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.     

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.     

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.     

An Improved Algorithm for Selecting Ground Motions to Match a Conditional Spectrum

This paper describes an algorithm to efficiently select ground motions from a database while matching a target mean, variance, and correlations of response spectral values at a range of periods. The approach improves an earlier algorithm by Jayaram et al. [2011]. Key steps in the process are to screen a ground motion database for suitable motions, statistically simulate response spectra from a target distribution, find motions whose spectra match each statistically simulated response spectrum, and then perform an optimization to further improve the consistency of the selected motions with the target distribution. These steps are discussed in detail, and the computational expense of the algorithm is evaluated. A brief example selection exercise is performed, to illustrate the type of results that can be obtained. Source code for the algorithm has been provided, along with metadata for several popular databases of recorded and simulated ground motions, which should facilitate a variety of exploratory and research studies.     

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.     

Application of Wavelet Transforms on Characterization of Inelastic Displacement Ratio Spectra for Pulse-Like Ground Motions

In this article, a simple and effective wavelet-based procedure is implemented for describing principle features of a special class of motions, pulse-like ground motions, on inelastic displacement ratio spectra (IDRS). The computed spectra supply a simple estimation of maximum inelastic displacement demand from the corresponding elastic one. The results of analysis in this work provide a suitable platform for quantification of pulse effects into IDRS and highlight the need to better understanding of this effect on demand estimation. It is concluded that the pulse has a significant influence on IDRS of pulse-like ground motions for systems with high ductility level.     

SITE AMPLIFICATION FACTOR IN ANCHORAGE,ALASKA BASED ON LONG PERIOD MICROTREMORS

Long period microtremors with periods ranging from 0.5 to 10 seconds were measured in the Anchorage metropolitan area. Two horizontal components of motion were recorded at 81 sites uniformly distributed throughout the basin with spatial resolution of about 2 km. Recording at each site was done for 300 seconds with a sampling rate of 20 Hz. Repeated measurements were performed at a bedrock reference site simultaneously with the measurements in the field. The measurements were completed in six days. In addition, multiple recordings were obtained concurrently at the reference bedrock site and a sediment site. Based on these measurements the Fourier spectra were calculated for each of the site. Ground motion amplification is determined in terms of spectral ratio of horizontal spectral amplitudes at a sediment site and the reference bedrock site. Mean spectral ratio contours were evaluated for different period bands. The results show that for period band 3 to 5 seconds the spectral ratio contours agree well with the ground failure susceptiblity map of Anchorage.     

Evaluation of 2D Seismic Site Response due to Hill-Cavity Interaction Using Boundary Element Technique

This paper deals with the evaluation of two-dimensional site-effects due to the seismic interaction between hills with various configurations and underground cavities. The time-domain boundary element method is used to evaluate the site-effects of hill-cavity interaction subjected to vertically propagating in-plane SV and P waves. The presence of an underground cavity and the hill topography are expected to induce significant effects on the surface ground motion. To further examine the contribution of the amplification ratio of the hill-cavity system, a fairly simple approach, which can compute the response spectra of the hill’s surface motion above a cavity based on the real input motions, is also used to input motions.     

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.     

Simulation of Spatially Variable Seismic Underground Motions in U-Shaped Canyons

This paper focuses on the study of simulations for spatially variable seismic underground motions in U-shaped canyons. First, a canyon ground cross-coherence function based on commonly used coherence function models of flat terrain, is deduced and presented. To further obtain the underground cross-coherence function, a mathematical expression, including its specific deduction process for describing the relationship between coherence functions of multi-support ground and underground motions, is also given in detail and adopted. Then, the key factors (i.e. canyon underground power spectrum density and canyon underground coherence function) for simulating the spatially variable seismic underground motions are obtained by a two-step transferring method from flat-ground to underground soil. Furthermore, a program is coded for generating the spatially variable seismic underground motions. The effectiveness of the generated seismic motions is further verified. Finally, two numerical examples are taken to validate the proposed simulation approach, illustrating the specific characteristics of canyon coherence function. The analysis results show the apparent differences of the simulated seismic motions using the canyon coherence function from those using conventional coherence function models of flat terrain. The proposed approach provides some insights for anti-earthquake analysis of soil-structure interaction or underground structures in canyon topography.     

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.     

A Method for Selecting Ground Motions that Considers Target Response Spectrum Mean and Variance as Well as Correlation Structure

This study proposes a method for selecting ground motions from a ground motion library with response spectra that match the target response spectrum mean, variance, and correlation structures. The proposed method is conceptually simple and straightforward. In this method, a desired number of ground motions are sequentially selected from first to last. The accuracy and consistency of the proposed method are verified through comparisons of the ground motions selected using the proposed method with those selected using conventional methods. This study shows that the seismic responses of the frames vary according to ground motion selection and correlation structures.     

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.     

Inelastic Demand Spectra of Bi-Linear Models for Capacity Spectrum Method and Response of Simple Structures under Near-Source Records

A very useful tool for the preliminary design of structures is the elastic demand spectrum that can be used in the capacity spectrum method. A pseudo-acceleration relationship has to be assumed when constructing a demand spectrum. This assumption results in large errors for long period structures with large damping ratios and the conventional demand spectra require a substitute elastic structure. In the present study, the conventional demand spectra are extended to bi-linear models. Pseudo-acceleration is still assumed but results in acceptably small errors, when a constant viscous damping coefficient for a single-degree-of-freedom (SDF) structure is calculated from the tangent stiffness and the damping ratio is set at 5% in both elastic and yield phases. For nonlinear structures, tangent stiffness dependency of damping force could be acceptable because energy absorption is primarily the result of structural nonlinear deformation. To extend the conventional demand spectra to a bi-linear model, effective period calculated from the secant stiffness has to be used. The use of effective period introduces no approximation because the peak displacement of the SDF structure is computed from nonlinear analysis in the time domain. The method presented in this study is also valid if damping coefficient proportional to initial elastic spectra is used. In this case, the pseudo-acceleration is defined as the base shear coefficient that is required to produce the peak displacement of the SDF structure in a static manner. We present demand spectra of bi-linear models for a number of near-source records from large earthquakes, and spectral ratios of two horizontal components. The effects of different types of ground motion on the response reduction factor due to inelastic deformation are investigated.     

SIMULATION OF THE FOURIER PHASE SPECTRUM FOR THE GENERATION OF SYNTHETIC ACCELEROGRAMS

This study presents the application of a new method for generating synthetic accelerograms based on statistical distributions for Fourier phase differences and Fourier amplitudes as functions of earthquake magnitude, hypocentral distance and site geology. Two important characteristics of the methodology are that it requires a small number of input parameters and that ground motion time histories can be simulated without any specific modulation function. Two areas with different tectonic patterns (North-Eastern and Central Italy) were selected for the application. The results of our analysis are reliable in the case of Central Italy because the data set is large and quite uniformly distributed, while for North-Eastern Italy our results should not be used for distances greater than 30 km.     

Study on Low-Frequency Characterizations of Pulse-Type Ground Motions through Multi-Resolution Analysis

This article makes an attempt to investigate the low-frequency characterizations of pulse-type ground motions through ground motion components instead of original records. A decomposed method based on multi-resolution analysis is introduced in this article. The accuracy and validity of the method is tested in frequency domain, time domain and dynamic response. A dataset of 398 low-frequency components is obtained after the decomposition of 91 typical pulse-type records. A probabilistic model to describe the proportion of low-frequency components in corresponding original ground motions is established. At last, the decomposed method is used to investigate the impulsive characterizations of pulse-type ground motions.     

The Strength Reduction Factors for Seismic-Isolated Bridges Characterized by SDOF Bilinear Systems in Far-Fault Areas

This article presents a statistical study on strength reduction factors for seismic-isolated bridges in far-fault areas. 1410 ground motions are selected and modified to be compatible with the recommended response spectra. Then, they are divided into 60 groups to investigate the effects of PGA/PGV ratios, soil conditions and post-to-pre-yield stiffness ratio. Results show that reduction factors are significantly affected by the PGA/PGV ratio, while the latter two items are not as important as the first one. Finally, an improved equation to estimate the reduction factor is proposed, and the accuracy of the equation is verified by additional records.     

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.     

An Investigation of Characteristic Periods of Seismic Ground Motions

The design seismic base shear was obtained from the spectral elastic acceleration S_a divided by a system behavior factor R, accounting for ductility and overstrength. The behavior factor is currently taken as a constant for a given type of structures in various codes regardless of structural periods. In fact, the behavior factor is also a spectrum varying with the natural periods of structures. In order to understand the relationship between the spectral values and the corresponding characteristic periods in these two spectra, S_a and R_μ, this article carries out an investigation into the characteristic periods of 370 seismic ground motions from 4 site types. It is found that the periods T_ga at which the peak values appear in the S_a spectra are much less than the periods T _gR at which the R_μ spectra take a maximum value. Two characteristic periods are necessary to determine the seismic action if a more elaborate procedure is required in practice. Statistical study on these two periods is carried out for the 370 records, and results are presented. For site types A–D, the ratio of these two periods has a statistically averaged value of 5.5–6.7.

The maximum input energy S _EI , relative velocity S _v , power density P _SD , and the Fourier amplitude F _S spectra were constructed to determine their characteristic periods, respectively. These four spectra predict similar characteristic periods to T _gR . T _gR is very close to the characteristic period T _gd of the elastic displacement spectra.

Analysis of SDOF systems under combined harmonic excitations shows that the S_a spectrum is more sensitive to high-frequency excitations, while the displacement spectrum is more sensitive to long period excitations. For the elastic-plastic S_a spectra, peak values tend to appear at shorter periods even the amplitudes of the longer periods are greater than that of the shorter period. This provides an explanation on different characteristic periods in the S_a and R_μ spectra.