Corner Period Research Articles

Comparison of Various Input Energy Spectra for the February 6th, 2023, Kahramanmaraş Earthquake Sequence

ABSTRACT This study aims to evaluate the success of various seismic input energy spectra equations in capturing the energy content of the ground motion records of the Türkiye earthquakes since the acceleration response spectra of some records exceeded the design spectra. Although most existing spectra had limited success, especially near the corner period, some recent equations yielded accurate results. Based on the obtained results, it is envisaged that the energy-based seismic design concept will have the maturity to be included in the next-generation seismic design codes as a reliable alternative to the current approaches.

A seismological method for estimating the long-period transition period TL in the seismic building code

Many changes have been made to the design response spectrum used in the ASCE 7 Standard in recent years. One parameter that has not been investigated or revisited since its first appearance in FEMA 450-1/2003 is the long-period transition period parameter, TL. The long-period transition period parameter was introduced and defined as the corner period that marks the transition from the constant velocity to the constant displacement segments of the design response spectrum. The long-period transition period parameter is primarily important for long-period structures such as high-rise buildings and bridges. The most current estimation of TL used in engineering design standards is loosely based on a correlation between modal magnitude Mw and TL that does not account for stress drop Δ σ or the crustal velocity in the source region β. This study aims to include both Δ σ and β in its estimation of TL. Modal magnitude is obtained from disaggregation data from the 2018 National Seismic Hazard Model (NSHM) for the conterminous United States (CONUS) and from the 2021 NSHM for Hawaii (HI). The parameter β is determined from previous literature. Then, inversion of ground motion models for Central and Eastern United States (CEUS) is used to determine Δ σ for CEUS events, and published information is used to determine Δ σ for Western United States (WUS) events and HI events. Then, the definition of the corner period is used to determine TL. The results yield a generally more conservative (or longer) estimation of TL than the estimation that is currently used in engineering design standards.

Development of elastic design response spectra with emphasis on far-source earthquakes for low to moderate seismic region

The development of design response spectra is crucial for earthquake design of structures. However, there are disagreements from the engineering community on the suitability of design values proposed by the existing design code which underestimates the long-period responses for flexible soils, typical of far-source earthquakes. This study uses soil response analysis to investigate the effect of near and far sources’ earthquakes on the response spectral acceleration of Malaysia in three seismically different regions, namely Peninsular Malaysia, Sabah and Sarawak. 1923 borehole data have been collected and analysed under 5 near and 4 far sources earthquakes, subjected to the intensity from the probabilistic seismic hazard analysis. The results show that for Peninsular Malaysia, the far-source earthquake will govern the response at a period of more than 1 s, indicating its importance for structures with long periods such as tall buildings. It is also found that the corner period TC is slightly higher than the code recommended and is dependent on the soil property, while TD is significantly higher for far-source earthquakes due to the larger magnitudes. The finding of this research shows that the Eurocode 8 supplemented by the Malaysian National Annex (MS-EN1998-1, 2017) can be used to design structures in Malaysia, with some adjustments to the longer period motion for Peninsular Malaysia. Finally, it is recommended to perform an enhanced analysis for important structures of long periods to ensure their loadings are not underestimated.

Evaluación de respuesta sísmica usando la teoría de vibraciones aleatorias en tres perfiles de suelo de Lima, Perú

Seismic response analyses are performed using a minimum number of seismic records as input motions in order to achieve a statistically strong estimation. Unfortunately, the available information recorded from the current seismic networks is still scarce regarding events with considerable magnitude. In this context, the Random Vibration Theory (RVT) arises as an alternative tool for performing site response analyses without the need of seismic records, since it only requires adequate probabilistic seismic hazard assessment.
 In this study, RVT was applied to three shear-wave velocity profiles in Lima city with distinct geomorphological origin. These profiles are characteristic for gravelly, sandy and fine deposits so the influence of each soil type in their corresponding transfer function was taken into account. In that sense, the three RVT-based normalized response spectra show good agreement with the design spectra specified in the Peruvian code, despite some amplification in the short (below 0.10 s) and long (above 0.80 s) period ranges related to noise or far-field effects. Furthermore, RVT-based response spectra for La Punta and Villa el Salvador show good agreement with the time-series based analyses from a previous study.
 In addition, spectral acceleration values surpass those specified in the Peruvian code for a range beyond the corner period. This could suggest that the soil profile characterization based on the time-averaged shear wave velocity from the upper 30 m might be insufficient to evaluate the overall seismic behavior of a soil deposit. Therefore, additional parameters that account for the deeper soil substructure might be required.

Spectral Characterization and Spatiotemporal Variability of the Background Seismic Noise in Italy

AbstractIn this study, we assess the spectral characteristics of seismic noise at the sites of the Italian Seismic Network and its spatio‐temporal variability. The evaluation of noise is crucial for the assessment of the detection capability of a seismic network. We selected a set of 233 stations, those equipped with broadband velocimeters (with corner period 40 s) and operating continuously for at least four consecutive years. The analysis was carried out in the frequency band from 0.025 to 30 Hz, in accordance with the seismic sensors bandwidth. We estimated the Power Spectral Density (PSD) of the seismic noise for fixed temporal windows and then we calculated the Probability Density Functions (PDF) at each station. Exploiting the large data set available, we have been able to: (a) describe the characteristics of the noise power at each site; (b) investigate both temporal and spatial variations of the background noise, revealing correlations of the noise levels with natural and anthropogenic noise sources; (c) propose an empirical relationship linking the “microseismic” noise (i.e., 0.12–1.2 Hz) with the geographical features of the site hosting the seismic station; (d) establish the baselines of a new seismic noise model that could be considered as a new reference for the Italian territory.

Damping reduction equation for the equivalent linear analysis of seismic isolated structures subjected to near fault ground motions

In this study, a new damping reduction equation is proposed to obtain reasonable estimates of the actual nonlinear responses of seismic isolated structures (SIS) subjected to near fault ground motions (NFGM) with forward-rupture-directivity effect, using equivalent linear analysis (ELA) procedure. For this purpose, first, a set of 29 NFGM are selected and grouped according to their site soil classification. Then, the average response spectra of the NFGM are plotted and a smoothed design response spectrum for each set of ground motions are obtained. Next, nonlinear time history analysis (NLTHA) and ELA of SIS are performed for the selected ground motions. Subsequently, the average of the isolator displacements calculated from the NLTHA are obtained for each set of NFGM considered in the analyses. Then, the damping reduction factor required to obtain an isolator displacement equal to the average isolator displacements obtained from the NLTHA of SIS is back calculated via the ELA procedure. Next, the variation of the damping reduction factor is plotted as a function of various combinations of the parameters considered in this research in dimensionless form and nonlinear regression analyses are performed to formulate the damping reduction equation. The isolator characteristic strength, post elastic period, the corner period of the response spectrum and peak ground acceleration are found to affect the damping reduction factor and hence, the displacements obtained from ELA. The proposed damping reduction equation is found to yield more reasonable estimates of the actual nonlinear responses compared to those available in the literature and design codes.

Investigating properties of vertical design spectra in Japan by applying differential evolution to KiK-net data

The vertical design spectrum plays an important role in seismic design whether of critical or ordinary structures. However, many studies focused on the vertical to horizontal response spectral ratio and less researchers investigated the properties of vertical design spectra directly. In this study, differential evolution and simulated annealing are firstly examined to determine an appropriate method to estimate the characteristic parameters of the vertical design spectra. Then, the properties of the vertical design spectra in Japan are investigated by applying differential evolution to about 10000 KiK-net seismic data. Compared with epicentral distance, the influence of earthquake magnitude is more obvious which shows up as the linear correlation between the corner period and earthquake magnitude. Moreover, we propose a loglog exponential formula which relates the corner period of vertical design spectra to that of horizontal design spectra, and the formula may be used in other regions.

An improved input energy spectrum verified by the shake table tests

SummaryInput energy is the principal component of the energy balance equation. It is beneficial to determine, through its components, how the recoverable and irrecoverable energies are distributed within the structural elements. Several equations and attenuation relations to define mass‐normalized input energy spectra exist in the literature. They are mainly proposed for elastic systems subjected to far‐fault EQs. There is a lack of experimental verification of these proposed spectra. In this paper, experimental assessment was performed to the existing spectra, and further improvements were accomplished. For this purpose, steel cantilever columns were tested on the shake table for two specific historical EQs coincidently having similar spectral acceleration values. Based on the experimental results, a three‐part mass‐normalized relative input energy spectrum was formulated including soil type, EQ (corner period, intensity, duration, spectral acceleration, and velocity), and structural behavioral characteristics (period and structural damping). The proposed input energy spectrum was experimentally calibrated and numerically validated for various EQs featuring near‐ and far‐field types. Analytical and experimental comparisons were made between the previously developed spectrum and the newly proposed one. The validation studies and the statistical evaluations exposed that the proposed spectrum yielded better agreement with the experimental and numerical results.

Empirical evaluation of peak ground velocity and displacement as a function of elastic spectral ordinates for design

SummaryIn the framework of the revision of Part 1 of Eurocode 8, this study aims at developing new empirical correlations to compute peak values of ground velocity (PGV) and displacement (PGD) as a function of elastic spectral ordinates for design. At variance with the expressions for PGV and PGD currently adopted in the Eurocode 8, based solely on the peak ground acceleration (PGA), in this paper reference is made to spectral ordinates of the short and intermediate period range, namely Ss, which is the constant acceleration spectral ordinate, and S1, which is the spectral ordinate at 1 s. On the one hand, a relationship between PGV and the product (Ss⋅S1) was found based on the regression analysis on a high‐quality strong‐motion dataset. On the other hand, the PGD was estimated by extrapolating to long periods the constant displacement branch of the elastic response spectrum, introducing a correlation between the corner period TD and S1. For this purpose, results of a long period probabilistic seismic hazard assessment study for Italy, encompassing low to high seismicity areas, were considered. Furthermore, verification of the proposed relationship against strong‐motion records was carried out, and differences justified in terms of the concept of uniform hazard spectrum.

An attempt to adapt the concept of seismic intensity to structural engineering needs

The interest for the topic dealt with was raised by the occurrence of the destructive Vrancea earthquake of 1977.03.04, when the first strong motion record of Romania was obtained at the Building Research Institute (INCERC) Bucharest. The attempt to assess the ground motion intensity on the basis of instrumental criteria of the MSK intensity scale failed, due to strongly divergent results obtained by means of alternatively using the peak ground acceleration (PGA) and peak ground velocity (PGV) criteria. This failure was due to the fact that the (inflexible) MSK criteria relied on the implicit, non-realistic, assumption that all ground motions are characterized by a velocity / acceleration corner period of 0.5 s. A flexible Spectral Intensity Assessment System (SIAS, relying on accelerographic information, was developed by the author. This makes it possible to estimate, according to needs, global intensity, frequency related intensity, intensity averaged upon a spectral band etc. Alternative basic kinematic ground motion characteristics for global intensities and for frequency related intensities were introduced. Correlation analysis was performed. Characteristic parameters were calibrated and alternative calibrations of them are discussed. Some illustrative cases and some comments and recommendations are finally presented.

The Comparative Analysis of Hydrodynamic Pressures in Cylindrical Tanks

Abstract This article presents a comparative study of the values of hydrodynamic pressure and their resultants occurred during the seismic action using P100-1/2013 technical rules and the relations defined in the papers: [1], [3], [5] and the Romanian standard [2] SR EN 1998-4 (silos, tanks and pipelines), which is implemented in Romania. Two cylindrical tanks placed in the same seismic zone have been chosen, with the same amount of storage (about 5000 m3), but of different geometries, to illustrate the influence of hydrodynamic pressures on the construction size (long and short wall behavior) as a function of ratio of the fluid height on the cylinder radius and ratio of corner period on the eigenperiod of the fluid mass. Also in the analyses, in order to evaluate the hydrodynamic convective pressure both the fundamental period of oscillation of the fluid mass and the first ten periods of oscillation were used.

Reduced Carbon Footprint with Composite Structures

The paper proposes to investigate the performances for composite structures made with fully encased steel-concrete composite columns in seismic zones in comparison with traditional solutions: concrete and steel to reduce carbon footprint. To achieve the proposed objectives a case study was developed on composite frames, with fully encased steel-concrete composite columns and steel beams. The case study included five types of structures, with two, six, eight, ten and twelve levels. The composite columns were designed with different types of steel contribution ratios: low, medium and high. The floor plan was the same for all composite frames used in the case study. The level height was also the same for all stories and composite frames. To evaluate the seismic performances on the studied composite frames were performed pushover and time history analysis, using the following parameters which control the chosen seismic zone: peak ground acceleration equal to 0.32g and the corner period equal to 1.6s. The results were compared with traditional similar structures of concrete and steel. The numerical model used in all analysis was developed at Technical University of Cluj-Napoca in 2013. The model was calibrated and validated using six experimental programs taken from the international literature on fully encased steel-concrete composite columns. The three types of structures: composite, concrete and steel are compared and the main advantages and disadvantages are presented. The main focuses of the paper include modality of reducing carbon footprint, also economical and structural improvement of composite structures in comparison with traditional ones.

Significant technical advances in broadband seismic stations in the Lesser Antilles

Abstract. In the last few years, French West Indies observatories from the Institut de Physique du Globe de Paris (IPGP), in collaboration with The UWI Seismic Research Centre (SRC, University of West Indies), have modernized the Lesser Antilles Arc seismic and deformation monitoring network. 15 new, permanent stations have been installed that strengthen and expand its detection capabilities. The global network of the IPGP-SRC consortium is now composed of 20 modernized stations, all equipped with broadband seismometers, strong motion sensors, Global Positioning System (GPS) sensors and satellite communication for real-time data transfer. To enhance the sensitivity and reduce ambient noise, special efforts were made to improve the design of the seismic vault and the original Stuttgart shielding of the broadband seismometers (240 and 120s corner period). Tests were conducted for several months, involving different types of countermeasures, to achieve the highest performance level of the seismometers. GPS data, realtime and validated seismic data (only broadband) are now available from the IPGP data centre (http://centrededonnees.ipgp.fr/index.php?&lang=EN). This upgraded network feeds the Caribbean Tsunami Warning System supported by UNESCO and establishes a monitoring tool that produces high quality data for studying subduction and volcanic processes in the Lesser Antilles arc.

Automated Detection of Long-Period Disturbances in Seismic Records; MouseTrap Code

Sudden disturbances in strong‐motion acceleration records, referred to as baseline offsets, are well known (Boore et al. , 2002; Javelaud et al. , 2011). The physical nature of this phenomenon remains unclear, although some cases are well explained by a permanent ground tilt (Graizer, 2010; Javelaud et al. , 2012). The ground tilt may be caused by near‐field source effects or a local tilt at a station produced by seismic vibrations in highly heterogeneous substrata (i.e., strong gradients of material properties at small scales). Tilts are frequently observed in volcanic areas (Wielandt and Forbriger, 1999; Wiens et al. , 2005). Delorey et al. (2008) performed an experiment showing that tilting of the instrument produces a long‐period disturbance of the characteristic shape. In these cases, the disturbances predominate on horizontal components. The disturbances can also have a purely instrumental origin (Iwan et al. , 1985; Shakal and Petersen, 2001; Boore, 2003). The latter is a more suitable explanation in cases where the disturbances are also strong on the vertical component. Similar artifacts have also been reported on different types of broadband seismometers worldwide (Zahradnik and Plesinger, 2005; Pillet and Virieux, 2007; Delorey et al. , 2008). A strong disturbance is frequently characterized by a one‐sided pulse in raw output velocity. A weaker disturbance is often masked by high‐frequency content of the velocity record. However, it can be easily visible in the integrated output of a broadband instrument (raw displacement) in which it looks like a baseline step, the duration of which is equal to the seismometer corner period (Fig. 1a). Figure 1. (a) Example of a steplike disturbance in the integrated output (raw displacement) of the Nanometrics Trillium T40 seismometer. The disturbance is well fitted by the simulated instrument response to an acceleration step of amplitude A =8.7×10−7 m·s−2, azimuth …

Bi-linear displacement response spectrum model for engineering applications in low and moderate seismicity regions

The second corner period has become a feature in the design response spectrum provisions in some major codes of practices with the general notion that the higher the value of the corner period the higher the design peak displacement demand value. Expressions recommended in the literature for determining the value of the corner period are very diverse. Ambiguities with the definition of the corner period and the manner in which its value is calculated as illustrated in the paper may well be contributors to the diversity. A generalized response spectrum model in the displacement format for providing predictions on rock sites in low and moderate seismic regions is proposed in this paper. The flat part of the spectrum of the bi-linear form defining the peak displacement limit is first constructed in accordance with functions of magnitude and distance of the earthquake (and is independent of the second corner period). Significantly, the displacement limits associated with local earthquake scenarios considered in this paper on soft rock/stiff soil sites were generally less than 100mm. The sloping part of the spectrum is then determined in accordance with the estimated second corner period value. The generic predictive capability of the model spectrum and its robustness due to the way it is constructed make the model distinctive. Importantly, the proposed model (based on 5s cut-off period limit) is suitable for applications where equivalent linearization techniques are employed to obtain approximate estimates of inelastic displacement demand in buildings structures.

High-frequency filtering of strong-motion records

The influence of noise in strong-motion records is most problematic at low and high frequencies where the signal to noise ratio is commonly low compared to that in the mid-spectrum. The impact of low-frequency noise (<1 Hz) on strong-motion intensity parameters such as ground velocities, displacements and response spectral ordinates can be dramatic and consequentially it has become standard practice to low-cut (high-pass) filter strong-motion data with corner frequencies often chosen based on the shape of Fourier amplitude spectra and the signal-to-noise ratio. It has been shown that response spectral ordinates should not be used beyond some fraction of the corner period (reciprocal of the corner frequency) of the low-cut filter. This article examines the effect of high-frequency noise (>5 Hz) on computed pseudo-absolute response spectral accelerations (PSAs). In contrast to the case of low-frequency noise our analysis shows that filtering to remove high-frequency noise is only necessary in certain situations and that PSAs can often be used up to 100 Hz even if much lower high-cut corner frequencies are required to remove the noise. This apparent contradiction can be explained by the fact that PSAs are often controlled by ground accelerations associated with much lower frequencies than the natural frequency of the oscillator because path and site attenuation (often modelled by Q and κ, respectively) have removed the highest frequencies. We demonstrate that if high-cut filters are to be used, then their corner frequencies should be selected on an individual basis, as has been done in a few recent studies.

Current empirical ground-motion prediction equations for Europe and their application to Eurocode 8

The first ground-motion prediction equation derived from European and Middle Eastern strong-motion data was published more than 30years ago; since then strong-motion networks and the resulting databank of accelerograms in the region have expanded signifi- cantly. Many equations for the prediction of peak ground-motion parameters and response spectral ordinates have been published in recent years both for the entire Euro-Mediter- ranean and Middle Eastern region as well as for individual countries within this region. Comparisons among empirical ground-motion models for these parameters, developed using large regional datasets, do not support the hypothesis of there being significant differences in earthquakeground-motionsfromoneareaofcrustalseismicitytoanother.However,thereare certain regions within Europe—affected by different tectonic regimes—for which the exist- ing pan-European equations may not be applicable. The most recent European equations make it possible to now implement overdue modifications to the presentation of seismic design actions in Eurocode 8 that allow an improved approximation to the target uniform hazard spectrum (UHS). Using these recent equations, this study outlines a new approach via which an approximation to the UHS may be constructed using hazard maps calculated for peak ground velocity and the corner period TD in addition to the maps for peak ground acceleration that underpin the current stipulations of Eurocode 8.

Using τc to estimate magnitude for earthquake early warning and effects of near‐field terms

This paper analyzes strong motion records of 24 large earthquakes to investigate the relationship between τc (the period parameter of the first motion) and moment magnitude. The records of some of the large‐magnitude events very close to the source include large near‐field terms. Therefore, if we include the data with large near‐field terms, we may overestimate the final size of the magnitude. We identified records with large near‐field terms and did not include these data in processing the records to compute τc for each event. Our analysis shows that the value of τc is between the earthquake corner period and the period determined by the record duration τ0. If the magnitude is less than 6, τc closely approximates the corner period, whereas τc for larger earthquakes depends on the rupture process and location of asperity. τc for large earthquakes provides a lower bound on the event magnitude and approaches the corner period if a longer record is used. We also propose a method to classify the records with and without large near‐field terms. If the peak displacement amplitude for the first 3 s (Pd3) exceeds 1 cm and τc exceeds 2 s, the record is more likely to include large near‐field terms. For the purpose of quick onsite warnings, stations observing large near‐field terms provide valuable information. Large near‐field terms can be observed only if the magnitude is large and the epicentral distance is small. Therefore, if the displacement exceeds a threshold (e.g., Pd = 0.5 cm), the ground motion at the site would likely become very large. This criterion will help to issue warnings to the blind zone, which is the region where there is insufficient time to issue a warning before the strong shaking arrives.

Distant-earthquake simulations considering source rupture propagation: refining the seismic hazard of Hong Kong

Deterministic and probabilistic seismic hazard analyses should be complementary, in the sense that probabilistic analysis may be used to identify the controlling deterministic design-level earthquake events, and more sophisticated models of these events may then be developed to account for uncertainties that could not have been included directly in the probabilistic analysis. De-aggregation of the tentative uniform hazard spectra (UHS) in Hong Kong resulting from a probabilistic seismic hazard assessment (PSHA) indicates that strong and major distant earthquakes, rather than moderate local earthquakes, make the largest contribution to the seismic hazard level within the natural-period range longer than 0.3 s. Ground-motion simulations of controlling events located 90 and 340 km from Hong Kong, taking into account uncertainties in the rupture process, reveal that the tentative UHS resulting from the PSHA may have significantly underestimated the mid-to-long period components. This is attributed mainly to the adoption of double-corner source-spectrum models in the attenuation relationships employed in the PSHA. The results of the simulations indicate clearly that rupture directivity and rupture velocity can significantly affect the characteristics of ground motions, even from such distant earthquakes. The rupture-directivity effects have profound implications in elongating the second corner period where the constant velocity intersects the constant displacement, thus increasing the associated displacement demand. However, demands for acceleration and velocity are found to be not sensitive to the presence of the directivity pulses. Ground pulses resulting from forward rupture directivity of distant earthquakes have longer predominant periods than the usual near-fault directivity pulses. These long-period pulses may have profound implications for metropolises, such as Hong Kong and others in Southeast Asia, having large concentration of high-rise buildings. Copyright © 2005 John Wiley & Sons, Ltd.

Estimation of Seismic Demands on Isolators Based on Nonlinear Analysis

A procedure based on rigorous nonlinear analysis that estimates the deformation and force of an isolator due to strong ground motion is presented. The procedure offers an alternative to the iterative equivalent-linear methods used by current U.S. building codes. The governing equation is reduced to a form such that the median normalized deformation of the system due to an ensemble of ground motions with a given corner period Td is found to depend on only two parameters: the natural period, defined from the postyield stiffness, and the normalized strength, or strength normalized by peak ground velocity. The dispersion of normalized deformation for an ensemble of ground motions is shown to be small, implying that the median normalized deformation is a meaningful estimate of response. The simple trends shown by the median normalized deformation led to the development of suitable design equations for isolator deformation. These design equations reflect a 13% increase when the excitation includes two lateral components of ground motion instead of just one component. For comparison, deformations estimated by the equivalent-linear method are unconservative by up to 50% compared to those found from the more accurate nonlinear spectrum, and building codes include at most a 4.4% increase for a second component.