Computational structural reliability - A major challenge and opportunity for concrete and other quasibrittle structures

An overview of several recent advances in reliability of quasibrittle structures, identifying the main challenges and pointing out opportunities for further progress, is presented. The paramount importance of reliability analysis is obvious if one notes that the load factors and understrength (capacity reduction) factors, still essentially empirical and physically poorly understood, are far larger than the typical errors of modern computer analysis of structures. An effect of particular interest for structural reliability is the transition from quasi-plastic to brittle response with increasing structure size and the effect of structure type and geometry (or brittleness). To simulate this effect in the sense of extreme value statistics, a hierarchical model of nano-scale interatomic bonds is proposed, simulating one representative volume element (RVE) of the heterogenous material. A chain-of-RVEs is used to model structures larger than one RVE size and the number of RVEs in the chain is related to structure size (as well as geometry). The model shows that the distribution of structural strength exhibits, at increasing size (or brittleness), a gradual transition from Gaussian distribution (except in far-out tails) to Weibull distribution. The fact that the distribution of interatomic bond strength must be governed by Maxwell-Boltzmann distribution of atomic energies and that the activation energy barriers are modified by applied stress leads to a physical proof that perfectly brittle failures must follow Weibull distribution. It also reveals a new physical meaning of Weibull modulus-the number of dominant bonds that must fail simultaneously to cause an RVE to fail. Observing that, for Weibull distribution of typical variance, the point of failure probability such as 10 ^-6 (a value tolerable in design) is about twice as far from the mean than it is for Gaussian distribution of the same mean and variance, one must conclude that the safety factor cannot be size-independent (as in current codes) but must be approximately doubled as the structure size changes from very small to very large. A way to capture it through reliability indices and through understrength factors applied to computational results is suggested. The brittleness factor, which needs to be made size dependent (contrary to current design codes), the material randomness factor, and the model error factor (both covertly implied by code provisions), need to be used as random variates in multi-variate Freudenthal-type reliability integral. At the same time, the size effect hidden in excessive self-weight factors currently imposed by codes has to be eliminated. The objective is to supplant realistic reliability estimates on deterministic computational mechanics. The paper concludes with examples of probabilistic structural analysis of some major structural disasters.