Nonlinear finite element reliability analysis of concrete

The nonlinear behavior of concrete is complex and is governed by a variety of parameters. As a result, there exist a number of constitutive models that try to predict concrete behavior beyond the linear elastic limit. A mature concrete model must not only remain operational under proportional and nonproportional loadings, but it should be capable of capturing the response behavior in the prepeak and postpeak regimes. Based on such a model, which resorts to an isotropic-hardening description of the prepeak behavior and to a fracture energy-based isotropic-softening description of the postpeak regime, the present paper develops a finite element reliability formulation of nonlinear stochastic concrete under both proportional and nonproportional loadings. The formulation accounts for randomness in loading and spatial variability of concrete properties. The proposed reliability formulation with focus on the prepeak regime uses analytical expressions to compute response gradients. In this manner, efficiency and accuracy concerns associated with perturbation methods are avoided. A computer code is developed for the application of the proposed method to concrete structures. Numerical results are also presented to demonstrate the capability of the computer code to evaluate the reliability of a nondeterministic concrete panel with respect to excessive plastic deformation under both proportional and nonproportional loadings.