Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB DETERMINATION OF STATISTICAL MATERIAL PARAMETERS OF CONCRETE USING FRACTURE TEST AND INVERSE ANALYSIS BASED ON FraMePID–3PB TOOL David Lehký, Zbyněk Keršner, Drahomír Novák Brno University of Technology, Brno, Czech Republic June, 13-15 5th REC, Brno, Czech Republic, 2012

Introduction, motivation Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Introduction, motivation Motivation for material parameters determination (strengths, fracture-mechanical): - comparison of different mixtures and composites (optimal content, type of fibres, etc.) - numerical modeling of structures (deterministic and statistical level) June, 13-15 5th REC, Brno, Czech Republic, 2012

Introduction, motivation Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Introduction, motivation The knowledge of fracture/mechanical parameters is fundamental for virtual modeling of elements and structures made of concrete. Key parameter: fracture energy and its variability Other important parameters of concrete are: modulus of elasticity, tensile and compressive strength, effective crack elongation, effective fracture toughness, etc. June, 13-15 5th REC, Brno, Czech Republic, 2012

Numerical modeling – parameters Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Numerical modeling – parameters Numerical model of structure appropriate material model (e.g. 3D Nonlinear Cementitious, Microplane model, etc.) – – many material parameters Information about parameters: experimental data recommended formulas engineering estimation June, 13-15 5th REC, Brno, Czech Republic, 2012

Numerical modeling – parameters Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Numerical modeling – parameters Primary calculation: Correction of parameters: „trial–and–error“ method sophisticated identification methods – artificial neural network based inverse analysis June, 13-15 5th REC, Brno, Czech Republic, 2012

5th REC, Brno, Czech Republic, 2012 Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Fracture experiment Testing configuration : 3-point bending test of beam with central edge notch Determination of parameters: effective crack model + work-of-fracture method ANN based inverse analysis Specimen parameter [mm] Nominal value Length of specimen 400 Width of specimen 100 Height of specimen Depth of notch 33 Span 300 L-d diagram June, 13-15 5th REC, Brno, Czech Republic, 2012

Statistical parameters identification Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Statistical parameters identification Two approaches: Load-deflection “one-by-one” identification approach Material parameters are identified individually for each specimen (individual l-d diagram is used as an input of ANN). Subsequently, statistical assessment of parameters of all specimens is carried out. Direct statistical parameters identification Random response of a structure is available in form of histograms and statistical moments (set of random l-d diagrams is used as an input of ANN). Statistical parameters are direct output of inverse analysis (ANN). June, 13-15 5th REC, Brno, Czech Republic, 2012

ANN based inverse analysis – deterministic parameters Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB ANN based inverse analysis – deterministic parameters Structural response Material model parameters Stochastic calculation (LHS) – training set for calibration of synaptic weights and biases June, 13-15 5th REC, Brno, Czech Republic, 2012

ANN based inv. anal. – statistical param. (direct approach) Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB ANN based inv. anal. – statistical param. (direct approach) Structural response Material model parameters Stochastic calculation (LHS) – training set for calibration of synaptic weights and biases June, 13-15 5th REC, Brno, Czech Republic, 2012

5th REC, Brno, Czech Republic, 2012 Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB FraMePID-3PB tool Developed for fully automatic and easy to use ANN based identification using 3PB experimental data (l-d diagrams) Designed for concretes of various strength and ages (large training set with relatively high variability of material parameters) Prepared for testing of specimens with various notch depth – study of fracture process zone development and corresponding changes of fracture energy Implemented experimental data filtering June, 13-15 5th REC, Brno, Czech Republic, 2012

5th REC, Brno, Czech Republic, 2012 Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB FraMePID-3PB tool Robust ANN implemented and trained – significant time reduction compared to general identification tasks FEM computational model implemented (ATENA software) – 3D Nonlinear Cementitious 2 material model Subject of identification: – modulus of elasticity Ec – tensile strength ft – fracture energy Gf Export of identified parameters to clipboard, text file, ATENA .ccm file Direct transfer to ATENA for verification via ATENA interface (in preparation) June, 13-15 5th REC, Brno, Czech Republic, 2012

Experimental testing campaign Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Experimental testing campaign Testing of stochastic properties of various concrete types, mixtures and ages (in cooperation with BOKU, Vienna and other industrial partners). Comparison of fracture–mechanical parameters obtained from several testing configurations: – 3-point bending test – wedge splitting test – compression test Development of stochastic properties database (statistical moments, distribution functions, correlation coefficients). Results of 4 sets of different concrete types tested in 3-point bending configuration will be shown here. June, 13-15 5th REC, Brno, Czech Republic, 2012

5th REC, Brno, Czech Republic, 2012 Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB 3-point bending tests Set I (C30/37 H) 9 specimens age 91 days Set II (C25/30 B3) 9 specimens age 87 days Set III (C25/30 XC1 GK16) 9 specimens age 67 days Set IV (C20/25 XC1 GK16) 8 specimens age 66 days June, 13-15 5th REC, Brno, Czech Republic, 2012

3-point bending tests – l-d diagrams Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB 3-point bending tests – l-d diagrams June, 13-15 5th REC, Brno, Czech Republic, 2012

Statistical parameters of set I (C30/37 H) Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Statistical parameters of set I (C30/37 H) Parameter of concrete/model Effective crack model, work-of-fracture method ANN identification Identif./ exp. Mean value COV [%] Modulus of elasticity [GPa] 35.5 7.4 40.3 16.6 1.14 Tensile strength [MPa] – 5.0 14.3 Compressive strength [MPa] 58.5 8.0 Fracture energy [J/m2] 235.9 18.6 281.5 19.5 1.19 Effective crack elongation [mm] 9.5 21.9 Effective fracture toughness [MPa.m1/2] 1.489 9.9 Effective toughness [J/m2] 62.3 13.7 Volume density [kg/m3] 2341.8 0.7 June, 13-15 5th REC, Brno, Czech Republic, 2012

Statistical parameters of set II (C25/30 B3) Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Statistical parameters of set II (C25/30 B3) Parameter of concrete/model Effective crack model, work-of-fracture method ANN identification Identif./ exp. Mean value COV [%] Modulus of elasticity [GPa] 30.8 8.6 35.0 8.2 1.14 Tensile strength [MPa] – 4.1 17.2 Compressive strength [MPa] 47.3 5.4 Fracture energy [J/m2] 188.9 11.5 211.8 18.1 1.12 Effective crack elongation [mm] 12.5 23.5 Effective fracture toughness [MPa.m1/2] 1.406 8.0 Effective toughness [J/m2] 65.2 21.8 Volume density [kg/m3] 2286.2 1.5 June, 13-15 5th REC, Brno, Czech Republic, 2012

Statistical parameters of set III (C25/30 XC1 GK16) Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Statistical parameters of set III (C25/30 XC1 GK16) Parameter of concrete/model Effective crack model, work-of-fracture method ANN identification Identif./ exp. Mean value COV [%] Modulus of elasticity [GPa] 35.4 5.6 40.4 9.5 1.14 Tensile strength [MPa] – 4.2 12.1 Compressive strength [MPa] 53.4 5.2 Fracture energy [J/m2] 183.3 5.5 214.0 6.0 1.17 Effective crack elongation [mm] 12.4 22.7 Effective fracture toughness [MPa.m1/2] 1.405 9.0 Effective toughness [J/m2] 56.3 19.9 Volume density [kg/m3] 2326.9 0.9 June, 13-15 5th REC, Brno, Czech Republic, 2012

Statistical parameters of set IV (C20/25 XC1 GK16) Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Statistical parameters of set IV (C20/25 XC1 GK16) Parameter of concrete/model Effective crack model, work-of-fracture method ANN identification Identif./ exp. Mean value COV [%] Modulus of elasticity [GPa] 31.2 4.3 34.8 5.3 1.12 Tensile strength [MPa] – 3.1 15.6 Compressive strength [MPa] 39.8 5.4 Fracture energy [J/m2] 146.2 13.3 166.8 15.4 1.14 Effective crack elongation [mm] 13.0 14.3 Effective fracture toughness [MPa.m1/2] 1.131 10.6 Effective toughness [J/m2] 41.4 20.7 Volume density [kg/m3] 2292.2 0.6 June, 13-15 5th REC, Brno, Czech Republic, 2012

Comparison of parameters among all 4 sets Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Comparison of parameters among all 4 sets Effective crack model + work-of-fracture method Modulus of elasticity Ec Compressive strength fc Fracture energy Gf June, 13-15 5th REC, Brno, Czech Republic, 2012

Comparison of parameters among all 4 sets Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Comparison of parameters among all 4 sets Effective crack model + work-of-fracture method Effective fracture toughness KIce Effective toughness Gce Volume density gc June, 13-15 5th REC, Brno, Czech Republic, 2012

Comparison of parameters among all 4 sets Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Comparison of parameters among all 4 sets ANN based identification method Modulus of elasticity Ec Tensile strength ft Fracture energy Gf June, 13-15 5th REC, Brno, Czech Republic, 2012

Comparison of l-d diagrams: experiment vs. identification Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Comparison of l-d diagrams: experiment vs. identification June, 13-15 5th REC, Brno, Czech Republic, 2012

5th REC, Brno, Czech Republic, 2012 Lehký, Keršner, Novák – Determination of concrete statistics using fracture test and inv. analysis based on FraMePID-3PB Conclusions Determination of fracture/mechanical parameters values: Effective crack model + work-of-fracture method ANN based identification method FraMePID-3PB – tool for fully automatic and time-effective ANN based identification using 3PB experimental data Recommended statistical parameters for stochastic nonlinear FEM analyses of beams/structures made of tested concretes   Distrib. I (C30/37 H) II (C25/30 B3) III (C25/30 XC1 GK16) IV (C20/25 XC1 GK16) Mean COV [%] Modulus of elasticity [GPa] LN (2 par) 40 17 35 9 10 6 Tensile strength [MPa] 5.0 15 4.1 18 4.2 12 3.1 16 Fracture energy [N/m] 282 20 212 214 167 June, 13-15 5th REC, Brno, Czech Republic, 2012