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