Determination of the Parameters of the Directivity Pulse Embedded in Near-Fault Ground Motions and Its Effect on Structural Response

Near-fault ground motions are affected by directivity phenomena, which produce important velocity pulses, mostly associated with the normal to the fault direction. Directivity pulses amplify the long period coherent component of the ground motions and are explicitly apparent in the velocity and the displacement time histories and the related response spectra. A number of methods are commonly used for the identification of the parameters of the velocity pulses, mainly their period and amplitude. Also, several mathematical expressions have been proposed for their mathematical representation, which vary from simple functions to more complicated wavelets. A very efficient wavelet is the one proposed by Mavroeidis and Papageorgiou (M&P), which, beyond the period and the amplitude, uses additional parameters related to the total duration and the phase shift of the pulse. In this chapter, a recently proposed new method is presented, which allows the explicit determination of the parameters of the pulse contained in pulse-like records. The M&P wavelet is used for the mathematical representation of the pulse but the proposed methodology can be easily modified to cover other types of wavelets as well. First, the period of the pulse is determined from the peak of the S _d  × S _ν product spectrum, a new concept defined as the product of the velocity and the displacement response spectra. The remaining parameters of the M&P wavelet are derived from the targeted response spectrum of the ground motion applying a relationship that is established between the Cumulative Absolute Displacement (CAD) of a wavelet and its peak spectral amplitude. The method follows a well-defined procedure that can be easily implemented in a computer code for the automatic determination of the pulse parameters of a given ground motion. In the last part of the chapter, the identified pulses, inherent in a wide set of ground motions, are used to study the effect of directivity pulses on the nonlinear response of SDOF structures. It is shown that, in a wide range of periods, the seismic behavior is dominated by the presence of the pulse, since the corresponding M&P wavelet alone can capture quite satisfactorily the nonlinear response.