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The numerical FE investigations of a deterministic and stochastic size effect in unnotched concrete beams of similar geometry under three point bending were performed within elasto-plasticity with non-local softening. Deterministic calculations were performed with the uniform distribution of a tensile strength. In turn, in stochastic calculations, the tensile strength took the form of spatially correlated random fields described by a truncated Gaussian distribution. In order to reduce the number of stochastic realizations without losing the calculation correctness, Latin hypercube sampling was applied. The numerical outcomes were compared with the size effect laws by Bazant.
Przeprowadzono analizę numeryczną MES deterministycznego i statystycznego efektu skali w belkach betonowych geometrycznie podobnych poddanych 3-punktowemu zginaniu. Zastosowano sprężysto-plastyczny model betonu z nielokalnym osłabieniem. Obliczenia deterministyczne wykonano z jednorodnym rozkładem wytrzymałości na rozciąganie. Symulacje stochastyczne przeprowadzono z wykorzystaniem przestrzennie skorelowanych pól losowych opisanych obciętym rozkładem Gaussa. W celu zredukowania liczby symulacji stochastycznych, przy zachowaniu poprawności obliczeniowej, zastosowano metodę próbkowania typu sześcianu łacińskiego. Wyniki numeryczne zostały porównane z prawem efektu skali wg Bazanta.
Czasopismo
Rocznik
Tom
Strony
67--78
Opis fizyczny
Bibliogr. 36 poz.
Twórcy
autor
autor
- Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Poland, esyroka@pg.gda.pl
Bibliografia
- [1] Bazant Z.P.; Size effect in blunt fracture: concrete, rock, metal. J. Engng. Mech. ASCE Vol.110, 1984; p.518-535
- [2] Carpinteri A.; Decrease of apparent tensile and bending strength with specimen size: two different explanations based on fracture mechanics. Int. J. Solids and Structures Vol.25, No.4, 1989; p.407-429
- [3] Bazant ZP, Planas J.; Fracture and size effect in concrete and other quasi-brittle materials. CRC Press LLC, 1998; p.1-640
- [4] Bazant Z.P.; Probability distribution of energetic-statistical size effect in quasi-brittle fracture. Probabilistic Engineering Mechanics Vol.19, 2004; p.307-319
- [5] Weibull W.; A statistical theory of the strength of materials. Journal of Applied Mechanics Vol.18, No.9, 1951; p.293-297
- [6] Bazant ZP, Pang SD, Vorechovsky M, Novak D.; Energetic-statistical size effect simulated by SFEM with stratified sampling and crack band model. Int. J. for Numerical Methods. in Engineering Vol.71, No.11, 2007; p.1297-1320
- [7] Carpinteri A, Chiaia B, Ferro G.; Multifractal scaling law: an extensive application to nominal strength size effect of concrete structures. In: Mihashi M, Okamura H, Bazant ZP, editors. Size effect of concrete. London: E&FN Spon; 1994; p.193-206
- [8] Wittmann FH, Mihashi H, Nomura N.; Size effect on fracture energy using three-point bend tests. Materials and Structures Vol.25, 1992; p.327-334
- [9] Walraven J, Lehwalter N.; Size effects in short beams loaded in shear. ACI Structural Journal Vol.91, No.5, 1994; p.585-593
- [10] Koide H, Akita H, Tomon M.; Size effect on flexural resistance on different length of concrete beams. In: Mihashi H, Rokugo K, editors. Fracture Mechanics of concrete structures. Freiburg: Aedificatio, 1998; p.2121-2130
- [11] van Vliet MRA.; Size effect in tensile fracture of concrete and rock. PhD Thesis. Delft (NL): University of Delft, 2000
- [12] Chen J, Yuan H, Kalkhof D.; A nonlocal damage model for elastoplastic materials based on gradient plasticity theory. Report Nr.01-13, Villigen(CH): Paul Scherrer Institute, 2001
- [13] Le Bellego C, Dube JF, Pijaudier-Cabot G, Gerard B.; Calibration of nonlocal damage model from size effect tests. European Journal of Mechanics A/Solids Vol.22, 2003; p.33-46
- [14] van Mier J, van Vliet M.; Influence of microstructure of concrete on size/scale effects in tensile fracture. Engineering Fracture Mechanics Vol.70, 2003; p.2281-2306
- [15] Bazant ZP, Yavari A.; Response to A. Carpinteri, B. Chiaia, P. Cornetti and S. Puzzi’s comments on „Is the cause of size effect on structural strength fractal or energetic-statistical”. Engineering Fracture Mechanics Vol.74, 2007; p.2897-2910
- [16] Vorechovsky M.; Interplay of size effects in concrete specimens under tension studied via computational stochastic fracture mechanics. Int. J. Solids and Structures, Vol. 44; 2007; p.2715-2731
- [17] Yu Q.; Size effect and design safety in concrete structures under shear. PhD Thesis. Illinois (US): Northwestern University, 2007
- [18] Walukiewicz H, Bielewicz E, Górski J.; Simulation of nonhomogeneous random fields for structural applications. Computers and Structures Vol.64, No.1-4, 1997; p.491-498
- [19] Bazant Z.P, Lin K.L.; Random creep and shrinkage in structures sampling. J. Structural Engineering ASCE Vol.115, No.5, 1985; p.1113-1134.
- [20] Florian A.; An efficient sampling scheme: Updated latin hypercube sampling. Probabilistic Engineering Mechanics Vol.2, 1992; p.123-130
- [21] Bazant ZP, Novak D.; Energetic-Statistical size effect in quasi-brittle failure at crack initiation. ACI Materials Journal Vol.97, No.3, 2000; p.381-392
- [22] Hordijk D.A.; Local approach to fatigue of concrete, PhD dissertation. Delft (NL): Delft University of Technology, 1991
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- [25] Brinkgreve R.B.J.; Geomaterial models and numerical analysis of softening. PhD Thesis. Delft (NL): Delft University of Technology, 1994
- [26] Syroka-Korol E.; Theoretical and experimental study on size effect in concrete beams reinforced with steel and basalt bars. PhD Thesis. Gdansk (PL): Gdansk University of Technology, 2012
- [27] Marzec I, Bobinski J, Tejchman J.; Simulations of crack spacing in reinforced concrete beams using elasticplasticity and damage with non-local softening. Computers and Concrete Vol.4, No.5, 2007; p.377-403
- [28] Majewski T, Bobinski J, Tejchman J.; FE-analysis of failure behaviour of reinforced concrete columns under eccentric compression. Engineering Structures Vol.30, No.2, 2008; p.300-317
- [29] Hibbit, Karlsson, Sorensen.; Abaqus, user’s manual, Version 5.8, Pawtucket (RI), 1998
- [30] Bobinski J, Tejchman J.; Numerical simulations of localization of deformation in quasi-brittle materials within non-local softening plasticity. Computers and Concrete Vol.4, 2004; p.433-455
- [31] Skarzynski L, Syroka E, Tejchman J.; Measurements and calculations of the width of the fracture process zones on the surface of notched concrete beams. Strain Vol.7, 2011; p.319-322
- [32] Tejchman J, Górski J.; Modeling of bearing capacity of footings on sand within stochastic micro-polar hypoplasticity. Int. Journal of Numerical and Analytical Methods in Geomechanics Vol.35, no.2, 2011; p.226-243
- [33] Bielewicz E, Górski J.; Shell with random geometric imperfections - simulation-based approach. International Journal of Non-linear Mechanics Vol.37, No.4-5, 2002; p.777-784
- [34] Vanmarcke E.H.; Random Fields: Analysis and Synthesis. Cambridge: MIT Press, 1983
- [35] Tejchman J, Górski J.; Computations of size effects in granular bodies within micro-polar hypoplasticity during plane strain compression. Int. J. for Solids and Structures Vol.45, No.6, 2007; p.1546-1569
- [36] Bazant ZP, Novak D.; Proposal for standard test of modulus of rupture of concrete with its size dependence. ACI Materials Journal Vol.98, No.1, 2001; p.79-87
Typ dokumentu
Bibliografia
Identyfikator YADDA
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