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.     

博物馆文物的防震保护研究（二）——设防地震动输入及结构地震动反应

通过对上海及邻近地区地震危害性分析,结合地震研究工作结果,根据上海博物馆文物防震保护的具体要求,研究确定了该博物馆文物防震保护的设防水准及地震动参数。场地地震动输入峰值加速度水准确定为50年超越概率3％,地震动反应谱采用上海市标准《建筑抗震设计规范》(DGJ08-9-92)中给出的地震影响系数曲线(阻尼比0.05),并将输入峰值加速度调整为180gal。研究采用了目前通用的拟合反应谱的方法,通过拟合选定的地震动反应标准谱,合成了6条人造地震波时程曲线,拟合精度控制在相对误差不大于5％;同时结合上海市《建筑抗震设计规范》(DGJ08-9-92)中所附的一条强震记录,共同作为上海博物馆结构地震反应分析的输入地震动。又根据上海博物馆建筑的结构特征分析,结合建筑结沟动力特征的实测结果,通过采用层模型结构时程分析计算方法,计算并获得了在遭遇设防地震时,上海博物馆建筑物每一层的地震动反应,表明上海博物馆建筑各楼层的地震动反应具有明显的楼层放大作用。对各楼层地震动反应的统计分析,给出了上海博物馆建筑物每一层的地震动参数,以此可作为今后文物地震危害性分析,及研究设计隔震装置等防震措施的依据。     

ESTIMATION OF GROUND MOTION ACCELERATION AND BUILDING RESPONSE TO A LONG DISTANCE EARTHQUAKE

In October 1995 an earthquake with a magnitude of 7 on the Richter scale occurred in Sumatra, 450 km from Singapore. Tremors were felt by occupants of several buildings in Singapore and were recorded as an RMS acceleration value by instruments installed in a high-rise condominium. Based on this value and considering instrumental effects, site conditions and building characteristics, this paper investigates the ground motion accelerations and the building response.     

Seismic Rotational Displacements of Gravity Quay Walls Considering Excess Pore Pressure in Backfill Soils

The effect of excess pore pressure developed in backfill soil during earthquake is an important consideration in rotational displacement prediction of gravity quay walls. Based on Newmark’s sliding block concept and stress-based excess pore pressure model, a new method is proposed to predict the critical rotational acceleration and angular acceleration time histories considering the development process of excess pore pressure in earthquake events. Then, the rotational displacement of gravity quay walls is predicted according to the calculated angular acceleration time histories. By using the proposed method, the effects of various parameters involved in the calculation have been studied by carrying out a parameter study. Analysis results reveal that the influence of excess pore pressure on the rotational displacement of gravity quay walls with saturated backfill soil is significant, so, can not be ignored; and rotational displacement is sensitive to the magnitude of earthquake, horizontal and vertical seismic accelerations of ground motion, wall and soil friction angle, and soil relative density. When the rotation and sliding of wall occur simultaneously, rotation and sliding will be inhibited by each other.     

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.     

Time-Domain Spectral Matching of Earthquake Ground Motions using Broyden Updating

Time-domain spectral matching of an earthquake ground motion consists of iteratively adding sets of wavelets to an acceleration history until the resulting response spectrum sufficiently matches a target spectrum. The spectral matching procedure is at its core a nonlinear problem because the addition of a wavelet often causes shifting in the time of peak response or creation of a larger second peak at a different time. A modification to existing time-domain spectral matching algorithms is proposed using Broyden updating for solving the set of nonlinear equations. Three wavelet bases are evaluated and the corrected tapered cosine wavelet is selected. The proposed algorithm is then tested and compared with other methods that are commonly used for spectral matching. The results show that the proposed algorithm is able to match the target spectrum while reasonably preserving the spectral nonstationarity, energy development, and the frequency content of the original time histories.     

Vector-valued Intensity Measures Incorporating Spectral Shape For Prediction of Structural Response

Vector-valued ground motion intensity measures (IMs) are developed and considered for efficiently predicting structural response. The primary IM considered consists of spectral acceleration at the first-mode structural period along with a measure of spectral shape which indicates the spectral acceleration value at a second period. For the IM to effectively predict response, this second period must be selected intelligently in order to capture the most relevant spectral shape properties. Two methods for identifying effective periods are proposed and used to investigate IMs for example structures, and an improvement in the efficiency of structural response predictions is shown. A method is presented for predicting the probability distribution of structural response using a vector IM while accounting for the effect of collapses. The ground motion parameter ε is also considered as part of a three-parameter vector. It is seen that although the spectral shape parameter increases the efficiency of response predictions, it does not fully account for the effect of ε. Thus, ε should still be accounted for in response prediction, either through informed record selection or by including ε in the vector of IM parameters.     

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.     

Implications of Thrown-Out Boulders for Earthquake Shaking

In the source areas of some large shallow earthquakes, we have found many dislodged boulders struck by severe ground shaking. Some boulders were located at quite distances from the former sockets, which remained undisturbed with surrounding clear edges. This fact indicates the possibility that vertically upward seismic acceleration exceeded the earth's gravity (1g). This phenomenon of upthrown boulders is investigated herein by examining the effects of waves, which emanate deep in the ground due to an earthquake, propagate through the ground and boulder, and reflect back to the ground, involving a variety of their interaction. An elastic dynamic analysis is carried out on the basis of a one-dimensional continuum model consisting of the ground and boulder. It is subjected to the input of the Ricker wave, which is intended to simulate an earthquake-generated wave, emanating from the bottom of the model ground. The upthrow of a boulder is taken to occur when the dynamic response at the bottom of the boulder satisfies certain conditions. It turns out that the possibility of upthrow occurrence is high when the period of the Ricker wave coincides with the fundamental period of the ground vibration. It leads to the conclusion that the upthrow takes place due to resonance in the response of the system of the ground and boulder to the external wave input. The upthrow possibility increases as the input acceleration increases. Trial is made of predicting the maximum acceleration and velocity of an earthquake, based on this consideration of the up throw phenomenon.     

Optimal Control of Structures under Earthquakes Including Soil-Structure Interaction

It is well known that the soil-structure interaction (SSI) changes the dynamic response of a structure supported on flexible soil. The analysis of optimally controlled SSI systems has certain difficulties due to the nature of the SSI and the optimal control problem. In this paper, a two-step iteration-based numerical algorithm is proposed to handle optimally controlled SSI systems under earthquakes. First, the optimal control forces are obtained by using a fixed-base system. Then, the optimal control forces are converted to the frequency domain by the Fourier transform technique to be used in the equations of the SSI system. The lateral displacement and the rocking of the foundation are obtained from the equations of the SSI system containing the optimal control forces in the frequency domain. The lateral displacement and rocking of the foundation are then converted to the time domain by the inverse Fourier transform technique, and the lateral accelerations and the rocking accelerations of the foundation are obtained by the forward finite difference method. During the second step, the optimal control forces are calculated again by using the lateral acceleration and the rocking acceleration of the foundation along with the earthquake ground motion. Using the method explained above, the optimal control forces obtained in the time domain are used in the equations of the soil-structure system from which the behavior of foundation and structure is obtained. In the final section of the paper, a numerical study is conducted for a controlled structure supported on flexible soil.     

Numerical Evaluation of Seismic Soil Pressures on Rigid Walls Fixed to the Bedrock

Seismic soil pressures developed on a 7 m rigid retaining wall fixed to the bedrock are investigated using a finite element model that engages nonlinear soil intended materials available in OpenSees. This allows incorporation of the inelastic behavior of the soil and wave propagation effects in the soil-wall system seismic response. The nonlinear response of the soil was validated using the well-stablished, frequency-domain, linear-equivalent approach. An incremental dynamic analysis was implemented to comprehensively examine the effect of soil nonlinearity and input motion on the induced seismic pressures and to evaluate current code equations/methodologies at different levels of earthquake intensity. The results show that soil nonlinearity and seismic wave amplification may play an important role in the response of the soil-wall system. Therefore, methodologies that rely only on peak ground acceleration may introduce large bias on the estimated seismic pressures in scenarios where high nonlinearity and site amplification are expected.     

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.     

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.     

The Response of Isolated Bridges Accounting for Spatial Variability of Ground Motion

The effects of the spatial variability of ground motion (loss of coherence, wave passage, and local site conditions) on the response of isolated bridges are investigated.

Therefore, a statistical approach is adopted to represent uncertainties in both the bridge configuration and the ground motion variability. The response of isolated bridges, designed for a standard input motion, under a spatially varying ground motion, is evaluated by nonlinear time-history analyses; the system performance is measured by the displacement demand on isolators.

Results show that the phenomenon affects the structural response considerably; the demand increases for the majority of isolators, irrespective of bridge configuration.     

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.     

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.     

INSTANTANEOUS OPTIMAL CONTROL FOR SEISMIC ANALYSIS OF NON-LINEAR STRUCTURES

In this paper, an effective active control algorithm is developed for the vibration control of non-linear structural systems subjected to earthquake excitation. It is an attempt to include the non-linear characteristics of the structural behaviour throughout the entire analysis (design and validation), accounting for the eventual cumulative structural damage and energy dissipation. This is a very important factor since, in current design practice, structures are assumed to behave nonlinearly when subjected to strong ground motion. The proposed algorithm focusses on the instantaneous optimal control approach for the development of the control algorithm where the nonlinearities are brought into the analysis through a non-linear state vector and a non-linear open loop term. A performance index that is quadratic in the control force and in the non-linear states and is subjected to a non-linear constraint equation, is minimised at every time step. The effectiveness of the proposed non-linear instantaneous optimal control (NIOC) strategy is critically evaluated in comparison with currently available active control techniques. Numerical simulation results indicate that the proposed approach provides a significant reduction of the peak response quantities, such as maximum response deformation, maximum response acceleration, ductility of the system, associated with a reduced maximum control force.     

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.     

Seismic Response of Base-Isolated Benchmark Building with Variable Sliding Isolators

The seismic response of base-isolated benchmark building with variable sliding isolators like variable friction pendulum system (VFPS), variable frequency pendulum isolator (VFPI), and variable curvature friction pendulum system (VCFPS), along with conventional friction pendulum system (FPS), was studied under the seven earthquakes. The earthquakes are applied bi-directionally in the horizontal plane ignoring vertical ground motion component. The shear type base-isolated benchmark building is modeled as three-dimensional linear elastic structure having three degrees of freedom at each floor level. Time domain dynamic analysis of the benchmark building was carried out with the help of constant average acceleration Newmark-Beta method and nonlinear isolation forces was taken care by fourth-order Runge-Kutta method. The base-isolated benchmark building is investigated for uniform isolation and hybrid isolation in combination with laminated rubber bearings through the performance criteria and time history response of important structural response parameters like floor accelerations, base displacement, etc. It is observed that variable sliding isolators performed better than conventional FPS due to their varying characteristic properties which enable them to alter the isolator forces depending upon their isolator displacements thus improves the performance of the structure. The VFPS efficiently controls large isolator displacements and VFPI and VCFPS improve super structural response on the cost of isolator displacement. It is also observed that the hybrid isolation is relatively better in comparison to the uniform isolation for the benchmark building.