Design Earthquake Ground Motion Prediction for Perth Metropolitan Area with Microtremor Measurements for Site Characterization

Perth is the largest city in Western Australia and home to three-quarters of the state's residents. In recent decades, there have been a lot of earthquake activities just east of Perth in an area known as the South-West Seismic Zone. Previous numerical results of site response analyses based on limited available geology information for PMA indicated that Perth Basin might amplify the bedrock motion by more than 10 times at some frequencies and at some sites. Hence, more detailed studies on site characterization and amplification are necessary. The microtremor method using spatial autocorrelation (SPAC) processing is a useful tool for gaining thickness and shear wave velocity (SWV) of sediments and has been adopted in many previous studies. In this study, the response spectrum of rock site corresponding to the 475-year return period for PMA is defined according to the probabilistic seismic hazard analysis (PSHA) based on the latest ground motion attenuation model of Southwest Western Australia. Site characterization in PMA is performed using two microtremor measurements, namely SPAC technique and H/V method. The clonal selection algorithm (CSA) is introduced to perform direct inversion of SPAC curves to determine the soil profiles of representative PMA sites investigated in this study. Using the simulated bedrock motion as input, the responses of the soil sites are estimated using numerical method based on the shear-wave velocity vs. depth profiles determined from the SPAC technique. The response spectrum of the earthquake ground motion on surface of each site is derived from the numerical results of the site response analysis, and compared with the respective design spectrum defined in the Australian Earthquake Loading Code. The comparison shows that the code spectra are conservative in the short period range, but may slightly underestimate the response spectrum at some long period range.     

COUPLED P-Y T-Z ANALYSIS OF SINGLE PILES IN COHESIONLESS SOIL UNDER VERTICAL AND/OR HORIZONTAL GROUND MOTION

Various approaches are currently used for the analysis of piles under vertical and lateral loading. Among these, the beam-on-a-nonlinear Winkler foundation (BNWF) approach using published P-y, T-z and Q-z curves is widely used in practice. In this approach, the P-y and T-z responses are generally uncoupled from each other. The objective of this paper is to investigate the influence that the coupling of the P-y and T-z responses has.on the cyclic and dynamic response of piles in cohesionless soil. A cyclic model is first developed and a parametric study is conducted to investigate the effect the initial confining pressure, angle of wall friction and effective vertical stiffness have on the lateral cyclic hysteretic response. A dynamic model is then developed, and used to study the response of a single pile in cohesionless soil under horizontal and/or vertical ground motion. Results from the parametric study showed that the three parameters did not have a significant influence on the lateral cyclic hysteretic response. Under horizontal and/or vertical ground motion, the horizontal ground motion was observed to dominate the inertial interaction response, and significantly affected both the horizontal and vertical displacement response, mainly due to second-order P-Δ and gapping effects.     

Estimation of the Displacement of Viscously Damped Pinching Hysteretic Structures Subjected to Near-fault Ground Motions

To fulfill a displacement-based design or response prediction for nonlinear structures, the concept of equivalent linearization is usually applied, and the key issue is to derive the equivalent parameters considering the characteristics of hysteretic model, ductility level, and input ground motions. Pinching hysteretic structures subjected to dynamic loading exhibit hysteresis with degraded stiffness and strength and thus reduced energy dissipation. In case of excitation of near-fault earthquake ground motions, the energy dissipation is further limited due to the short duration of vibration. In order to improve the energy dissipation capability, viscous-type dampers have been advantageously incorporated into these types of structures. Against the viscously damped pinching hysteretic structure under the excitation of near-fault ground motions, this study aims to develop a seismic response estimation method using an equivalent linearization technique. The energy dissipation of various hysteretic cycles, including stationary hysteretic cycle, amplitude expansion cycle, and amplitude reduction cycle, is investigated, and empirical formulas for the equivalent damping ratio is proposed. A damping modification factor that accounts for the near-fault effect is introduced and expanded to ensure its applicability to structures with damping ratios less than 5%. An approach for estimating the maximum displacement of a viscously damped pinching hysteretic structure, in which the pinching hysteretic effect of a structure and the near-fault effect of ground motions are considered, is developed. A time history analysis of an extensive range of structural parameters is performed. The results confirm that the proposed approach can be applied to estimate the maximum displacement of a viscously damped pinching hysteretic structure that is subjected to near-fault ground motions.     

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.     

GROUND MOTION DOMINANT FREQUENCY EFFECT ON THE DESIGN OF MULTIPLE TUNED MASS DAMPERS

Utilising the Kanai-Tajimi and Clough-Penzien spectrums and the pseudo-excitation algorithm in the frequency domain, parametric study is performed to examine the effect of the dominant frequency of ground motion on the optimum parameters and effective-ness of multiple tuned mass dampers (MTMD) with identical stiffness and damping coefficient but with unequal mass. The examination of the optimum parameters is con-ducted through the minimisation of the minimum values of the maximum displacement and acceleration dynamic magnification factors of the structure with the MTMD. The optimum parameters of the MTMD include the optimum frequency spacing reflecting the robustness, the average damping ratio and the tuning frequency ratio. Minimisation of the minimum values of the maximum displacement and acceleration dynamic mag-nification factors, nondimensionalised respectively by the maximum displacement and acceleration dynamic magnification factors of the structure without the MTMD, is used to measure the effectiveness of the MTMD. The results indicate that in the two cases where both the total mass ratio is below 0.02 and the total mass ratio is above 0.02, but the dominant frequency ratio of ground motion is below unity (including unity), the earthquake ground motion can be modelled by a white noise. It is worth noting, however, that for the total mass ratio above 0.02, the Kanai-Tajimi Spectrum or Clough-Penzien spectrum needs to be employed to design the MTMD for seismic structures in situations where the dominant frequency ratio of ground motion is beyond unity.     

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 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.     

IDENTIFICATION AND VERIFICATION OF SEISMIC DEMAND FROM DIFFERENT HYSTERETIC MODELS

The goal of this paper is to develop a modified Bouc-Wen hysteretic model from cyclic loading test data for reinforced columns, including the behavior of stiffness degradation, strength deterioration, pinching and softening effects of RC members. Seismic demands on this inelastic single degree of freedom system when subjected to both near-fault ground motion and far-field ground motion excitations were examined.

The cyclic loading test of reinforced concrete columns was experimentally observed and a system identification computer program was developed to solve each control parameter of the hysteretic model. A least-squared method for identifying parameters of the model is proposed in this paper. The hysteretic constitutive law produces a smoothly varying hysteresis such as the control-parameters for strength deterioration, stiffness degradation, pinching and softening effects. Two implementations of (1) flexure damage and (2) shear damage were conducted to provide better understanding of hysteretic behavior of RC structural members. A pseudo-dynamic experiment was also developed to verify the model parameters.

Based on the developed hysteretic model, the seismic demand of this inelastic model was investigated by using both near-fault ground motion data and far-field ground motion data as input motion. An R-μT inelastic response spectrum from different hysteretic models was generated.     

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.     

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.     

Influence of Collapse Definition and Near-Field Effects on Collapse Capacity Spectra

In the present article, the impact of both near fault ground motions and a finite ductility threshold on the collapse capacity is studied. Single-degree-of-freedom systems with non-deteriorating bilinear hysteretic behavior, vulnerable to P-delta effects, are considered. Defining collapse as excessive ductility is investigated, and the difference to collapse associated with instability is elaborated. Medians of individual record dependent collapse capacities are presented as function of the initial structural period for characteristic structural and ground motion parameters. Analytical expressions for influence coefficients, which account for a differing ground motion set, and finite ductility thresholds, respectively, are derived via non-linear regression analysis.     

GROUND MOTION ANALYSIS IN THE ANCHORAGE BASIN: 1-D APPROACH

Understanding the dynamic behaviour of soil in the Anchorage basin in southcentral Alaska is essential for seismic hazard assessment of this highly seismically active region. The analysis of site responses for 40 sites from weak-motion and strong-motion data with amplitudes less than 0.1 g showed a strong influence of subsurface geological conditions on the characteristics of ground motion. Particularly, the sites in the central part of the city, including the downtown area, showed prominent resonance peaks around 1 Hz with amplification values up to about 4. The numerical analysis, based on one-dimensional multi-layer soil models shows that site response characteristics, and especially aforementioned peaks, are largely related to the thick, soft layer of Quaternary deposits, particularly cohesive fades of Bootlegger Cove Formation. The computed transfer functions for soil profiles of six representative sites are in accord with the site responses in the frequency range from 1 to 5 Hz. There is no significant change in amplification values below 2 Hz corresponding to large-amplitude (up to 0.38 g) ground motions; however, above 2-3 Hz the amplification values are greatly reduced in this case.     

Equivalent Damping in Support of Direct Displacement-Based Design

The concept of equivalent linearization of nonlinear system response as applied to direct displacement-based design is evaluated. Until now, Jacobsen's equivalent damping approach combined with the secant stiffness method has been adopted for the linearization process in direct displacement-based design. Four types of hysteretic models and a catalog of 100 ground motion records were considered. The evaluation process revealed significant errors in approximating maximum inelastic displacements due to overestimation of the equivalent damping values in the intermediate to long period range. Conversely, underestimation of the equivalent damping led to overestimation of displacements in the short period range, in particular for effective periods less than 0.4 seconds. The scatter in the results ranged between 20% and 40% as a function of ductility. New equivalent damping relations for four structural systems, based upon nonlinear system ductility and maximum displacement, are proposed. The accuracy of the new equivalent damping relations is assessed, yielding a significant reduction of the error in predicting inelastic displacements. Minimal improvement in the scatter of the results was achieved, however. While many significant studies have been conducted on equivalent damping over the last 40 years, this study has the following specific aims: (1) identify the scatter associated with Jacobsen's equivalent damping combined with the secant stiffness as utilized in Direct Displacement-Based Design; and (2) improve the accuracy of the Direct Displacement-Based Design approach by providing alternative equivalent damping expressions.     

SYSTEM IDENTIFICATION OF FEI-TSUI ARCH DAM FROM FORCED VIBRATION AND SEISMIC RESPONSE DATA

This paper presents the experimental investigation of the Fei-Tsui arch dam using the forced vibration test and its seismic response data. A forced vibration test was conducted on Fei-Tsui dam, this study presents the identified dynamic properties of the dam from these test data. For the identification of dam properties from seismic response data, in order to consider the nonuniform excitation of the seismic input and to describe the global behavior of the dam, the multiple input/multiple output discrete-time ARX model with least square estimation is applied to identify the dynamic characteristics of the dam. The system modal frequency, damping ratio and frequency response function are identified from both the forced vibration and seismic response data. To verify the accuracy of the identification result, comparison between discrete-time ARX model and a frequency domain conditioned spectral analysis was made. Finally, the spatial variation of ground motion across the free-field canyon surface is also studied.     

Predicting Probabilistic-Based Strong Ground Motion Time Series for Citadel of Arg-E-Bam (South-East of Iran)

The main objective of this article is to present a probabilistic-based strong motion compatible with the source-path and site soil condition given the probability of exceedence for citadel of Arg-e-Bam site bed rock (South-East of Iran). A Fourier amplitude spectral attenuation relation for bed rock beneath the site is proposed which permits the estimation of time-histories through a probabilistic seismic hazard analysis procedure. Due to lack of data, the two well-known simulation techniques, point source and finite fault models have been used for generating hundreds of strong motion as input data. Tens of model parameter values such as stress-drop nucleation points were used, in each specified magnitude-distance, to reduce the uncertainty effects inherently existing in seismological/geological parameters. The proposed attenuation relation is validated by comparing the estimated strong motion, in the form of Fourier amplitude spectral, using the proposed attenuation relation with those of recorded ground motion data at three stations far away from the assumed source so that the results would not be influenced by the near source problems such as directivity and fling step. The results of proposed technique is assessed by comparing the estimated response spectra, with 10% probability of exceedence and 5% damping ratio, with those of traditional uniform hazard spectra. The proposed technique is supposed to be used in retrofitting procedure of international historical adobe structures in Arg-e-Bam site, which have been damaged during the destructive Bam earthquake 2003, Iran     

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.     

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.     

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.     

A Ground Motion Record Selection Approach Based on Multiobjective Optimization

The evaluation of the seismic safety and reliability of buildings and building contents within a probabilistic framework often requires response history analyses using site-specific ground motion records. The ground motion selection method proposed in this paper addresses this issue by a stochastic search procedure in which record sets are selected such that first- and second-order statistics (median and dispersion) satisfy predefined ground motion spectrum targets over a wide period range. Once a ground motion record set is selected, it can be used for seismic assessment of a broad class of buildings within the target period range at the given location.     

EFFECTS OF SOIL LAYERING ON THE CHARACTERISTICS OF BASIN-EDGE INDUCED SURFACE WAVES AND DIFFERENTIAL GROUND MOTION

This paper studies the effects of soil layering in the basin based on the characteristics of basin-edge induced surface waves and associated differential ground motion. Seismic responses of various basin-edge models were simulated using software based on parsimonious finite difference staggered grid approximation of 2.5D eiastodynamic wave equation. Seismic responses of various models with different number of soil/soft rock layers but for a fixed thickness of deposit, fundamental frequency and impedance contrast revealed a decrease of surface wave amplitude with an increase in the number of layers in the basin. Shifting of dominant frequency towards the higher values was obtained with an increase of number of layers. An increase of dispersion of surface waves with an increase of number of soil layers in the basin was observed. A minor increase of Rayleigh wave velocity with an increase of number of soil layers was also obtained, but in the case of Love wave it was almost negligible.

Spectral analysis of the edge-induced surface waves revealed that the anomalous earthquake intensity may arise in a zone of width of 2.5–3.0 km, parallel to basin-edge and at an offset of 0.5–0.7 km from the edge. Maximum horizontal differential ground motion (HDGM) developed by Love wave (≈4.9×10^?2) was more than that of Rayleigh wave (≈9.4×10^?3). Large variation in HDGM caused by the surface waves was obtained with a change in the number of layers in the basin and maximum HDGM was observed when there were only two layers in the basin. It was inferred that the effect of soil layering in the basin was more on the Rayleigh wave as compared to the Love wave. Development of large HDGM near the basin-edge and its dependency on the number of soil layers reveals that basin-edge induced surface waves need special attention during seismic microzonation or seismic hazard prediction.