VIRTUAL TESTING OF BRIDGES FOR LIFE CYCLE RELIABILITY...
Transcript of VIRTUAL TESTING OF BRIDGES FOR LIFE CYCLE RELIABILITY...
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VIRTUAL TESTING OF BRIDGES FOR LIFE CYCLE RELIABILITY ASSESSMENT
Radomír
Pukl
and Vladimír ČervenkaČervenka
Consulting, Prague, Czech Republic
Drahomír
Novák and Břetislav TeplýBrno University of Technology, Czech Republic
Konrad
Bergmeister
and Alfred StraussUniversity of Natural Resources and Applied Life Sciences, Vienna, Austria
Outline:SARA software system –
Structural Analysis and Reliability Assessment –
modeling of structural behavior
three core components:Nonlinear computer simulation of damage in concrete structures
Probabilistic-based assessment of structural safety and reliabilityProbabilistic modeling of material degradation
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SARA projectStructural Analysis and Reliability Assessment
assessment of structural reliability based on nonlinear finite element analysisinternational research team –
Italy, Austria, Czech Republicleader -
Prof. Konrad Bergmeisteroriginal purpose –
safety of bridges –
Brennero
highway
presentation at: IABMAS, Euro-C, ICASP, ICOSSAR, SHMII, IALCCE, …next projects: Sustainable bridges, VITESPO, …
SARA system -
integration
of nonlinear FEM and advanced probabilistic methods (LHS)open architecture:
degradation analysis –
life-cycle reliabilityspatial variability of structural (material) properties
dynamic damage identification
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SARA main
components:
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Nonlinear finite element analysis of reinforced concrete structures -
software
ATENA
Numerical
core
is
based
on realistic
material
model for concrete
Text
Computer simulation of damage
in engineering
structures
–
VIRTUAL TESTING
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Model for concrete:
damage mechanics
objectivity (FE mesh independent)deterministic size-effect
Concrete
in tension
smeared crack approach
nonlinear fracture mechanicstensile softening after crackingcrack band method
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Solid
finite
elements
in ATENA
nodal points with 3 displacement DOFs
layered integration points
• brick
• tetrahedron
• wedge
• linear
• quadratic
• layered
shell/plate elements
• higher
order
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Steel reinforcement in concrete
in ATENA
• discrete reinforcing bars
• smeared reinforcement
• perfect
bond
• bond-slip law
• prestressing
cables
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Program ATENA
Well-balanced approach
for practical applications
of advanced FEM in civil engineering
Numerical core
-
state-of-art background + Graphical user environment-
visualization + interaction
-2.431E+00
-2.200E+00
-2.000E+00
-1.800E+00
-1.600E+00
-1.400E+00
-1.200E+00
-1.000E+00
-8.000E-01
-6.000E-01
-4.000E-01
-2.000E-01
0 000E+00 M2:
Rea
ctio
ns C
ompo
nent
2
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Fields of application:
structural detailsanchorsframe corners
precast elements
transport infrastructuretunnelsbridges
buildings (high rise)hallscontainments (nuclear power plants)
examples
from Prague, Czech Republic
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Analysis of structural details
fasteners in concrete –
pull out test Step 32, RILEM axi A2, d=150, a=2d, K=oo Scalar: rendering, Basic material, in nodes, Tensile Strength, Sig T(2), <3.000E-03;3.000E+00>[MPa]
3.000E-033.300E-016.600E-019.900E-011.320E+00
1.680E+002.010E+002.340E+002.670E+003.000E+00
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Charles bridge
in Prague, Czech Republic, founded
1357 -
650 years
old
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c
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S tep 26, NSf-UZL - nevyztuzene osteni 300, MSU, zima, liniove pruzne ulozeni Scalars:iso-areas, Basic material, in nodes, Principal Stress, Max., <-5.027E-01;9.964E-01>[MP a]
-5.027E-01-4.500E-01-3.000E-01-1.500E-010.000E+001.500E-013.000E-014.500E-016.000E-017.500E-019.000E-019.964E-01
-5.0
37E
-04
1.78
4E-0
2 8
.076
E-03
8.516E-03
-2.745E-02
-1.00
6E-03 -8
.330
E-03 5.324E-03
-2.763E-02
1.752E-02
-5.0
99E
-04
1.2
52E
-04
-1.248E-01
-4.2
36E-
02
-4.766E-02
-4.427E-02
-6.749E-02 -6.697E-02
-1.258E-01 1.0
81E
-04
Tunnels
of
New Railway Connection in Prague Analysis
of plain
concrete
tunnel
lining
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Shopping
Mall
in Prague heavy reinforced girder with large openings
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Shopping
Mall
in Prague heavy reinforced girder with large openings
LOAD-DISPLACEMENT RESPONSE
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60
deflection [mm]
load
inte
nsity
[kN
/m2]
full
circular opening strong
circular opening, ties
circular opening
service load 12 kN/m2
dead load 7.75 kN/m2
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Prestressed
concrete containment in nuclear power plant
SAFETY
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Features of virtual testing of structures (nonlinear computer simulation):
detailed information about structural response
and behavior under various actions
ultimate load-carrying capacity,
resistance
against expected load, overloading
mechanical damage
in reinforced concrete structures (cracking, crushing)
serviceability
simulating failureexplanation of reasons
predictionprevention
avoidance
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VIRTUAL TESTING
Nonlinear computer simulation of damage in concrete structures
Probabilistic-based assessment of structural safety and reliability
uncertainty, randomness, stochastic evaluation
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SARA main
components:
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Stochastic methods
Improved results:
statistical characteristics of structural responsesensitivity analysisassessment of
structural
safety, reliability, failure
probabilitystatistical size-effect
Improved input parameters
for nonlinear analysis:
reflects real material and structural properties uncertain (lack of information)set
of
random
data measured in material tests
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Repeated nonlinear analysis
standard stochastic method: Monte Carlo high number of realizations
required
demanding nonlinear FE analysis
-
contradiction
probabilistic methods suitable for nonlinear analysis
stratified Monte Carlo -
Latin Hypercube Sampling
(LHS)small number of realizations
for acceptable accurate results
methodology:random sets of input parameters are generated
and used in nonlinear analysis
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Latin Hypercube Sampling (LHS)
statistical correlation
between random variables –
undesired, desired –
correlation matrix
random variables
real
izat
ions
permutation of samples
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probabilitydensity
load,
resistanceR=2.5 MN,COV 0.102
Load E
assumption: normal distribution
ERZ μμμ −=222ERZ σσσ +=
Z
Zσμβ =
Reliability assessment -
Cornell’s β-index
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012345678
0.5 1 1.5 2 2.5
Load [MN]
Rel
iabi
lity
inde
x COV of load = 0.1COV of load = 0.2Eurocode
Reliability index β
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Software FReET
Feasible Reliability Engineering Tooldeveloped by Reliability group at TU Brno (Prof. Drahomír
Novák)designed for
computationally intensive applications
main functions:
randomization of input databuilt-in database of statistic parameters of concrete and reinforcement propertiessimulated annealing method for imposing statistical correlation
(weighted, non-positive definite correlation matrix)
stochastic evaluation
of results (structural resistance, crack width)histogram, mean, COV, distribution type
(suitability
check), limit state function
sensitivity
analysis (importance of input parameters)based on nonparametric rank-order statistical correlation
reliability and safety assessmentusing reliability index and theoretical failure probability
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Software FReET
reliability techniques:
Cornell’s reliability β-indexFORMSORMdesign pointHasofer-Lind reliability indexresponse surface methodology in failure region – polynomial approximation (Bucher-Bourgund approach) importance sampling (around mean values or around design point)
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SARA system
Virtual testing of bridges for life cycle reliability assessment
open architecture:identification of optimal input parametersdamage identification
life-cycle
reliability assessment:
degradation and deterioration analysisprediction of structural reliability evolutionlife-cycle analysis, retrofitting and rehabilitation, cost optimization
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SARA main
components:
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Degradation of structures –
FReET–D
developed at TU Brno by group of Prof. Břetislav Teplý
phenomenological models for material degradation
Carbonation of Concrete (depasivation):
• Papadakis
1992
• Papadakis
2002
• Morinaga 1988
• Morinaga 2002
• Linhua+Jiang
–
OPC
• Linhua+Jiang
–
HVFA
• Bob+Affana
• Kishitany
• fib Model Code
Chloride Ingress:
• Papadakis
1992
• fib Model Code
Reinforcement Corrosion:
• Andrade
Stress
Corrosion Cracking – prestressed
steel
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Papadakis
1992
( ) tccρaρ
cwρ
RHf
cwρ
.cw
ρ.x COa
cc
ccc
61044
8.231000
1
10001
30350
2
−⎟⎟⎠
⎞⎜⎜⎝
⎛++
⎟⎟⎠
⎞⎜⎜⎝
⎛+
⎟⎠⎞
⎜⎝⎛ −
=
Papadakis
2002
)(218.0
1044
8.232 6, 22
kPc
tcDx
COCOe
c +=
−
Morinaga
1988
Morinaga
2002
for w/c ≤
0.6:
for w/c > 0.6:
21
61044
8.23)(38.016502
⎟⎠⎞
⎜⎝⎛ ⋅⋅⎟
⎠⎞
⎜⎝⎛ −≈ − tcRHfcwx COc
( )( )[ ]
21
6
21
1044
8.23)(6.21
25.01650
2⎟⎠⎞
⎜⎝⎛ ⋅⋅
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
+
−≈ − tcRHf
cw
cwx COc
for w/c ≥
0.6:
for w/c ≤
0.6:
tWTRHRCOxc )76.16.4)(0217.0174.0391.1(44.25/2 −+−⋅⋅=
( )( ) tWWTRHRCOxc 315.1/)25.09.4)0217.0174.0391.1(44.25/2 +−+−⋅⋅=
Carbonation of Concrete
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Linhua+Jiang
-
OPC
Bob+Affana
Kishitany
Linhua+Jiang
-
HVFA
( ) tccrr
crw
RHx COcHD
cc ⋅⋅
−⋅−= −41.1 10
448.23
34.01839
2
( ) nCOc tc
ckBWRHx ⋅⋅
−⋅−⋅= −4
'
*1.1 10
448.2334.0/1839
2α
tfdkCx
cc 150=
for w/c < 0.6:
for w/c > 0.6:
( )[ ] tcwRxc ⋅−⋅
=2.7
76.1/6.410
( )[ ]( )[ ]
tcw
cwRxc ⋅+−⋅
=/315.13.025.0/10
fib
Model Code
( ) WTcRkkkTx COtOACCtcec ⋅⋅⋅+⋅⋅⋅⋅= −− 61, 102)(
2ε
Input parameters –
random and/or uncertain
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Linhua+Jiang
-
OPC
Bob+Affana
Kishitany
Linhua+Jiang
-
HVFA
( ) tccrr
crw
RHx COcHD
cc ⋅⋅
−⋅−= −41.1 10
448.23
34.01839
2
( ) nCOc tc
ckBWRHx ⋅⋅
−⋅−⋅= −4
'
*1.1 10
448.2334.0/1839
2α
tfdkCx
cc 150=
for w/c < 0.6:
for w/c > 0.6:
( )[ ] tcwRxc ⋅−⋅
=2.7
76.1/6.410
( )[ ]( )[ ]
tcw
cwRxc ⋅+−⋅
=/315.13.025.0/10
fib
Model Code
( ) WTcRkkkTx COtOACCtcec ⋅⋅⋅+⋅⋅⋅⋅= −− 61, 102)(
2ε
Parametric function library in FReET
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Andrade
( ) ( )( )⎪
⎩
⎪⎨
⎧
+>+≤<−−
≤=
ααα
corrii
corriiiicorri
ii
idTtidTtTTtid
Ttdtd
116.0/0116.0/116.0)(
Results
of the degradation analysis
–
probability distribution function
used for the stochastic nonlinear FE analysis
Chaining of the models:
1. Depassivation
time
2. Steel Corrosion
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Summary
and
Conclusions
Combination of efficient methods:
• virtual testing (nonlinear FE analysis)
• reliability assessment (stochastic evaluation)
• degradation models
(life cycle analysis)
Evaluation
of existing
structures (reliability, probability of failure) –
relative
comparison
Life-cycle
analysis
–
degradation
+ retrofitting
Traces
evolution
of structural
reliability
in time
Design for durability
(Performance Based
Design)
Mean service life
Sevice life density
TimeFailure probability
Target service life
Distribution ofS(t)
S(t)
R(t)
R,SPf
Pf
Distribution of R(t)
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Precast prestressed
bridge girder AASHTO Type IV
damaged by hydrogen induced SCC (Stress Corrosion Cracking)
Illustrative example:
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• 26 prestressing
strands
• 2D plane stress with variable thickness
• about 3000 elements and 4500 nodes
• continuous loading (cov
= 0.0 and 0.2)
•
nonlinear solution using Newton-
Rhapson
algorithm
Illustrative example:
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Material properties
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Correlation matrix
upper right triangle = prescribed, lower left triangle = generated for 40 realizations)
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Deterministic and stochastic analysis
Several alternatives calculated:
• virgin state
• 2 strands ruptured
• 6 strands ruptured
• bond renewed
Typical
crack
pattern
at
ultimate
load
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Load-deflection
diagrams
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Failure
probability
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Reliability
index
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Thank you for your attention
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