• Structural Engineering and Mechanics
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• v.9 no.2
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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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• 2008.02a
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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.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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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.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.34 no.1
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• pp.91-98
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• 2016

In order to apply Kriging methods for geostatistics of spatial data, an estimation of spatial coherency functions is required priorly based on the spatial distance between measurement points. In the study, the typical coherency functions, such as semi-variogram, homeogram, and covariance function, were estimated using the national geoid model. The test area consisting of 2°×2° and the Unified Control Points (UCPs) within the area were chosen as sampling measurements of the geoid. Based on the distance between the control points, a total of 100 sampling points were grouped into distinct pairs and assigned into a bin. Empirical values, which were calculated with each of the spatial coherency functions, resulted out as a wave model of a semi-variogram for the best quality of fit. Both of homeogram and covariance functions were better fitted into the exponential model. In the future, the methods of various Kriging and the functions of estimated spatial coherency need to be studied to verify the prediction accuracy and to calculate the Mean Squared Prediction Error (MSPE).

• Structural Engineering and Mechanics
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• v.73 no.6
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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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• v.36 no.1
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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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• v.17 no.6
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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.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.3
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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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.35 no.4
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• pp.759-768
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• 2015

The ground motions of large dimensional structures such as long span bridges at different stations during an earthquake, are inevitably different, which is known as the ground motion spatial variation effect. There are many causes that may result in the spatial variability in seismic ground motion, e.g., the wave passage effect due to the different arrival times of waves at different locations; the loss of coherency due to seismic waves scattering in the heterogeneous medium of the ground; the site amplification effect owing to different local soil properties. In previous researches, the site amplification effects have not been considered or considered by a single-layered soil model only. In this study, however, the ground motion amplification and filtering effects are evaluated by multi-layered soil model. Spatially varying ground motion at the sites with different number of layers, depths, and soil characteristics are generated and the variation characteristics of ground motion time histories according to the correlation of coherency loss function and soil conditions are evaluated. For the bridge system composed of two unit bridges, seismic behavior characteristics are analyzed using the generated seismic waves as input ground motion. Especially, relative displacement due to coherency loss and site effect which can cause the unseating and pounding between girders are evaluated. As a result, considering the soil conditions of each site are always important and should not be neglected for an accurate structural response analysis.

• Steel and Composite Structures
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• v.22 no.5
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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.