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
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Introduction, motivation
Motivation for material parameters determination (strengths, fracturemechanical):
- 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
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Numerical modeling – parameters
Numerical 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
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Numerical modeling – parameters
Load [kN]
6
5
Experiment
4
Primary calculation
3
2
1
Primary calculation:
0
0
June, 13-15
0.2
0.3
0.4
Deflection [mm]
0.5
0.6
6
Experiment
5
Load [kN]
Correction of parameters:
• „trial–and–error“ method
• sophisticated identification methods
– artificial neural network based
inverse analysis
0.1
Identification
4
3
2
1
0
0
5th REC, Brno, Czech Republic, 2012
0.1
0.2
0.3
0.4
Deflection [mm]
0.5
0.6
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Fracture experiment
Testing configuration :
3-point bending test of beam with
central edge notch
Specimen parameter [mm]
Nominal value
Length of specimen
400
Width of specimen
100
Height of specimen
100
Depth of notch
33
Span
300
L-d diagram
Determination of parameters:
• effective crack model +
work-of-fracture method
• ANN based inverse analysis
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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 identification
Random 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
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
ANN based inverse analysis – deterministic parameters
Structural response
Material
model
parameters
Stochastic calculation (LHS) – training set for
calibration of synaptic weights and biases
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
ANN based inv. anal. – statistical param. (direct approach)
Structural response
Material
model
parameters
Stochastic calculation (LHS) – training set for
calibration of synaptic weights and biases
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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)
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
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
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
3-point bending tests – l-d diagrams
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Statistical parameters of set I (C30/37 H)
Effective crack model,
work-of-fracture method
Parameter of concrete/model
ANN identification
Identif./
exp.
Mean
value
COV [%]
Mean
value
COV [%]
35.5
7.4
40.3
16.6
1.14
–
–
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
9.5
21.9
–
–
–
Effective fracture toughness [MPa.m1/2]
1.489
9.9
–
–
–
Effective toughness [J/m2]
62.3
13.7
–
–
–
2341.8
0.7
–
–
–
Modulus of elasticity [GPa]
Tensile strength [MPa]
Effective crack elongation [mm]
Volume density [kg/m3]
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5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Statistical parameters of set II (C25/30 B3)
Effective crack model,
work-of-fracture method
Parameter of concrete/model
ANN identification
Identif./
exp.
Mean
value
COV [%]
Mean
value
COV [%]
30.8
8.6
35.0
8.2
1.14
–
–
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
–
–
–
2286.2
1.5
–
–
–
Modulus of elasticity [GPa]
Tensile strength [MPa]
Volume density [kg/m3]
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Statistical parameters of set III (C25/30 XC1 GK16)
Effective crack model,
work-of-fracture method
Parameter of concrete/model
ANN identification
Identif./
exp.
Mean
value
COV [%]
Mean
value
COV [%]
35.4
5.6
40.4
9.5
1.14
–
–
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
–
–
–
2326.9
0.9
–
–
–
Modulus of elasticity [GPa]
Tensile strength [MPa]
Volume density [kg/m3]
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Statistical parameters of set IV (C20/25 XC1 GK16)
Effective crack model,
work-of-fracture method
Parameter of concrete/model
ANN identification
Identif./
exp.
Mean
value
COV [%]
Mean
value
COV [%]
31.2
4.3
34.8
5.3
1.12
–
–
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
–
–
–
2292.2
0.6
–
–
–
Modulus of elasticity [GPa]
Tensile strength [MPa]
Volume density [kg/m3]
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Comparison of parameters among all 4 sets
Effective crack model + work-of-fracture method
Compressive
strength fc
Modulus of
elasticity Ec
Mean Value
COV
Mean Value
40
25
COV
Mean Value
60
25
COV
250
25
225
20
10
15
10
5
5
20
200
40
15
30
10
20
5
10
Fracture Energy in J/m2 .
15
Compressive Strength in MPa .
25
COV in %
30
20
175
150
15
125
100
10
75
50
5
25
0
0
I
II
June, 13-15
III
IV
0
0
I
II
III
IV
5th REC, Brno, Czech Republic, 2012
0
0
I
II
III
IV
19
COV in %
50
20
COV in %
35
Modulus of Elasticity in GPa.
Fracture
energy Gf
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Comparison of parameters among all 4 sets
Effective crack model + work-of-fracture method
Effective
toughness Gce
Effective fracture
toughness KIce
COV
Mean Value
25
Mean Value
70
1.4
25
2340
0.4
5
15
40
30
10
20
0.0
0
I
June, 13-15
II
III
IV
1.5
2330
2320
1.0
2310
2300
0.5
5
2290
10
0.2
Volume Density in kg/m3.
10
0.6
50
COV in %
0.8
Effective Toughness in J/m2.
15
2.0
20
1.2
1.0
COV
2350
60
20
COV in %
Effective Fracture Toughness in MPa.m1/2.
1.6
COV
0
0
I
II
III
IV
5th REC, Brno, Czech Republic, 2012
2280
0.0
I
II
III
IV
20
COV in %
Mean Value
Volume
density gc
Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Comparison of parameters among all 4 sets
ANN based identification method
Modulus of
elasticity Ec
June, 13-15
Tensile
strength ft
5th REC, Brno, Czech Republic, 2012
Fracture
energy Gf
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Comparison of l-d diagrams: experiment vs. identification
June, 13-15
5th REC, Brno, Czech Republic, 2012
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Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB
Conclusions
Determination 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.
Modulus of
LN (2 par)
elasticity [GPa]
Tensile
LN (2 par)
strength [MPa]
Fracture
LN (2 par)
energy [N/m]
June, 13-15
III (C25/30 XC1 IV (C20/25 XC1
GK16)
GK16)
Mean COV [%] Mean COV [%] Mean COV [%] Mean COV [%]
I (C30/37 H)
II (C25/30 B3)
40
17
35
9
40
10
35
6
5.0
15
4.1
18
4.2
12
3.1
16
282
20
212
18
214
6
167
16
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