BASED ON FraMePID3PB TOOL

concretecakeΠολεοδομικά Έργα

29 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

1

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

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.

June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

4

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

5

Numerical modeling



parameters


„trial

and

error“ method


sophisticated identification methods




artificial neural network based
inverse analysis

Correction of parameters:

0
1
2
3
4
5
6
0
0.1
0.2
0.3
0.4
0.5
0.6
Deflection [mm]
Load [kN]
Experiment
Primary calculation
0
1
2
3
4
5
6
0
0.1
0.2
0.3
0.4
0.5
0.6
Deflection [mm]
Load [kN]
Experiment
Identification
Primary calculation
:

June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

6

Fracture experiment

Testing 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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

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

7

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

8

Stochastic calculation (LHS)


training set for

calibration of synaptic weights and biases

Material

model

parameters

ANN based inverse analysis


deterministic parameters

Structural response


June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

9

Stochastic calculation (LHS)


training set for

calibration of synaptic weights and biases

Material

model

parameters

Structural response


ANN based inv. anal.


statistical
param
. (direct approach)

June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

10

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

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

11

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB


Subject of identification:


modulus of elasticity

E
c



tensile strength
f
t





fracture energy
G
f


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 function
s
, correlation coefficients).


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

June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

13

3
-
point bending tests

Set I (C30/37 H)


9 specimens


age 91 days

June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

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

14

3
-
point bending tests


l
-
d

diagrams

June, 13
-
15

5
th

REC
,
Brno
,
Czech Republic
, 201
2

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

15

S
tatistical parameters of set I (C30/37 H)

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 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/m
2
]

235.9

18.6

281.5

19.5

1.19

Effective crack elongation [mm]

9.5

21.9







Effective fracture toughness [
MPa.m
1/2
]

1.489

9.9







Effective toughness [
J/m
2
]

62.3

13.7







Volume density [
kg/m
3
]

2341.8

0.7







Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

16

S
tatistical parameters of set II (C25/30 B3)

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 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/m
2
]

188.9

11.5

211.8

18.1

1.12

Effective crack elongation [mm]

12.5

23.5







Effective fracture toughness [
MPa.m
1/2
]

1.406

8.0







Effective toughness [
J/m
2
]

65.2

21.8







Volume density [
kg/m
3
]

2286.2

1.5







Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

17

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 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/m
2
]

183.3

5.5

214.0

6.0

1.17

Effective crack elongation [mm]

12.4

22.7







Effective fracture toughness [
MPa.m
1/2
]

1.405

9.0







Effective toughness [
J/m
2
]

56.3

19.9







Volume density [
kg/m
3
]

2326.9

0.9







Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

18

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 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/m
2
]

146.2

13.3

166.8

15.4

1.14

Effective crack elongation [mm]

13.0

14.3







Effective fracture toughness [
MPa.m
1/2
]

1.131

10.6







Effective toughness [
J/m
2
]

41.4

20.7







Volume density [
kg/m
3
]

2292.2

0.6







Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

19

Comparison of parameters among all 4 sets

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 13
-
15

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

Modulus of
elasticity
E
c

Compressive
strength
f
c

Fracture
energy
G
f

0
5
10
15
20
25
30
35
40
I
II
III
IV
Modulus of Elasticity in GPa
.
0
5
10
15
20
25
COV in %
Mean Value
COV
0
10
20
30
40
50
60
I
II
III
IV
Compressive Strength in MPa
.
0
5
10
15
20
25
COV in %
Mean Value
COV
0
25
50
75
100
125
150
175
200
225
250
I
II
III
IV
Fracture Energy in J/m2
.
0
5
10
15
20
25
COV in %
Mean Value
COV
Effective crack model + work
-
of
-
fracture method

20

Comparison of parameters among all 4 sets

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 13
-
15

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

Effective fracture
toughness
KI
ce

Effective
toughness
G
ce

Volume
density
g
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
Effective Fracture Toughness in MPa.m1/2
.
0
5
10
15
20
25
COV in %
Mean Value
COV
0
10
20
30
40
50
60
70
I
II
III
IV
Effective Toughness in J/m2
.
0
5
10
15
20
25
COV in %
Mean Value
COV
2280
2290
2300
2310
2320
2330
2340
2350
I
II
III
IV
Volume Density in kg/m3
.
0.0
0.5
1.0
1.5
2.0
COV in %
Mean Value
COV
21

Comparison of parameters among all 4 sets

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 13
-
15

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

Modulus of
elasticity
E
c

Tensile
strength
f
t

Fracture
energy
G
f

ANN based identification method

22

Comparison of
l
-
d

diagrams: experiment vs. identification

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 13
-
15

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

based on FraMePID
-
3PB

23

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

5
th

REC
,
Brno
,
Czech Republic
, 201
2

June, 13
-
15

Lehký,
Keršner
, Novák


Determination of concrete stat
istics

using fracture test and
inv
.

anal
ysis

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