An empirical approach of accounting for the amplification effects induced by near-fault directivity

How to incorporate near-fault directivity effect into the ground motion prediction equations (GMPEs) is an active research topic in recent years. Many studies demonstrated that the directivity could amplify the spectral accelerations (S_a) in a range close to the pulse period (T_p). This study intends to propose a new empirical narrowband model for including such effects. The ratio of the S_a from the original ground motions to the S_a from the residual ground motions is employed to quantify this amplification effects, under the assumption that the S_a from the residual ground motions are well predicted by the non-directivity-included GMPEs. Differing from previous models that suggested the amplified S_a arise in a smooth bell-shaped pattern, the proposed model assumes that the peak amplification occurs as a plateau in the intermediate range. This plateau, having a constant ordinate of about 3.31, starts and ends at the period of 0.75 and 1.09 times the T_p, respectively; while in the other ranges the amplification decreases away from the two sides of this plateau. To further simplify the proposed model, two additional controlling periods are derived to determine the period range with significant amplification effects. Then the proposed model is expressed in the form of a piecewise function comprising five line segments. Finally, it is concluded that the non-directivity-included GMPEs, when multiplying the proposed model, can reasonably approximate the S_a of the original ground motions in the statistical sense within the T_p-related range.