Energy-based collapse assessment of concrete structures subjected to random damage evolutions

Abstract

The assessment of structural capacity against collapse is conducive to the optimal design of new structures as well as checking the safety of existing structures. However, the evaluation cannot be typically carried out by means of destructive tests on prototype or reduced scale structures. In this regard, the numerical models that adequately represent the prototype structures can be alternatively used. Specifically, both the nonlinearities and randomness as well as their coupling effect of materials need to be represented in a unified manner in structural analysis. The present paper aims at providing an effective approach to incorporate the stochastic nature of damage constitutive relationships in collapse analysis and assessment of concrete structures subjected to earthquake ground motions. Within the framework of stochastic damage mechanics, the spatial variability of concrete is represented by a two-scale stationary random fields. The concept of covariance constraint is introduced to bridge the two-scale random fields such that the scale-of-fluctuation of the random material property is satisfied at both scales. Random damage evolution induced structural collapse analysis is achieved via the nonlinear stochastic finite element method. To address the randomness propagation across scales, the probability density evolution method is employed. By exerting the absorbing boundary condition associated with an energy-based collapse criterion on the generalized probability density evolution equation, the anti-collapse reliability of concrete structures can be evaluated with fair accuracy and efficiency. Numerical investigation regarding an actual high-rise reinforced concrete frame-shear wall structure indicates that the random damage evolution of concrete dramatically affects the structural nonlinear behaviors and even leads to entirely different collapse modes. The proposed method provides a systematic treatment of both uncertainties and nonlinearities in collapse assessment of complex concrete structures.