The objective of this research is to develop a new probabilistic framework to facilitate reliability-based analysis and design of reinforced concrete (RC) buildings against progressive collapse. In this study, a two-scale numerical model is developed to investigate the probabilistic collapse behavior of RC buildings subjected to local structural damage. In this model, a set of coarse-scale cohesive elements is used to model the failure behavior of potential damage zones (PDZ) in various RC structural members. The constitutive properties of the cohesive elements and their probability distributions are determined from detailed stochastic finite element simulations of the PDZs by taking into account the uncertainties in various material properties. The two-scale model is validated both experimentally and numerically for different types of structural subassemblages. With this two-scale model, the nonlinear dynamic analysis is applied to study the collapse behavior of a 2D 30-story RC frame structure and a 3D 10-story RC building subjected to sudden column removal. The results of the present probabilistic analysis are discussed in comparison with the existing deterministic approach, which reveals the importance of the probabilistic method for analysis of progressive collapse. To further improve the computational efficiency of the proposed probabilistic method for reliability-based design optimization against progressive collapse, a linear elastic cohesive model inspired by the concept of energetic equivalence is developed based on the two-scale model. In this simplified method, the damage status of the PDZ is determined by comparing the elastic energy stored in the cohesive element with the actual energy dissipation capacity of the PDZ. This linear elastic cohesive model is combined with a sequential analysis method to identify different possible failure paths that could lead to collapse initiation. This energetic-equivalent model is applied to analyze the collapse initiation risk of a prototype RC building. The results are compared with those obtained by using the nonlinear dynamic analysis. It is shown that the simplified model is far more efficient than the conventional nonlinear dynamic analysis, and it yields a reasonable upper bound of the collapse probability. Finally, this energetic-equivalent cohesive model is incorporated into a general optimization method for the optimum retrofitting of RC buildings to achieve a target collapse risk.
University of Minnesota Ph.D. dissertation. October 2015. Major: Civil Engineering. Advisor: Jia-Liang Le. 1 computer file (PDF); xi, 152 pages.
Reliability-Based Analysis and Design of Reinforced Concrete Buildings against Progressive Collapse.
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