1. Reliability assessment of concrete structures Software package under development: -Project GA 1O3/02/1030 (Czech Grand Agency) -International project SARA BUT, Faculty of Civil Engineering, Brno Cervenka Consulting, Prague BOKU and TU Vienna

2. SARA studio ATENA FREET Modular concept ATENA Interface

3. Nonlinear fracture mechanics – FEM software ATENA (Červenka Consulting) SBETA material model for concrete damage: 2D failure criterion Tension: –nonlinear fracture mechanics, exponential softening –smeared cracks: fictitious crack approach, crack band theory –two crack models: fixed and rotated cracks Compression: –non-linear behaviour including softening (crushing) –compressive strength reduction after crack propagation Shear: –shear strength reduction of cracked concrete Solution methods (equations of equilibrium): –Newton Raphson, Arc-length.

4. Failure criterion for concrete in 2D plane stress state

5. Crack Band Model Independence of FEM mesh (localization limiter) (Bažant and Oh, 1983).

6. Uncertainties modelling - random variables by PDF, described by mean value, variance and other statistical parameters. Statistical simulation - random input parameters are generated according to their PDF using LHS. Generated realizations of random parameters are then used as inputs for ATENA computational model. The complex nonlinear solution is performed and results (response) are saved. Previous two steps are repeated N-times (N is the number of simulations used). Statistical assessment - the resulting set of structural responses is statistically evaluated: Mean value, variance, coefficient of skewness, histogram, empirical cumulative probability density function of structural response, etc. Probabilistic module - FREET implementation into ATENA

10. Practical example - PORR bridge in Vienna SARA studio

11. Longitudinal section Ground plan Cross section PORR bridge

13. Correlation between variables using simulated annealing upper triangle - presribed correlation matrix lower triangle - generated correlation matrix (8 samples)

14. Left -Load-deflection curves (8 samples), right - Histogram of ultimate loads (32 samples)

16. Reliability assessment (Prof. Novak and Mrs. Eichinger)