Physically-driven GE-GDEE and its application to stochastic seismic response and dynamic reliability analyses of practical engineering structures

Abstract

Stochastic seismic response and dynamic reliability analyses of large-scale high-rise building structures under earthquake actions is one of the most challenging problems in engineering field. Both the randomness from structural parameters and external excitations have significant effects on the stochastic dynamic behaviors of structures with complex nonlinearity. In such a case, it is difficult to evaluate the first-passage reliability, especially the small probability of failure under rare events. A feasible approach for this problem is developed via the physically-driven globally-evolving-based generalized density evolution equation (GE-GDEE), where the double randomness is characterized in a one- or two-dimensional partial differential equation (PDE) governing the probability density function (PDF). In the developed unified formalism of GE-GDEE, an absorbing boundary process (ABP) of the critical response quantity indicating structural failure or not can be constructed. Its transient PDF satisfies the GE-GDEE, a two-dimensional PDE. The effective drift coefficient in the GE-GDEE essentially represents the physically driving force for the evolution of transient PDF, and can be identified via the observed data given by some representative deterministic dynamic analyses. Then, the GE-GDEE with the determined effective drift coefficient can be solved numerically to capture the transient PDF of the ABP, and obtain the time-variant reliability by integration further. In the present paper, the stochastic seismic response and dynamic reliability analyses of a 24-story reinforced concrete (RC) shear wall structure with nearly 280,000 degrees of freedom are performed. There are fourteen concrete material parameters considered as probabilistically dependent random variables characterized by vine copulas. The ground motion is modelled by the non-stationary Clough-Penzien spectrum. The time-variant reliability curves of the structure under different thresholds are given, which cannot be achieved by the general Monte Carlo simulation (MCS) due to the limitation of computational cost.

Keywords: high-rise reinforced concrete (RC) shear wall structure; seismic reliability analysis; Globally-evolving-based generalized density evolution equation (GE-GDEE); Physically-driven; Rare event.