Seismic spatial effects for long-span bridges, using the pseudo excitation method

Seismic analysis of long-span bridges subjected to multiple ground excitations is very important. The conventional response spectrum method that has been widely used in earthquake engineering neglects the spatial effects of ground motion, and so may lead to incorrect results. The random vibration approach has been widely regarded as a good alternative, and many scholars have worked hard to develop new seismic analysis methodology based on the MIMO (multi-input-multi-output) random differential equations of motion. An efficient method, known as the pseudo excitation method (PEM), for solving the high-degree stochastic differential equations with multiple excitations is established and presented in this paper. It includes wave passage effects, incoherence effects and the cross-correlation terms between the participating modes and between the excitations. It has been successfully used in the three dimensional analysis of a long-span cable-stayed bridge with thousands of degrees of freedom and dozens of supports, to give numerical results which are compared with those computed by the response spectrum and time history methods. These computations show that the seismic spatial effects, and most particularly the wave passage effect, are very important in evaluating the safety of long-span bridges.