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Reliable/reliability computing for concrete structures: Methodology and software tools. D. Novak R. Pukl. Brno University of Technology Brno, Czech Republic. Cervenka Consulting, Prague, Czech Republic. + many co-workers!. Outline. - PowerPoint PPT Presentation
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D. Novak
R. Pukl
Reliable/reliability computing for concrete structures: Methodology and software tools
Brno University of Technology Brno, Czech Republic
Cervenka Consulting, Prague, Czech Republic
+ many co-workers!
Outline• A complex and systematic methodoloy for concrete
structures assessment– Experiment– Deterministic computational model development to capture
experiment– Inverse analysis – Deterministic nonlinear computational model of a structure– Stochastic model of a structure– Statistical, sensitivity and reliability analyses
• Methods and software– Uncertainties simulation– Nonlinear behaviour of concrete
• Application
2/182/25
Experiment
2/183/25
• The key part of the methodology, carefully performed and evaluated
• Material parameters of concrete: compressive strength, modulus of elasticity…
• Fracture-mechanical parameters: tensile strength, fracture energy…
• Eg. three-point bending…
Experiment
2/184/25
• The meaning of „experiment“ in a broader sense• Laboratory experiment• In-situ experiment on a real structure (a part of health monitoring)
• At elastic level only• Other parameters, eg. eigenfrequencies…
0,0
0,5
1,0
1,5
2,0
0,00 0,05 0,10 0,15 0,20deformation [mm]
forc
e [k
N]
experiment
4th modeshape (damaged state)
-1.25
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
0 10 20 30 40 50 60 70
Distance along girder [m]
Norm
alized d
ispla
cem
ent
uz [
-]
Exp.: frontExp.: centerExp.: backModel: front
Model: centerModel: back
Deterministic computational model
2/185/25
12 3
4
5
6 78
910
1 2 3 45
67 89
10
1112 131415
16
17 18
19
20 21 2223 24
25
2627
2829301 2 34 5 6
7 8 910 11 12
131415
16171819
2021
1
12
X
Y
Inverse analysis
2/186/25
Numerical model of structure
appropriate material modelmany (material) parameters
Information aboutparameters:
• experimental data• recommended formulas• engineering estimation
Correction of parameters:• „trial – and – error“ method• sofisticated identification methods
– artificial neural network + stochastic calculations (LHS)artificial neural network + stochastic calculations (LHS)
Artificial neural network
2/187/25
Modeling of processes in brain(1943 - McCulloch-Pitts Perceptron)
Various fields of technical practice
Neural network type – Multi-layer perceptron:- set of neurons arranged in several layers- all neurons in one layer are connected with all neurons of the following layer
kkk bpwfxfy
Output from 1 neuron:
Artificial neural network
2/188/25
Two phases:active period (simulation of
process)adaptive period (training)
Training of network:- training set, i.e. ordered pair [pi, yi]
Minimization of criterion:
N
i
K
kik
vik yyE
1 1
2*
2
1N – number of ordered pairs input - output in
training set; – required output value of k-th output neuron
at i-th input; – real output value (at same input).
*iky
viky
Scheme of inverse analysis
2/189/25
Stochastic calculation (LHS) – training set for calibration of synaptic weights and biases
Materialmodelparameters
Structural response
Computational model of structure
2/1810/25
• The result of inverse analysis – the set of idetified computational model parameters
• For calculation of a real structure, first at deterministic level
Stochastic model of structure
2/1811/25
Variable UnitMean value
COV [–] PDF
Modulus of elasticity
GPa10.1 R 0.195 Rayleigh
7.8 D 0.199 Weibull min (3 par)
…………etc.
1 0 0.8
1 0
1
Table of basic random variables
+ correlation matrix
For calculation of a real structure, second at stochastic level
LHS: Step 1 - simulation
2/1814/25
b
Sim
a
N x f x dx
Huntington & Lyrintzis (1998)
• Mean value: accurately
• Stand. deviation: significant improvement
LHS: Step 2 – imposing statistical correlation
2/1815/25
x1 y 1 … z1
x2 y 2 … z2
x3 y 3 … z3
x4 y 4 … z4
x5 y 5 … z5
x6 y 6 … z6
x7 y 7 … z7
x8 y 8 … z8
… … … …
xNSim yNSim … zNSim
variable
sim
ula
tio
n
• Simulated annealing: Probability to escape from local minima
• Cooling - decreasing of system excitation
• Boltzmann PDF, energetic analogy
b
E
k TrP E e
LHS: Step 2 – imposing statistical correlation
2/1816/25
x1 y 1 … z1
x2 y 2 … z2
x3 y 3 … z3
x4 y 4 … z4
x5 y 5 … z5
x6 y 6 … z6
x7 y 7 … z7
x8 y 8 … z8
… … … …
xNSim yNSim … zNSim
variable
sim
ula
tio
n
Sensitivity analysis
2/1817/25
Nonparametric rank-order correlation between input variables ane output response variable• Kendall tau• Spearman
• Robust - uses only orders• Additional result of LHS simulation, no extra effort • Bigger correlation coefficient = high sensitivity• Relative measure of sensitivity (-1, 1)
R1x1,1
……
……
……
R, Nx1,N
OUTPUTINPUT
p1q1,1
……
……
……
p Nq1,N
OUTPUTINPUT
Nj,pqττ jjii ,,2,1,
11
61 1
2
nnn
dr
n
ii
s
Reliability analysis
2/1818/25
• Simplified – as constrained by extremally small number of simulations (10-100)!• Cornell safety index • Curve fitting• FORM, importance sampling
response surface…
ATENA
2/1822/25
• Well-balanced approach for practical applications of advanced FEM in civil engineering
• Numerical core – state-of-art background• User friendly Graphical user environment
visualization + interaction
Material models for concrete: ATENA software
2/1819/25
Numerical core – advanced nonlinear material models
concrete• damage based models• SBETA model• fracture-plastic model• microplane M4 (Bažant)
steel• multi-linear uniaxial law• von Mises
cc1
c2f
cf
tf
te f
ce fcfcf
tf
b iax ia l fa ilu re su rface e ffec tiv e 1 D s tre ss
eq
Material models for concrete: ATENA software
2/1820/25
Numerical core – advanced nonlinear material models
concrete in tension• tensile cracks• post-peak behavior• smeared crack approach • crack band method• fracture energy• fixed or rotated cracks• crack localization• size-effect is captured
Software tools: SARA Studio
2/1821/25
+
Probabilistic software FReEThttp://www.freet.cz
Software for nonlinear fracture mechanics analysis ATENA
FREET
2/1823/25
Response/Limit state function• Closed form (direct) using implemented Equation Editor (simple problems)• Numerical (indirect) using user-defined DLL function prepared practically in ..any programming language (C++, Fortran, Delphi, etc.)• General interface to third-parties software using user-defined *.BAT or *.EXE
Probabilistic techniques• Crude Monte Carlo simulation• Latin Hypercube Sampling (3 types)• First Order Reliability Method (FORM)• Curve fitting• Simulated Annealing• Bayesian updating
http://www.freet.cz
Software tools: SARA Studio
2/1824/25
Designed FRC facade panels
• glass fibre-reinforced cement based composite
• dimensions 2050×1050×13.5 mm• vacuum-treated laboratory
experiment
10/18
Test of FRC facade panel
deflectometer
TEST T3Va/I
0
0.5
1
1.5
2
2.5
3
0 2 4 6 8 10 12
deflection [mm]
load
[kN
/m2]
11/18
180mmSpan15mmNotch depth40mmWidth
40mmHeight200mmLength
ValueUnit
Experiment
Three point bending tests of notched specimens (40 reference, 40 degraded)
4/18
Materiálové parametryExperiment – summary
Load-deflection diagrams – reference specimens
Load-deflection diagrams – degraded specimens
6/18
Inverse analysis
0.0
0.5
1.0
1.5
2.0
0.0 0.1 0.2 0.3 0.4 0.5deflection [mm]
load
[k
N]
experimentsimulation
Based on coupling of nonlinear fracture mechanics FEM modelling (ATENA), probabilistic stratified simulation for training neural network (FREET) and artificial neural network (DLLNET):
Scheme of numerical model of three point bending test
8/18
Synthesis of experimental results
Variable UnitMean value
COV [–] PDF
Modulus of elasticity
GPa10.1 R 0.195 Rayleigh
7.8 D 0.199 Weibull min (3 par)
Compressivestrength
MPa53.5 R 0.250 Log-normal (2 par)
31.5 D 0.250 Log-normal (2 par)
Tensile strength MPa6.50 R 0.250 Weibull min (2 par)
3.81 D 0.250 Weibull min (2 par)
Fractureenergy
J/m2
816.2 R 0.383 Weibull max (3 par)
195.8 D 0.418 Log-normal (2 par)
9/18
Nonlinear numerical model
ATENA 3D:• smeared cracks
(Crack Band Model)
• material model 3D Non Linear Cementitious
• continuous loading – wind intake • Newton-Raphson solution method• the loading increment step of 1 kN/m2
12/18
• Latin hypercube sampling; simulated annealing; ATENA/FREET/SARA
• Correlation matrix of basic random variables for reference panel (R) and for degraded panel (D):
Stochastic model – introduction
E fc ft GF
Modulus of elasticity E 1 0.9 (R) 0.7 (R) 0.647 (R)
Compressive strength fc
0.9 (D) 1 0.8 (R) 0.6 (R)
Tensile strength ft
0.7 (D) 0.8 (D) 1 0.9 (R)
Fractureenergy GF
0.376 (D) 0.6 (D) 0.9 (D) 1
13/18
0
5
10
15
20
0 2 4 6 8
deflection [mm]
load
[kN
/m2 ]
0
5
10
15
20
0 2 4 6 8
deflection [mm]
load
[kN
/m2 ]
Stochastic model – summary
Random l-d curves – reference panel
Random l-d curves – panel after degradation
14/18
Statistical analysis
Ultimate load – reference panel
Ultimate load – panel after degradation
15/18
Statistical and sensitivity analysis
ParameterSpearman’s correlation
coefficient:
Reference panel
Degraded panel
Modulus of elasticity
0.82 0.73
Compressive strength
0.79 0.85
Tensile strength
0.95 0.99
Fracture energy
0.95 0.91
Ultimate loadMean value
[kN/m2]COV [%]
Reference panel
13.23 26.5
Degraded panel
6.52 27.6
Results of statistical analysis: Results of sensitivity analysis:
16/18
Theoretical failure probabilities
17/18
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0 5 10 15
load [kN/m2]
pro
bab
ilit
y o
f fa
ilu
re [
–]
reference specimens
degraded specimens
Conclusions
2/1825/25
• Efficient techniques of both nonlinear analysis and stochastic simulation methods were combined bridging:• theory and praxis• reliability and nonlinear computation
• Software tools (SARA=ATENA+FREET) for the assessment of real behavior of concrete structures
• A wide range of applicability both practical and theoretical - gives an opportunity for further intensive development
• Procedure can be applied for any problem of quasibrittle modeling of concrete structures