Influence of high-pass filtering of near-fault earthquake record on the responses of base-isolated building

Highlights

• As the cutting frequency closes to pulse frequency, the pulse identification results of near-fault records may be changed.

• The inelastic response is more significantly affected by the high-pass filter, in terms of larger variation and dispersion.

• The responses of the superstructure and isolated floor are both sensitive to the high-pass filter, but slightly different.

• The cutting frequencies of 0.2 and 0.1 Hz were suggested for short-to-mid and mid-to-long period pulse records respectively.

Abstract

Filtering is one of the critical steps of earthquake ground motion processing before its application to engineering practice, and high-pass filtering is particularly important due to rich contents of low frequency in ground motion signals. In particular, the impulsive properties of the ground motion recorded in near-fault zones are susceptible to the high-pass filtering, and thus selecting a reasonable filtering method becomes a critical issue that determines the reliability of the structural analysis results. This study investigates how the high-pass filtering of pulse-like ground motions affect the subsequent responses of long-period base-isolated building. A set of near-fault ground motions were selected and classified into short-to-mid and mid-to-long period groups, with 2 s being the threshold, and they were subjected to filter with varied parameters. The filtering induced variations of elastic response spectra, inelastic response spectra, and the impulsive property identification were analyzed. The highest cutting frequency of 0.20 Hz and 0.10 Hz of the high-pass filter were recommended for short-to-mid and mid-to-long period pulse records, respectively, while the impulse properties and spectral properties of engineering interest were not disturbed considerably. The ground motions were input to a high-rise base-isolated building, and the responses were computed from different filtering settings and compared, which further verified the suggested high-pass filtering method for pulse-like ground motions.

Introduction

As the most common way currently used, ground motions are recorded by accelerometers mounted on the ground surface. During recording, the valid signal is inevitably accompanied by both the low-frequency and high-frequency noise. Low-frequency noise usually results from the transducer hysteresis [1], instrument and background noise, ground rotation and tilting [2], lateral movements of the film [3], and the procedure of analog-to-digital conversion particularly for analog signals [3,4]. Hence, extracting the right part from a recorded signal becomes an essential procedure for both digital signal and analog signal before the application of a signal to engineering practice. On the other hand, high-frequency noise might be caused by the neighboring environmental disturbances [5], the lower resolution of the analog-to-digital converter, as well as the noise magnifications of instrument correction [6]. Filtering of high-frequency noise is usually unnecessary, as only a minor effect may be observed in the high-frequency range of the pseudo-spectral acceleration [5]. Earthquake ground motion is a wide-band signal, and it is usually hard to decompose the recorded signal into pure ground motion and noise. That means filtering processing will unavoidably bring error into the structural analysis results, and thus how to select a reasonable filter is a critical issue in the processing of ground motion signals.

Depending on the recording instruments and methods, various filtering method has been adopted among different seismology institutes, and researchers have proposed continuously new approaches. For instance, within the manual of a strong motion processing software released by USGS (United States Geological Survey) [6], a high-pass filtering cutting frequency between 0.2–0.5 Hz was suggested. CSMIP (California Strong Motion Instrumentation Program) suggested the frequency between 0.05–0.07 Hz, on the basis of corner period equaling to 15 s for correcting errors due to instrument noise [7]. PRISM (Processing and Review Interface for Strong-Motion Data) [8] adopted the method initially proposed by Massa et al. [9], which suggested the cutting frequency depending on the earthquake magnitude. According to the recommendation, a lower cutting frequency should be defined for larger earthquakes, in which long-period contents are dominant in ground motions. Jafar [10] proposed a method for determining the cutting frequency, which was related to the duration of ground motion. In source spectrum models developed by seismologists, either the single-corner source spectrum model [11,12] or the double-corner source spectrum model [[13], [14], [15], [16], [17]], the determination of cutting frequency was based on the earthquake parameters such as magnitude, stress drop, and shear wave velocity. For digitally recorded signal, the high-pass filter cutting frequency is usually located near the intersection of the f² and 1/f trend lines (f: the frequency at Fourier amplitude spectrum) and finally determined by the signal-to-noise ratio method, combined with the digital noise spectrum model proposed by Lee and Trifunac [18].

Compared to the far-fault ground motions, those recorded in near-fault zones are characterized by rich contents of low-frequency, and very high velocity can be recorded on the ground surface, and some of them are identified as pulse-like signals. Based on the current understanding, the impulsive property can result from either the directivity effect or the fling step effect [[19], [20], [21], [22]], and the pulse-like ground motions are supposed to impose considerable energy into civil structures in a short time interval and thus cause severe damage to engineering structures [[22], [23], [24], [25], [26]]. The damaging effect is particularly severe for long-period structures, such as long-span bridges or base-isolated buildings [[27], [28], [29], [30]]. The pulse period T_p and the corresponding ratio of the pulse period to the structural period play essential roles in the structural responses [[23], [24], [25]]. It should be fully considered during the seismic design of structures located in near-fault zones. The cutting frequencies of high-pass filters currently used by institutes may be very close to the periods of pulse-like records obtained in earthquake events. For example, the signal processing scheme first developed at the California Institute of Technology adopted band-pass processing with the lower and higher cutting frequency being 0.20 Hz and 25 Hz, respectively [31]; PRISM adopted 0.10 Hz and 0.30 Hz as high-pass cutting frequencies for earthquakes with local magnitude ML ≥ 5.5 and 5.5 > ML ≥ 3.5, respectively [8]. Even though the pulse period is correlated with magnitude [21,32,33], an earthquake of a specified magnitude may produce ground motions with pulse periods ranging widely. The periods of the pulse-like records currently recorded in the PEER (Pacific Earthquake Engineering Research Center) strong motion database can be as small as less than 1 s or as large as over 13 s. Inappropriate processing may weaken the pulse effect and thus cause an unexpected error in the numerical results compared to the “true” response. Structural engineers are interested in understanding the effect of filtering of ground motions on particularly the long-period base-isolated buildings and apply the filtering during the processing of the ground motions in their numerical analysis practice so that the structural response estimation can be achieved accurately as much as possible. Therefore, it is essential to clarify the effect of high-pass filtering on the properties of pulse records, as well as on the structural responses.

Several pieces of literature regarding the filtering of pulse-like ground motions have served valuable guidelines [27,28,34,35]. Mccallen et al. [27] compared the responses of a bridge subjected to broadband and band-pass near-fault ground motions with permanent displacement, and they emphasized that the band-pass processing of near-fault ground motion might result in an underestimation of bridge force. Yang et al. [28] filtered the Landers record at Lucerne Valley Station by fourth-order high-pass acausal Butterworth filter with a cutting frequency of 0.08 Hz and analyzed the dynamic response of a seismically isolated bridge with and without fault crossing considerations. They also concluded that the response of the long-span bridge was significantly underestimated when the high-pass filtered ground motion was used and suggested that caution should be utilized to the high-pass filtering process of near-fault ground motions. Burks and Baker [34] estimated the effect of a fling on the collapse capacity of SDOF systems, and they concluded that filtering at a frequency approaching the structural period might lead to an unconservative estimate. Hamidi et al. [35] also investigated the effect of a fling on the responses of reinforced concrete structures, including the idealized SDOF structures and two multi-story building structures. The results showed that the ductility demands might or might not increase after the permanent displacement was removed from the ground motions, depending on the ground motion utilized. In these research works, even though only a few numbers of ground motions were utilized, the results brought insights into the effect of pulse, particularly the fling step pulse, of the near-fault ground motions on structural responses.

The forward directivity has a different mechanism with the fling step and thus imposes a different impact on structures. During engineering practice, how to select a reasonable cutting frequency of high-pass filter for forward directivity pulse-like ground motions is of great interest. Therefore, this study aims to reveal the high-pass filter effect of this type of ground motion. In the following sections, a set of ground motions is selected from recent earthquake events and applied to the high-pass filter with different cutting frequencies. The effect of filtering on the impulsive property identification and the pulse periods are investigated. The influence on the elastic and inelastic response spectra is examined, and the reasonable cutting frequencies are recommended for pulse-like records according to their pulse periods. The ground motions are further input to a high-rise base-isolated building, and time history analysis is carried out to verify the effect of the high-pass filter on responses of functional engineering structures.