modeling of concrete materials and …bechtel.colorado.edu/~willam/cclass7-07.pdf · triaxial...

MODELING OF CONCRETE MATERIALS AND STRUCTURES

Kaspar Willam, University of Colorado at BoulderWith contributions by Dr. Inkyu Rhee, Dr. Jaesung Lee and Keun Lee, UC-Boulder

Class Meeting #7: Discrete Interface Formulations

Zero-Thickness Interface Models:Cohesive Damage and Elasto-Plastic Traction-Separation Models

Inherent Length Scale:Fracture Energy Basis GI

f and GIIf of Softening

Example Problems:- Thermal Softening of Axial Strength due Mismatch- High Temperature Bond: Pull-Out Experiment vs FE Model

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

MULTI-SCALE ASPECTS OF CONCRETE MATERIALS

Four Scales of Observation, Continuum vs Particle Models-Size Effects?

(Real Structure)Meter Level

Millimeter Level(Concrete)

Micrometer Level(Cement Paste)

Nanometer Level(Calcium Silicate Hydr

X1000

X1000

X1000

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

HIGH TEMPERATURE EFFECTS IN CONCRETE MATERIALS

Concrete Spalling: Temperature gradient vs pore pressure effects.

Transient Effects: Load-induced thermal strains-LITS.

Andersen and Thelandersen [1984]: Thermal sweep experiments.

0

0.2

0.4

0.6

0.8

1

0 200 400 600 800 1000

Temperature, C

/ f'c

TEST 1 C / min

TEST 5 C / min

−σ

11

-10

-5

0

5

10

0 200 400 600 800 1000

Temperature, C

Str

ain

[%

]

σ a

= -0.675 f'c σ a

= -0.45 f'c

σ a

= -0.225 f'c

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

THERMAL MISMATCH OF CONCRETE MATERIALS

Heterogeneity of Mesostructure:

Aggregate vs Cement Paste and Bond of ITZ

x

y

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

ZERO-THICKNESS INTERFACE FORMULATION

Weak ITZ-Cohesive Traction-Separation Relations:Softening Damage and Plasticity Models

Fracture Energy Basis:Coupling of Mode I and Mode II Softening Damage/Plasticity Models(softening of tensile bond vs tangential shear strength).

x

y[|un

|]1

n

s

[|u s|]1

ξ[|u n|]2

[|u s|]2

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

BIMATERIAL INTERFACE CONDITIONS

Perfect Bond:

[|uN |] = uaN − uc

N = 0 and [|tN |] = taN − tc

N = 0

Weak Discontinuities: all strain components exhibit jumps across interfaceexcept for εa

TT = εcTT restraint.

Note: Jump of tangential normal stress, σaTT 6= σc

TT .

Imperfect Contact:

[|uN |] = uaN − uc

N 6= 0 whereas [|tN |] = taN − tc

N = 0

Strong Discontinuities: all displacement components exhibit jumps acrossinterface.

Note: FE Displacement method enforces traction continuity in ‘weak’ senseonly, hence [|tN |] 6= 0.

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

ZERO-THICKNESS INTERFACE FORMULATION

Deformed FE Mesh after Thermal Sweep:

Diagonal separation of RVE due to slip.

x

y

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

ZERO-THICKNESS INTERFACE FORMULATION

Axial Thermal Stress due to Temperature Sweep:

Experimental observations vs computational results.

0 200 400 600 800Temperature [

oC]

0

0.2

0.4

0.6

0.8

1

- σ11

/ f’

c

TEST 1oC/min

TEST 5oC/min

T

ε 11 = 0

0 200 400 600 800Temperature [C]

-40

-30

-20

-10

0

Stre

ss_Y

Y[M

pa]

at O

uter

Edg

e of

Con

fine

d Su

rfac

es

ContinuumDiscrete, b=0.1Discrete, b=0.5Discrete, b=1.0

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

HIGH TEMPERATURE BOND

Pull-Out Test Setup: Residual Experiments after Cooling.

Test Variables:

- Coated-Uncoated Rebars- Slow-Rapid Heating Rates- Target Temperatures: 20oC, 200oC, 400oC, 600oC- Natural-Water Cooling

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

HIGH TEMPERATURE BOND

Pull-Out Test Program: Residual Experiments after Cooling.

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

HIGH TEMPERATURE BOND

Pull-Out Test Results:

Bond-Slip Relationships for T=20, 200, 400, 600C (rapid heating)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 0.01 0.02 0.03 0.04 0.05 0.06Slip (inch)

Bon

d st

reng

th (k

si)

Uncoated ref.UR15_200NUR15_400NUR15_600N

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

HIGH TEMPERATURE BOND

Pull-Out Test Results:

Bond Strength of slow heating tests up to T = 20o, 200o, 400o, 600oC

1.29

1.11

0.36

0.00

0.99

1.44

0.29

0.60

1.67

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

25 200 400 600 800

Temperature (˚C)

Bon

d st

reng

th (k

si)

UR2 test series (Natural cooling)CR2 test series (Natural cooling)

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

HIGH TEMPERATURE BOND

Pull-Out Test Results:

Bond Strength of rapid heating tests up to T = 20o, 200o, 400o, 600oC

0.94

0.00

0.99

0.35

1.29

1.27

0.160.33

1.44

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

25 200 400 600 800

Temperature (˚C)

Bon

d st

reng

th (k

si)

UR15 test series (Natural cooling)CR15 test series (Natural cooling)

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Finite Element Model of Pull-Out Test Specimen

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

BIMATERIAL INTERFACE CONDITIONS

Perfect Bond:

[|uN |] = ustN − uco

N = 0 and [|tN |] = tstN − tco

N = 0

Weak Discontinuities: all strain components exhibit jumps across interfaceexcept for εst

TT = εcoTT restraint.

Note: Jump of tangential normal stress, σstTT 6= σco

TT .

Imperfect Bond:

[|uN |] = ustN − uco

N 6= 0 whereas [|tN |] = tstN − tco

N = 0

Strong Discontinuities: all displacement components exhibit jumps acrossinterface.

Note: FE Displacement method enforces traction continuity in ‘weak’ senseonly, hence [|tN |] 6= 0.

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

MISMATCH OF THERMAL EXPANSION

3-D Thermoelastic Response:

∆εεεco = EEE−1co : ∆σσσco + αααco∆T and ∆εεεst = EEE−1

st : ∆σσσst + αααst∆T

Interface Bond Kinematics: ∆εstz = ∆εco

z

Interface Bond Traction: ∆σstr = ∆σco

r

Radial Contact Stress:

σr =EcoEst

Estνcon − Ecoνst[αco − αst]∆T + HO

0 100 200 300 400 500Temperature

0.00001

0.0000125

0.000015

0.0000175

0.00002

0.0000225

alpha

0 100 200 300 400 500Temperature

0

50

100

150

200

250

Radial stress@MPaD

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

TRIAXIAL CONCRETE MODEL

Damage-Plasticity Model in ABAQUS: Lee & Fenves [1998]

Damage-Plasticity Model in ABAQUS Standard

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PLANE STRESS FAILURE ENVELOPE

Damage-Plasticity Model: Lee & Fenves [1998]

Triaxial Concrete Model in ABAQUS-Standard

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Evolution of Tensile Damage at Different Outside TemperaturesT = 100, 300, 580oC

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Evolution of Compression Damage at Different Outside TemperaturesT = 100, 300, 580oC

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Circumferential Stress Distribution at Outside TemperaturesT = 100, 300, 580oC

-25

-20

-15

-10

-5

0

5

0 10 20 30 40 50 60

Radius [mm]

Stre

ss [M

Pa]

stress_t at T=108

stress_t at T=300

stress_t at T=580

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Circumferential Stress Contours at Outside Temperature T = 580oC

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Bond Stress-Axial Slip Response (cold vs hot conditions)

0

5

10

15

20

25

0 1 2 3 4 5

Bond stress

τ b in MPa

Displacement in mm

cold

warm

cooled

cold exp. Kurz

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Axial Stress Contours after Heating to T = 580oC

S, S22

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

PULL-OUT PROBLEM

Compression Damage after Heating to T = 580oC

DAMAGEC

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007

CONCLUDING REMARKS

Thermal Mismatch of Steel and Concrete:Full Bond vs Cohesive Interface Formulation - Loss of Confinement.

Mesoscale Analysis of Concrete RVE:Interaction of tensile cracking and shear debonding along weakzero-thickness interface layers-ITZ.

High Temperature Pull-Out:Residual experiments and axisymmetric FE simulation ofsteel-concrete contact separation.

Class #7 Concrete Modeling, UNICAMP, Campinas, Brazil, August 20-28, 2007