Coupled systems mechanics

  • 제12권5호
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  • Pages.429-444
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  • 2023
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  • 2234-2184(pISSN)
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  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Stochastic identification of masonry parameters in 2D finite elements continuum models

  • Giada Bartolini (Department of Energy, Systems, Territory and Construction Engineering, University of Pisa) ;
  • Anna De Falco (Department of Civil and Industrial Engineering, University of Pisa) ;
  • Filippo Landi (Department of Civil and Industrial Engineering, University of Pisa)
  • 투고 : 2023.04.01
  • 심사 : 2023.07.29
  • 발행 : 2023.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

The comprehension and structural modeling of masonry constructions is fundamental to safeguard the integrity of built cultural assets and intervene through adequate actions, especially in earthquake-prone regions. Despite the availability of several modeling strategies and modern computing power, modeling masonry remains a great challenge because of still demanding computational efforts, constraints in performing destructive or semi-destructive in-situ tests, and material uncertainties. This paper investigates the shear behavior of masonry walls by applying a plane-stress FE continuum model with the Modified Masonry-like Material (MMLM). Epistemic uncertainty affecting input parameters of the MMLM is considered in a probabilistic framework. After appointing a suitable probability density function to input quantities according to prior engineering knowledge, uncertainties are propagated to outputs relying on gPCE-based surrogate models to considerably speed up the forward problem-solving. The sensitivity of the response to input parameters is evaluated through the computation of Sobol' indices pointing out the parameters more worthy to be further investigated, when dealing with the seismic assessment of masonry buildings. Finally, masonry mechanical properties are calibrated in a probabilistic setting with the Bayesian approach to the inverse problem based on the available measurements obtained from the experimental load-displacement curves provided by shear compression in-situ tests.

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참고문헌

  1. Angelillo, M., Lourenco, P.B. and Milani, G. (2014), "Masonry behaviour and modelling", Mech. Masonry Struct., 1-26. https://doi.org/10.1007/978-3-7091-1774-3_1.
  2. Asteris, P.G. and Plevris, V. (2015), Handbook of Research on Seismic Assessment and Rehabilitation of Historic Structures, IGI Global.
  3. Beconcini, M.L., Croce, P., Formichi, P., Landi, F. and Puccini, B. (2021), "Experimental evaluation of shear behavior of stone masonry wall", Mater., 14(9), 2313. https://doi.org/10.3390/ma14092313.
  4. Berto, L., Saetta, A., Scotta, R. and Vitaliani, R. (2002), "An orthotropic damage model for masonry structures", Int. . Numer. Meth. Eng., 55(2), 127-157. https://doi.org/10.1002/nme.495.
  5. Bosiljkov, V.Z., Totoev, Y.Z. and Nichols, J.M. (2005), "Shear modulus and stiffness of brickwork masonry: An experimental perspective", Struct. Eng. Mech., 20(1), 21-43. https://doi.org/10.12989/sem.2005.20.1.021.
  6. Bracchi, S., Rota, M., Magenes, G. and Penna, A. (2016), "Seismic assessment of masonry buildings accounting for limited knowledge on materials by Bayesian updating", Bull. Earthq. Eng., 14(8), 2273-2297. https://doi.org/10.1007/s10518-016-9905-8.
  7. Clemente, R. (2006), "Structural analysis of historical buildings by localized cracking models", PhD Thesis, Universitat Politecnica de Catalunya, Barcelona, Spain.
  8. Clemente, R., Roca, P. and Cervera, M. (2006), "Damage model with crack localization-application to historical buildings", Structural Analysis of Historical Constructions, New Delhi, India.
  9. Como, M. and Grimaldi, A. (1985), "A unilateral model for the limit analysis of masonry walls", Unilateral Problems in Structural Analysis: Proceedings of the Second Meeting on Unilateral Problems in Structural Analysis, Ravello, September.
  10. Croce, P., Beconcini, M.L., Formichi, P., Landi, F., Puccini, B. and Zotti, V. (2021a), "Evaluation of partial safety factors for the structural assessment of existings masonry buildings", 18th International Probabilistic Workshop, 153, 341-352. https://doi.org/10.1007/978-3-030-73616-3_25.
  11. Croce, P., Beconcini, M.L., Formichi, P., Landi, F., Puccini, B. and Zotti, V. (2021b), "Bayesian methodology for probabilistic description of mechanical parameters of masonry walls", ASCE-ASME J. Risk Uncertain. Eng. Syst., Part A: Civil Eng., 7(2), 04021008. https://doi.org/10.1061/AJRUA6.0001110.
  12. Del Piero, G. (1989), "Constitutive equation and compatibility of the external loads for linear elastic masonry-like materials", Meccanica, 24(3), 150-162. https://doi.org/10.1007/BF01559418.
  13. Di Pasquale, S. (1982), "Questioni di meccanica dei solidi non reagenti a trazione", Atti VI Convegno Nazioale AIMETA, Genova, 7-9.
  14. Di Pasquale, S. (1984), "Statica dei solidi murari: Teoria ed esperienze", Dipartimento di Costruzioni, Universita di Firenze.
  15. Dragon, A. and Mroz, Z. (1979), "A continuum model for plastic-brittle behaviour of rock and concrete", Int. J. Eng. Sci., 17(2), 121-137. https://doi.org/10.1016/0020-7225(79)90058-2.
  16. Formisano, A., Sorrentino, L. and Zucconi, M. (2023), "Editorial of the special issue "Seismic vulnerability and strengthening of unreinforced masonry buildings"", Geosci., 13(3), 62. https://doi.org/10.3390/geosciences13030062.
  17. Ghanem, R. and Red-Horse, J. (2017), Polynomial Chaos: Modeling, Estimation, and Approximation, Eds. R. Ghanem, D. Higdon, and H. Owhadi, Handbook of Uncertainty Quantification, Springer International Publishing.
  18. 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", Cement Concrete Res., 6(6), 773-781. https://doi.org/10.1016/0008-8846(76)90007-7.
  19. Italian Ministry of Infrastructures and Transportation (2018), NTC 2018-Italian Building Code.
  20. Italian Public Works Council (2019), "Memorandum for application of italian building code, N. 7", Italian Official Journal, Istituto Poligrafico e Zecca dello Stato, Rome, Italy. (in Italian)
  21. Kachanov, L.M. (2004), Fundamentals of the Theory of Plasticity, Courier Corporation.
  22. Krentowski, J.R., Knyziak, P., Pawlowicz, J.A. and Gavardashvili, G. (2023), "Historical masonry buildings' condition assessment by non-destructive and destructive testing", Eng. Fail. Anal., 146, 107122. https://doi.org/10.1016/j.engfailanal.2023.107122.
  23. Landi, F., Marsili, F., Friedman, N. and Croce, P. (2021), "gPCE-Based stochastic inverse methods: A benchmark study from a civil engineer's perspective", Infrastruct., 6(11), 158. https://doi.org/10.3390/infrastructures6110158.
  24. Lee, J. and Fenves, G.L. (1998), "Plastic-damage model for cyclic loading of concrete structures", J. Eng. Mech., 124(8), 892-900. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:8(892).
  25. Loland, K.E. (1980), "Continuous damage model for load-response estimation of concrete", Cement Concrete Res., 10(3), 395-402. https://doi.org/10.1016/0008-8846(80)90115-5.
  26. Lourenco, P.B., Rots, J.G. and Blaauwendraad, J. (1998), "Continuum model for masonry: Parameter estimation and validation", J. Struct. Eng., 124(6), 642-652. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:6(642).
  27. Lubliner, J., Oliver, J., Oller, S. and Onate, E. (1989), "A plastic-damage model for concrete", Int. J. Solid. Struct., 25(3), 299-326. https://doi.org/10.1016/0020-7683(89)90050-4.
  28. Lucchesi, M., Padovani, C., Pasquinelli, G. and Zani, N. (2008), Masonry Constructions: Mechanical Models and Numerical Applications, Springer Science & Business Media.
  29. Lucchesi, M., Pintucchi, B. and Zani, N. (2017), "Modelling masonry structures through the MADY code", Proceedings of the 2nd International Conference on Recent Advances in Nonlinear Models-Design and Rehabilitation of Structures, 10.
  30. Lucchesi, M., Pintucchi, B. and Zani, N. (2018a), "Bounded shear stress in masonry-like bodies", Meccanica, 53(7), 1777-1791. https://doi.org/10.1007/s11012-017-0719-9.
  31. Lucchesi, M., Pintucchi, B. and Zani, N. (2018b), "Masonry-like material with bounded shear stress", Eur. J. Mech.-A/Solid., 72, 329-340. https://doi.org/10.1016/j.euromechsol.2018.05.001.
  32. Marzouk, Y.M., Najm, H.N. and Rahn, L.A. (2007), "Stochastic spectral methods for efficient Bayesian solution of inverse problems", J. Comput. Phys., 224(2), 560-586. https://doi.org/10.1016/j.jcp.2006.10.010.
  33. Matthies, H.G., Zander, E., Rosic, B.V. and Litvinenko, A. (2016), "Parameter estimation via conditional expectation: A Bayesian inversion", Adv. Model. Simul. Eng. Sci., 3(1), 24. https://doi.org/10.1186/s40323-016-0075-7.
  34. Matthies, H.G., Zander, E., Rosic, B.V., Litvinenko, A. and Pajonk, O. (2016), "Inverse problems in a Bayesian setting", Ed. A. Ibrahimbegovic, Computational Methods for Solids and Fluids, 41, 245-286. https://doi.org/10.1007/978-3-319-27996-1_10.
  35. Mazars, J. (1984), "Application de la mecanique de l'endommagement au comportement non lineaire et a rupture du beton de structure", PhD Thesis, Universite Pierre et Marie Curie-CNRS.
  36. Papa, E. (1996), "A unilateral damage model for masonry based on a homogenisation procedure", Mech. Cohes.-Frict. Mater., 1(4), 349-366. https://doi.org/10.1002/(SICI)1099-1484(199610)1:4<349::AID-CFM18>3.0.CO,2-M.
  37. Roca, P., Cervera, M., Gariup, G. and Pela', L. (2010), "Structural analysis of masonry historical constructions. Classical and advanced approaches", Arch. Comput. Meth. Eng., 17(3), 299-325. https://doi.org/10.1007/s11831-010-9046-1.
  38. Romano, G. and Romano, M. (1985), "Elastostatics of structures with unilateral conditions on stress and displacement fields", Unilateral Problems in Structural Analysis: Proceedings of the Second Meeting on Unilateral Problems in Structural Analysis, Ravello, September.
  39. Rosic, B.V., Kucerova, A., Sykora, J., Pajonk, O., Litvinenko, A. and Matthies, H.G. (2013), "Parameter identification in a probabilistic setting", Eng. Struct., 50, 179-196. https://doi.org/10.1016/j.engstruct.2012.12.029.
  40. Saloustros, S., Pela, L. and Cervera, M. (2015), "A crack-tracking technique for localized cohesive-frictional damage", Eng. Fract. Mech., 150, 96-114. https://doi.org/10.1016/j.engfracmech.2015.10.039.
  41. Saloustros, S., Pela, L., Cervera, M. and Roca, P. (2018), "An enhanced finite element macro-model for the realistic simulation of localized cracks in masonry structures: A large-scale application", Int. J. Arch. Heritage, 12(3), 432-447. https://doi.org/10.1080/15583058.2017.1323245.
  42. Saltelli, A. (2008), Global Sensitivity Analysis: The Primer, John Wiley.
  43. Saltelli, A. and Sobol', I.M. (1995), "About the use of rank transformation in sensitivity analysis of model output", Reliab. Eng. Syst. Saf., 50(3), 225-239. https://doi.org/10.1016/0951-8320(95)00099-2.
  44. Sanchez, A., Varum, H., Martins, T. and Fernandez, J. (2022), "Mechanical properties of adobe masonry for the rehabilitation of buildings", Constr. Build. Mater., 333, 127330. https://doi.org/10.1016/j.conbuildmat.2022.127330.
  45. Sarhosis, V., Garrity, S.W. and Sheng, Y. (2015), "Influence of brick-mortar interface on the mechanical behaviour of low bond strength masonry brickwork lintels", Eng. Struct., 88, 1-11. https://doi.org/10.1016/j.engstruct.2014.12.014.
  46. Sobol, I.M. (2001), "Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates", Math. Comput. Simul., 55(1-3), 271-280. https://doi.org/10.1016/s0378-4754(00)00270-6.
  47. Sudret, B. (2008), "Global sensitivity analysis using polynomial chaos expansions", Reliab. Eng. Syst. Saf., 93(7), 964-979. https://doi.org/10.1016/j.ress.2007.04.002.
  48. Sudret, B. (2015), Polynomial Chaos Expansions and Stochastic Finite-Element Methods, In Risk and Reliability in Geotechnical Engineering, CRC Press.
  49. Sudret, B. and Mai, C.V. (2015), "Computing derivative-based global sensitivity measures using polynomial chaos expansions", Reliab. Eng. Syst. Saf., 134, 241-250. https://doi.org/10.1016/j.ress.2014.07.009.
  50. Sykora, M. and Holicky, M. (2010), "Probabilistic model for masonry strength of existing structures", Eng. Mech., 17(1), 61-70.
  51. Sykora, M., Cejka, T., Holicky, M. and Witzany, J. (2013), "Probabilistic model for compressive strength of historic masonry", Safety, Reliability and Risk Analysis, CRC Press.
  52. Tarantola, A. (2005), Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM.
  53. Tierney, L. (1994), "Markov chains for exploring posterior distributions", Ann. Stat., 22(4), 1701-1728. https://doi.org/10.1214/aos/1176325750.
  54. Tomazevic, M. (2009), "Shear resistance of masonry walls and Eurocode 6: Shear versus tensile strength of masonry", Mater. Struct., 42(7), 889-907. https://doi.org/10.1617/s11527-008-9430-6.
  55. Turnsek, V. and Cacovic, F. (1971), "Some experimental results on the strength of brick masonry walls", Proceedings of the 2nd International Brick Masonry Conference, British Ceramic Research Association, Stoke-on-Trent, UK.
  56. Wei, D.L., Cui, Z.S. and Chen, J. (2008), "Uncertainty quantification using polynomial chaos expansion with points of monomial cubature rules", Comput. Struct., 86(23-24), 2102-2108. https://doi.org/10.1016/j.compstruc.2008.07.001.
  57. Wiener, N. (1938), "The homogeneous chaos", Am. J. Math., 60(4), 897. https://doi.org/10.2307/2371268.
  58. Xiu, D. (2010), Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press.
  59. Xiu, D. and Karniadakis, G.E. (2002), "The Wiener-Askey polynomial chaos for stochastic differential equations", SIAM J. Scientif. Comput., 24(2), 619-644. https://doi.org/10.1137/s1064827501387826.