1. 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!

2. 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
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3. Experiment
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…
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4. Experiment 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…
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5. Deterministic computational model
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6. Inverse analysis Numerical model of structure
appropriate material model
many (material) parameters
Information about
parameters:
experimental data
recommended formulas
engineering estimation
Correction of parameters:
„trial – and – error“ method
sofisticated identification methods
– artificial neural network + stochastic calculations (LHS)
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7. Artificial neural network
Modeling of processes in brain
( 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
Output from 1 neuron:
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8. Artificial neural network
active period (simulation of process)
Two phases:
adaptive period (training)
Training of network:
- training set, i.e. ordered pair [pi, yi]
Minimization of criterion:
N – 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).
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9. Scheme of inverse analysis
Structural response
Material
model
parameters
Stochastic calculation (LHS) – training set for
calibration of synaptic weights and biases
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10. Computational model of structure
The result of inverse analysis – the set of idetified computational model parameters
For calculation of a real structure, first at deterministic level
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11. Stochastic model of structure
For calculation of a real structure, second at stochastic level
Variable
Unit
Mean
value
COV [–]
PDF
Modulus of
elasticity
GPa
10.1 R
0.195
Rayleigh
7.8 D
0.199
Weibull min (3 par)
…………etc.
Table of basic random variables
+ correlation matrix 1
0.8
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12. LHS: Step 1 - simulation Huntington & Lyrintzis (1998)
Mean value: accurately
Stand. deviation: significant improvement
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13. LHS: Step 2 – imposing statistical correlation
variable
Simulated annealing: Probability to escape from local minima
Cooling - decreasing of system excitation
Boltzmann PDF, energetic analogy 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
simulation
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14. LHS: Step 2 – imposing statistical correlation
variable 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
simulation
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15. Sensitivity analysis 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) R1
x1,1 …
R, N
x1,N
OUTPUT
INPUT p1
q1,1 …
p N
q1,N
OUTPUT
INPUT
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16. Reliability analysis Simplified – as constrained by extremally small
number of simulations (10-100)!
Cornell safety index
Curve fitting
FORM, importance sampling
response surface…
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17. ATENA
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
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18. Material models for concrete: ATENA software
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
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19. Material models for concrete: ATENA software
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
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20. + Software tools: SARA Studio Probabilistic software FReET +
Software for nonlinear fracture mechanics analysis ATENA
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21. FREET http://www.freet.cz Probabilistic techniques
Crude Monte Carlo simulation
Latin Hypercube Sampling (3 types)
First Order Reliability Method (FORM)
Curve fitting
Simulated Annealing
Bayesian updating
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
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22. Software tools: SARA Studio
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23. Designed FRC facade panels
glass fibre-reinforced cement based composite
dimensions 2050×1050×13.5 mm
vacuum-treated laboratory experiment
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24. Test of FRC facade panel
deflectometer
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25. Experiment
Three point bending tests of notched specimens (40 reference, 40 degraded)
Unit
Value
Length mm
200
Height mm 40
Width mm 40
Notch depth mm 15
Span mm
180
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26. Materiálové parametry
Experiment – summary
Materiálové parametry
Load-deflection diagrams – reference specimens
Load-deflection diagrams – degraded specimens
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27. Inverse analysis
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
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28. Synthesis of experimental results
Variable
Unit
Mean
value
COV [–]
PDF
Modulus of
elasticity
GPa
10.1 R
0.195
Rayleigh
7.8 D
0.199
Weibull min (3 par)
Compressive
strength
MPa
53.5
0.250
Log-normal (2 par)
31.5
Tensile strength
6.50
Weibull min (2 par)
3.81
Fracture
energy
J/m2
816.2
0.383
Weibull max (3 par)
195.8
0.418
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29. 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
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30. Stochastic model – introduction
Latin hypercube sampling; simulated annealing; ATENA/FREET/SARA
Correlation matrix of basic random variables for reference panel (R) and for degraded panel (D): E fc ft GF
Modulus of
elasticity E 1
0.9 (R)
0.7 (R)
0.647 (R)
Compressive
strength fc
0.9 (D)
0.8 (R)
0.6 (R)
Tensile
strength ft
0.7 (D)
0.8 (D)
Fracture
energy GF
0.376 (D)
0.6 (D)
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31. Stochastic model – summary
Random l-d curves
– reference panel
Random l-d curves
– panel after degradation
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32. Statistical analysis Ultimate load – reference panel
Ultimate load – reference panel
Ultimate load – panel after degradation
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33. Spearman’s correlation coefficient:
Statistical and sensitivity analysis
Results of statistical analysis:
Results of sensitivity analysis:
Ultimate load
Mean value
[kN/m2]
COV
[%]
Reference
panel
13.23
26.5
Degraded
6.52
27.6
Parameter
Spearman’s correlation coefficient:
Reference
panel
Degraded
Modulus of
elasticity
0.82
0.73
Compressive
strength
0.79
0.85
Tensile
0.95
0.99
Fracture
energy
0.91
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34. Theoretical failure probabilities
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35. Conclusions
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
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