Spectral Representation-Based Multidimensional Nonstationary Ground Motion Model for Seismic Reliability Analysis of Frame Structures

A framework for a multidimensional nonstationary ground motion model based on spectral representation theory is proposed in this paper. The multidimensional nonstationary ground motion model is built from a local target to fit the multidimensional response spectrum. A four-stage modulation function takes into account the multidimensional intensity correlation and the modified Clough–Penzien (C-P) power spectrum with parameter correlation, which represent the two main aspects, the modulation function and the power spectrum of constructing the multidimensional nonstationary ground motion model. A multidimensional response spectrum constructed according to the standardizing response spectrum is used as the fitting target response spectrum. Samples of random ground motion for random seismic response and dynamic reliability study are finally obtained. The random seismic responses are then combined with the probability density evolution method (PDEM) to carry out the seismic reliability analysis of a randomly base-excited moment-resisting frame structure. In the numerical analysis, the nonlinear seismic responses and reliability of a 10-story reinforced concrete frame structure are carefully investigated in accordance with the Egyptian seismic code. As a result, the effectiveness of the proposed method is fully demonstrated.