Stochastic nonlinear dynamic analysis and system reliability evaluation of RC structures involving spatial variation under stochastic ground motions

Dynamic analysis and system reliability evaluation are crucial in the design of seismic-resilient reinforced concrete (RC) structures. Uncertainties in earthquake ground motions (EGM) and the spatial variation of heterogeneous concrete must be thoroughly considered. However, implementing these analyses poses significant challenges due to the inherent complexity and high computational costs associated with stochastic nonlinear dynamic analysis and the quantification of concrete's spatial variation through random field theory. To address these issues, we propose a novel methodology for the stochastic dynamic analysis and system reliability evaluation of RC structures involving spatial variation under stochastic ground motions. In the methodology, a two-scale random field model developed within the framework of stochastic damage mechanics is adopted to capture the coupling effects of the nonlinearity and the spatial variation of concrete. Additionally, a physical-based stochastic ground motion model is utilized to represent the randomness of EGM. Furthermore, the probability density evolution method is employed to derive probabilistic information (statistical moments, and probability density function (PDF), etc.) of dynamic responses, and the system reliability is evaluated by the physical synthesis method. A well-designed five-story RC frame structure is analyzed to demonstrate the efficacy of the proposed methodology and to investigate the influence of concrete's spatial variation and randomness of EGM on structural responses. The results indicate that the proposed methodology can effectively obtain the probabilistic information of stochastic responses and system reliability, and the concrete's spatial variation has a non-negligible impact on the structural responses and system reliability.