subjected to severe initial damage.” J. Struct. Eng., 893–902.
Sasani, M., and Sagiroglu, S. (2008). “Progressive collapse resistance of Hotel San Deigo” J. Struct. Eng., 478–488.
Seffen, K. A. (2008). “Progressive collapse of the World Trade Center: Simple analysis.” J. Eng. Mech., 125–132.
Sezen, H., and Moehle, J. P. (2003). “Bond-slip behavior of reinforced concrete members.” fib–Symp. (CEB-FIP); Concrete Structures in Seismic Regions, Athens, Greece.
Shanley, F. R. (1947). “Inelastic column theory.” J. Aerosp. Sci., 14(5), 261–268.
Song, B. I., and Sezen, H. (2013). “Experimental and analytical progressive collapse assessment of a steel frame building.” Eng. Struct., 56, 664–672.
Szyniszewski, S., and Krauthammer, T. (2012). “Energy flow in progressive collapse of steel framed buildings.” Eng. Struct., 42, 142–153.
Vlassis, A. G., Izzuddin, B. A., Elghazouli, A. Y., and Nethercot, D. A. (2009). “Progressive collapse of multi-storey buildings due to failed floor impact.” Eng. Struct., 31(7), 1522–1534.
Xiao, Y., Zhao, Y. B., Li, F. W., Kunnath, S., and Lew, H. S. (2013). “Collapse test of a 3-story half-scale RC frame structures.” Proc., Structures Congress, ASCE, Reston, VA, 11–19.
Xu, G., and Ellingwood, B. R. (2011a). “An energy-based partial pushdown analysis procedure for assessment of disproportionate collapse potential.” J. Constr. Steel Res., 67(3), 547–555.
Xu, G., and Ellingwood, B. R. (2011b). “Probabilistic robustness assessment of pre-Northridge steel moment resisting frames.” J. Struct. Eng., 925–934.
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Published In
Journal of Structural Engineering
Volume 142 • Issue 7 • July 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: May 24, 2015
Accepted: Nov 25, 2015
Published online: Feb 8, 2016
Published in print: Jul 1, 2016
Discussion open until: Jul 8, 2016
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