Calculation of free field response spectrum from bed rock response spectrum directly for horizontally-layered site using equivalent linear method

A stable relationship between the peak ground velocity (PGV) and the 5%-damped maximum pseudo-spectral velocity (maxPSV) is presented based on analysis of horizontal records of PEER NGA project as well as those strong motion records of Wenchuan M8.0 Earthquake (2008) and the M9.0 Earthquake near the East Coast of Honshu, Japan. The validity and the applicability of this relationship are inspected using near-source records. This relationship is validated by comparison with the former work. A new approach to calculate the free field response spectrum directly from the bed rock response spectrum at a horizontal layered site is presented using the following iterative procedure firstly, using the standard equivalent linear method model and the assumed strain level at the center of each layer, the transfer functions are determined for a unit input specified at the bed rock. Secondly, treating the earthquake motions as a stationary stochastic process with power spectral density (PSD) function which is converted from the bed rock response spectrum, the PSD functions of every layer are calculated by the transfer functions. Finally, the equivalent strain of every layer, which is used to get a new shear modulus and damping to determine new transfer function, is obtained by converting the PSD functions to response spectra, evaluating the PGV from the results, and calculating strain using the relationship between the shear strain and the particle velocity of homogeneous medium. The applicability and the validity of the proposed approach are demonstrated by comparing the results with those of other methods for the same project site, as well as with the response spectra of the down-hole array records in Japan.