Stationary earthquake motion input at bedrock is evaluated by a two-step inversion method. Firstly, the stationary power spectral density （PSD） of acceleration at the ground level is obtained by an iterative approach of equivalence of peak acceleration according to the response spectrum in the Chinese seismic code （GB 50011—2001）. Secondly, after the stiffness and damping ratio of each soil layer were calculated by the equivalent linearization technique, the stationary PSD of acceleration at the ground level was applied as the pseudo stationary inputs. By the use of the one-dimensional wave propagation function on the semi-finite shear beam, the stationary earthquake motion at bedrock under nonlinear layered ground was evaluated iteratively. It provides relatively reliable and accurate earthquake motion inputs at the bedrock for the stochastic seismic analysis of dams, tunnels and pipelines at regions for which few acceleration observation data at the ground level or bedrock are obtained, and it can also estimate the stationary dynamic response such as peak acceleration and peak shear strain under the ground as a primarily reference value for further dynamic analysis. The results show that the method is practical.
Journal of Vibration Engineering
power spectral density
earthquake motion input