Reliable/reliability computing for concrete structures: Methodology and software tools

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 2/18 2/25

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… 2/18 3/25

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… 2/18 4/25

5. Deterministic computational model 2/18 5/25

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) 2/18 6/25

7. Artificial neural network Modeling of processes in brain (1943 - McCulloch-Pitts Perceptron) Various fields of technical practice Neural network type – Multi-layer perceptron: - set of neurons arrangedin several layers - all neurons in one layer are connected with all neurons of the following layer Output from 1 neuron: 2/18 7/25

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 pairsinput - outputin training set; – required output value ofk-thoutputneuron ati-thinput; – real output value (at same input). 2/18 8/25

9. Scheme of inverse analysis Structural response Material model parameters Stochastic calculation (LHS) – training set for calibration of synaptic weights and biases 2/18 9/25

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 2/18 10/25

11. Stochastic model of structure For calculation of a real structure, second at stochastic level Table of basic random variables + correlation matrix 2/18 11/25

12. LHS: Step 1 - simulation Huntington & Lyrintzis (1998) • Mean value: accurately • Stand. deviation: significant improvement 2/18 14/25

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 simulation 2/18 15/25

14. LHS: Step 2 – imposing statistical correlation variable simulation 2/18 16/25

15. Sensitivity analysis INPUT INPUT OUTPUT OUTPUT x1,1 q1,1 R1 p1 … … … … … … … … … … … … x1,N q1,N R, N pN • 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) 17/25 2/18

16. Reliability analysis • Simplified – • as constrained by extremally small • number of simulations (10-100)! • Cornell safety index • Curve fitting • FORM, importance sampling • response surface… 2/18 18/25

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 2/18 22/25

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 2/18 19/25

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 2/18 20/25

20. Software tools: SARA Studio Probabilistic software FReET http://www.freet.cz + Software for nonlinear fracture mechanics analysis ATENA 2/18 21/25

21. FREET • 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 (simpleproblems) • Numerical (indirect) using user-defined DLL function preparedpractically in..any programming language (C++, Fortran, Delphi, etc.) • General interface to third-parties software using user-defined *.BAT or *.EXE http://www.freet.cz 2/18 23/25

22. Software tools: SARA Studio 2/18 24/25

23. Designed FRC facade panels • glass fibre-reinforced cement based composite • dimensions 2050×1050×13.5 mm • vacuum-treated laboratoryexperiment 10/18

24. Test of FRC facade panel deflectometer 11/18

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 4/18

26. Experiment – summary Materiálové parametry Load-deflection diagrams –reference specimens Load-deflection diagrams – degraded specimens 6/18

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 8/18

28. Synthesis of experimental results 9/18

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 12/18

30. Stochastic model – introduction • Latin hypercube sampling; simulated annealing; ATENA/FREET/SARA • Correlation matrix of basic random variables for reference panel (R) and fordegraded panel (D): 13/18

31. Stochastic model – summary Random l-d curves –reference panel Random l-d curves – panel after degradation 14/18

32. Statistical analysis Ultimate load –reference panel Ultimate load – panel after degradation 15/18

33. Statistical and sensitivity analysis Results of statistical analysis: Results of sensitivity analysis: 16/18

34. Theoretical failure probabilities 17/18

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 2/18 25/25