Spatial Variability Of Ground Motion Research Articles

Seismic Response of a Steel Trussed Arch Structure to Spatially Varying Earthquake Ground Motions Including Site Effect

This paper investigates seismic response of a realistic large dimension steel trussed arch structure subjected to the combined spatially varying horizontal and vertical ground motions. The ground motion spatial variations associated with wave passage effect, coherency loss effect and local site effect are considered. In numerical calculations, the simulated spatially varying ground motions are individually compatible with response spectrum defined in Chinese Seismic Design Code, and are compatible with an empirical coherency loss function between each other. Compared with structural responses calculated using uniform and delayed excitations, numerical results show that seismic response is amplified when spatially varying ground motions including local site effect are considered. Each factor of ground motion spatial variations has a significant effect on the dynamic response of the structure. Numerical results also indicate that considering simultaneous vertical and horizontal ground motions will lead to more accurate response predictions of the trussed arch as compared with those obtained by considering horizontal excitations only. Therefore, to have an accurate structural response assessment and a better design of long span steel trussed arch structures, a reliable ground motion spatial variation model is essential.

The Effect of the Spatially Varying Earthquake Ground Motion on Random Hydrodynamic Pressures

In this paper, the effects of the spatially varying earthquake ground motion on random hydrodynamic pressures are investigated considering dam-reservoir-foundation interaction by Lagrangian approach. For this purpose, variable-number-nodes two-dimensional fluid finite elements based on the Lagrangian approach is programmed in FORTRAN language and incorporated into a general-purpose computer program SVEM, which is used for stochastic dynamic analysis of solid systems under spatially varying earthquake ground motion. The spatial variability of ground motion is taken into account with the incoherence, wave-passage and site response effects. As the effect of the wave-passage is investigated by using wave velocities of 1000 m/s, 1500 m/s and 2000 m/s, the incoherence effect is examined by considering the Harichandran-Vanmarcke and Luco Wong coherency models. The changing of the soil conditions from firm to soft soil types are selected for considering the site-response effect where the foundation supports are constructed. The effects of transient response and the water compressibility on hydrodynamic pressures are also investigated. The ground motion is described by filtered white noise and applied to each support point of the two dimensional finite element model of the dam-reservoir-foundation system in horizontal direction. It is observed that the spatially varying earthquake ground motion affects the mean of maximum values of random hydrodynamic pressures considerably.

Influence of ground motion spatial variation, site condition and SSI on the required separation distances of bridge structures to avoid seismic pounding

AbstractIt is commonly understood that earthquake ground excitations at multiple supports of large dimensional structures are not the same. These ground motion spatial variations may significantly influence the structural responses. Similarly, the interaction between the foundation and the surrounding soil during earthquake shaking also affects the dynamic response of the structure. Most previous studies on ground motion spatial variation effects on structural responses neglected soil–structure interaction (SSI) effect. This paper studies the combined effects of ground motion spatial variation, local site amplification and SSI on bridge responses, and estimates the required separation distances that modular expansion joints must provide to avoid seismic pounding. It is an extension of a previous study (Earthquake Engng Struct. Dyn. 2010; 39(3):303–323), in which combined ground motion spatial variation and local site amplification effects on bridge responses were investigated. The present paper focuses on the simultaneous effect of SSI and ground motion spatial variation on structural responses. The soil surrounding the pile foundation is modelled by frequency‐dependent springs and dashpots in the horizontal and rotational directions. The peak structural responses are estimated by using the standard random vibration method. The minimum total gap between two adjacent bridge decks or between bridge deck and adjacent abutment to prevent seismic pounding is estimated. Numerical results show that SSI significantly affects the structural responses, and cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.

Influence of irregular topography and random soil properties on coherency loss of spatial seismic ground motions

AbstractCoherency functions are used to describe the spatial variation of seismic ground motions at multiple supports of long span structures. Many coherency function models have been proposed based on theoretical derivation or measured spatial ground motion time histories at dense seismographic arrays. Most of them are suitable for modelling spatial ground motions on flat‐lying alluvial sites. It has been found that these coherency functions are not appropriate for modelling spatial variations of ground motions at sites with irregular topography (Struct. Saf. 1991; 10(1):1–13). This paper investigates the influence of layered irregular sites and random soil properties on coherency functions of spatial ground motions on ground surface. Ground motion time histories at different locations on ground surface of the irregular site are generated based on the combined spectral representation method and one‐dimensional wave propagation theory. Random soil properties, including shear modulus, density and damping ratio of each layer, are assumed to follow normal distributions, and are modelled by the independent one‐dimensional random fields in the vertical direction. Monte‐Carlo simulations are employed to model the effect of random variations of soil properties on the simulated surface ground motion time histories. The coherency function is estimated from the simulated ground motion time histories. Numerical examples are presented to illustrate the proposed method. Numerical results show that coherency function directly relates to the spectral ratio of two local sites, and the influence of randomly varying soil properties at a canyon site on coherency functions of spatial surface ground motions cannot be neglected. Copyright © 2010 John Wiley & Sons, Ltd.

A method for generating fully non-stationary and spectrum-compatible ground motion vector processes

Earthquake ground motion spatial variability can influence significantly the response of certain structures. In order to accurately evaluate probabilistic characteristics of the seismic response of structures, the Monte Carlo simulation technique is still the only universal method of analysis when strong nonlinearities and input uncertainties are involved. Consequently, realizations of ground motion time histories taking into account both time and spatial variability need to be generated. Furthermore, for some design applications, the generated time histories must also satisfy the provision imposed by certain seismic codes stating that they have to be also response-spectrum-compatible. For these purposes, a spectral-representation-based methodology for generating fully non-stationary and spectrum-compatible ground motion vector processes at a number of locations on the ground surface is proposed in this paper. The simulated time histories do not require any iterations on the individual generated sample functions so that Gaussianity and prescribed coherence are suitably preserved. The methodology has also the advantage of providing the fully non-stationary and spectrum-compatible cross-spectral density matrix of the ground motion time-histories that can be used for reliability studies in an analytic stochastic fashion.

Response of a frame structure on a canyon site to spatially varying ground motions

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.

Wave Passage and Ground Motion Incoherency Effects on Seismic Response of an Extended Bridge

This paper investigates the implications of ground motion spatial variability on the seismic response of an extended highway bridge. An existing 59-span, 2,164-meter bridge with several bearing types and irregularity features was selected as a reference structure. The bridge is located in the New Madrid Seismic Zone and supported on thick layers of soil deposits. Site-specific bedrock input ground motions were selected based on a refined probabilistic seismic hazard analysis of the bridge site. Wave passage and ground motion incoherency effects were accounted for after propagating the bedrock records to the ground surface. The results obtained from inelastic response-history analyses confirm the significant impact of wave passage and ground motion incoherency on the seismic behavior of the bridge. The amplification in seismic demands exceeds 150%, whereas the maximum suppression of these demands is less than 50%. The irregular and unpredictable changes in structural response owing to asynchronous earthquake records necessitate in-depth seismic assessment of major highway bridges with advanced modeling techniques to realistically capture their complex seismic response. DOI: 10.1061/(ASCE)BE.1943-5592.0000155. © 2011 American Society of Civil Engineers. CE Database subject headings: Bridges, highway; Wave action; Seismic analysis; Inelasticity; Dynamic analysis. Author keywords: Extended highway bridges; Seismic assessment; Wave passage; Ground motion incoherence; Site effects; Inelastic dynamic analysis.

The Influence of Geographical Resolution of Urban Exposure Data in an Earthquake Loss Model for Istanbul

Exposure data available to developers of earthquake loss models are often very crudely aggregated spatially, and in such cases very considerable effort can be required to refine the geographical resolution of the building stock inventory. The influence of the geographical resolution of the exposure data for the Sea of Marmara region in Turkey is explored using several different levels of spatial aggregation to estimate the losses due to a single earthquake scenario. The results show that the total damage over an urban area, expressed as a mean damage ratio (MDR), is rather insensitive to the spatial resolution of the exposure data if a sufficiently large number of ground-motion simulations are used. However, the variability of the MDR estimates does reduce as the spatial resolution becomes higher, reducing the number of simulations required, although there appears to be a law of diminishing returns in going to very high exposure data resolution. This is largely due to the inherent and irreducible spatial variability of ground motion, which suggests that if only mean MDR estimates are needed, the effort required to refine the spatial definition of exposure data is not justified.

Effect of material uncertainty on stochastic response of dams

The present research considers the effect of uncertain material parameters on the stochastic dynamic response of an asphaltic lining dam–foundation system subjected to both stationary and non-stationary random excitation. The uncertain material parameters of interest are the shear modulus and mass density, which are modelled using a log-normal distribution. The Monte Carlo simulation method determines the stochastic seismic response of the dam–foundation system to spatially varying ground motion with uncertain material parameters. Consideration of the spatial variability of ground motion incorporates incoherence and wave passage effects from both stationary and non-stationary random excitations. A Heaviside modulating function is used throughout the study for the non-stationary responses. The results obtained indicate that variability of the shear modulus should be included in a stochastic dynamic analysis of an asphaltic lining dam–foundation system, but variability of the mass density can be neglected. Also, from the results, stationarity is a reasonable assumption for asphaltic lining dams in response to typical durations of strong shaking.

Deconvolved Stochastic Seismic Excitation Effect on the Nonlinear Response of Asphaltic Lining Dam-Foundation Interaction Systems

The effect of the deconvolved stochastic seismic excitation on the nonlinear response of dam-foundation interaction systems is investigated in this paper using the equivalent linear method. For this purpose, three different earthquake input mechanisms are used: the standard-rigid-base input model, the massless-foundation input model and the deconvolved-base-rock input model. The spatial variability of ground motion including the incoherence and wave-passage effects are taken into account in the analyses. The Izmit earthquake in 1999 is selected as sample ground motion. Two-dimensional interface finite elements are used between the dam-soil deposit and the asphalt face and also between the foundation-soil deposit and the cut-off wall. The mean of the absolute maximum displacement and stress values obtained from the three earthquake input models are compared with each other.

Seismic Response of Power Transmission Tower‐Line System Subjected to Spatially Varying Ground Motions

The behavior of power transmission tower‐line system subjected to spatially varying base excitations is studied in this paper. The transmission towers are modeled by beam elements while the transmission lines are modeled by cable elements that account for the nonlinear geometry of the cables. The real multistation data from SMART‐1 are used to analyze the system response subjected to spatially varying ground motions. The seismic input waves for vertical and horizontal ground motions are also generated based on the Code for Design of Seismic of Electrical Installations. Both the incoherency of seismic waves and wave travel effects are accounted for. The nonlinear time history analytical method is used in the analysis. The effects of boundary conditions, ground motion spatial variations, the incident angle of the seismic wave, coherency loss, and wave travel on the system are investigated. The results show that the uniform ground motion at all supports of system does not provide the most critical case for the response calculations.

Evaluation of Two Approaches to Simulate Spatially Variable Ground Motions

Spatial variability of ground motions has significant influence on dynamic response of extended structures such as bridges and tunnels. This study systematically evaluates two commonly used procedures for developing spatially variable ground motion time series considering incoherency effect, wave passage effect, and effect of intermediate stations. The evaluation included the methods' ability to: handle general forms of incoherency function, correctly account for wave passage, conserve energy, and be minimally influenced by the presence of intermediate stations. The method that can mostly satisfy these requirements is identified in this article.

Required separation distance between decks and at abutments of a bridge crossing a canyon site to avoid seismic pounding

AbstractMajor earthquakes in the past indicated that pounding between bridge decks may result in significant structural damage or even girder unseating. With conventional expansion joints, it is impossible to completely avoid seismic pounding between bridge decks, because the gap size at expansion joints is usually not big enough in order to ensure smooth traffic flow. With a new development of modular expansion joint (MEJ), which allows a large joint movement and at the same time without impeding the smoothness of traffic flow, completely precluding pounding between adjacent bridge decks becomes possible. This paper investigates the minimum total gap that a MEJ must have to avoid pounding at the abutments and between bridge decks. The considered spatial ground excitations are modelled by a filtered Tajimi‐Kanai power spectral density function and an empirical coherency loss function. Site amplification effect is included by a transfer function derived from the one‐dimensional wave propagation theory. Stochastic response equations of the adjacent bridge decks are formulated. The effects of ground motion spatial variations, dynamic characteristics of the bridge and the depth and stiffness of local soil on the required separation distance are analysed. Soil–structure interaction effect is not included in this study. The bridge response behaviour is assumed to be linear elastic. Copyright © 2009 John Wiley & Sons, Ltd.

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.

Seismic design of bridge structures with allowance for large relative girder movements to avoid pounding

Pounding between bridge girders have been observed in almost all previous major earthquakes. This is because the gap size of conventional bridge expansion joint is usually only a few centimetres, which is not sufficient to preclude poundings owing to large relative displacements between bridge girders caused by the effect of varying vibration properties of adjacent bridge spans, varying ground motions at bridge supports and varying soil-structure interaction (SSI). In this work a new design of bridge expansion joint is introduced. Instead of tolerating pounding and providing possible mitigating measures, this new design approach enables large movement between bridge girders which makes a complete pounding preclusion possible. The new expansion joint is called Modular Expansion Joint (MEJ). The large movability is achieved by installing a number of small gaps in the joint. In this study, the MEJ gap size required to completely avoid girder pounding is investigated. The most significant influence factors – the varying vibration properties of adjacent bridge spans, the effect of SSI and ground motion spatial variation on expansion joint size required to preclude pounding- are calculated. Discussions on the relative importance of various structural and ground motion properties in generating relative displacements of adjacent bridge girders are made.

Deterministic Seismic Scenarios for Imphal City

In this article, the spatial variation of ground motion in Imphal City has been estimated by the finite-fault seismological model coupled with site response analysis. The important seismic sources around Imphal City have been identified from the fault map and past seismicity data. The rock level acceleration time histories at Imphal City for the 1869 Cachar (Mw 7.5) earthquake and a hypothetical Mw 8.1 event in the Indo-Burma subduction zone have been estimated by a stochastic finite-fault model. Soil investigation data of 122 boreholes have been collected from several construction projects in Imphal City. Site response analysis has been carried out and the surface level ground motion has been determined for Imphal City for these two earthquake events. The results are presented in the form of peak ground acceleration (PGA) contour map. From the present study it has been ascertained that the maximum amplification for PGA over Imphal City is as high as 2.5. The obtained contour maps can serve as guidelines for identifying vulnerable areas and disaster mitigation in Imphal City.

Evaluation of seismic response of bridges under asynchronous excitation and comparisons with Eurocode 8-2 provisions

The paper aims to evaluate the way Eurocode 8 treats the consideration of asynchronous earthquake ground motion during the seismic design of bridges, and to discuss alternative solutions for cases wherein existing provisions do not lead to satisfactory results. The evaluation of EC8-2 new provisions and simplified methods is performed through comparison with a more refined approach whereas an effort is made to quantitatively assess the relative importance of various design and analysis assumptions that have to be made when spatial variability of ground motion is taken into consideration, based on the study of the dynamic response of 27 different bridges. It is concluded that, despite the complexity of the problem, there are specific cases where EC8 provisions can be safely and easily applied in practice, while in other cases ignoring the effect of asynchronous excitation or performing simplified calculations can significantly underestimate the actual seismic demand.

Random vibration analysis of long-span structures subjected to spatially varying ground motions

On the basis of the pseudo-excitation method (PEM), a random vibration methodology is formulated for the seismic analysis of multi-supported structures subjected to spatially varying ground motions. The ground motion spatial variability consists of the wave passage, incoherence and site–response effects. Advantages of this method are that less computation effort is required and that the cross-correlations both between normal modes and between excitations are automatically included. Random seismic responses of a realistic long-span bridge due to the wave passage, incoherence and site–response effects are extensively investigated. It is shown that all these effects have significant influence on the seismic response of the structure.

Response of a Rc Bridge in WA to Simulated Spatially Varying Seismic Ground Motions

In this paper, numerical results from a non-linear dynamic response analysis of a 50 m long two-span RC bridge in the Perth Metropolitan Area (PMA) to simulated spatially varying seismic ground motions are presented and discussed. Spatially varying ground motions are stochastically simulated to be compatible with the design spectrum for different site conditions given in the Draft Australian Earthquake Loading Code, and are compatible with an empirical coherency loss function representing highly, intermediately and weakly correlated spatial ground motions. Effects of ground motion spatial variation, bridge bearing stiffness, gap size of the expansion joint, and soil stiffness on impact force between the girders, and bending moment and shear force of the pier are investigated. Discussions on the influence of ground motion spatial variations on bridge structure response are made.

Significance of SSI and non-uniform near-fault ground motions in bridge response II: Effect on response with modular expansion joint

This is the second part of the study of soil–structure interaction (SSI) and ground motion spatial variation effects on bridge pounding responses. The first part [Chouw N, Hao H. Significance of SSI and non-uniform near-fault ground motions in bridge response I: Effect on response with conventional girder gap. J Eng Struct. [in press]] concentrated on studying the responses of bridges with a traditional expansion joint between adjacent girders. The main objective of this second paper is to investigate the influence of spatial variation of ground motions and SSI on the minimum total gap that a modular expansion joint system (MEJS) between two bridge frames must have to prevent any pounding between the adjoined girders. This minimum total gap is critical in a MEJS design because it ensures intact expansion joint and adjacent girders. Additional investigations of pounding response with a large total gap of a MEJS are performed to study the characteristics of pounding responses when collision does occur e.g. due to unintended underestimation of the ground excitation magnitude, which may be different from the pounding responses between bridge girders with a small gap of a conventional expansion joint. The spatially varying ground excitations are simulated stochastically based on an empirical near-source response spectrum and an empirical coherency loss function. The investigation reveals that neglecting spatial variation of ground motions and SSI can significantly underestimate the total gap of a MEJS required to avoid pounding between the adjacent bridge girders. The results also show that pounding between girders with a large gap of a MEJS in general causes stronger impact forces. Compared with the results reported in the first part of this study, using a MEJS with a large gap is likely to completely preclude bridge girder pounding, and consequently to prevent local damage at the girder ends. However, a large girder movement results in large bending moment in bridge piers, which compensates the advantages of using MEJS in bridges to resist earthquake loading.