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The experimental results for quasi‐brittle materials such as concrete and fibre‐reinforced concrete exhibit high variability due to the heterogeneity of their aggregates, additives and general composition. An accurate assessment of the fracture‐mechanical parameters of such materials (e.g. compressive strength fc and specific fracture energy Gf) turns out to be much more difficult and problematic than for other engineering materials. The practical design of quasi‐brittle material‐based structures requires virtual statistical approaches, simulations and probabilistic assessment procedures in order to be able to characterize the variability of these materials. A key parameter of non‐linear fracture mechanics modelling is the specific fracture energy Gf and its variability, which has been a research subject for numerous authors although we will mention only [1, 2] at this point. The aim of this contribution is the characterization of stochastic fracture‐mechanical properties of four specific, frequently used classes of concrete on the basis of a comprehensive experimental testing programme.

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A new general inverse reliability analysis approach based on artificial neural networks is proposed. An inverse reliability analysis is a problem of obtaining design parameters corresponding to a specified reliability (reliability index or theoretical failure probability). Design parameters can be deterministic or they can be associated with random variables. The aim is to generally solve not only single design parameter cases but also multiple parameter problems with given multiple reliability constraints. Inverse analysis is based on the coupling of a stochastic simulation of the Monte Carlo type (the small-sample simulation method Latin hypercube sampling) and an artificial neural network. The validity and efficiency of this approach is shown using numerical examples with single as well as multiple reliability constraints and with single as well as multiple design parameters, and with independent basic random variables as well as random variables with prescribed statistical correlations.

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