Progressive collapse of 2D reinforced concrete structures under sudden column removal

doi:10.1007/s11709-020-0645-0

Front. Struct. Civ. Eng.

2020, Vol. 14

Issue (6) : 1387-1402 https://doi.org/10.1007/s11709-020-0645-0

RESEARCH ARTICLE

Progressive collapse of 2D reinforced concrete structures under sudden column removal

El Houcine MOURID¹(

), Said MAMOURI¹, Adnan IBRAHIMBEGOVIC²

¹. Mechanics of Structures Laboratory, Mechanics, Modeling and Experimentation Laboratory, Department of Mechanical Engineering, University of Tahri Mohamed-Bechar, Bechar 08000, Algeria
². Roberval Mechanics laboratory, Alliance Sorbonne University, Compiegne 60203, France

Download: PDF(1546 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Once a column in building is removed due to gas explosion, vehicle impact, terrorist attack, earthquake or any natural disaster, the loading supported by removed column transfers to neighboring structural elements. If these elements are unable to resist the supplementary loading, they continue to fail, which leads to progressive collapse of building. In this paper, an efficient strategy to model and simulate the progressive collapse of multi-story reinforced concrete structure under sudden column removal is presented. The strategy is subdivided into several connected steps including failure mechanism creation, MBS dynamic analysis and dynamic contact simulation, the latter is solved by using conserving/decaying scheme to handle the stiff nonlinear dynamic equations. The effect of gravity loads, structure-ground contact, and structure-structure contact are accounted for as well. The main novelty in this study consists in the introduction of failure function, and the proper manner to control the mechanism creation of a frame until its total failure. Moreover, this contribution pertains to a very thorough investigation of progressive collapse of the structure under sudden column removal. The proposed methodology is applied to a six-story frame, and many different progressive collapse scenarios are investigated. The results illustrate the efficiency of the proposed strategy.

Keywords failure mechanism MBS dynamic analysis gravity loads structure-ground contact structure-structure contact energy conserving/decaying scheme

Corresponding Author(s): El Houcine MOURID

Just Accepted Date: 18 August 2020 Online First Date: 28 September 2020 Issue Date: 12 January 2021

Cite this article:

El Houcine MOURID,Said MAMOURI,Adnan IBRAHIMBEGOVIC. Progressive collapse of 2D reinforced concrete structures under sudden column removal[J]. Front. Struct. Civ. Eng., 2020, 14(6): 1387-1402.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-020-0645-0
https://academic.hep.com.cn/fsce/EN/Y2020/V14/I6/1387

Fig.1 Jump in rotation.

Fig.2 Constitutive laws: (a) moment-curvature diagram; (b) moment-rotation jump diagram.

Fig.3 Replacing softening plastic hinges with revolute joints for (a) beam and (b) frame.

Fig.4 Two-story frame.

Fig.5 Response of the two-story frame up to the complete failure comparing to different studies.

Fig.6 Location of plastic hinges in two-story frame.

Fig.7 Six story frame.

Fig.8 Response of a six story frame using different meshes.

Fig.9 Response of the six story frame and softening plastic hinges creation.

Fig.10 Locations of softening plastic hinges in a six-story frame. (a) Groups and (b) location of softening plastic hinges.

Fig.11 Six-story frame with removed column.

Fig.12 Response of six-story frame: time step effect.

Fig.13 Response of six-story frame: time step effect (zoomed).

Fig.14 Six-story frame progressive collapse: no gravity load and no contact between elements.

Fig.15 Response of the six-story frame: no gravity load and no contact between elements.

Fig.16 Response of the six-story frame: no gravity load and no contact between elements (zoomed zone).

Fig.17 Six-story frame progressive collapse: with gravity load and no contact between elements.

Fig.18 Response of the six-story frame: with gravity load and no contact between elements.

Fig.19 Response of the six-story frame: with gravity load and no contact between elements (zoomed zone).

Fig.20 Six-story frame progressive collapse: with gravity load and contact between elements.

Fig.21 Response of six-story frame: with gravity load and contact between elements.

Fig.22 Response of six-story frame: with gravity load and contact between elements (zoomed zone).

Fig.23 Response of the six-story frame: comparison between the three cases.

Fig.24 Partial collapse of the six-story frame with structural masses and additional masses of 900 kg/m.

Fig.25 Partial collapse of the six-story frame with structural masses and additional masses of 900 kg/m.

Fig.26 Progressive collapse of the six-story frame under only the gravity loads taking into account contact between elements.

Fig.27 Response of the six-story frame under only the gravity loads taking into account the contact between elements.

1	V M Janssens. Modelling progressive collapse in steel structures. Dissertation for the Doctoral Degree. Dublin: Trinity College Dublin, 2012
2	A Vlassis, B Izzuddin, A Elghazouli, D Nethercot. Progressive collapse of multi-storey buildings due to sudden column loss, part II: Application. Engineering Structures, 2008, 30(5): 1424–1438 https://doi.org/10.1016/j.engstruct.2007.08.011
3	B Luccioni, R Ambrosini, R Danesi. Analysis of building collapse under blast loads. Engineering Structures, 2004, 26(1): 63–71 https://doi.org/10.1016/j.engstruct.2003.08.011
4	Y Shi, Z X Li, H Hao. A new method for progressive collapse analysis of RC frames under blast loading. Engineering Structures, 2010, 32(6): 1691–1703 https://doi.org/10.1016/j.engstruct.2010.02.017
5	S Mattern, G Blankenhorn, K Schweizerhof. Numerical investigation on collapse kinematics of a reinforced concrete structure within a blasting process. In: Proceedings of the 5th German LS-DYNA Forum. Ulm: DYNAmore GmbH, 2006, 15–24
6	D Hartmann, F Stangenberg, R Melzer, R. BlumComputer-based Planning of Demolition of Reinforced Concrete Smokestacks by Means of Blasting and Implementation of a Knowledge Based Assistance System. Bochum: Ruhr-Universität Bochum, 1994 (in German)
7	Y Toi, D Isobe. Finite element analysis of Quasi-static and dynamic collapse behaviors of framed structures by the adaptively shifted integration technique. Computers & Structures. 1996, 58:947–955 10.1016/0045-7949(95)00195-M.
8	R. Abbasnia, , F. M. Nav, , N. Usefi, , & O Rashidian, . A new method for progressive collapse analysis of RC frames. Structural Engineering and Mechanics, 2016, 60(1): 31–50.
9	D Hartmann, M Breidt, V Nguyen, F Stangenberg, S Höhler, K Schweizerhof, S Mattern, G Blankenhorn, B Möller, M Liebscher. Structural collapse simulation under consideration of uncertainty-fundamental concept and results. Computers & Structures, 2008, 86(21–22): 2064–2078 https://doi.org/10.1016/j.compstruc.2008.03.004
10	B Möller, M Liebscher, K Schweizerhof, S Mattern, G Blankenhorn. Structural collapse simulation under consideration of uncertainty–improvement of numerical efficiency. Computers & Structures, 2008, 86(19–20): 1875–1884 https://doi.org/10.1016/j.compstruc.2008.04.011
11	L Kwasniewski. Nonlinear dynamic simulations of progressive collapse for a multi-story building. Engineering Structures, 2010, 32(5): 1223–1235 https://doi.org/10.1016/j.engstruct.2009.12.048
12	D Grierson, L Xu, Y Liu. Progressive-failure analysis of buildings subjected to abnormal loading. Computer-Aided Civil and Infrastructure Engineering, 2005, 20(3): 155–171 https://doi.org/10.1111/j.1467-8667.2005.00384.x
13	A G Vlassis. Progressive collapse assessment of tall buildings. Dissertation for the Doctoral Degree. London: Imperial College London, 2007
14	B Izzuddin, A Vlassis, A Elghazouli, D Nethercot. Progressive collapse of multi-storey buildings due to sudden column loss. Part I: Simplified assessment framework. Engineering Structures, 2008, 30(5): 1308–1318 https://doi.org/10.1016/j.engstruct.2007.07.011
15	S Zhou, X Zhuang, T Rabczuk. Phase-field modeling of fluid-driven dynamic cracking in porous media. Computer Methods in Applied Mechanics and Engineering, 2019, 350: 169–198 https://doi.org/10.1016/j.cma.2019.03.001
16	S Zhou, T Rabczuk, X Zhuang. Phase field modeling of quasi-static and dynamic crack propagation: Comsol implementation and case studies. Advances in Engineering Software, 2018, 122: 31–49 https://doi.org/10.1016/j.advengsoft.2018.03.012
17	M H Tsai, B H Lin. Investigation of progressive collapse resistance and inelastic response for an earthquake-resistant RC building subjected to column failure. Engineering Structures, 2008, 30(12): 3619–3628 https://doi.org/10.1016/j.engstruct.2008.05.031
18	J Kim, T Kim. Assessment of progressive collapse-resisting capacity of steel moment frames. Journal of Constructional Steel Research, 2009, 65(1): 169–179 https://doi.org/10.1016/j.jcsr.2008.03.020
19	H S Kim, J Kim, D W An. Development of integrated system for progressive collapse analysis of building structures considering dynamic effects. Advances in Engineering Software, 2009, 40(1): 1–8 https://doi.org/10.1016/j.advengsoft.2008.03.011
20	G Kaewkulchai, E B Williamson. Beam element formulation and solution procedure for dynamic progressive collapse analysis. Computers & Structures, 2004, 82(7–8): 639–651 https://doi.org/10.1016/j.compstruc.2003.12.001
21	Y Bao, S K Kunnath, S El-Tawil, H S Lew. Macro-model-based simulation of progressive collapse: RC frame structures. Journal of Structural Engineering, 2008, 134(7): 1079–1091 https://doi.org/10.1061/(ASCE)0733-9445(2008)134:7(1079)
22	F Fu. Progressive collapse analysis of high-rise building with 3-D finite element modeling method. Journal of Constructional Steel Research, 2009, 65(6): 1269–1278 https://doi.org/10.1016/j.jcsr.2009.02.001
23	K Galal, T El-Sawy. Effect of retrofit strategies on mitigating progressive collapse of steel frame structures. Journal of Constructional Steel Research, 2010, 66(4): 520–531 https://doi.org/10.1016/j.jcsr.2009.12.003
24	U Gsa. Progressive collapse analysis and design guidelines for new federal office buildings and major modernization projects. Washington, D.C.: General Service Administration, 2003
25	E H Mourid, S Mamouri, A Ibrahimbegović. A controlled destruction and progressive collapse of 2D reinforced concrete frames. Coupled Systems Mechanics, 2018, 7(2): 111–139
26	F J Vecchio, M B Emara. Shear deformations in reinforced concrete frames. ACI Structural Journal, 1992, 89(1): 46–56
27	A Ibrahimbegović, F Frey. Stress resultant finite element analysis of reinforced concrete plates. Engineering Computations, 1993, 10(1): 15–30 https://doi.org/10.1108/eb023892
28	A Ibrahimbegović, F Frey. An efficient implementation of stress resultant plasticity in analysis of Reissner-Mindlin plates. International Journal for Numerical Methods in Engineering, 1993, 36(2): 303–320 https://doi.org/10.1002/nme.1620360209
29	A Cipollina, A López-Inojosa, J Flórez-López. A simplified damage mechanics approach to nonlinear analysis of frames. Computers & Structures, 1995, 54(6): 1113–1126 https://doi.org/10.1016/0045-7949(94)00394-I
30	M E Marante, R Picón, J Flórez-López. Analysis of localization in frame members with plastic hinges. International Journal of Solids and Structures, 2004, 41(14): 3961–3975 https://doi.org/10.1016/j.ijsolstr.2004.02.014
31	M E Marante, L Suárez, A Quero, J Redondo, B Vera, M Uzcategui, S Delgado, L R León, L Núñez, J Flórez-López. Portal of damage: a web-based finite element program for the analysis of framed structures subjected to overloads. Advances in Engineering Software, 2005, 36(5): 346–358 https://doi.org/10.1016/j.advengsoft.2004.06.017
32	P Nanakorn. A two-dimensional beam-column finite element with embedded rotational discontinuities. Computers & Structures, 2004, 82(9–10): 753–762 https://doi.org/10.1016/j.compstruc.2004.02.008
33	T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758 https://doi.org/10.1016/j.engfracmech.2008.06.019
34	T Rabczuk, T Belytschko. Cracking particles: a simplified mesh-free method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343 https://doi.org/10.1002/nme.1151
35	T Rabczuk, T Belytschko. A three-dimensional large deformation mesh-free method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799 https://doi.org/10.1016/j.cma.2006.06.020
36	T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455 https://doi.org/10.1016/j.cma.2010.03.031
37	A Ibrahimbegović, D Brancherie. Combined hardening and softening constitutive model of plasticity: precursor to shear slip line failure. Computational Mechanics, 2003, 31(1–2): 88–100 doi:10.1007/s00466-002-0396-x
38	A Ibrahimbegović, S Melnyk. Embedded discontinuity finite element method for modeling of localized failure in heterogeneous materials with structured mesh: an alternative to extended finite element method. Computational Mechanics, 2007, 40(1): 149–155 https://doi.org/10.1007/s00466-006-0091-4
39	M Jukić, B Brank, A Ibrahimbegović. Embedded discontinuity finite element formulation for failure analysis of planar reinforced concrete beams and frames. Engineering Structures, 2013, 50: 115–125 https://doi.org/10.1016/j.engstruct.2012.07.028
40	M Jukić, B Brank, A Ibrahimbegović. Failure analysis of reinforced concrete frames by beam finite element that combines damage, plasticity and embedded discontinuity. Engineering Structures, 2014, 75: 507–527 https://doi.org/10.1016/j.engstruct.2014.06.017
41	J Dujc, B Brank, A Ibrahimbegović. Multi-scale computational model for failure analysis of metal frames that includes softening and local buckling. Computer Methods in Applied Mechanics and Engineering, 2010, 199(21–22): 1371–1385 https://doi.org/10.1016/j.cma.2009.09.003
42	N N Bui, M Ngo, M Nikolic, D Brancherie, A Ibrahimbegović. Enriched Timoshenko beam finite element for modeling bending and shear failure of reinforced concrete frames. Computers & Structures, 2014, 143: 9–18 doi:10.1016/j.compstruc.2014.06.004
43	S Zhou, X Zhuang, T Rabczuk. Phase field modeling of brittle compressive-shear fractures in rock-like materials: A new driving force and a hybrid formulation. Computer Methods in Applied Mechanics and Engineering, 2019, 355: 729–752 https://doi.org/10.1016/j.cma.2019.06.021
44	S Zhou, X Zhuang, T Rabczuk. A phase-field modeling approach of fracture propagation in poroelastic media. Engineering Geology, 2018, 240: 189–203 https://doi.org/10.1016/j.enggeo.2018.04.008
45	S Zhou, X Zhuang, H Zhu, T Rabczuk. Phase field modelling of crack propagation, branching and coalescence in rocks. Theoretical and Applied Fracture Mechanics, 2018, 96: 174–192 https://doi.org/10.1016/j.tafmec.2018.04.011
46	C Anitescu, E Atroshchenko, N Alajlan, T Rabczuk. Artificial neural network methods for the solution of second order boundary value problems, Computers. Materials & Continua, 2019, 59(1): 345–359 https://doi.org/10.32604/cmc.2019.06641
47	H Guo, X Zhuang, T Rabczuk. A deep collocation method for the bending analysis of Kirchhoff plate. Computers, Materials & Continua, 2019, 59(2): 433–456 https://doi.org/10.32604/cmc.2019.06660
48	A Cardona, M Geradin. Time integration of the equations of motion in mechanism analysis. Computers & Structures, 1989, 33(3): 801–820 https://doi.org/10.1016/0045-7949(89)90255-1
49	T Laursen, V Chawla. Design of energy conserving algorithms for frictionless dynamic contact problems. International Journal for Numerical Methods in Engineering, 1997, 40(5): 863–886 https://doi.org/10.1002/(SICI)1097-0207(19970315)40:5<863::AID-NME92>3.0.CO;2-V
50	A Ibrahimbegović, S Mamouri. On rigid components and joint constraints in nonlinear dynamics of flexible multibody systems employing 3d geometrically exact beam model. Computer Methods in Applied Mechanics and Engineering, 2000, 188(4): 805–831 https://doi.org/10.1016/S0045-7825(99)00363-1
51	N M Newmark. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division, 1959, 85(3): 67–94
52	A Ibrahimbegović, S Mamouri. Nonlinear dynamics of flexible beams in planar motion: formulation and time-stepping scheme for stiff problems. Computers & Structures, 1999, 70(1): 1–22 https://doi.org/10.1016/S0045-7949(98)00150-3
53	A Ibrahimbegović, S Mamouri. Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations. Computer Methods in Applied Mechanics and Engineering, 2002, 191(37–38): 4241–4258 https://doi.org/10.1016/S0045-7825(02)00377-8
54	S Mamouri, R Kouli, A Benzegaou, A Ibrahimbegović. Implicit controllable high-frequency dissipative scheme for nonlinear dynamics of 2d geometrically exact beam. Nonlinear Dynamics, 2016, 84(3): 1289–1302 https://doi.org/10.1007/s11071-015-2567-2
55	O Bauchau, N Theron. Energy decaying scheme for nonlinear elastic multi-body systems. Computers & Structures, 1996, 59(2): 317–331 https://doi.org/10.1016/0045-7949(95)00250-2
56	D Kuhl, M Crisfield. Energy-conserving and decaying algorithms in non-linear structural dynamics. International Journal for Numerical Methods in Engineering, 1999, 45(5): 569–599 https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<569::AID-NME595>3.0.CO;2-A
57	F Armero, I Romero. On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part I: low-order methods for two model problems and nonlinear elasto-dynamics. Computer Methods in Applied Mechanics and Engineering, 2001, 190(20–21): 2603–2649 https://doi.org/10.1016/S0045-7825(00)00256-5
58	A Signorini. On some issues elastostatic . Proceedings of the Italian Society for the Progress of Sciences, 1933 , 21(2):143–148 (in Italian)
59	G Fichera. Elastostatic Problems with Unilateral Constraints: The Signorini Problem with Ambiguous Boundary Conditions. United States: Aerospace Research Laboratories, 1964
60	J J Moreau. Quadratic programming in mechanics: Dynamics of one-sided constraints. SIAM Journal on Control, 1966, 4(1): 153–158 https://doi.org/10.1137/0304014
61	E Reissner. On one-dimensional finite-strain beam theory: The plane problem . Journal of Applied Mathematics and Physics (ZAMP), 1972, 23(5): 795–804
62	B R Ellingwood, R Smilowitz, D O Dusenberry, D Duthinh, H S Lew, N J Carino. Best Practices for Reducing the Potential for Progressive Collapse in Buildings . Technical Report No. 7396. 2007
63	A Ibrahimbegović. Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods. Dordrecht: Springer , 2009, 160
64	J Huang, W Zhu. Nonlinear dynamics of a high-dimensional model of a rotating Euler Bernoulli beam under the gravity load. Journal of Applied Mechanics, 2014, 81(10): 101007 https://doi.org/10.1115/1.4028046
65	P Wriggers. Finite element algorithms for contact problems. Archives of Computational Methods in Engineering, 1995, 2(4): 1–49 https://doi.org/10.1007/BF02736195
66	B Brank, J Korelc, A Ibrahimbegović. Dynamics and time-stepping schemes for elastic shells undergoing finite rotations. Computers & Structures, 2003, 81(12): 1193–1210 https://doi.org/10.1016/S0045-7949(03)00036-1
67	B Pham, D Brancherie, L Davenne, A Ibrahimbegović. Stress-resultant models for ultimate load design of reinforced concrete frames and multi-scale parameter estimates. Computational Mechanics, 2013, 51(3): 347–360 https://doi.org/10.1007/s00466-012-0734-6
68	I Imamovic, A Ibrahimbegović, C Knopf-Lenoir, E Mesic. Plasticity-damage model parameters identification for structural connections. Coupled Systems Mechanics, 2015, 4(4):337–364

[1]	Baoyun ZHAO, Yang LIU, Dongyan LIU, Wei HUANG, Xiaoping WANG, Guibao YU, Shu LIU. Research on the influence of contact surface constraint on mechanical properties of rock-concrete composite specimens under compressive loads[J]. Front. Struct. Civ. Eng., 2020, 14(2): 322-330.

Viewed

Full text

Abstract

Cited

Shared

Discussed