david lehký , zbyněk keršner , drahomír novák

June, 13-15 5th REC, Brno, Czech Republic, 2012 1

Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB

DETERMINATION OF STATISTICAL MATERIAL

PARAMETERS OF CONCRETE USING

FRACTURE TEST AND INVERSE ANALYSIS

BASED ON FraMePID–3PB TOOL

David Lehký, Zbyněk Keršner, Drahomír Novák

Brno University of Technology, Brno, Czech Republic

2

Introduction, motivation

Motivation for material parameters determination (strengths, fracture-mechanical): - comparison of different mixtures and composites (optimal content, type of fibres, etc.) - numerical modeling of structures (deterministic and statistical level)

June, 13-15 5th REC, Brno, Czech Republic, 2012


3

Introduction, motivation

The knowledge of fracture/mechanical parameters is fundamental for virtual modeling of elements and structures made of concrete.

Key parameter: fracture energy and its variability

Other important parameters of concrete are: modulus of elasticity, tensile and compressive strength, effective crack elongation, effective fracture toughness, etc.



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Numerical modeling – parametersNumerical model of structure

appropriate material model (e.g. 3D Nonlinear Cementitious,

Microplane model, etc.) –– many material parameters

Information about parameters:• experimental data• recommended formulas• engineering estimation



5

Numerical modeling – parameters

• „trial–and–error“ method• sophisticated identification methods

– artificial neural network based inverse analysis

Correction of parameters:

0

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0 0.1 0.2 0.3 0.4 0.5 0.6Deflection [mm]

Load

[kN

]

Experiment

Primary calculation

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2

3

4

5

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0 0.1 0.2 0.3 0.4 0.5 0.6Deflection [mm]

Load

[kN

]

Experiment

Identification

Primary calculation:



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Fracture experimentTesting configuration :3-point bending test of beam with central edge notch

Determination of parameters:• effective crack model + work-of-fracture method• ANN based inverse analysis



L-d diagram

Specimen parameter [mm] Nominal value

Length of specimen 400

Width of specimen 100

Height of specimen 100

Depth of notch 33

Span 300

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Statistical parameters identification

Two approaches:•Load-deflection “one-by-one” identification approach

Material parameters are identified individually for each specimen (individual l-d diagram is used as an input of ANN). Subsequently, statistical assessment of parameters of all specimens is carried out.

• Direct statistical parameters identificationRandom response of a structure is available in form of histograms and statistical moments (set of random l-d diagrams is used as an input of ANN). Statistical parameters are direct output of inverse analysis (ANN).



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Stochastic calculation (LHS) – training set for calibration of synaptic weights and biases

Materialmodelparameters

ANN based inverse analysis – deterministic parametersANN based inverse analysis – deterministic parameters

Structural response



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Stochastic calculation (LHS) – training set for calibration of synaptic weights and biases

Materialmodelparameters

Structural response

ANN based inv. anal. – statistical param. (direct approach)ANN based inv. anal. – statistical param. (direct approach)



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FraMePID-3PB tool• Developed for fully automatic and easy to use ANN based identification

using 3PB experimental data (l-d diagrams)• Designed for concretes of various strength and ages (large training set

with relatively high variability of material parameters)



• Prepared for testing of specimens with various notch depth – study of fracture process zone development and corresponding changes of fracture energy

• Implemented experimental data filtering

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FraMePID-3PB tool• Robust ANN implemented and trained – significant time reduction

compared to general identification tasks• FEM computational model implemented (ATENA software) –

3D Nonlinear Cementitious 2 material model



• Subject of identification: – modulus of elasticity Ec – tensile strength ft – fracture energy Gf

• Export of identified parameters to clipboard, text file, ATENA .ccm file

• Direct transfer to ATENA for verification via ATENA interface (in preparation)

12

Experimental testing campaign• Testing of stochastic properties of various concrete types, mixtures

and ages (in cooperation with BOKU, Vienna and other industrial partners).

• Comparison of fracture–mechanical parameters obtained from several testing configurations: – 3-point bending test – wedge splitting test – compression test

• Development of stochastic properties database (statistical moments, distribution functions, correlation coefficients).

Results of 4 sets of different concrete types tested in 3-point bending configuration will be shown here.



13

3-point bending tests

Set I (C30/37 H)•9 specimens•age 91 days



Set II (C25/30 B3)•9 specimens•age 87 days

Set III (C25/30 XC1 GK16)•9 specimens•age 67 days

Set IV (C20/25 XC1 GK16)•8 specimens•age 66 days

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3-point bending tests – l-d diagrams



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Statistical parameters of set I (C30/37 H)

5th REC, Brno, Czech Republic, 2012June, 13-15

Parameter of concrete/model

Effective crack model, work-of-fracture method ANN identification

Identif./exp.Mean

value COV [%] Mean value COV [%]

Modulus of elasticity [GPa] 35.5 7.4 40.3 16.6 1.14

Tensile strength [MPa] – – 5.0 14.3 –

Compressive strength [MPa] 58.5 8.0 – – –

Fracture energy [J/m2] 235.9 18.6 281.5 19.5 1.19

Effective crack elongation [mm] 9.5 21.9 – – –

Effective fracture toughness [MPa.m1/2] 1.489 9.9 – – –

Effective toughness [J/m2] 62.3 13.7 – – –

Volume density [kg/m3] 2341.8 0.7 – – –


16

Statistical parameters of set II (C25/30 B3)




Identif./exp.Mean











17

Statistical parameters of set III (C25/30 XC1 GK16)




Identif./exp.Mean











18

Statistical parameters of set IV (C20/25 XC1 GK16)




Identif./exp.Mean











19

Comparison of parameters among all 4 sets



Modulus of elasticity Ec

Compressive strength fc

Fracture energy Gf

0

5

10

15

20

25

30

35

40

I II III IV

Mod

ulus

of

Ela

stic

ity in

GP

a .

0

5

10

15

20

25

CO

V in

%Mean Value COV

0

10

20

30

40

50

60

I II III IV

Com

pres

sive

Str

engt

h in

MP

a .

0

5

10

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20

25

CO

V in

%

Mean Value COV

0

25

50

75

100

125

150

175

200

225

250

I II III IV

Fra

ctur

e E

nerg

y in

J/m

2 .

0

5

10

15

20

25

CO

V in

%

Mean Value COV

Effective crack model + work-of-fracture method

20




Effective fracture toughness KIce

Effective toughness Gce

Volume density c

Effective crack model + work-of-fracture method

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

I II III IV

Eff

ectiv

e F

ract

ure

Tou

ghne

ss in

MP

a.m

1/2

.

0

5

10

15

20

25

CO

V in

%Mean Value COV

0

10

20

30

40

50

60

70

I II III IV

Eff

ectiv

e T

ough

ness

in J

/m2

.

0

5

10

15

20

25

CO

V in

%

Mean Value COV

2280

2290

2300

2310

2320

2330

2340

2350

I II III IV

Vol

ume

Den

sity

in k

g/m

3 .

0.0

0.5

1.0

1.5

2.0

CO

V in

%

Mean Value COV

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Modulus of elasticity Ec

Tensile strength ft

Fracture energy Gf

ANN based identification method

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Comparison of l-d diagrams: experiment vs. identification



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ConclusionsDetermination of fracture/mechanical parameters values:

• Effective crack model + work-of-fracture method • ANN based identification method

FraMePID-3PB – tool for fully automatic and time-effective ANN based identification using 3PB experimental data

Recommended statistical parameters for stochastic nonlinear FEM analyses of beams/structures made of tested concretes



Distrib. I (C30/37 H) II (C25/30 B3) III (C25/30 XC1

GK16)IV (C20/25 XC1

GK16)Mean COV [%] Mean COV [%] Mean COV [%] Mean COV [%]

Modulus of elasticity [GPa] LN (2 par) 40 17 35 9 40 10 35 6

Tensile strength [MPa] LN (2 par) 5.0 15 4.1 18 4.2 12 3.1 16

Fracture energy [N/m] LN (2 par) 282 20 212 18 214 6 167 16

david lehký , zbyněk keršner , drahomír novák

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