Extreme Value Distribution Estimation Method for Nonlinear Seismic Response of Bridge Structures

To study the extreme value distribution (EVD) of nonlinear seismic response of bridges subjected to near-fault impulse ground motion and accurately estimates the dynamic reliability of bridges at small failure probability level, an effective method is proposed and validated. Considering the nonlinearity of bridge structures and the uncertainty of ground motions, the random parameters of near-fault impulse ground motion and structure are sampled by Latin hypercube sampling (LHS). The required number of seismic samples is determined by the relative error between the mean square value of simulated high-frequency ground motion and the exact value. Using synthetic near-fault impulse ground motions as seismic excitation, the structural nonlinear dynamic equation is solved by time history analysis, and the structural nonlinear seismic response extreme value samples are obtained. Then, the improved maximum entropy principle with fraction moment is adopted to obtain the EVD of bridges. The accuracy and efficiency of the proposed method are verified by a single degree freedom system and a three-story shear frame structure in comparison with the Monte Carlo simulation. Results indicate that the proposed method can not only effectively simulate the EVD of dynamic response of bridge under the double uncertainties influence of structure and ground motion, but also accurately estimate the tail distribution of the extreme value of nonlinear seismic response of bridge structure, with a balanced between efficiency and calculation accuracy. This method provides an effective way for evaluating the non-linear dynamic reliability of bridge structures.