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
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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.
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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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0 0.1 0.2 0.3 0.4 0.5 0.6Deflection [mm]
Load
[kN
]
Experiment
Identification
Primary calculation:
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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).
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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)
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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)
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
• 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
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
• 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)
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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.
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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3-point bending tests
Set I (C30/37 H)•9 specimens•age 91 days
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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
June, 13-15 5th REC, Brno, Czech Republic, 2012
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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 – – –
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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Statistical parameters of set II (C25/30 B3)
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] 30.8 8.6 35.0 8.2 1.14
Tensile strength [MPa] – – 4.1 17.2 –
Compressive strength [MPa] 47.3 5.4 – – –
Fracture energy [J/m2] 188.9 11.5 211.8 18.1 1.12
Effective crack elongation [mm] 12.5 23.5 – – –
Effective fracture toughness [MPa.m1/2] 1.406 8.0 – – –
Effective toughness [J/m2] 65.2 21.8 – – –
Volume density [kg/m3] 2286.2 1.5 – – –
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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Statistical parameters of set III (C25/30 XC1 GK16)
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] 35.4 5.6 40.4 9.5 1.14
Tensile strength [MPa] – – 4.2 12.1 –
Compressive strength [MPa] 53.4 5.2 – – –
Fracture energy [J/m2] 183.3 5.5 214.0 6.0 1.17
Effective crack elongation [mm] 12.4 22.7 – – –
Effective fracture toughness [MPa.m1/2] 1.405 9.0 – – –
Effective toughness [J/m2] 56.3 19.9 – – –
Volume density [kg/m3] 2326.9 0.9 – – –
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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Statistical parameters of set IV (C20/25 XC1 GK16)
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] 31.2 4.3 34.8 5.3 1.12
Tensile strength [MPa] – – 3.1 15.6 –
Compressive strength [MPa] 39.8 5.4 – – –
Fracture energy [J/m2] 146.2 13.3 166.8 15.4 1.14
Effective crack elongation [mm] 13.0 14.3 – – –
Effective fracture toughness [MPa.m1/2] 1.131 10.6 – – –
Effective toughness [J/m2] 41.4 20.7 – – –
Volume density [kg/m3] 2292.2 0.6 – – –
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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Comparison of parameters among all 4 sets
5th REC, Brno, Czech Republic, 2012June, 13-15
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Modulus of elasticity Ec
Compressive strength fc
Fracture energy Gf
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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
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10
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60
I II III IV
Com
pres
sive
Str
engt
h in
MP
a .
0
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10
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20
25
CO
V in
%
Mean Value COV
0
25
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75
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125
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I II III IV
Fra
ctur
e E
nerg
y in
J/m
2 .
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CO
V in
%
Mean Value COV
Effective crack model + work-of-fracture method
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Comparison of parameters among all 4 sets
5th REC, Brno, Czech Republic, 2012June, 13-15
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Effective fracture toughness KIce
Effective toughness Gce
Volume density c
Effective crack model + work-of-fracture method
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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
.
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25
CO
V in
%Mean Value COV
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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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Comparison of parameters among all 4 sets
5th REC, Brno, Czech Republic, 2012June, 13-15
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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
5th REC, Brno, Czech Republic, 2012June, 13-15
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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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
5th REC, Brno, Czech Republic, 2012June, 13-15
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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