• Structural Engineering and Mechanics
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• 제9권2호
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• pp.141-152
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• 2000

Based on the discussion about some empirical coherency models resulted from earthquake-induced ground motion recordings at the SMART-1 array in Taiwan, and a heuristic model of the coherency function from elementary notions of stationary random process theory and a few simplifying assumptions regarding the propagation of seismic waves, a practical coherency model for spatially varying ground motions, which can be applied in aseismic analysis and design, is proposed, and the regressive coefficients are obtained using least-square fitting technique from the above recordings.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2008년도 정기총회 및 학술발표대회
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• pp.265-268
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• 2008

The safety of a tunnel under seismic motion is most often evaluated by ovalling deformation of tunnel. This paper research about tunnel's longitudinal deformation. Because of spatial variation of seismic ground motion, the longitudinal structures like tunnel are likely to experience relative displacements along longitudinal direction. The spatially variable ground motion can be estimated by coherency function obtained empirically, and can be considered from different arrival times of ground motion. As a result of estimating tunnel's relative displacements at maximum curvature of tunnel, the displacements and curvatures estimated by coherency function affect the tunnel's safety more than different arrival times. However, if tunnel's displacements by coherency function superpose on displacements by different arrival times, the relative displacements and curvatures of tunnel will be more severe. Therefore, to estimate accurately tunnel's deformation in longitudinal direction has to consider both coherency and wave passage effects.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2006년도 춘계 학술발표회 논문집
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• pp.625-633
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• 2006

Spatial variability of ground motions has significant influence on dynamic response of longitudinal structures such as bridges and tunnels. The coherency function, which quantifies the degree of positive or negative correlation between two ground motions, is often used to describe the spatially variable ground motions. This paper compares two available procedures for developing spatially variable ground time histories from a given coherency function. Hao's method shows serious limitation, resulting in unrealistic decrease in coherency with increase in distance Abrahamason's method, on the other hand, preserves important characteristics of the reference ground motion. Therefore, the Abrahamason's method is recommended to be used in developing spatially varying ground motions.

• 한국측량학회지
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• 제34권1호
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• pp.91-98
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• 2016

지구통계학적인 공간분석의 대표적인 방법인 크리깅(kriging)을 적용하기 위해서는 두 관측점 사이의 거리에 기반한 상관성을 나타내는 공간상관함수의 추정이 우선적으로 이루어져야 한다. 본 연구에서는 다양한 크리깅에 적용할 수 있는 대표적인 상관함수인 semi-variogram, homeogram, covariance function에 대하여 국가지오이드 모델을 기반으로 추정하였다. 경위도 각각 2°의 대상지역 내 통합기준점의 지오이드고를 이용하였으며, 선형모델을 이용하여 공간적인 편향성을 제거하였다. 전체 100개의 샘플 포인트에 대해서 중복되지 않은 두 점 간의 거리를 기준으로 구간을 나누고, 각 함수에 대한 경험적인 값을 계산하였다. 공간상관함수의 경험적인 값은 각각 두 개의 모델에 최소제곱조정 방법으로 피팅한 결과 semi-variogram의 wave 모델 적합도가 가장 높았으며, homeogram과 covariance function은 exponential 모델이 상대적으로 좋은 피팅 결과를 보였다. 본 연구에서 결정한 공간상관함수는 추후 다양한 크리깅 방법을 통해 임의 지점에서의 예측값에 대한 정확도 검증과 이에 대한 평균제곱예측오차(Mean Squared Prediction Error, MSPE)를 계산함으로써 각 함수의 활용성에 대한 추가적인 연구가 수행되어야 한다.

• Structural Engineering and Mechanics
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• 제73권6호
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• pp.651-666
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• 2020

In this study, the spatial variation mechanisms of large far-field earthquakes at engineering scales are first investigated with data from the 2008 Ms 8.0 Wenchuan earthquake. And a novel 'coherency cut-off frequency' is proposed to distinguish the spatial variations in ground motions in the low-frequency and high-frequency ranges. Then, a practical piecewise coherency model is developed to estimate and characterize the spatial variation in earthquake ground motions, including the effects of source-to-site distances, site conditions and neighboring topography on these variations. Four particular earthquake records from dense seismograph arrays are used to investigate values of the coherency cut-off frequency for different source-to-site distances. On the basis of this analysis, the model is established to simulate the spatial variations, whose parameters are suitable for both near- and far-field earthquake conditions. Simulations are conducted to validate the proposed model and method. The results show that compared to the existing models, the proposed model provides an effective method for simulating the spatial correlations of ground motions at local sites with known source-to-site distances.

• Structural Engineering and Mechanics
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• 제36권1호
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• pp.111-127
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• 2010

This paper studies the effects of spatially varying ground motions on the responses of a bridge frame located on a canyon site. Compared to the spatial ground motions on a uniform flat site, which is the usual assumptions in the analysis of spatial ground motion variation effects on structures, the spatial ground motions at different locations on surface of a canyon site have different intensities owing to local site amplifications, besides the loss of coherency and phase difference. In the proposed approach, the spatial ground motions are modelled in two steps. Firstly, the base rock motions are assumed to have the same intensity and are modelled with a filtered Tajimi-Kanai power spectral density function and an empirical spatial ground motion coherency loss function. Then, power spectral density function of ground motion on surface of the canyon site is derived by considering the site amplification effect based on the one dimensional seismic wave propagation theory. Dynamic, quasi-static and total responses of the model structure to various cases of spatially varying ground motions are estimated. For comparison, responses to uniform ground motion, to spatial ground motions without considering local site effects, to spatial ground motions without considering coherency loss or phase shift are also calculated. Discussions on the ground motion spatial variation and local soil site amplification effects on structural responses are made. In particular, the effects of neglecting the site amplifications in the analysis as adopted in most studies of spatial ground motion effect on structural responses are highlighted.

• Earthquakes and Structures
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• 제17권6호
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• pp.557-566
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• 2019

The evaluation of the seismic hazard for a given site is to estimate the seismic ground motion at the surface. This is the result of the combination of the action of the seismic source, which generates seismic waves, the propagation of these waves between the source and the site, and site local conditions. The aim of this work is to evaluate the sensitivity of dynamic response of extended structures to spatial variable ground motions (SVGM). All factors of spatial variability of ground motion are considered, especially local site effect. In this paper, a method is presented to simulate spatially varying earthquake ground motions. The scheme for generating spatially varying ground motions is established for spatial locations on the ground surface with varying site conditions. In this proposed method, two steps are necessary. Firstly, the base rock motions are assumed to have the same intensity and are modelled with a filtered Tajimi-Kanai power spectral density function. An empirical coherency loss model is used to define spatial variable seismic ground motions at the base rock. In the second step, power spectral density function of ground motion on surface is derived by considering site amplification effect based on the one dimensional seismic wave propagation theory. Several dynamics analysis of a curved viaduct to various cases of spatially varying seismic ground motions are performed. For comparison, responses to uniform ground motion, to spatial ground motions without considering local site effect, to spatial ground motions with considering coherency loss, phase delay and local site effects are also calculated. The results showed that the generated seismic signals are strongly conditioned by the local site effect. In the same sense, the dynamic response of the viaduct is very sensitive of the variation of local geological conditions of the site. The effect of neglecting local site effect in dynamic analysis gives rise to a significant underestimation of the seismic demand of the structure.

• 전자공학회논문지S
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• 제34S권3호
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• pp.74-83
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• 1997

In this paper, a new stereo matching algorithm is proposed which uses th econstrainted optimization technique and the matching measures between the segments extracted from zero-crossing edges. The initial matching measures and average disparities are calculated by the features of segments on the searching window of the left and right images. The matching measure is calculated by applying an exponential function using the differences of slope, overlapped length and intensity. The coherency constraint is that neighbouring image points corresponding to the same object should have nearly the same disparities. The matching measures are iteratively updated by applying the coherency constraint. Simulation results on various images show that the proposed algorithm more acculately extracts the segment disparity.

• 대한토목학회논문집
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• 제35권4호
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• pp.759-768
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• 2015

장대교량과 같이 길이가 긴 다 지점 구조물에서는 각 지점에서의 지반운동은 차이가 난다. 이것은 지반운동의 공간적 변화로 알려져 있다. 지반운동의 공간적 변화는 각각 다른 위치에서의 지진파 도착시간의 차이에 의해 발생하는 파동전파 효과, 이질적인 지반매체에서의 지진파 산란에 의한 일관성손실, 부지의 지반특성에 따른 부지증폭 효과 등의 이유에 의해 발생한다. 기존연구에서는 부지증폭 효과를 고려하지 않거나, 지반을 단층으로 모델링하여 이를 고려하였으나, 본 연구에서는 다층의 지반에 의한 지반운동의 증폭 및 필터링이 구조물의 지진거동에 미치는 영향을 평가하였다. 서로 다른 지층의 수와 깊이 그리고 지반특성을 가지고 있는 부지에서 공간적으로 변화하는 지반운동을 생성하였고, 일관성손실 함수의 상관성 정도와 각 부지의 지반조건에 따른 지반운동의 시간이력의 변화특성을 평가하였다. 또한, 두 개의 단위 교량으로 이루어진 교량시스템을 대상으로 각각의 부지 조건에 맞게끔 생성된 지진파를 입력으로 하는 교량해석을 통해 각 단위교량 및 단위교량 간 지진거동 특성을 비교분석하였다. 특히, 일관성손실과 지반조건이 두 교량 간 충돌 및 낙교를 유발할 수 있는 상대변위에 미치는 영향을 평가하였다. 해석결과 각 부지의 지반조건의 고려는 아주 중요하며 실제 구조해석에서 무시되어서는 안 될 것으로 판단된다.

• Steel and Composite Structures
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• 제22권5호
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• pp.1001-1018
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• 2016

The purpose of this paper is to compare the structural responses obtained from the stochastic analysis of a suspension bridge subjected to uniform and partially correlated seismic ground motions, using different spatial correlation functions commonly used in the earthquake engineering. The spatial correlation function employed in this study consists of a term that characterizes the loss of coherency. To account for the spatial variability of ground motions, the widely used four loss of coherency models in the literature has been taken into account in this study. Because each of these models has its own characteristics, it is intended to determine the sensitivity of a suspension bridge due to these losses of coherency models which represent the spatial variability of ground motions. Bosporus Suspension Bridge connects Europe to Asia in Istanbul is selected as a numerical example. The bridge has steel towers that are flexible, inclined hangers and a steel box-deck of 1074 m main span, with side spans of 231 and 255 m on the European and Asian sides, respectively. For the ground motion the filtered white noise model is considered and applied in the vertical direction, the intensity parameter of this model is obtained by using the S16E component of Pacoima Dam record of 1971 San Fernando earthquake. An analytically simple model called as filtered white noise ground motion model is chosen to represent the earthquake ground motion. When compared with the uniform ground motion case, the results obtained from the spatial variability models with partial correlation outline the necessity to include the spatial variability of ground motions in the stochastic dynamic analysis of suspension bridges. It is observed that while the largest response values are obtained for the model proposed by Harichandran and Vanmarcke, the model proposed by Uscinski produces the smallest responses among the considered partially correlated ground motion models. The response values obtained from the uniform ground motion case are usually smaller than those of the responses obtained from the partially correlated ground motion cases. While the response values at the flexible parts of the bridge are totally dominated by the dynamic component, the pseudo-static component also has significant contributions for the response values at the rigid parts of the bridge. The results also show the consistency of the spatial variability models, which have different characteristics, considered in this study.