DOI QR코드

DOI QR Code

Homogenized limit analysis of masonry structures with random input properties: polynomial Response Surface approximation and Monte Carlo simulations

  • Milani, G. (DIS, Dipartimento di Ingegneria Strutturale, Politecnico di Milano) ;
  • Benasciutti, D. (DIEGM, Dipartimento di Ingegneria Elettrica Gestionale Meccanica, University of Udine)
  • 투고 : 2008.09.03
  • 심사 : 2009.11.16
  • 발행 : 2010.03.10

초록

The uncertainty often observed in experimental strengths of masonry constituents makes critical the selection of the appropriate inputs in finite element analysis of complex masonry buildings, as well as requires modelling the building ultimate load as a random variable. On the other hand, the utilization of expensive Monte Carlo simulations to estimate collapse load probability distributions may become computationally impractical when a single analysis of a complex building requires hours of computer calculations. To reduce the computational cost of Monte Carlo simulations, direct computer calculations can be replaced with inexpensive Response Surface (RS) models. This work investigates the use of RS models in Monte Carlo analysis of complex masonry buildings with random input parameters. The accuracy of the estimated RS models, as well as the good estimations of the collapse load cumulative distributions obtained via polynomial RS models, show how the proposed approach could be a useful tool in problems of technical interest.

키워드

참고문헌

  1. Apostolakis, G. (1990), "The concept of probability in safety assessments of technological systems", Science, 250(4986), 1359-1364. https://doi.org/10.1126/science.2255906
  2. Bicanic, N., Stirling, C. and Pearce, C.J. (2003), "Discontinuous modelling of masonry bridges", Comput. Mech., 31, 60-68. https://doi.org/10.1007/s00466-002-0393-0
  3. Brencich, A. and Gambarotta, L. (2005), "Mechanical response of solid clay brickwork under eccentric loading. Part I: Unreinforced masonry", Mater. Struct., 38(276), 257-266. https://doi.org/10.1617/14134
  4. Eurocode 6 (1996), Design of Masonry Structures, EN 1996.
  5. Florian, A. (1992), "An efficient sampling scheme: Updated Latin Hypercube sampling", Probabilist, Eng. Mech., 7, 123-130. https://doi.org/10.1016/0266-8920(92)90015-A
  6. Giunta, A.A. and Watson, L.T. (1998), "A comparison of approximation modeling techniques: polynomial versus interpolating models", Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, September.
  7. Giunta, A.A., Wojtkiewicz, S.F. and Eldred, M.S. (2003), "Overview of modern design of experiments methods for computational simulations", Proceedings of the 41st AIAA, Aerospace Sciences Meeting and Exhibit, Reno, January.
  8. Glynn, P.W. and Iglehart, D.L. (1989), "Importance sampling for stochastic simulations", Manage. Sci., 35(11), 1367-1392. https://doi.org/10.1287/mnsc.35.11.1367
  9. Goodman, L.A. (1960), "On the exact variance of products", J. Am. Stat. Assoc., 55(292), 708-713. https://doi.org/10.2307/2281592
  10. Goyal, A., Shahabuddin, P., Heidelberger, P., Nicola, V.F. and Glynn, P.W. (1992), "A unified framework for simulating Markovian models of highly dependable systems", IEEE T. Comput., 41(1), 36-51. https://doi.org/10.1109/12.123381
  11. Haan, C.T. (1989), "Parametric uncertainty in hydrologic modeling", Trans. ASAE, 32(1), 137-146. https://doi.org/10.13031/2013.30973
  12. Heidelberger, P. (1995), "Fast simulation of rare events in queueing and reliability models", ACM T. Model. Comput. Simul., 5(1), 43-85. https://doi.org/10.1145/203091.203094
  13. Helton, J.C. (1994), "Treatment of uncertainty in performance assessments for complex systems", Risk Anal., 14(4), 483-511. https://doi.org/10.1111/j.1539-6924.1994.tb00266.x
  14. Helton, J.C. (1997), "Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty", J. Stat. Comput. Simul., 57(1-4), 3-76. https://doi.org/10.1080/00949659708811803
  15. Helton, J.C. and Burmaster, D.E. (1996), "Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems", Reliab. Eng. Syst. Safe., 54(2-3), 91-94. https://doi.org/10.1016/S0951-8320(96)00066-X
  16. Helton, J.C. and Davis, F.J. (2003), "Latin Hypercube and the propagation of the uncertainty in analyses of complex systems", Reliab. Eng. Syst. Safe., 81, 23-69. https://doi.org/10.1016/S0951-8320(03)00058-9
  17. Helton, J.C., Davis, F.J. and Johnson, J.D. (2005), "A comparison of uncertainty and sensitivity analysis results obtained with random and Latin Hypercube sampling", Reliab. Eng. Syst. Safe., 89(3), 305-330. https://doi.org/10.1016/j.ress.2004.09.006
  18. Hoffman, F.O. and Hammonds, J.S. (1994), "Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability", Risk Anal., 14(5), 707-712. https://doi.org/10.1111/j.1539-6924.1994.tb00281.x
  19. Hradil, P., Zak, J., Novak, D. and Lavicky, D. (2001), "Stochastic analysis of historical masonry structures", Hist. Construct., Lourenco P.B., Roca, P. (eds), Guimaraes.
  20. Huntington, D.E. and Lyrintzis, C.S. (1998), "Improvements to and limitations of Latin Hypercube sampling", Probabilist, Eng. Mech., 13(4), 245-253. https://doi.org/10.1016/S0266-8920(97)00013-1
  21. Iman, R.L. (1981), "Statistical methods for including uncertainties associated with the geologic isolation of radioactive waste which allow for a comparison with licensing criteria", Proceedings of the Symposium on Uncertainties Associated with the Regulation of the Geologic Disposal of High-Level Radioactive Waste (Ed. Kocher, D.C.), Gatlinburg, March.
  22. Jin, R., Chen, W. and Simpson, T.W. (2001), "Comparative studies of metamodelling techniques under multiple modeling criteria", Struct. Multidiscip. O., 23, 1-13. https://doi.org/10.1007/s00158-001-0160-4
  23. Krabbenhoft, K., Lyamin, A.V., Hjiaj, M. and Sloan, S.W. (2005), "A new discontinuous upper bound limit analysis formulation", Int. J. Numer. Meth. Eng., 63, 1069-1088. https://doi.org/10.1002/nme.1314
  24. Lofti, H.R. and Shing, B.P. (1994), "Interface model applied to fracture of masonry structures", J. Struct. Eng., 120, 63-80. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:1(63)
  25. Lourenco, P.B., de Borst, R. and Rots, J.G. (1997), "A plane stress softening plasticity model for orthotropic materials", Int. J. Numer. Meth. Eng., 40, 4033-4057. https://doi.org/10.1002/(SICI)1097-0207(19971115)40:21<4033::AID-NME248>3.0.CO;2-0
  26. Lourenco, P.B. (1999), "Anisotropic softening model for masonry plates and shells", J. Struct. Eng., 126(9), 1008-1016.
  27. Lourenco, P.B. and Pina-Henriques, J. (2006), "Validation of analytical and continuum numerical methods for estimating the compressive strength of masonry", Comput. Struct., 84(29-30), 1977-1989. https://doi.org/10.1016/j.compstruc.2006.08.009
  28. Magenes, G. and Calvi, G.M. (1997), "In-plane seismic response of brick masonry walls", Earth. Eng. Struct. D., 26, 1091-1112. https://doi.org/10.1002/(SICI)1096-9845(199711)26:11<1091::AID-EQE693>3.0.CO;2-6
  29. McKay, M.D., Conover, W.J. and Beckman, R.J. (1979), "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technometrics, 21, 239-245. https://doi.org/10.2307/1268522
  30. Melchers, R.E. (1990), "Search-based importance sampling", Struct. Safe., 9(2), 117-128. https://doi.org/10.1016/0167-4730(90)90003-8
  31. Milani, G., Lourenco, P.B. and Tralli, A. (2006a), "Homogenization approach for the limit analysis of out-of-plane loaded masonry walls", J. Struct. Eng., 132(10), 1650-1663. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:10(1650)
  32. Milani, G., Lourenco, P.B. and Tralli, A. (2006b), "Homogenised limit analysis of masonry walls. Part I: failure surfaces", Comput. Struct., 84, 166-180. https://doi.org/10.1016/j.compstruc.2005.09.005
  33. Milani, G., Lourenco, P.B. and Tralli, A. (2006c), "Homogenised limit analysis of masonry walls. Part II: structural examples", Comput. Struct., 84, 181-195. https://doi.org/10.1016/j.compstruc.2005.09.004
  34. Milani, G., Lourenco, P.B. and Tralli, A. (2007a), "3D homogenized limit analysis of masonry buildings under horizontal loads", Eng. Struct., 29(11), 3134-3148. https://doi.org/10.1016/j.engstruct.2007.03.003
  35. Milani, G., Zuccarello, F.A., Olivito, R.S. and Tralli, A. (2007b), "Heterogeneous upper-bound finite element limit analysis of masonry walls out-of-plane loaded", Comput. Mech., 40(6), 911-931. https://doi.org/10.1007/s00466-006-0151-9
  36. Mood, A., Graybill, F. and Boes, D. (1974), Introduction to the Theory of Statistics, McGraw-Hill.
  37. Neves, R.A., Chateauneuf, A., Venturini, W.S. and Lemaire, M. (2006), "Reliability analysis of reinforced concrete grids with nonlinear material behavior", Reliab. Eng. Syst. Safe., 91, 735-744. https://doi.org/10.1016/j.ress.2005.07.002
  38. Nicola, V.F., Shahabuddin, P. and Nakayama, M.K. (2001), "Techniques for fast simulation of models of highly dependable systems", IEEE T. Reliab., 50(3), 246-264. https://doi.org/10.1109/24.974122
  39. Olsen, P.C. (1999), "Evaluation of triangular elements in rigid-plastic finite element analysis of reinforced concrete", Comput. Meth. Appl. Mech. Eng., 179, 1-17. https://doi.org/10.1016/S0045-7825(99)00038-9
  40. Olsen, P.C. (2001), "Rigid-plastic finite element analysis of steel plates, structural girders and connections", Comput. Meth. Appl. Mech. Eng., 191, 761-781. https://doi.org/10.1016/S0045-7825(01)00284-5
  41. Owen, A. and Zhou, Y. (2000), "Safe and effective importance sampling", J. Am. Stat. Assoc., 95(449), 135-143. https://doi.org/10.2307/2669533
  42. Parry, G.W. and Winter, P.W. (1981), "Characterization and evaluation of uncertainty in probabilistic risk analysis", Nucl. Safe., 22(1), 28-42.
  43. Pate-Cornell, M.E. (1996), "Uncertainties in risk analysis: six levels of treatment", Reliab. Eng. Syst. Safe., 54(2-3), 95-111. https://doi.org/10.1016/S0951-8320(96)00067-1
  44. Pendola, M., Mohamed, A., Lemaire, M. and Hornet, P. (2000), "Combination of finite element and reliability methods in nonlinear fracture mechanics", Reliab. Eng. Syst. Safe., 70, 15-27. https://doi.org/10.1016/S0951-8320(00)00043-0
  45. Ramu, P., Kim, N.H. and Haftka, R.T. (2007), "Error amplification in failure probability estimates due to small errors in response surface", SAE paper 2007-01-0549.
  46. Sejnoha, J., Sejnoha, M., Zeman, J., Sykora, J. and Vorel, J. (2008), "Mesoscopic study on historic masonry", Struct. Eng. Mech., 30(1), 99-117. https://doi.org/10.12989/sem.2008.30.1.099
  47. Shahabuddin, P. (1994), "Importance sampling for the simulation of highly reliable Markovian systems", Manage. Sci., 40(3), 333-352. https://doi.org/10.1287/mnsc.40.3.333
  48. Simpson, T.W., Peplinski, J.D., Koch, P.N. and Allen, J.K. (2001), "Metamodels for Computer-based Engineering Design: Survey and recommendations", Eng. Comput., 17, 129-150. https://doi.org/10.1007/PL00007198
  49. Simpson, T.W., Lin, D.K.J. and Chen, W. (2002), "Sampling strategies for computer experiments: design and analysis", Int. J. Rel. Appl., 2(3), 209-240.
  50. Sloan, S.W. and Kleeman, P.W. (1995), "Upper bound limit analysis using discontinuous velocity fields", Comput. Meth. Appl. Mech. Eng., 127(1-4), 293-314. https://doi.org/10.1016/0045-7825(95)00868-1
  51. Storlie, C.B. and Helton, J.C. (2008a), "Multiple predictor smoothing methods for sensitivity analysis: description of techniques", Reliab. Eng. Syst. Safe., 93(1), 28-54. https://doi.org/10.1016/j.ress.2006.10.012
  52. Storlie, C.B. and Helton, J.C. (2008b), "Multiple predictor smoothing methods for sensitivity analysis: example results", Reliab. Eng. Syst. Safe., 93(1), 55-77. https://doi.org/10.1016/j.ress.2006.10.013
  53. Storlie, C.B., Swiler, L.P., Helton, J.C. and Sallaberry, C.J. (2009), "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models", Reliab. Eng. Syst. Safe., 94(11), 1735-1763. https://doi.org/10.1016/j.ress.2009.05.007
  54. Suquet, P. (1983), "Analyse limite et homogeneisation", CR Acad. Sci., 296, 1355-1358 (in French).
  55. Sutcliffe, D.J., Yu, H.S. and Page, A.W. (2001), "Lower bound limit analysis of unreinforced masonry shear walls", Comput. Struct., 79, 1295-1312. https://doi.org/10.1016/S0045-7949(01)00024-4
  56. Swiler, L.P., Slepoy, R. and Giunta, A.A. (2006), "Evaluation of sampling methods in constructing response surface approximations", Proceedings of 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Newport, Rhode Island.
  57. van der Pluijm, R. (1999), Out-of-plane Bending of Masonry. Behaviour and Strength, PhD Thesis, Eindhoven University of Technology.
  58. Vermeltfoort, A. (2006), Brick-mortar Interaction in Masonry Under Compression, PhD Thesis, Eindhoven University of Technology.
  59. Winkler, R.L. (1996), "Uncertainty in probabilistic risk assessment", Reliab. Eng. Syst. Safe., 54(2-3), 127-132. https://doi.org/10.1016/S0951-8320(96)00070-1
  60. Yu, X. and Tin-Loi, F. (2006), "A simple mixed finite element for static limit analysis", Comput. Struct., 84, 1906-1917. https://doi.org/10.1016/j.compstruc.2006.08.019

피인용 문헌

  1. Lesson learned after the Emilia-Romagna, Italy, 20–29 May 2012 earthquakes: A limit analysis insight on three masonry churches vol.34, 2013, https://doi.org/10.1016/j.engfailanal.2013.01.001
  2. Capabilities of stochastic response surface method and response surface method in reliability analysis vol.49, pp.1, 2014, https://doi.org/10.12989/sem.2014.49.1.111
  3. Consideration of modelling uncertainties in the seismic assessment of masonry buildings by equivalent-frame approach vol.13, pp.11, 2015, https://doi.org/10.1007/s10518-015-9760-z
  4. Analyzing the effect of workmanship quality on performance of unreinforced masonry walls through numerical methods vol.167, 2016, https://doi.org/10.1016/j.compstruc.2016.01.013
  5. A unified level set based methodology for fast generation of complex microstructural multi-phase RVEs vol.223-224, 2012, https://doi.org/10.1016/j.cma.2012.02.018
  6. Safety Assessment of Four Masonry Churches by a Plate and Shell FE Nonlinear Approach vol.27, pp.1, 2013, https://doi.org/10.1061/(ASCE)CF.1943-5509.0000321
  7. Characterization of the response of quasi-periodic masonry: Geometrical investigation, homogenization and application to the Guimarães castle, Portugal vol.56, 2013, https://doi.org/10.1016/j.engstruct.2013.05.040
  8. Homogenized and Heterogeneous Limit Analysis Model for Pushover Analysis of Ancient Masonry Walls with Irregular Texture vol.7, pp.3, 2013, https://doi.org/10.1080/15583058.2011.640737
  9. Automatic fragility curve evaluation of masonry churches accounting for partial collapses by means of 3D FE homogenized limit analysis vol.89, pp.17-18, 2011, https://doi.org/10.1016/j.compstruc.2011.04.014
  10. Global sensitivity analysis of unreinforced masonry structure using high dimensional model representation vol.33, pp.4, 2011, https://doi.org/10.1016/j.engstruct.2011.01.008
  11. Gene expression programming approach to cost estimation formulation for utility projects vol.23, pp.1, 2017, https://doi.org/10.3846/13923730.2016.1210214
  12. Novel Approach to Strength Modeling of Concrete under Triaxial Compression vol.24, pp.9, 2012, https://doi.org/10.1061/(ASCE)MT.1943-5533.0000494
  13. Parametric sensitivity study on regional seismic damage prediction of reinforced masonry buildings based on time-history analysis vol.15, pp.11, 2017, https://doi.org/10.1007/s10518-017-0168-9
  14. Seismic Vulnerability Reduction of Masonry Churches: A case study vol.199, 2017, https://doi.org/10.1016/j.proeng.2017.09.026
  15. A homogenization approach for uncertainty quantification of deflection in reinforced concrete beams considering microstructural variability vol.38, pp.4, 2010, https://doi.org/10.12989/sem.2011.38.4.503
  16. In-plane response of masonry infilled RC framed structures: A probabilistic macromodeling approach vol.68, pp.4, 2010, https://doi.org/10.12989/sem.2018.68.4.423
  17. Ambient vibration test and numerical investigation on the St. Giuliano church in Poggio Picenze (L’aquila, Italy) vol.9, pp.4, 2010, https://doi.org/10.1007/s13349-019-00346-7
  18. Identification of critical mechanical parameters for advanced analysis of masonry arch bridges vol.16, pp.2, 2020, https://doi.org/10.1080/15732479.2019.1655071
  19. An iterative rectification procedure analysis for historical timber frames: Application to a cultural heritage Chinese Pavilion vol.227, pp.None, 2021, https://doi.org/10.1016/j.engstruct.2020.111415
  20. Probabilistic-based structural assessment of a historic stone arch bridge vol.17, pp.3, 2010, https://doi.org/10.1080/15732479.2020.1752261
  21. In-plane structural performance of dry-joint stone masonry Walls: A spatial and non-spatial stochastic discontinuum analysis vol.242, pp.None, 2021, https://doi.org/10.1016/j.engstruct.2021.112620