Correlations Between Frequency Content Indicators of Strong Ground Motions and PGV

The frequency content of ground motions seems to be one of the most important parameters to explain the structural damage experienced during worldwide strong earthquakes. The frequency content of ground motions can be characterized by various stochastic and/or deterministic indicators: the frequency bandwidth indicator ? (Cartwright & Longuet-Higgins) related to the power spectral density function and, respectively, the control (corner) period T_c of the structural response spectra or the mean period T_M . Peak ground velocity (PGV) and the ratio PGA/PGV can be used as either damage potential parameters or frequency content indicators. A comparative analysis of stochastic and deterministic frequency content indicators and of PGV is applied to a set of 30 strong ground motion records having peak ground acceleration (PGA) from 0.2–0.8 g and recorded on 4 continents during the last 70 years.     

Estimation of Strong Ground Motions in Southwest Western Australia with a Combined Green's Function and Stochastic Approach

As only a very limited number of earthquake strong ground motion records are available in southwest Western Australia (SWWA), it is difficult to derive a reliable and unbiased strong ground motion attenuation model based on these data. To overcome this, in this study a combined approach is used to simulate ground motions. First, the stochastic approach is used to simulate ground motion time histories at various epicentral distances from small earthquake events. Then, the Green's function method, with the stochastically simulated time histories as input, is used to generate large event ground motion time histories. Comparing the Fourier spectra of the simulated motions with the recorded motions of a ML6.2 event in Cadoux in June 1979 and a ML5.5 event in Meckering in January 1990, provides good evidence in support of this method. This approach is then used to simulate a series of ground motion time histories from earthquakes of varying magnitudes and distances. From the regression analyses of these simulated data, the attenuation relations of peak ground acceleration (PGA), peak ground velocity (PGV), and response spectrum of ground motions on rock site in SWWA are derived.     

A PROCEDURE FOR ESTIMATING INPUT ENERGY SPECTRA FOR SEISMIC DESIGN

In this paper, the damage potential of an earthquake ground motion is evaluated in terms of the total power of the acceleration of the ground motion. By assuming an appropriate spectral shape for the input energy spectrum, and using the well-known Parseval theorem for evaluating the total power of a random signal, the peak amplification factor for the equivalent input energy velocity spectrum can be determined. It is shown that the peak amplification factor for the input energy spectrum depends on the peak-ground-acceleration to peak-ground-velocity ratio and duration of the strong motion phase of the ground motion. Values for the equivalent input energy velocity amplification factor vary from about 2 to 10 for most of the recorded ground motions used in this study. Although a considerable scatter of data is observed in this study, the peak amplification factor predicted by the Fourier amplitude spectrum of the ground acceleration provides a fairly good estimate of the mean value of the peak input energy compared to that determined from inelastic dynamic time history analyses, particularly for systems with high damping and low lateral strength. The peak amplification factor derived in this paper provides a more consistent approach for estimation of seismic demand when compared to an earlier empirical expression used for the formulation of duration-dependent inelastic seismic design spectra, even though only a slight difference in the required lateral strength results from the use of the new formula.     

AN EVALUATION OF THE STRONG GROUND MOTION RECORDED DURING THE MAY 1, 2003 BINGÖL TURKEY,EARTHQUAKE

An important record of ground motion from a M6.4 earthquake occurring on May 1, 2003, at epicentral and fault distances of about 12 and 9 km, respectively, was obtained at a station near the city of Bingöl, Turkey. The maximum peak ground values of 0.55 g and 36 cm/s are among the largest ground-motion amplitudes recorded in Turkey. From simulations and comparisons with ground motions from other earthquakes of comparable magnitude, we conclude that the ground motion over a range of frequencies is unusually high. Site response may be responsible for the elevated ground motion, as suggested from analysis of numerous aftershock recordings from the same station. The mainshock motions have some interesting seismological features, including ramps between the P-and S-wave that are probably due to near- and intermediate-field elastic motions and strong polarisation oriented at about 39 degrees to the fault (and therefore not in the fault-normal direction). Simulations of motions from an extended rupture explain these features. The N10E component shows a high-amplitude spectral acceleration at a period of 0.15 seconds resulting in a site specific design spectrum that significantly overestimates the actual strength and displacement demands of the record. The pulse signal in the N10E component affects the inelastic spectral displacement and increases the inelastic displacement demand with respect to elastic demand for very long periods.     

YIELDING OSCILLATOR UNDER TRIANGULAR GROUND ACCELERATION PULSE

An analytical solution is presented for the response of a bilinear inelastic simple oscillator to a symmetric triangular ground acceleration pulse. This type of motion is typical of near-fault recordings generated by source-directivity effects that may generate severe damage. Explicit closed-form expressions are derived for: (i) the inelastic response of the oscillator during the rising and decaying phases of the excitation as well as the ensuing free oscillations; (ii) the time of structural yielding; (iii) the time of peak response; (iv) the associated ductility demand. It is shown that when the duration of the pulse is long relative to the elastic period of the structure and its amplitude is of the same order as the yielding seismic coefficient, serious damage may occur if significant ductility cannot be supplied. The effect of post-yielding structural stiffness on ductility demand is also examined. Contrary to presently-used numerical algorithms, the proposed analytical solution allows many key response parameters to be evaluated in closed-form expressions and insight to be gained on the'response of inelastic structures to such motions. The model is evaluated against numerical results from actual near-field recorded motions. Illustrative examples are also presented.     

Empirical Correlations of Frequency-Content Parameters of Ground Motions with Other Intensity Measures

Empirical correlations between the frequency-content parameters of earthquake ground motions and amplitude-, cumulative-, and duration-based intensity measures (IMs) are examined in this study. Three commonly used scalar frequency-content parameters are considered, namely the mean period (T_m), the average spectral period (T_avg), and the smoothed spectral predominant period (T₀). It is found that the frequency-content parameters have weakly negative correlations with high-frequency IMs such as peak ground acceleration (PGA) and spectral accelerations (SAs) at periods smaller than 0.3 s, low-to-moderate positive correlations with peak ground velocity (PGV) and SA within a period range of 0.5 s–10 s, negligible correlations with cumulative-based IMs, and weakly positive correlations (in the vicinity of 0.1–0.3) with significant durations. Simple piecewise parametric equations are proposed to fit the empirical correlations of T_m, T_avg, and T₀ with SA over the entire period range. The presented correlation results and parametric models enable the frequency-content parameters to be easily used in various applications such as ground-motion selection and vector-based probabilistic seismic hazard analysis.     

NONLINEAR SHAKE TABLE IDENTIFICATION AND CONTROL FOR NEAR-FIELD EARTHQUAKE TESTING

The primary focus of a structural shake table system is the accurate reproduction of acceleration records for testing. However, many systems deliver variable and less than optimal performance, particularly when reproducing large near-field seismic events that require extreme table performance. Improved identification and control methods are developed for large hydraulic servo-actuated shake table systems that can exhibit unacceptable tracking response for large, near-field seismic testing. The research is presented in the context of a 5-tonne shake table facility at the University of Canterbury that is of typical design. The system is identified using a frequency response approach that accounts for the actual magnitudes and frequencies of motion encountered in seismic testing. The models and methods developed are experimentally verified and the impact of different feedback variables such as acceleration, velocity and displacement are examined.

The methods show that shake table control in testing large near-field seismic events is often a trade off between accurate tracking and nonlinear velocity saturation of the hydraulic valves that can result in severe acceleration spikes. Control methods are developed to improve performance and include both acceleration and displacement feedback to reduce the acceleration spikes, and record modification, where the reference signal is modified to conform to the shake table's operational parameters. Results show record modification gives exact tracking for near-field ground motions, and optimal system response for reference signals with velocity components greater then the system capabilities. Overall, the research presents a methodology for simple effective identification, modelling, diagnosis and control of structural shake table systems that can be readily generalised and applied to any similar facility.     

Influence of Time Step of Ground Motions on Site Effect and Structural Response Analyses for Long-Duration Earthquakes

Long-duration ground motions may be down-sampled to speed up the computational process. However, using ground motions with large time step (Δt) would inevitably bring in numerical errors. The influence of Δt on the site effect and structural response analyses was quantitatively examined in this study. The results show that the nonlinear site response method is more sensitive to a change of Δt than the equivalent-linear method. For the structural analysis, the impact of Δt is highly dependent on the magnitude of damage parameters. Thus, using input motions with Δt as 0.005 s is recommended for structures subjected to strong shakings.     

SEISMIC HAZARD ASSESSMENT IN FLORENCE CITY ITALY

A seismic hazard analysis of Florence city was performed in the frame of a project concerning the dynamic behaviour of cable-stayed bridges. Both a probabilistic approach and a methodology based on the use of a local macroseismic catalogue were applied. A local catalogue was expressly compiled for this purpose, to collect the macroseismic intensities actually observed at the site as a result of past earthquakes. This sort of catalogue is an independent tool to verify the assumptions of the probabilistic approach (seismic zoning, earthquake recurrence relation, attenuation model), though it can supply results in terms of macroseismic intensity only and reflects the effective seismic history at the site, without taking into account any variability. The Cornell' methodology was used to assess probabilistic hazard in terms of macroseismic intensity, peak ground acceleration, peak ground velocity, and pseudovelocity uniform response spectra. The local catalogue points out level VII of the Mercalli-Cancani-Sieberg scale (MCS) as the maximum intensity historically observed in Florence. The probabilistic approach leads to the consideration of intensity VIII MCS as the maximum credible for the city. The probabilistic analysis in terms of ground motion was performed using attenuation relations estimated for alluvium sites, since the geology of Florence area is represented by fluvial and lacustrine deposits of various thickness. Peak ground acceleration values with 90% non exceedence probability in 50 and 500 years are respectively 145 and 219 cm/s's for a shallow alluvium site, and 95 and 157 cm/s's for a deep alluvium site; the corresponding peak ground velocity values for sites located on alluvium are 6.41 and 11.76 cm/s. Uniform response spectra are provided for shallow and deep alluvium sites, according to frequency-dependent attenuation relations estimated from strong Italian earthquakes.     

Maximum Possible Ground Motion for Linear Structures

This article develops a method to generate ground motion time histories that maximize the response of a given linearly elastic structure. The root mean square (RMS) level of the input power spectral density (PSD) is used as a strong motion parameter. It is related to seismological data that is readily available. An empirical relation to estimate RMS value of the PSD from peak ground acceleration, magnitude, rupture distance, and shear wave velocity is derived from world-wide strong motion data. The ground motion is obtained by solving the inverse problem such that the structural response is maximized under the constraint of fixed value of RMS level of the input PSD enforced using a Lagrange multiplier. The proposed methodology is illustrated for a single-degree of freedom system, a six storey building and an earthen dam. It is shown that the critical PSD obtained in all the cases is a narrow band process resulting in stochastic resonance and not a Dirac-delta function with the entire energy of the system concentrated at its natural frequency. Moreover, the critical excitation samples generated using this critical PSD resembles actual earthquake acceleration time histories.     

Floor Spectra of Inelastic RC Frame Buildings Considering Ground Motion Characteristics

A range of reinforced concrete frame buildings with different levels of inelasticity as well as periods of vibration is analyzed to study the floor response. The derived floor acceleration response spectra are normalized by peak ground acceleration, peak floor acceleration, and ground response spectrum. The normalization with respect to ground response spectrum leads to the lowest coefficients of variation. Based on this observation as well as previous studies, an amplification function is proposed that can be used to develop design floor spectra from the ground motion spectrum, considering the building’s dynamic characteristics and level of inelasticity.     

A Fast and Efficient Simulation of the Far-Fault and Near-Fault Earthquake Ground Motions Associated with the June 17 and 21, 2000, Earthquakes in South Iceland

The two M_w 6.5 earthquakes on June 17 and 21, 2000, respectively, in the populated South Iceland Seismic Zone (SISZ) significantly augmented the Icelandic database of strong ground motions, and several strong velocity pulses were recorded at near-fault sites. The strong motions are interpreted via the Specific Barrier Model (SBM) and a mathematical model of near-fault velocity pulses. The data indicates self-similar source scaling and significantly greater attenuation of seismic waves than in other interplate regions. Through inversion of the data a new attenuation function for the SISZ has been adopted, which results in unbiased simulations. For the first time, the characteristics of the recorded near-fault pulses have been identified and compared to the worldwide database of such records. The SBM and the near-fault pulse model combine naturally in a fast and efficient synthesis of realistic, broad-band strong ground motions in the far-fault and near-fault region. Such simulations are showcased for the June 2000 earthquakes and indicate that the modeling approach adopted in this study is an effective tool for the estimation of realistic earthquake ground motions in the SISZ.     

SIGNIFICANT GROUND MOTION PARAMETERS FOR EVALUATION OF THE SEISMIC PERFORMANCE OF SLENDER MASONRY TOWERS

The evaluation of seismic risk of masonry monuments requires to study the combination of vulnerability and hazard. In the present work, the global seismic response of slender masonry towers has been studied by means of a specific 3-D fibre model. Accounting for the particular behaviour of such structures, the hazard should also be described by a suitable measure of intensity of the seismic action. A variety of different parameters relating with the ground acceleration recordings have been investigated for what regards their correlation with the damage indicators of the model. The combination of the peak ground velocity of the horizontal component and of the significant duration is an effective measure of intensity. This measure can be improved by considering the accord of the frequency content of the ground motion with the dynamical characteristics of the tower. Since in some cases the effect of the vertical component proved to be important, a further improvement can be obtained by taking into account also the vertical ground motion intensity.     

THE USE OF SIMPLE PULSES TO ESTIMATE INELASTIC RESPONSE SPECTRA

Inelastic response spectra are estimated for elasto-plastic SDOF systems subjected to strong earthquake ground motions by applying the strength reduction factors determined for a simple pulse to the elastic response spectrum of the ground motion. This approach relies upon similarities in the strength reduction factors computed for earthquake ground motions and for short duration pulses. The accuracy of the estimated inelastic spectra obtained using 24 simple pulse waveforms is assessed in order to identify subsets of just several pulse waveforms that are suited for this purpose. Based upon the ground motions and pulses investigated, this approach appears to be equally applicable to short and long duration ground motions and those having near-fault forward directivity features.     

Influence of Uncertain Source Parameters on Strong Ground Motion Simulation with the Empirical Green's Function Method

A combined stochastic and Green's function approach was developed to simulate strong ground motions in Southwest Western Australia (SWWA) in a previous study. Although it was demonstrated that adopting the source parameters derived from other regions yielded reasonable simulation of ground motions in SWWA as compared with a few available strong motion records, the effect of source parameter variations on simulated ground motions was not known. This article performs a statistical study of the effects of random fluctuations of the seismic source parameters on simulated strong ground motions. The uncertain source parameters, i.e., stress drop ratio, rupture velocity, and rise time corresponding to the empirical source models are assumed to be the respective mean value of the parameter and normally distributed with an assumed coefficient of variation. The Rosenblueth's point estimate method [Rosenblueth, 1981 Rosenblueth, E. 1981. Two-point estimates in probabilities. Applied Mathematical Modelling, 5: 329–335. [Crossref], [Web of Science ®] , [Google Scholar]] is used to calculate the statistics of the simulate ground motion parameters corresponding to different magnitudes and epicentral distances. The accuracy of the Rosenblueth's point estimate method in estimating the mean and standard deviation of ground motion PGA, PGV, and response spectrum is proven by simulating the ground motions from an ML6.0 and epicentral distance 100 km event with both the Rosenblueth's point estimate method and the Monte Carlo simulation method. A sensitivity analysis is preformed to investigate the effect of random fluctuations of each source parameters on strong ground motion simulation. A coefficient of variation model for ground motion parameters is developed based on the simulated data as a function of the variations of the three source parameters and earthquake magnitude, which can be used in probabilistic predictions of earthquake ground motions with uncertain source parameters.     

A NON-PARAMETRIC APPROACH TO ATTENUATION RELATIONS

Abstract

A non-parametric multidimensional regression method is proposed for the prediction of seismic ground motion parameters. The main features which distinguish the method from standard regression procedures are: (1) The relationship between the input and output variables is not selected a priori by a prediction law, (2) an arbitrary number of input variables Can be taken into account, provided that an appropriate data base exists, and (3) the computational procedure is very simple. The results can be easily updated when new information becomes available. The method has been applied for the derivation of attenuation relations by using a combination of databases compiled by other researchers. In the majority of the cases discussed in this paper, the method was used for the prediction of horizontal peak ground acceleration as a function of magnitude and distance. In some cases, ground conditions were also taken into account. Some results on the attenuation relations of peak ground velocity and displacement, as well as Arias intensity, are also presented.     

FRICTION DAMPED STEEL MOMENT-RESISTING FRAMES SUBJECTED TO LONG-DISTANCE EARTHQUAKES: INFLUENCE OF WELD FRACTURES

It has been generally accepted that steel moment-resisting frames behave in a ductile manner under seismic excitations. However, during the 1994 Northridge earthquake in California, weld fractures at the beam-to-column connections occurred in many steel buildings. Such brittle failures obviously precluded the traditional ductile-behaviour assumption and had a significant effect on the responses of steel moment-resisting frames. In this paper, the performance of a friction damping system for retrofitting steel moment-resisting frames was investigated under long-distance earthquakes. For this purpose, the 1985 Mexico City (SCT), the 1995 Bangkok, or the 1977 Romania ground motions, all scaled to a peak ground acceleration of 0.17 g, were considered in this study. Responses of the building under the 1940 El Centro N-S component were also included for comparison. The results of the study show that a friction damping system can reduce the seismic responses significantly. The devices can also prevent the total collapse and joint failures of the building equipped with friction dampers, while the one without dampers would collapse, even under a peak ground acceleration of only 0.17 g.     

Impact of Vertical Ground Excitation on a Bridge with Footing Uplift

Ground motions recorded in the epicentral region of an earthquake often have a strong vertical component with dominant high frequencies. Damage to bridges in near-source regions due to strong vertical ground motion has been reported. The beneficial effects of footing uplift on structural performance in form of reduction of seismic response of structural members have been confirmed in previous research. The uplift of bridge piers has been utilised in a very limited number of bridge structures, e.g., the South Rangitikei railway bridge in New Zealand. However, the near-fault seismic behaviour of bridges with footing uplift has been even less addressed. In this study shake table investigations were carried out on the response of a single-span bridge model with footing uplift subjected to simultaneous vertical and horizontal excitations. Near-fault ground motions recorded in the Canterbury earthquake sequences of 2010 and 2011 were used. The experimental results show that inclusion of vertical ground motions produce stronger axial force in the pier and larger bending moment in the deck. Concurrent horizontal and vertical excitations may also cause more frequent footing uplift than the solely horizontal excitations.     

Study of a Ground-Motion Simulation Method using a Causality Relationship

The causality of natural ground motions is evaluated through statistical values for the phase difference. The causality is expressed in terms of the Hilbert transform relationship between the real and imaginary parts of the Fourier transform of the ground motion. We find that ground motions with a shorter duration have a higher degree of causality. Furthermore, we propose a ground-motion simulation algorithm that incorporates causality. The simulated ground motions, compatible with design response spectra, have almost the same spectrum conversion factors as those estimated from natural ground motions.     

A THEORETICAL ATTENUATION MODEL FOR EARTHQUAKE-INDUCED GROUND MOTION

A theoretical attenuation model of earthquake-induced ground motion is presented and discussed. This model is related directly to physical quantities such as source and wave motion parameters. An attenuation formula for rms acceleration of ground motion is derived and verified using acceleration data from moderate-sized earthquakes recorded in Iceland from 1986 to 1997. The source parameters and the crustal attenuation are computed uniformly for the applied earthquake data. Furthermore, attenuation formulas for peak ground acceleration are put forward.