• 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.

• 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.

• Structural Engineering and Mechanics
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• v.43 no.5
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• pp.637-655
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• 2012

In this study, stochastic responses of a cable-stayed bridge subjected to the spatially varying earthquake ground motion are investigated by the finite element method taking into account soil-structure interaction (SSI) effects. The considered bridge in the analysis is Quincy Bay-view Bridge built on the Mississippi River in between 1983-1987 in Illinois, USA. The bridge is composed of two H-shaped concrete towers, double plane fan type cables and a composite concrete-steel girder deck. In order to determine the stochastic response of the bridge, a two-dimensional lumped masses model is considered. Incoherence, wave-passage and site response effects are taken into account for the spatially varying earthquake ground motion. Depending on variation in the earthquake motion, the response values of the cable-stayed bridge supported on firm, medium and soft foundation soil are obtained, separately. The effects of SSI on the stochastic response of the cable-stayed bridge are also investigated including foundation as a rigidly capped vertical pile groups. In this approach, piles closely grouped together beneath the towers are viewed as a single equivalent upright beam. The soil-pile interaction is linearly idealized as an upright beam on Winkler foundation model which is commonly used to study the response of single piles. A sufficient number of springs on the beam should be used along the length of the piles. The springs near the surface are usually the most important to characterize the response of the piles surrounded by the soil; thus a closer spacing may be used in that region. However, in generally springs are evenly spaced at about half the diameter of the pile. The results of the stochastic analysis with and without the SSI are compared each other while the bridge is under the sway of the spatially varying earthquake ground motion. Specifically, in case of rigid towers and soft soil condition, it is pointed out that the SSI should be significantly taken into account for the design of such bridges.

• Earthquakes and Structures
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• v.26 no.5
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• pp.401-416
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• 2024

Long-span structures, such as bridges, can experience different seismic excitations at the supports due to spatially variability of ground motion. Regarding current bridge designing codes, it is just EC 2008 that suggested some regulations to consider it and in the other codes almost ignored while based on some previous studies it is found that the effect of mentioned issue could not be neglected. The current study aimed to perform a comprehensive study about the effect of spatially varying ground motions on the dynamic response of a reinforced concrete bridge under asynchronous input motions considering soil-structure interactions. The correlated ground motions were generated by an introduced method that contains all spatially varying components, and imposed on the supports of the finite element model under different load scenarios. Then the obtained results from uniform and non-uniform excitations were compared to each other. In addition, the effect of soil-structure interactions involved and the corresponding results compared to the previous results. Also, to better understand the seismic response of the bridge, the responses caused by pseudo-static components decompose from the total response. Finally, an incremental dynamic analysis was performed to survey the non-linear behavior of the bridge under assumed load scenarios. The outcomes revealed that the local site condition plays an important role and strongly amplifies the responses. Furthermore, it was found that a combination of wave-passage and strong incoherency severely affected the responses of the structure. Moreover, it has been found that the pseudo-static component's contribution increase with increasing incoherent parameters. In addition, regarding the soil condition was considered for the studied bridge, it was found that a combination of spatially varying ground motions and soil-structure interactions effects could make a very destructive scenarios like, pounding and unseating.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.143-152
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• 2019

In this study, stochastic responses of a cable-stayed bridge subjected to the spatially varying earthquake ground motion are investigated for variable local soil cases and wave velocities. Quincy Bay-view cable-stayed bridge built on the Mississippi River in Illinois, USA selected as a numerical example. The bridge is composed of two H-shaped concrete towers, double plane fan type cables and a composite concrete-steel girder deck. The spatial variability of the ground motion is considered with the coherency function, which is represented by the components of incoherence, wave-passage and site-response effects. The incoherence effect is investigated by considering Harichandran and Vanmarcke model, the site-response effect is outlined by using hard, medium and soft soil types, and the wave-passage effect is taken into account by using 1000, 600 and 200 m/s wave velocities for the hard, medium and soft soils, respectively. Mean of maximum response values obtained from the analyses are compared with those of the specific cases of the ground motion model. It is concluded that the obtained results from the bridge model increase as the differences between local soil conditions cases of the bridge supports change from firm to soft. Moreover, the variation of the wave velocity has important effects on the responses of the deck and towers as compared with those of the travelling constant wave velocity case. In addition, the variability of the ground motions should be considered in the analysis of long span cable-stayed bridges to obtain more accurate results in calculating the bridge responses.

• Structural Engineering and Mechanics
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• v.82 no.3
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• pp.325-341
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• 2022

Previous major earthquakes indicated that the earthquake induced ground motions are typical non-stationary processes, which are non-stationary in both amplification and frequency. For the convenience of aseismic design and analysis, it usually assumes that the ground motions at structural supports are stationary processes. The development of time-frequency analysis technique makes it possible to evaluate the non-stationary responses of engineering structures subjected to non-stationary inputs, which is more general and realistic than the analysis method commonly used in engineering. In this paper, the wavelet-based stochastic vibration analysis methodology is adopted to calculate the non-stationary responses of multi-support structures. For comparison, the stationary response based on the standard random vibration method is also investigated. A frame structure and a two-span bridge are analyzed. The effects of non-stationary spatial ground motion and local site conditions are considered, and the influence of structural property on the structural responses are also considered. The analytical results demonstrate that the non-stationary spatial ground motions have significant influence on the response of multi-support structures.

• Structural Engineering and Mechanics
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• v.44 no.5
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• pp.663-680
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• 2012

Previous major earthquakes revealed that most damage of the buried segmented pipelines occurs at the joints of the pipelines. It has been proven that the differential motions between the pipe segments are one of the primary reasons that results in the damage (Zerva et al. 1986, O'Roueke and Liu 1999). This paper studies the combined influences of ground motion spatial variations and local soil conditions on the seismic responses of buried segmented pipelines. The heterogeneous soil deposits surrounding the pipelines are assumed resting on an elastic half-space (base rock). The spatially varying base rock motions are modelled by the filtered Tajimi-Kanai power spectral density function and an empirical coherency loss function. Local site amplification effect is derived based on the one-dimensional wave propagation theory by assuming the base rock motions consist of out-of-plane SH wave or combined in-plane P and SV waves propagating into the site with an assumed incident angle. The differential axial and lateral displacements between the pipeline segments are stochastically formulated in the frequency domain. The influences of ground motion spatial variations, local soil conditions, wave incident angle and stiffness of the joint are investigated in detail. Numerical results show that ground motion spatial variations and local soil conditions can significantly influence the differential displacements between the pipeline segments.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.6
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• pp.35-47
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• 2003

Seismic ground motion can vary significantly over distances comparable to the length of a majority of highway bridges on multiple supports. This paper presents results of fragility analysis of two actual highway bridges under ground motion with spatial variation. Ground motion time histories are artificially generated with different amplitudes, phases, as well as frequency contents at different support locations. Monte Carlo simulation is performed to study dynamic responses of the bridges under these ground motions. The effect of spatial variation on the seismic response is systematically examined and the resulting fragility curves are compared with those under identical support ground motion. This study shows that ductility demands for the bridge columns can be underestimated if the bridge is analyzed using identical support ground motions rather than differential support ground motions. Fragility curves are developed as functions of different measures of ground motion intensity including peak ground acceleration(PGA), peak ground velocity(PGV), spectral acceleration(SA), spectral velocity(SV) and spectral intensity(SI). This study represents a first attempt to develop fragility curves under spatially varying ground motion and provides information useful for improvement of the current seismic design codes so as to account for the effects of spatial variation in the seismic design of long-span bridges.

• Structural Engineering and Mechanics
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• v.54 no.1
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• pp.169-188
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• 2015

This study presents the effects of the spatial variation of ground motions in a hard rock site on the seismic responses of a base-isolated nuclear power plant (BI-NPP). Three structural models were studied for the BI-NPP supported by different number of lead rubber bearing (LRB) base isolators with different base mat dimensions. The seismic responses of the BI-NPP were analyzed and investigated under the uniform and spatial varying excitation of El Centro ground motion. In addition, the rotational degrees of freedom (DOFs) of the base mat nodes were taken to consider the flexural behavior of the base mat on the seismic responses under both uniform and spatial varying excitation. Finally, the seismic response results for all the analysis cases of the BI-NPP were investigated in terms of the vibration periods and mode shapes, lateral displacements, and base shear forces. The analysis results indicate that: (1) considering the flexural behavior of the base mat has a negligible effect on the lateral displacements of base isolators regardless of the number of the isolators or the type of excitation used; (2) considering the spatial variation of ground motions has a substantial influence on the lateral displacements of base isolators and the NPP stick model; (3) the ground motion spatial variation effect is more prominent on lateral displacements than base shear forces, particularly with increasing numbers of base isolators and neglecting flexural behavior of the base mat.

• 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.