Structural Engineering and Mechanics

  • 제38권4호
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  • Pages.503-516
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  • 2011
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A homogenization approach for uncertainty quantification of deflection in reinforced concrete beams considering microstructural variability

  • Kim, Jung J. (Department of Civil Engineering, University of New Mexico) ;
  • Fan, Tai (Department of Civil Engineering, University of New Mexico) ;
  • Reda Taha, Mahmoud M. (Department of Civil Engineering, University of New Mexico)
  • 투고 : 2010.04.22
  • 심사 : 2011.04.06
  • 발행 : 2011.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

Uncertainty in concrete properties, including concrete modulus of elasticity and modulus of rupture, are predicted by developing a microstructural homogenization model. The homogenization model is developed by analyzing a concrete representative volume element (RVE) using the finite element (FE) method. The concrete RVE considers concrete as a three phase composite material including: cement paste, aggregate and interfacial transition zone (ITZ). The homogenization model allows for considering two sources of variability in concrete, randomly dispersed aggregates in the concrete matrix and uncertain mechanical properties of composite phases of concrete. Using the proposed homogenization technique, the uncertainty in concrete modulus of elasticity and modulus of rupture (described by numerical cumulative probability density function) are determined. Deflection uncertainty of reinforced concrete (RC) beams, propagated from uncertainties in concrete properties, is quantified using Monte Carlo (MC) simulation. Cracked plane frame analysis is used to account for tension stiffening in concrete. Concrete homogenization enables a unique opportunity to bridge the gap between concrete materials and structural modeling, which is necessary for realistic serviceability prediction.

키워드

참고문헌

  1. ACI Committee 318 (2008), Building Code Requirements for Structural Concrete (318-08), and Commentary (318R-08), American Concrete Institute, Farmington Hills, USA.
  2. An, D., Choi, J.H., Kim, N.H. and Pattabhiraman, S. (2011), "Fatigue life prediction based on Bayesian approach to incorporate field data into probability model", Struct. Eng. Mech., 37(4), 427-442. https://doi.org/10.12989/sem.2011.37.4.427
  3. Bear, J. and Bachmat, Y. (1990), Introduction to the Modelling of Transport Phenomena in Porous Media, Kluwer Academic Dordrecht.
  4. Beer, M. and Spanos, P.D. (2009), "A neural network approach for simulating stationary stochastic processes", Struct. Eng. Mech., 32(1), 71-94. https://doi.org/10.12989/sem.2009.32.1.071
  5. Branson, D.E. (1977), Deformation of Concrete Structures, McGraw-Hill Book Co., NY, USA.
  6. Cavdar, O., Bayraktar, A., Cavdar, A. and Adanur, S. (2008), "Perturbation based stochastic finite element analysis of the structural systems with composite sections under earthquake forces", Steel Compos, Struct., 8(2), 129-144. https://doi.org/10.12989/scs.2008.8.2.129
  7. Cavdar, O., Bayraktar, A., Çavdar, A. and Kartal, M.E. (2009), "Stochastic finite element analysis of structural systems with partially restrained connections subjected to seismic loads", Steel Compos, Struct., 9(6), 499-518. https://doi.org/10.12989/scs.2009.9.6.499
  8. CEP-FIP Model Code 90 (1993), Model Code for Concrete Structures, Comite Euro-International du Beton (CEB) - Federation Internationale de la Precontrainte (FIP), Thomas Telford Ltd., London, UK.
  9. Christiansen, K. (1988), "Eight-year deformation tests on reinforced concrete beams", Mater. Struct. (RILEM), 21, 172-178. https://doi.org/10.1007/BF02473052
  10. Choi, B.S., Scanlon, A. and Johnson, A.P. (2004), "Monte Carlo simulation of immediate and time-dependent deflections of reinforced concrete beams and slabs", ACI Struct. J., 101, 633-641.
  11. CSA A23.3-M04 Technical Committee (2004), Design of Concrete Structures, Canadian Standards Association, Toronto, Canada.
  12. Dormieux, L., Kondo, D. and Ulm, F.J. (2006), Microporo Mechanics, John Wiley & Sons, UK.
  13. Fling, R.S. (1992), "Practical considerations in computing deflection of reinforced concrete", ACI Special Publication, 133, 69-91.
  14. Ghali, A. and Favre, R. (2002), Concrete Structures: Stresses and Deformations, 3rd Edition, Spon Press, London, UK.
  15. Ghali, A., Elbadry, M. and Megally, S. (2000), "Two-year deflections of the confederation bridge", Can. J. Civil Eng., 27(6), 1139-1149. https://doi.org/10.1139/l00-050
  16. Gardner, N.J. (1990), "Design and construction interdependence", Concrete Int., 12(11), 32-38.
  17. Hashin, Z. (1983), "Analysis of composite materials - A survey", J. Appl. Mech., 50, 481-505. https://doi.org/10.1115/1.3167081
  18. Hall, P.L. and Strutt, J.E. (2003), "Probabilistic physics-of-failure models for component reliabilities using Monte Carlo simulation and Weibull analysis: a parametric study", Reliab. Eng. Syst. Safe., 80(3), 233-242. https://doi.org/10.1016/S0951-8320(03)00032-2
  19. Jain, J.R. and Ghosh, S. (2008), "Homogenization based continuum damage mechanics model for monotonic and cyclic damage evolution in 3D composites", Interact. Multis. Mech., 1(2), 279-301. https://doi.org/10.12989/imm.2008.1.2.279
  20. Jokinen, E.P. and Scanlon, A. (1985), "Field-measured two-way slab deflections", Proceeding of the Annual Conference of the Canadian Society for Civil Engineering, Saskatoon, Saskatchewan, 43-58.
  21. Ju, J.W. and Chen, T.M. (1994), "Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogenities", Acta Mech., 103, 123-144. https://doi.org/10.1007/BF01180222
  22. Khisaeva, Z.F. and Ostoja-Starzewski, M. (2006), "On the size of RVE in finite elasticity of random composites", J. Elast., 85, 153-173. https://doi.org/10.1007/s10659-006-9076-y
  23. Kalali, A. and Kabir, M.Z. (2010), "Modeling of unreinforced brick walls under in-plane shear & compression loading", Struct. Eng. Mech., 36(3), 247-278. https://doi.org/10.12989/sem.2010.36.3.247
  24. Kim, J.J. (2009), "Uncertainty quantification for serviceability of reinforced concrete structures", PhD Dissertation, Department of Civil Engineering, University of New Mexico, USA.
  25. Kim, J.J. and Reda Taha, M.M. (2009), "Robustness-to-uncertainty: An alternative perspective in realizing uncertainty in modeling deflection of reinforced concrete structures", J. Struct. Eng.-ASCE, 135(8), 998-1001. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:8(998)
  26. Kim, J.J., Reda Taha, M.M. and Ross, T.J. (2010), "Establishing concrete cracking strength interval using possibility theory with an application to predict the possible reinforced concrete deflection interval", Eng. Struct., 32, 3592-3600. https://doi.org/10.1016/j.engstruct.2010.08.003
  27. Kim, J. and Muliana, A. (2010), "Time-dependent and inelastic behaviors of fiber- and particle hybrid composites", Struct. Eng. Mech., 34(4), 525-539. https://doi.org/10.12989/sem.2010.34.4.525
  28. Le Pape, Y., Toulemonde, C. and Sanahuja, J. (2009), "Upscaling concrete properties: a rational approach to account for the material complexity and variability", Int. J. Mater. Struct. Integrity, 3, 227-246. https://doi.org/10.1504/IJMSI.2009.028616
  29. Kurukuri, S. (2005), "Homogenization of damaged concrete meso-structure using representative volume elements: implementation and application to slang", MS Thesis, University Weimar, Germany.
  30. Mehta, K., and Monterio, P.J.M. (2006), Concrete: Microstructure, Properties and Materials, Third Edition. McGraw-Hill Professional, New York, USA.
  31. Milani, G. and Benasciutti, D. (2010), "Homogenized limit analysis of masonry structures with random input properties: polynomial Response Surface approximation and Monte Carlo simulations", Struct. Eng. Mech., 34(4), 417-447. https://doi.org/10.12989/sem.2010.34.4.417
  32. Muzzammil, M., Siddiqui, N.A. and Siddiqui, A.F. (2008), "Reliability considerations in bridge pier scouring", Struct. Eng. Mech., 28(1), 1-18. https://doi.org/10.12989/sem.2008.28.1.001
  33. Nowak, A.S. and Szerszen, M.M. (2003), "Calibration of design code for buildings (ACI 318): Part I-Statistical models for resistance", ACI Struct. J., 100(3), 377-382.
  34. Ostoja-Starzewski, M. (2006), "Material spatial randomness: From statistical to representative volume element", Probabilist. Eng. Mech., 21, 112-132. https://doi.org/10.1016/j.probengmech.2005.07.007
  35. Ostoja-Starzewski, M. (2007), Microstructural Randomness and Scaling in Mechanics of Materials, Chapman & Hall/CRC/Taylor & Francis, USA.
  36. Pellissetti, M.F. (2009), "Parallel processing in structural reliability", Struct. Eng. Mech., 32(1), 95-126. https://doi.org/10.12989/sem.2009.32.1.095
  37. Qiu, G. and Li, X. (2009), "Design of materials with prescribed elastic properties using D-functions", Struct. Eng. Mech., 33(1), 109-112. https://doi.org/10.12989/sem.2009.33.1.109
  38. Scanlon, A. and Pinheiro, L. (1992), "Allowable deflections: the other side of the equation", ACI Special Publication, 133, 111-120.
  39. Schueller, G.I. (2009), "Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis - recent advances", Struct. Eng. Mech., 32(1), 1-20. https://doi.org/10.1111/j.1460-2695.2008.01300.x
  40. Smit, R.J.M., Brekelmans, W.A.M. and Meijer, H.E.H. (1998), "Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling", Comput. Meth. Appl. Mech. Eng., 155, 181-192. https://doi.org/10.1016/S0045-7825(97)00139-4
  41. Thompson, D.P. and Scanlon, A. (1988), "Minimum thickness requirements for control of two-way slab deflections", ACI Struct. J., 85, 12-22.
  42. Torquato, S. (2002), Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer Science & Business Media, LLC., New York, USA.
  43. Vorel, J. and Šejnoha, M. (2009), "Evaluation of homogenized thermal conductivities of imperfect carbon-carbon textile composites using the Mori-Tanaka method", Struct. Eng. Mech., 33(4), 429-446. https://doi.org/10.12989/sem.2009.33.4.429
  44. Wu, W., Yuan, Z. and Fish, J. (2010), "Eigendeformation-based homogenization of concrete", Int. J. Multiscale Com., 8, 1-15. https://doi.org/10.1615/IntJMultCompEng.v8.i1.20
  45. Zundelevich, S., Hamada, H.S. and Chiu, A.N. (1974), "Variability of deflections of simply supported precast prestressed concrete beams", ACI Special Publication, 43, 547-571.

피인용 문헌

  1. Modelling of Alkali-Silica Reaction Effects on Mechanical Property Changes of Concrete vol.8, pp.2, 2015, https://doi.org/10.7782/IJR.2015.8.2.042
  2. 3D Microstructure Simulation of Reactive Aggregate in Concrete from 2D Images as the Basis for ASR Simulation vol.14, pp.11, 2011, https://doi.org/10.3390/ma14112908