Aging, Cracking and Shaking of Concrete Dams

Transcription

1 Aging, Cracking and Shaking of Concrete Dams Victor Saouma University of Colorado, Boulder Acknowledgements: Tokyo Electric Power Service Company (TEPSCO)

2 Dams are BIG! 9,000 m, m 2,335 m, 185 m 2

3 Major Issues Cracking: Massive un-reinforced concrete. Aging: Alkali-Aggregate Reactions Shaking: Earthquakes 3

4 Some Relevant Publications 1. Puntel, E., Bolzon, G. Saouma, V., A Fracture mechanics Based Model for Joints Under Cyclic Loading, November 2006, ASCE J. of Engineering Mechanics, Vol. 132, No. 11, pp Puntel, E., Saouma, V., Experimental Behavior of Concrete Joints Under Cyclic Loading, in print, ASCE J. of Structural Engineering, Saouma, V., Perotti, L., Shimpo, T. Stress Analysis of Concrete Structures Subjected to Alkali Aggregate Reactions, American Concrete Institute Structural Journal, Vol. 104, No. 5, pp , September-October, Saouma, V. Perotti, L., Constitutive Model for Alkali Aggregate Reactions, American Concrete Institute, Materials Journal, Vol. 103, No. 3, pp , May- June, Uchita, Y., Shimpo, T., Saouma, V., Dynamic Centrifuge Tests of Concrete Dams, Earthquake Engineering and Structural Dynamics, Vol. 34, pp , Oct Uchita, Y., Noguchi, Y. and Saouma, V. Seismic Dam Safety Research International Water Power \& Dam Construction, pp , Dec Saouma, V., Miura, F., Lebon, G., Yagome, Y., A Simplified 3D Model for Rock- Structure Interaction with Radiation Damping and Free Field, Submitted for Publication. 6. Lebon, G., Saouma, V., Uchita, Y., 3D rock-dam seismic interaction, Dam Engineering, Sept

5 Cracking Aging Shaking 5

6 Joints & Cracks 6

7 Testing Joints; Monotonic Dry Static; Different Sizes Mixed-Mode Dry and Wet Dynamic 7

8 Testing Joint Cyclic 8

9 Interface Crack Model (ICM) At the heart of our numerical model, is an interface/joint element. Hyperbolic Failure Envelope τ 1 1 tan( φ f ) tan( φ f ) c Initial Failure Function Failure Function Final Failure Function ( 1 2) Cohesion and Tensile Strength F Displacement decomposition: Softening parameter: u = τ + τ 2ctan( φ )( σ σ) tan( φ ) ( σ σ ) = f t f t ieff ieff ( ) σt σt ( ) c= cu = u e i i p f u= u + u u = u + u ( u u u ) = u = + + ieff i i i i x y z Irreversible 1 2 Fracturing σ 9

10 Cyclic Model The asymptotes of the hyperbola rotate of angle α. Analytical expression of an asperity representative of the joint roughness ϕ 2 µ p ( c p µ ) + ( c χ µ ) p 0 β t β n β β β β t µ β+ α = 2 µ β pt cβ pn µ β + cβ χ β µ β pt < µ β α ( ) ( ) 0 Asperity degradation depends on confinement p n and shear work L i t w i n ( i p L ) y( w ) = f, n t i t L = p w i i t t t 10

11 Validation 1: Interface COD (mm) COD Distribution (t=3.260sec) Case3: Linear Case2: Constant COD (mm) COD Distribution (t=4.005sec) Case3: Linear Case2: Constant COD (mm) COD Distribution (t=4.190sec) Case3: Linear Case2: Constant COD (mm) COD Distribution (t=4.230sec) Case3: Linear Case2: Constant Ligament Length (m) Ligament Length (m) Ligament Length (m) Ligament Length (m) Normal Stress Distribution (t=3.260sec) 2 Normal Stress Distribution (t=4.190sec) 2 Normal Stress (MPa) Case3: Linear -8 Case2: Constant Ligament Length (m) Normal Stress (MPa) Case3: Linear -8 Case2: Constant Ligament Length (m) Note: 1. No crack overlap; 2. Crack advances; 3. Cohesive tensile stresses 11

12 Application 1 Diagonal and horizontal cracks t 6 = m t 5 = m t 4 = m t 3 = m t 2 = m t 1 = m Base Concrete 6.06 m 12

13 Laboratory Tests to model reinforced joints 13

14 3D Nonlinear Numerical Simulation 14

15 Crack Modeling 10 buttress-buttress cracks x z y 14 beams 28 beamsbuttress cracks Interface cracks z x y 15

16 16

17 Application 2 17

18 Cracking Aging Shaking 18

19 AAR Over 10 cm US movement since 1940 Over 7.5-cm VERTICAL expansion since 1940 Unit misalignment problems in Powerhouse Alkali-Aggregate Reaction causes an expansion of concrete which may lead to structural cracks Slice the dam to relieve stresses due to expansion Courtesy R. Charlwood 19

20 Reaction is Sensitive to RH What we know Thermodynamically driven (Temperature). Laboratory tests at LCPC have shown that Expansion follows a typical sigmoidal curve Expansion is inhibited in presence of confinement (~8 MPa). There is a redistribution of expansion. Cracks reduce expansion Degradation of tensile strength and Young s modulus 20

21 AAR ( ) ( ' ) ( ' ε ) ( ) ( ) vol t Γt ft w c, σi CODmax Γ c σ, fc f h ξ t, θ ε = t, = 1 e 1 1 τ c( θ) = τc( θ0)exp U C ; θ θ0 ' ' 1 1 τ L( θ, Iσ, fc ) = f( Iσ, fc ) τl( θ0)exp U L ; θ θ0 ε,, τ τ c C t L, I, f 1 C L e t ' c Model 1 if Iσ 0 ' f( Iσ, fc ) = I ; I σ σ = σ + σ + σ 1 + α if I ' σ > I II III 0 3fc U U C L ξ ( t) These parameters must be determined (possibly through an inverse analysis or laboratory Tests) τ L 2 τ c Time [day] θ θ = 5, 400 ± 500 K Activation energy for the char. time = 9, 400 ± 500 K Activation energy for the lat. time f ( h ) m H = 1 in general for dams 0 21

22 TENSION ε AAR vol AAR gel absorption ' ' ( tγ ) = Γ,f ( f fw h, COD ) ( ) ( ) ξ( t, ) t t c σ I max c σ c θ ε θ= θ 0 Tension causes cracks which absorb the gel and inhibit expansion Γ t ' 1 if σi γt ft Linear elastic fictitious γ t ft ' Γr + ( 1 Γr) if γt ft < σi σ I = 1 if CODmax γ twc Smeared crack γ twc Γr + ( 1 Γ) if γ r t w c < COD max COD max ' f t t 1 Linear Analysis t 1 G F Non-Linear Analysis w c r r γ f = f fictitious ' t t t σ I t w c COD max 22

23 COMPRESSION ε AAR vol ' ' ( tγ ) = Γ,f ( f fw h, COD ) ( ) ( ) ξ( t, ) t t c σ I max c σ c θ ε θ= θ 0 Reactive aggregate Crack There is a reduction in expansion under biaxial or triaxial state of stress Gamma 2 versus Hydrostatic stress 1 1 if σ 0 Tension β Γc = e σ 1 if σ 0 Compression β > 1+ ( e 1) σ I II III σ σ + σ + = σ Principal Stresses ' 3 f c Gamma β=-2 β= β=0 0.4 β=1 β= *f 3*f c t Hydrostatic stress [MPa] 23

24 Redistribution of volumetric strain AAR i ε ( t) = W ε ( t) i AAR Vol Assumptions Uniaxial/Biaxial load: the AAR-expansion in direction i is reduced (or eliminated if σ < σ u ) in presence of compression. Triaxial load: the AAR-expansion is reduced in the direction of the highest compression; Note: we can have expansion if f c < σ < σ u ) The AAR volumetric expansion is redistributed into the three principal directions on the basis of the multiaxial state of (principal) stresses. Reduction of AAR volumetric strain accounted for by Γ c 24

25 k Weights l m Must consider different scenarios; based on f t, σ u and f c 1 σ 0 σ < σ < 0 σk σu 2 σ k 0 σu < σk < 0 σk σu k u k σ l = σ u W k = 1/3 W l =1/3 W m =1/3 0 < W k < 1/3. W l = (1-W k )/2 W m = (1-W k )/2 W k = 0 W l = 1/2 W m = 1/2 W k =1/2 W l = 0 W m = 1/2 0 < W k < 1/2 W l = 0 W m = 1-W k W k = 0 W l = 0 W m = 1 3 σ 0 σ < σ < 0 σk = σu k u k f < σ < σ ' c k u σ k = f c W k = 1 W l = 0 W m = 0 1/3 < W k < 1 W l = (1-W k )/2 W m = (1-W k )/2 W k = 1/3 W l = 1/3 W m = 1/3 σ l = σ u σ m = σ u Wk= 0 W k < 1/3 W l = (1-W k )/2 W m = (1-W k )/2 W l = 1/2 W m = 1/2 25

26 Degradation of Young s modulus and tensile strength ( ) E = E 1 1 β ξ (, θ ) 0 E t β E residual fraction of Young`s modulus ( ) f = β ξ θ,0 1 1 (, ) t ft f t β f residual fraction of tensile strength ξ( t, θ ) = 1 e 1 + e t τ ( θ ) C ( t τl ( θ ) ) τ ( θ ) C E/E 0 ; f t /f t β = β = 70% E f τ lat τ lat +2τ car 0.6 Time Time [days] 26

27 Arch-gravity dam. 27

28 Data Preparation for Stress Analysis Increments Initialization Incr Displacement / Boundary condition Body force Full on the curve 11 Dam Hydrostatic Uplift Pool Elevation Pool Elevation Incremental Elevation Incremental Elevation \ \ Temperature Temperature None AAR AAR None Incremental Elevation Temperature [ o C] AAR Incr. Body force Pool Elevation January February March April May June dam Hydrostatic Uplift Air Water AAR Activated Incremental Elevation Temperature [ o C] AAR Incr. Body force Pool Elevation July August September October November December dam Hydrostatic Uplift Air Water AAR Activated 28

29 Matlab Based System Identification for Key parameters Program Merlin GUI 29

30 Principal stresses: maximum Cracks inside the dam The presence of high tensile stresses inside the dam can explain the origin of the cracks which appeared along the upper gallery. Other cracks can exist inside the dam and may not be yet identified. Crack along the upper gallery Crack inside core borehole in the upper gallery 30

31 Application 2 AAR Localized C b C a c T d T 6,900 3,700 1,500 1,700 c 15,750 2,000 11,750 2,000 1,500 1, d 2,000 8, ,500 1,700 3,000 3,550 c d 8,000 3,000 3,000 b a cable TENSION column D column A Loading a 脚 b 脚 c 脚 d 脚 Units Load T 1.52E E E E+06 N Area m 2 Traction 3.798E E E E+05 Pa 3.798E E E E-01 Mpa column C TENSION transmission cable column B column C,D COMPRESSION column A,B 31

32 Analyses 4.40E-03 Observation Upper side 4.67E-03 C 脚 4.40E E E E E E E E-05 D 脚 (MPa) 9.00E-04 Lower side 4.33E E E E E E E E E E E E-05 解析結果との比較 C 脚 D 脚 Facing North 1.18E E E E E E E E E E E E-05 C C 脚 D 脚 Facing South 3.33E E E E E E E E E E E E E-03 Maximum principal strain D C 脚 C D 脚 32

33 Cracking Aging Shaking 33

34 Earthquakes & Dams 34

35 LOADS Thermal Deconvolution INTERACTIONS Initial Stresses MODELS TESTS APPLICATIONS TOOLS 35

36 Modes of heat transfer in a dam analysis Conductivity T qi = ki x Convection i ( ) qconv = htsurface Tfluid, Time varying prescribed T Reservoir Absorption Incident solar radiation Reflection Convection Radiation 4 4 ( ) qr = ecs Tsurf T fluid, Isolation Dam Foundation Radiation Isolation 36

37 Deconvolution Details O I Observe (or determine a synthetic) earthquake on surface O Must apply the seismic record at I Must model (elastic) foundation Q: Which record should be applied at base of foundation such that the computed one at O will match the desired earthquake? A: Need to Deconvolute the signal 37

38 ( t) Time Domain; ( ) Frequency Domain (via FFT) 1 -i2 t i2 t X( ) xt () e dt ; x() t X( ) e - - FFT FFT FFT xt () X( ) FFT 1 d FFT FFT -1 i(t) I(ω) Excitation h (t) H (ω) o(t) O(ω) Transfer Function (Fourier Spectral Ratio) (1D) 1. FFT input, I(t) and output O(t) signal to go from time to frequency domain; I(ω) and O(ω); 2. Determine the TF by dividing amplitudes of each frequency of the Output by the corresponding one of the input: TF I-O = O(ω)/ I(ω) 38

39 1D Deconvolution a (t) a(t) Physical model i (t)=a (t) Numerical model i(t)? FFT 1. i'( t) I '( ); a( t) A( ) A( ) 2. TF I '( ) 1 I '( ) 3. I( ) TF A'( ) A'( ) A( ) FFT 1 4. I( ) it ( ) FFT 39

40 Input FFT x Deconvolved FFT x Deconvolution; Frequency X 0.05 Amplitude Frequency Input data x Deconvolved Ix Deconvolution; Time X Acceleration Time 40

41 Initial Stress Analysis; Staged Construction Simulation; Static-Dynamic Analysis Weight in one block Staged Construction of individual monoliths (2D) Grouting (3D) Static Analysis followed by a Dynamic Analysis (change in material properties & Boundary Conditions) Excessive Deformation and Stresses (tensile) More realistic initial stresses 41

42 Reservoir-Structure LOADS Fluid-Fracture/Joint INTERACTIONS Foundation-Free Field MODELS TESTS APPLICATIONS TOOLS 42

43 Uplift L = 0 Lcr < Lg cr al Lcr D eff > = L gal 0. L D cr gal eff > L = 1.0 In a nonlinear analysis, uplift is automatically adjusted in accordance with crack opening/failure 43

44 Uplift must be adjusted as crack propagates in a nonlinear analysis; In Dynamic analysis as d(cod)/dt, p and d(cod)/dt, p UDyn U Dynamic Uplift Stat Model must be calibrated with Boulder and Montreal Tests 1 dcod dt 44

45 1 0.8 Initial Uplift on Dam/Foundation Interface Dynamic Uplift Validation Uplift (MPa) We note that: Uplift (MPa) Ligament (m) Uplift Distribution on Dam/Foundation Interface t=0sec t=3.26sec t=4.005sec t=4.19sec t=4.23sec 1. Uplift is non-zero for an open (or previously opened) crack 2. Water/crack front advances with time Ligament (m) 45

46 Base of the dam excited by a seismic wave. Wave will travel through the model, and eventually hit the boundary. As with all waves, it will be reflected by the free surface. In actuality, it keeps propagating in the foundation. Seismic Wave Reflection Reflected wave may either amplify or decrease seismic excitation, in either case, it must be eliminated. Reflection can be eliminated either by a) infinitely large mesh (expensive), b) infinite (boundary) element ; or through Radiation Damping which will absorb the incident waves (P and S). 46

47 Radiation Damping M 0; g 0 M=0; g=0 It is erroneous not to account for the mass in the rock Current Practice 47

48 Lysmer M 0; g 0 Ω C dp s F C M 0; g = 0 C dp n u Ω Lysmer Assumes rigid support, no effect of free field Current Practice 2; Lysmer t = ρvu; t = ρvv; n P s1 S µ 1 V = ; V = V ρ s s S P S 2 1 2ν = 2(1 ν ) ; 48

49 Free Field Γ - Displacements Velocities u Γ u Γ K S K N C dp n C dp s F K F R F C u Ω Lysmer Γ + Ω Miura-Saouma Analyse Free Field First F F F F F F M u + C u +Κ u = t F F Solve u and u along boundary Γ F Account for free field analysis results, and analyse foundation-structure next ( ) ( ) + + Ω u + u + u Ω Ω Ω Ω Ω dp Γ Γ dp Γ Γ dp Ω M C K Clft u lft u lft Crgt u rgt u rgt Cbotu bot = ( R Γ Γ u + ) ( R Γ Γ ) lft ft Crgtu rgt + K rgtu rgt Ω t bot Clft lft K u l Left Virtual Interface Right Virtual Interface Ω Ω Ω M u C u K u C u C u C u Ω Ω Ω dp Ω dp Ω dp Ω lft lft + lft rgt + bot bot t + F + F + F + F + F + F Ω C K R C K R bot lft lft lft rgt rgt rgt Derived from Principle of Virtual Work = 49

50 Meshing ff, L ff, L { u }, { u } F F ff, R ff, R { u }, { u } dp C bot Free Field Free Field

51 Validation; Harmonic excitation at Base Free Boundaries Lysmer Miura-Saouma 51

52 3D Validation Lysmer Miura-Saouma 52

53 Effect of Boundary Conditions Criteria Radiation Damping No Lysmer Miura Rocking Yes Yes No No Yes No Gravity Load Transfer Yes Yes No Yes No Yes Perform static analysis with supports Determine reactions Restart a dynamic analysis with initial stress, zeroed displacements, remove supports and replace them by forces (i.e. no BC) 53

54 Case Study STUDY No Rad. Damp. Lysmer Miura Foundation Size BC Type Miura vs Lysmer Small Large Fixed Free f (1, 4, 8 Hz) Interface Effect of E Reaction to Load Comp. (with Interface) E/10 Foundation Size Exact E 10E Small Large No RD; 10% Rayl. Effect of M Effect of M Massless Mass Massless Mass Mesh Size Inter./Ext. Small Medium Interior Exterior Large f (1, 4, 8 Hz) Detailed parametric study of Folsom Dam subjected to harmonic excitation (different frequencies), and 1971 San Fernando Earthquake, 0.30 peak ground acceleration) 54

55 Observations 1. If no radiation damping is present, very large foundations should be used, 2. For soft rock, the mass of the foundation should be modeled as we can have substantial amplification of the input signal. 3. When the mass is modeled, we have a larger inertia and thus slightly reduced dam accelerations. However this effect is mitigated by deconvolution of the input signal which should be performed. 4. Massless foundation will generate larger response than when the foundation mass is accounted for. 5. One should not apply vertical support in a seismic analysis of a massive concrete structures with its foundation as rocking will induce additional accelerations (and stresses). 6. When radiation damping is present we greatly reduce the dependency on the size of the foundation. 7. Even when radiation damping is present, the height of the foundation should be carefully selected to correspond to a multiplier (one should be enough) of the shear wave length. 8. Interface (or joint) elements between the dam and the foundation may not substantially reduce the accelerations but will reduce the stresses. 9. A model based on Saouma-Miura with interface element is equivalent to a simpler model (with no interfaces, no radiation damping) with a Rayleigh damping of about 15%. 55

56 Beaver (Dam Definition) LOADS Pre-Processor: KUMO Analysis: MERLIN INTERACTIONS Post-Processor: SPIDER MODELS Analysis Sequence TESTS APPLICATIONS TOOLS 56

57 MERLIN 57

58 58

59 Profiles_of_crack_002,Crack opening 'C:\Tepsco\Analyses\Kasho-Gravity\Data-Files\3D\kas-3-f-ss_dyn2.xyzvdat' Profiles_of_crack_003,Uplift 2e-07 values 1e-07 'C:\Tepsco\Analyses\Kasho-Gravity\Data-Files\3D\kas-3-f-ss_dyn2.xyzvdat' e-07 values -1.39e-17 2e-07 1e e-07-2e-07-2e-07-3e e Z X Z X -54 Time-Accel_Crv,_Increment_ 'C:\Tepsco\Analyses\Kasho-Gravity\Data-Files\3D\kas-3-f-ss_dyn2.dat' Acceleration Time Time-Accel_Crv,_Increment_555-FFT 1.2 'C:\Tepsco\Analyses\Kasho-Gravity\Data-Files\3D\kas-3-f-ss_dyn2.dat' Acceleration, magnitude Time, frequency 59

60 LOADS INTERACTIONS Boulder Tests (Misc) Centrifuge Dynamic test (Short) MODELS Centrifuge Dynamic Tests (Detailed) TESTS APPLICATIONS TOOLS 60

61 CENTRIFUGE Maxi Payload: 7 t Platform Size: 2.2 x 2.2 m Model Height: 2.5 m Max. Accel. 120 g Max. Payload: 700 g-t Shaking Table 4 Electro-Hydraulic Actuators (1,176 kn Total) Max. Payload: Platform: 3 t 2.2 x 1.07 m Max. Accel. 500 m/s 2 Max. Freq. 200 Hz 61

62 Centrifuge Test of Dam Place Specimen on Shaking table Place shaking table on centrifuge Prototype 100 m 10 sec. Model 1m 0.1 sec. 62

63 載荷 加振条件 遠心力場 (g) ならし運転空虚時 最大加速度 : 6 段階 加振波形 6 段階で加速度を増加させる 最大加速度 450m/s 2 湛水振動実験 振動実験 満水時 加振波形 :4 段 階 経過時間 (min) 加振 1 段階当たりの波形イメージ加速度(m/s2) sec 167Hz 漸増正弦波 t(s) 0.1 時間 (s) 63

64 基盤に対する天端の伝達関数 第 3 波 増幅率 第 4 波 増幅率 Transfer Functions to Detect Cracks 周波数 (Hz) 周波数 (Hz) 第 5 波 30 第 6 波 増幅率 増幅率 急増 周波数 (Hz) 周波数 (Hz) 64

65 加速度応答の比較 天端 基盤 Acceleration (m/sec 2 ) Acceleration (m/sec 2 ) Time (sec) 解析実験 解析 Anal 実験 ysis Experi ment ( 同定値 ) 弾性係数 : 9,370MPa 引張強度 : 1.01MPa 減衰定数 : 7% Time (sec) 基盤に対する天端の伝達関数の比較 増幅率 弾性領域での応答 解析 12 実験 ( 同定値 ) 弾性係数 : 9,370MPa 減衰定数 :7% Finite Element Simulation captured the experimental response; Validation of FEM Code 周波数 (Hz) 65

66 For How Long Can we Ignore the Problem? John Hendrix 66

67 END Thank you for your Attention 67

68 Bilinear Evolution Laws σ t c σ t0 c 0 s1 σ I G F s 1c w1 σ w uieff σ II G F w1c wc uieff Energy dissipated in shear test under high confinement p ( ) Constitutive Equation: σ = α E: u u σ + σ Integrity Parameter: α = 1 2 σ σ AF K ns Damage Parameter: D = = 1 A K K ns σ = u u p 1 if > 0; 0 otherwise 0 n0 Stiffness Degradation D σ t K no K ns u σ i σ t u p I G F u i = γ u i u i = u ieff 68

69 Dilatancy & Damping Φ d Φ d 0 σ n dcod = η dt 1 u u ieff dil Maybe difficult to calibrate. Useful to dissipate energy 69

70 User input data ε Maximum volumetric strain at temperature θ θ= θ 0 0 τc ( θ0) Characteristic time at temperature θ0 τl ( θ0, σ / f ' c) Γr Residual value in tension for Γt α Retardation factor due to compressive stresses β Coefficient that determines the shape of Γc γ t Fraction of σt or w c prior to reduction of AAR expansion σ U Upper compressive stress before zero AAR expansion in uniaxial load ' f c Compressive strength ' f t Tensile strength G f Fracture energy βe Reduction coefficient for Elastic modulus βf Reduction coefficient for tensile strength U C Activation energy associated with τc( θ0), default value 5,400 K U L Activation energy associated with τl( θ0), default value 9,400 K T0 Laborator y temperature for determination of ε, τc( θ0) and τl( θ0) θ= θ0 Reference dam temperature 70

71 Representative year cycle Generate mesh for thermal analysis (without cracks or foundation). T water (t) T air (t) T(x,y,t) y t (x,y) t t x Computed temperatures at location T10007 Temperature [ o C] Carry out a transient thermal analysis for 4 years (2 week increments). Select last year as typical thermal load Time [ATU] 71

72 Air temperature and pool elevation For 1 year Cyclic load generation Air temperature [o C ] Water level [m m.s.l.] , , , , , , , , , , ,00 Time [ATU] Air temperature is necessary to determine the temperature on the upstream and downstream surfaces exposed to the air 1584, Time [ATU] Water level is necessary to determine the upstream surface below water level during a year Air temperature [o C ] Water level [m m.s.l.] 14,00 12,00 10,00 8,00 6,00 4,00 2,00 0, ,00-4,00-6,00 Time [ATU] 1606, , , , , , , , , , , , Time [ATU] Ti [ATU] 72

73 January Yearly temperature variation (should add 7 o C) February March April May June 73

74 Mesh for 3D stress analysis Mesh for 3D stress analysis Only the dam body with joint between each cantilever 7,552 nodes 5,196 elements (tetrahedral, pyramidal and hexahedral linear elements) Interface elements (Joints) Hexahedral elements Pyramidal elements Tetrahedral elements 74

75 Parameter identification process Field Measurements U Initial Parameters X o Computation of U f(x)=u ( ) U U' X ε No Computation of new parameter vector Yes Final parameters X A Matlab driver for Merlin analysis has been written It reads experimental/field measurements, and then seeks to determine the primary parameters through a least square nonlinear optimization function Driver (AARSI), will internally read Merlin output file to extract numerical predictions, and edit Merlin input file to write new set of input parameters Graphical user interface. 75

76 Areas of Research 1. Can we extract cores from a dam, perform laboratory tests, and characterize the remaining expansion curve (kinetics) of the concrete (i.e. what is the maximum AAR expansion, and when would it stop)? 2. Improve our understanding of AAR expansion when concrete is subjected to uniaxial, biaxial or triaxial confinement. 76

77 ASR Expansion ε Field ε field ε 0?? t 0? Problem Mathematical Formulation tlab + t 0 ε lab τcar 1 e ε Lab ( tlab ) = ε ε ( t 0 Lab + t0 τ lat ) τcar ε Coring Field () t = Laboratory coordinate system 1 e Field coordinate system 1+ e In Laboratory coordinate system tfield τcar ( tfield τ lat ) τcar 1+ e In field coordinate system ε t field t lab ε field ε 0?? ε t 1 lab T1? 0 ε 2 lab T 1 T 2 t T2? 0 ε t 3 lab T3? 0 t field The red curve is with respect to global coordinates and is what we are seeking We can obtain the blue curve with respect to the laboratory coordinate system We want to get the entire curve with respect to the global coordinate system Thus we have 5 unknowns for each test: τ lat, τ char, ε, t 0, ε 0 Will need to perform at least 3 tests at 3 different temperatures to also determine UL and UC (activation Energies) T 3 t, t, t lab lab lab 77

78 AAR Expansion Under Controlled Triaxial Confinement Check validity of AAR redistribution when concrete is subjected to uniaxial, biaxial or triaxial confinement under controlled temperature and 100% humidity 78

79 Actual Frame 79

80 Display Panel Web Based Monitoring 80