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 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 2/25 2/18

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

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

Deterministic computational model 5/25 2/18

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

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 arranged in several layers - all neurons in one layer are connected with all neurons of the following layer Output from 1 neuron: 7/25 2/18

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). 2/18 8/25

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

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

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 2/18 11/25

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

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 2/18 15/25

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 16/25 2/18

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 17/25 2/18

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

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

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

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

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

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 http://www.freet.cz 23/25 2/18

Software tools: SARA Studio 24/25 2/18

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 11/18

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

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

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

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 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

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) 13/18

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 – reference panel Ultimate load – panel after degradation 15/18

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 16/18

Theoretical failure probabilities 17/18

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