Simulação computacional da RAA em estruturas de concreto

Transcription

1 imulação computacional da RAA em estruturas de concreto Eduardo M. R. Fairbairn, Marcos M. ilvoso, Romildo D. Toledo Filho, Fernando L. B. Ribeiro, COPPE/UFRJ Márcia F. F. Aguas FURNA CENTRAI ELÉTRICA.A. FURNA 1

2 Physical principles of the model (Glasser and Kataoka mechanism) Reactive aggregate Inert aggregate Cement matrix Pore Pore + gel (eventual crack) 2

3 Courtney Collins. Jason Ideker. Gayle Willis. Jessica Hurst, Virginia Tech 3

4 Physical principles of the model Nicole P. Hasparyk, M.c. Thesis, UFG, Brasil,

5 Physical principles of the model 5

6 Problems in an hydropower plant 6

7 Problems in an hydropower plant 7

8 Problems in an hydropower plant Leger et al, Canadian Journal of Civil Engineering, vol 22, 1995,

9 Problems in an hydropower plant Leger et al, Canadian Journal of Civil Engineering, vol 22, 1995,

10 Problems in an hydropower plant Leger et al, Canadian Journal of Civil Engineering, vol 22, 1995,

11 Problems in an hydropower plant Leger et al, Canadian Journal of Civil Engineering, vol 22, 1995,

12 Problems in an hydropower plant Leger et al, Canadian Journal of Civil Engineering, vol 22, 1995,

13 Bases of the model (some experimental evidences) AAR occurs if the structure is in contact with water. The reaction is thermo-activated. The extension of the reaction is independent on stress levels ranging from 0 to 10 MPa. There is an anisotropy induced by the stress fields. 13

14 Cracking free expansion LCPC tests s=0 (Larive, C., Apports combinés de l alkali-réaction et de ses effets mécaniques, thèse de dotorat, E.N.P.C., Paris, France, 1997.} 14

15 Cracking free expansion - LCPC tests s=0 (Larive, C., Apports combinés de l alkali-réaction et de ses effets mécaniques, thèse de dotorat, E.N.P.C., Paris, France, 1997.) 15

16 Cracking free expansion 16

17 Cracking free expansion 17

18 Cracking free expansion 18

19 tress induced anisotropy - Cracking s = 5 MPa - LCPC tests s=5mpa (Larive, C., Apports combinés de l alkali-réaction et de ses effets mécaniques, thèse de dotorat, E.N.P.C., Paris, France, 1997.) 19

20 tress induced anisotropy - Cracking s = 10 MPa - LCPC tests s=10mpa (Larive, C., Apports combinés de l alkali-réaction et de ses effets mécaniques, thèse de dotorat, E.N.P.C., Paris, France, 1997.) 20

21 tress induced anisotropy 21

22 tress induced anisotropy 22

23 tress induced anisotropy 23

24 LCPC tests for stresses levels untill s = 10 MPa DV/V does not change. DV/V Larive Adeghe s(mpa) (Larive, C., Apports combinés de l alkali-réaction et de ses effets mécaniques, thèse de dotorat, E.N.P.C., Paris, France, 1997.) 24

25 Mechanical model (1D think model) Model at the micro structural level 25

26 Mechanical model (1D think model) Model at the micro structural level 26

27 Thermo-chemo-mechanical model (1D think model) The model is based on Ulm and Coussy (elastic and plastic) models 27

28 Thermo-chemo-mechanical model - cracking 28

29 Thermo-chemo-mechanical model - cracking (1D think model) s s D g s < f ct D s, g f e f / ct D f ct p g g f cr s f ct D s e f / D ct g 1 D g g p g s s 0 0 L L +2 c 500 t 29

30 Model (thermo-hygro-chemo-mechanical) for AAR The reaction depends on: umidity and temperature. 1 t 1 exp t c 1 exp t c L c c exp U c 0 c l exp U l 0 l L L +2 c 500 t g k k f (h) 30

31 Determination of parameters 31

32 Test for the determination of Young s modulus D g s < f ct, e g f D s =D c f / D ct g =0 p g =0 s s =s 32

33 Test for the determination of fracture parameters s cr D g > f ct, e g f D s =D c f / D ct g =0 p g =0 s s =s 33

34 Test for the determination of AAR parameters free expansion s D g = fe < f ct D s, g f e f / D ct g p g s s Uncracked specmen 34

35 Test for the determination of AAR parameters free expansion s = fe cr D g > f ct D s, g f e f / D ct g p g s s Cracked specmen 35

36 Test for the determination of AAR parameters free expansion Robots (RMDV1 e RMDV2) for measuring volumetric delayed strains 36

37 Test for the determination of AAR parameters free expansion Laboratory dedicated to delayed strain measurements 37

38 38 Generalization: Classical fixed orthogonal smeared crack model Decomposition of total deformation for the cracked material in a crack deformation and in a deformation of the uncracked material between the cracks: cr e ε ε ε ε tresses equilibrium: 1 σ σ g p Constitutive relations for the gel and for the skeleton: V g V g g K p, e ε D σ Overall stress-strain relation: cr ε D σ, cr cr D N N D N D N D D D T -1 T ˆ,

39 Implementation: FEM 3D code The model was implemented in a reference program developed in FORTRAN for non-linear analysis of three dimensional problems via Finite Element Method through four nodes tetrahedral elements. The resulting non-linear equations system is solved by means of a Newton-Raphson iterative-incremental technique. The initial stiffness matrix is used as an approximation for the discrete Jacobian. The solution of the linearized system employs the Pre-Conditioned Conjugated Gradients Method, which was implemented under an Element- By-Element technique avoiding global stiffness matrix assembling and factorization. 39

40 Validation: Larive s tests (LCPC France) 40

41 Validation: Larive s tests elements 9120 elements 2160 elements (FEM convergence test) 41

42 Def. volumétrica (%) Inverse analysis: amplitude k = 0.196% k = 0.180% k = 0.160% k = 0.150% Experimental Tempo (dias) 42

43 Def. volumétrica (%) Inverse analysis: kinetics tauc = 33.4 taul = 82.9 tauc = 40.0 taul = 60.0 tauc = 40.0 taul = 50.0 tauc = 40.0 taul = 40.0 tauc = 40.0 taul = 30.0 tauc = 50.0 taul = 30.0 Experimental Tempo (dias) 43

44 Volumetric Deformation (%) LCPC Larive s tests Numerical and experimental results Tc = 50.0 Tl = 30.0 k = 0.150% Experimental Time (days) 44

45 Longitudinal Def. longitudinal deformation(%) Transversal Deformação deformation(%) Transversal Numerical simulation of LCPC Larive s tests Displaying stress-induced anisotropy MPa 10 MPa MPa 5 MPa Time Tempo (days) (dias) Time Tempo (days) (dias) Longitudinal deformation Transversal deformation 45

46 imulation: hypothetical discharge ring 46

47 imulation: hypothetical discharge ring 47

48 imulation: hypothetical discharge ring 48

49 Application: Furnas MW hydroelectric power plant in Minas Gerais - Brazil 49

50 Application FURNA dam 50

51 51

52 Application FURNA dam (upstream view) 52

53 Application FURNA dam (downstream view) 53

54 Field measurements 54

55 55

56 FURNA dam Field measurements: displacements at the crest 56

57 FURNA dam Field measurements: displacements at the crest: statistical modeling 57

58 Displacement at the crest (m) FURNA dam Displacements at the crest (m) : creep simulation 16 years Time (years) 58

59 Furnas dam: FEM modeling thetrahedral elements 59

60 Furnas dam: thermal fields averaged steady state 60

61 Furnas dam: moisture fields averaged steady state 61

62 Displacement Deslocamento at the crest (mm) (mm) Furnas dam: displacements at the crest Time Tempo (years) (anos) Numerical: Emax = k=0.30%; Tc = tc=15.0; Tl tl=12.0 = 12.0 Measured Experimental 62

63 Displacement Deslocamento at the crest (mm) (mm) Furnas dam: displacements at the crest Time Tempo (years) (anos) Emax Numerical: = 0.30% k=0.30%; Tc = tc=15.0; Tl tl=12.0 = 12.0 Experimental Measured 63

64 Concluding remarks Model thermo-hygro-chemo-mechanical with stress-induced anisotropy: Can simulate the evolution of the chemical reaction and of its mechanical effects, considering temperature, moisture and cracking effects on the evolution of swelling. Numerical modeling (Finite Element Method): 3D operational FEM computer code allows for the execution of real analysis on complex geometries with a large number of degree of freedom. It is then possible to predict the evolution of the effects of the rezaction. Inverse analysis (experimental and numerical): Allows for the identification of parameters structural ol local levels. 64

65 Acknowledgements FURNA CENTRAI ELÉTRICA.A.

66 FIM