Equivalent linear method with complex frequency for response analyses of the ground subject to fling-step displacements

The equivalent linear (EL) method is one of the most commonly used methods for seismic ground response analyses in engineering practice. However, it cannot be used to directly calculate the displacement response of the ground subject to fling-step displacements because these are characterized by non-zero final values and ordinary Fourier transform with real frequency breaks down. This article shows that this difficulty can be overcome by introducing a complex frequency in the equivalent linear method. The technique of using complex frequency was used in existing studies for analyses of undamped structures and is known as the exponential window method (EWM). In essence, the same approach is effective for the analysis of fling-step displacement. Herein, why this works for fling-step displacements is described and an application to a vertical array record which captured near-fault fling-step displacements is shown. The reasonable agreement between the observed and synthetic time histories, both for acceleration and displacement, illustrates the applicability of the method to the response analyses of the ground subject to fling-step displacements.

Automated summary

The equivalent linear (EL) method, commonly used for seismic ground response analyses, is not directly applicable to calculate displacement response of the ground subject to fling-step displacements. This article introduces the use of complex frequency in the EL method to overcome this limitation and shows its effectiveness in analyzing fling-step displacements. The reasonable agreement between observed and synthetic time histories of acceleration and displacement demonstrates the applicability of the method for response analyses of ground subject to fling-step displacements.