FUZZY PATTERN CLASSIFICATION OF STRONG GROUND MOTION RECORDS

Classification of earthquake strong ground motion (SGM) records is performed using fuzzy pattern recognition to exploit knowledge in the data that is utilised in a genetic algorithm (GA) search and scaling program. SGM records are historically treated as “fingerprints” of certain event magnitude and mechanism of faulting systems recorded at different distances on different soil types. Therefore, databases of SGM records of today present data of complex nature in high dimensions (many of the dimensions—or SGM parameters in time and frequency domain—are presently available from different archives). In this study, simple ground motion parameters were used but were combined and scaled nonlinearly such that the physical properties of the data could be preserved while reducing its dimensionality. The processed data was then analysed using fuzzy c-means (FCM) clustering method to explore the possibility of meaningfully representing earthquake SGM data in lower dimensions through finding subsets of mathematically similar vectors in a benchmark database. This representation can be used in practical applications and has a direct influence on the processes of synthesising ground motion records, identifying unknown ground motion parameters (e.g. soil type in this study), improving the quality of matching SGM records to design target spectra, and in rule generalisation for response. The results showed that the stochastic behaviour of earthquake ground motion records can be accurately simplified by having only a few of motion parameters. The very same parameters may also be utilised to derive unknown characteristics of the motion when the classification task on “training” records is performed carefully. The clusters are valid and stable in time and frequency domain and are meaningful even with respect to seismological features that were not included in the classification task.     

SEISMIC AMPLIFICATION AT A SOFT SOIL SITE WITH LIQUEFIABLE LAYER

It is well known that local soil conditions play a key role in the amplification of earthquake waves. In particular, a liquefiable shallow soil layer may produce a significant influence on ground motion during strong earthquakes. In this paper, the response of a liquefiable site during the 1995 Kobe earthquake is studied using vertical array records, with particular attention on the effects of nonlinear soil behaviour and liquefaction on the ground motion. Variations of the characteristics of the recorded ground motions are analysed using the spectral ratio technique, and the nonlinearity occurring in the shallow liquefied layer during earthquake is identified. A fully coupled, inelastic finite element analysis of the response of the array site is performed. The calculated stress-strain histories of soils and excess pore water pressures at different depths are presented, and their relations to the characteristics of the ground motions are addressed.     

Identification of Modal Parameters of a Multistoried RC Building Using Ambient Vibration and Strong Vibration Records of Bhuj Earthquake, 2001

Modal parameters of an instrumented multi-storied reinforced concrete building (G +9) have been studied using strong motion records of Bhuj Earthquake, 2001. The Ambient Vibration Testing (AVT) is also conducted to measure the modal parameters of the same building under ambient environmental forces. Frequency Domain Decomposition (FDD) or Peak Picking (PP) in frequency domain and Stochastic Subspace Identification (SSI) technique in time domain is used for extracting the modal parameters. The observed natural frequencies during strong motion are smaller than the ambient vibration testing. The difference in the frequencies may be caused by interaction between structure and soil due to high level of strain during strong motion earthquake. The modal pattern of first five modes obtained from strong motion records and ambient vibration records are identical.     

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.     

VERTICAL EARTHQUAKE GROUND MOTION RECORDS: AN OVERVIEW

Recent research clearly shows the importance of including the vertical component of earthquake ground motion in seismic analysis and design. In addition, pioneering studies [e.g., Elnashai and Papazoglou (1997)] have explored and documented the characteristics of available near-field vertical ground motion records. As a follow-up, this paper complements earlier studies, and investigates additional far-field records and available downhole array vertical motion records. A total of 111 free-field strong motion records (from California) and available downhole array records are employed. Compared to near-field records, far-field records generally contain more energy at longer periods. Based on the available data, response spectra are presented for near-field and far-field records respectively. The currently scarce downhole-array vertical motion records show that significant amplification may occur within the top 10-20 m soil layers. A simple one-dimensional (ID) vertical wave propagation model did not appear adequate for modelling the observed downhole array response. In using such a simplified model, very high viscous damping in the range of 15-25% was needed to match the recorded downhole vertical response, even for small tremors. Additional data and research are required [Beresnev et al., 2002] towards the development of a rational vertical motion site response analysis procedure.     

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.     

STRONG MOTION VERSUS WEAK MOTION: IMPLICATIONS FOR MICROZONATION STUDIES

A set of mainshock and aftershock data following the Chamoli earthquake of March 29, 1999, recorded at a single station viz. Gopeshwar, has been studied. Particularly, the utility of the use of aftershock/weak motion data for site characterisation in seismic microzonation studies is investigated. The analysis of aftershock and mainshock data indicates that the spectral shape and amplification is quite different during the main-shock and the aftershock. This, in turn, implies that the use of weak motion/aftershock records may lead to erroneous conclusions regarding the expected ground motion during a strong earthquake. Further, it has been shown that the site characteristics estimated from H/V ratios are not stable in the near field conditions, even for weak motion data.     

Influence of Ground Motion Duration on Damping Reduction Factor

This article investigates the influences of the effective ground motion duration (GMD) on damping reduction factor. The GMD are associated with 25 Chi-chi earthquake ground motion records and harmonic sine wave. The study shows that damping reduction factor decreases with the increasing of the damping ratio, and decreases with the increasing of the effective duration of the ground motion and the number of cycles of harmonic excitation. A nonlinear multiple regression analysis based on the statistical mean values of the present study is employed, and a modified damping reduction factor considering the effects of GMD is suggested.     

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.     

SEISMIC HAZARD IN GREECE BASED ON DIFFERENT STRONG GROUND MOTION PARAMETERS

The available Greek strong ground motion records to date are used in order to study the duration of strong-motion in Greece, covering magnitudes between 4.5 and 6.9 and distances from 1 km to 128 km. An attenuation relation of strong-motion duration is calculated and compared to earlier existing similar relations proposed for Greece and Japan. Furthermore, the seismic hazard for the area of Greece is assessed, using the strong-motion parameters of duration and peak ground acceleration. The results are presented in the form of a map according to which Greece is classified in four different categories of equal seismic hazard.     

THE EFFECTIVE DURATION OF EARTHQUAKE STRONG MOTION

The duration of strong ground shaking during earthquakes can play an important role in the response of foundation materials and structures, particularly when strength or stiffness degradation is encountered. A thorough seismic hazard assessment should therefore include an estimation of the expected duration of strong motion, which first requires criteria to define the part of an accelerogram considered to represent the duration of strong ground motion. Some 30 different definitions of strong motion duration are reviewed and classified into generic groups. Problems that arise with the use of these definitions for duration are highlighted. A new definition of duration is presented using a previously unexplored option which identifies the part of the record where the main energy is contained and constrains this strong shaking phase by absolute criteria. This new definition is shown to give consistently meaningful durations for strong earthquake accelerograms from an engineering viewpoint. The correlations between the new definition of duration and magnitude, soil conditions and distance are explored as a first step towards the development of predictive equations.     

Derivation of New Equations for Prediction of Principal Ground-Motion Parameters using M5′ Algorithm

In this study, M5′ model tree is used to develop a model for prediction of peak time-domain strong ground motion parameters. The main advantages of model trees are that can be easily developed and their formulas are simple and understandable. Selected data from Pacific Earthquake Engineering Research Center (PEER) are used to train the proposed model. Earthquake magnitude, earthquake source to site distance, average shear-wave velocity, and faulting mechanisms are used as input parameters. The developed M5′ based formulas are compared with those of well-known empirical and soft computing based models. The accuracy of the model is evaluated by statistical error parameters.     

AN ANALYTICAL RESPONSE OF CHURCH BELLS TO EARTHQUAKE EXCITATION

Occasionally there is an earthquake in the UK during which church bells are reported to have been set ringing. The motion of a medium sized church bell has been simulated and the response to earthquake records from the Parkfield earthquake of 1966 has been calculated. The response of the bells is found to depend on the mechanical properties of the bell and the tower in which it is hung. The analyses do show that for a bell to ring in an earthquake the peak ground acceleration is in the range 0.97 to 29.4 m s^?2 considerably in excess of the range indicated by the MMI VI “church and school bells ring” of 0.4 to 1.5 m s^?2. The best correlation between recognised earthquake parameters and the ringing of the bell was obtained by combining the spectral values for clapper-bell angle, obtained from the linearised set of equations, at the bells natural frequencies using the SRSS method. The values of this parameter to set the bell ringing was in the range 0.25 and 0.38 rad, compared with the actual striking angle 0.54 rad.     

Establishment of a Time-Varying Modified Kanai-Tajimi Non Stationary Stochastic Model of Seismic Records Based on the S-transform

This article investigates the time-varying characteristics of seismic records. Time-varying amplitude and energy spectrums are defined to reflect the time-frequency dependence, and a general formulation of the S-transform is introduced. The S-transform is tested with various window functions to analyse the Kobe seismic records. The results indicate that using a complex window function with properly adjusted parameters gives favorable outcomes. Analyses of three soil sites show that sites with hard soil feature seismic records with shorter stationary durations, higher frequency centers, and broader frequency bands than other soil sites. The average time-varying spectrums of the seismic records are simulated using a uniform non stationary stochastic model and a time-varying modified non stationary Kanai-Tajimi stochastic model. Empirical formulas are established for the time-varying spectrums of the earthquake records from these sites by nonlinearly fitting stochastic models to the record data. The values of the time-varying spectrum factors for different earthquake intensities and sites agreeing with the Chinese Seismic Code are obtained. Based on these analyses and observations, we propose using the solutions to the stochastic models to simulate non stationary ground motions.     

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.     

Dynamic Stability and Design of C-Bent Columns

Symmetrically reinforced bridge columns with a horizontal cantilever in one direction, called C-bent columns, tend to deform predominantly in the direction of applied moment when subject to strong earthquake shaking. For this reason, the strength in the direction of applied moment is generally increased in design. This article describes the use of inelastic dynamic time history analyses with a suite of ground motion records to quantify the amount of strength increase required to minimize likely peak and permanent displacement demands. It is shown that the strength should be increased by approximately 2.3 times the applied moment in design.     

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.     

Attenuation Relationships for Iran

The purpose of this study is to derive the attenuation relationships for PGA, PGV, and EPA parameters for areas within the seismic zones of Zagros, Alborz and Central Iran with rock and soil substructures. In order to do so, at first the available scientific data including the methods used for deriving attenuation relationships and the parameters involved have been gathered. Afterwards, all the efforts have been focused on gathering a thorough catalogue of earthquakes occurred in Iran. In this regard, a majority of the available catalogs in Iran have been gathered and corrected through different methods and finally a set of 89 earthquake events including 307 earthquake records with reliable data was chosen.

Since in order to derive the attenuation relationships it is essential to extract the parameters from the acceleration records, a great effort was placed on gathering the earthquake acceleration records of Iran. This resulted in building a database of a majority of the earthquake records up to the year of 2004. Afterwards, correction methods applicable to earthquakes records of Iran considering the type of machines used and the ground type were examined which resulted in certain guidelines for correction of earthquake acceleration record data related to Iran.

In the next step the needed parameters were extracted from the earthquake acceleration record data which were consequently divided into two seismic zones of Zagros, and Alborz and Central Iran according to tectonic conditions. After examination of the parameters and choosing the most appropriate among them, the attenuation relationships were derived for such parameters.     

A PROCEDURE FOR COMBINING VERTICAL AND HORIZONTAL SEISMIC ACTION EFFECTS

The vertical component of earthquake ground motion has generally been neglected in the earthquake-resistant design of structures. This is gradually changing due to the increase in near-source records obtained recently, coupled with field observations confirming the possible destructive effect of high vertical vibrations.

In this paper, simple procedures are suggested for assessing the significance of vertical ground motion, indicating when it should be included in the determination of seismic actions on buildings. Proposals are made for the calculation of elastic and inelastic vertical periods of vibration incorporating the effects of vertical and horizontal motion amplitude and the cross-coupling between the two vibration periods. Simplified analysis may then be used to evaluate realistic vertical forces by employing the vertical period of vibration with pertinent spectra without resorting to inelastic dynamic analysis.

Finally, a procedure is suggested for combining vertical and horizontal seismic action effects which accounts for the likelihood of coincidence, or otherwise, of peak response in the two directions.     

SEGMENTAL CROSS-SPECTRUM AS A NEW TECHNIQUE IN SITE RESPONSE ESTIMATION USING SPECTRAL RATIO ANALYSIS

Different aspects of spectral analysis for site response evaluation are investigated in this study. The segmental cross-spectrum is proposed in spectral analysis of earthquake ground motions. The performance of segmental cross-spectrum in contrast with the conventional methods is investigated through the mathematical modelling, numerical analysis and application to earthquake data recorded at Chiba and Shinfuji downhole arrays in Japan. In analysis of earthquake data, the soil amplification function is identified using both uphole/downhole (U/D) and H/V spectral ratios. The advantage of seg-mental cross-spectrum is assessed by comparing identified amplification functions using different spectral methods and theoretical soil response. The reliability of site response estimations obtained by H/V spectral ratio using segmental cross- and Fourier spectra is also examined by means of cross-validation with the U/D spectral ratio of earthquake motion and theoretical soil response. Furthermore, the application of segmental cross-spectrum in nonlinear soil response is examined by comparing the amplification function of weak and strong motions for both methods. The results validate the advantage of segmental cross-spectrum in both linear and nonlinear soil response, particularly, when it used with H/V technique.