Empirical Coherency Loss Function Research Articles

Simulation of Spatially Varying Ground Motions in V-shaped Symmetric Canyons

A method of simulating spatially varying ground motions in V-shaped symmetric canyon is presented. The topographic amplification effect is taken into account by considering a 2-dimension wave propagation model. Two approaches are developed to simulate spatially varying ground motions. First, the spatially varying ground motions are simulated by using the power spectral density and an empirical coherency loss function. Second, the spatially varying ground motions are simulated by using given ground motions and an empirical coherency loss function. These two proposed methods are validated by comparing statistical characteristics of the synthetic motions with target theoretical models.

Field Tests on Total Gap of Modular Expansion Joints to Avoid Bridge Pounding

Modular expansion joints (MEJs) are used for accommodating large relative displacements of adjacent bridge segments and for completely eliminating pounding. However, the minimum total gap that an MEJ needs to avoid pounding is not well investigated. To provide guidance for the seismic gap of MEJs, the maximum relative displacement of adjacent bridge segments subject to strong earthquakes was studied experimentally. To date, no experimental investigation of excitation spatial variation effect on bridge on natural soil has been reported. This research addressed a bridge with three identical segments of 100 m. A 1:22 scale bridge model founded on compacted beach sand was tested using electro-magnetic inertial exciters. Different ground motions were applied to the model to simulate the effect of spatially varying ground motions. Soil-structure interaction (SSI) was studied by comparing the minimum total gaps with those obtained from the fixed-based experiments in the laboratory. The spatially varying ground motions were simulated based on the New Zealand design spectra for soft soil, shallow soil and strong rock conditions using an empirical coherency loss function. SSI was found to reduce the minimum total gap of an MEJ needed to avoid pounding between adjacent segments. Under spatially varying ground motions designing adjacent bridge segments with identical or similar fundamental frequencies is still recommended even if it does not necessarily preclude an out-of-phase movement of adjacent structures.

Effect of soil flexibility on bridges subjected to spatially varying excitations

Pounding is a major cause of bridge damage during earthquakes. In an extreme situation, it can even contribute to the unseating of bridge girders. Long-span bridges will inevitably experience spatially varying ground motions. Soil-structure interaction (SSI) may play a significant role in the structural response of these structures. The objective of this research is to experimentally investigate the effect of spatially varying ground motions on the response of a three-segment bridge considering SSI and pounding. To incorporate SSI, the model was placed on sand contained in sandboxes. The sandboxes were fabricated using soft rubber in order to minimise the rigid wall effect. The spatially varying ground motion inputs were simulated based on the New Zealand design spectra for soft soil, shallow soil and strong rock conditions, using an empirical coherency loss function. The results show that with pounding, SSI can amplify the pier bending moments and the relative opening displacements.

Effect of abutment excitation on bridge pounding

Bridge damage due to pounding at joints of girders and abutments has been observed in many major earthquakes. One reason that this pounding phenomenon is so common is due to the differences between the dynamic characteristics of a girder and the relatively rigid adjoining abutments. Hence, a good understanding of girder–abutment pounding is critical for bridge design. However, the studies on this topic have mainly been numerical and abutment excitation was rarely considered. Very limited experimental investigations were conducted, none of which considered the effect of abutment motion on bridge pounding response. The objective of this study is to experimentally evaluate the influence of abutment excitations on the pounding behaviour of a system consisting of a single bridge span with various fundamental frequencies and its abutments using three shake tables. The excitations are applied in the longitudinal direction of the bridge span. The spatially varying ground excitations are simulated based on the New Zealand design spectra for soft soil, shallow soil and strong rock conditions using an empirical coherency loss function. Results show that with the spatial variation effect of ground motions, a consideration of movable rather than fixed abutments leads to greater relative opening displacement with its adjacent structure and larger pounding potential.

Influence of ground motion spatial variations and local soil conditions on the seismic responses of buried segmented pipelines

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.

Experimental investigation of spatially varying effect of ground motions on bridge pounding

SUMMARYPounding between adjacent bridge structures with insufficient separation distance has been identified as one of the primary causes of damage in many major earthquakes. It takes place because the closing relative movement is larger than the structural gap provided between the structures. This relative structural response is controlled not only by the dynamic properties of the participating structures but also by the characteristics of the ground excitations. The consequence of the spatial variation of ground motions has been studied by researchers; however, most of these studies were performed numerically. The objective of the present research is to experimentally evaluate the influence of spatial variation of ground motions on the pounding behaviour of three adjacent bridge segments. The investigation is performed using three shake tables. The input spatially varying ground excitations are simulated based on the New Zealand design spectra for soft soil, shallow soil and strong rock using an empirical coherency loss function. Results confirm that the spatially nonniform ground motions increase the relative displacement of adjacent bridge girders and pounding forces. Copyright © 2012 John Wiley & Sons, Ltd.

Modelling and simulation of spatially varying earthquake ground motions at sites with varying conditions

In a flat and uniform site, it is reasonable to assume that the spatially varying earthquake ground motions at various locations have the same power spectral density or response spectrum. If an engineering site with varying soil conditions at different structural supports is considered, this assumption is no longer valid because of different local site amplification effect. This paper presents an approximate method to model and simulate spatially varying ground motions on the surface of an uneven site with non-uniform conditions at different locations in two steps. In the first step, the base rock motions at different locations are assumed to have the same intensity, and are modelled by a filtered Tajimi–Kanai power spectral density function or other stochastic ground motion attenuation models. The base rock ground motion spatial variation is modelled by an empirical coherency loss function. The power spectral density functions of the surface motions on the site with multiple soil layers are derived based on the deterministic 1D wave propagation theory, neglecting the wave scattering on the uneven canyon surface, and assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SVwaves propagating into the site with an assumed incident angle. In the second step, a stochastic method to generate spatially varying time histories compatible with non-uniform spectral densities and a coherency loss function is developed to generate ground motion time histories on an uneven site. Two numerical examples are presented to demonstrate the proposed method. Each generated ground motion time history is compatible with the derived power spectral density at a particular point on the site or response spectrum corresponding to the respective site conditions, and any two of them are compatible with a model coherency loss function.

Seismic Response Analysis of Transmission Tower-Line System on a Heterogeneous Site to Multi-Component Spatial Ground Motions

This paper studies the nonlinear responses of a coupled transmission towerline system on a heterogeneous site subjected to multi-component spatially varying ground motions. The three-dimensional finite element model of the transmission tower-line system is established with consideration of the geometric nonlinearity of the transmission lines. The spatial variation of ground motions associated with the wave passage, coherency loss and local site effects are considered. The spatial ground motions on ground surface are derived by modelling the base rock motion propagating through the local soil sites. The base rock motions are assumed consisting of out-of-plane and in-plane waves and are simulated stochastically based on an empirical coherency loss function and the filtered Tajimi-Kanai power spectral density function. The effects of multi-component, spatial variations of ground motions and varying site conditions at multiple tower foundations on seismic response of the transmission tower-line system are analysed. The study reveals that for a reliable seismic response analysis and safe and economic seismic resistance design of transmission tower-line systems, the multi-support and multi-component earthquake excitations with consideration of the effects of local site conditions on ground motion spatial variations should be considered.

Seismic behaviour of isolated multi-span continuous bridge to nonstationary random seismic excitation

This paper concentrates on the results of responses of a multi-span continuous bridge isolated with double concave friction pendulum bearings subjected to non-stationary random seismic excitation characterized by the incoherence, the wave-passage, and the site-response effects. The earthquake excitation is modelled as a non-stationary random process as uniformly modulated broad-band excitation. To perform the seismic isolation procedure, the double concave friction pendulum bearings which are sliding devices that utilize two spherical concave surfaces are placed at each of the six support points of the deck. The non-stationary response of the isolated bridge is compared with the corresponding stationary response in order to study the effects of non-stationary characteristics of the earthquake input motion. Solutions obtained from the stationary and non-stationary stochastic analyses for the isolated bridge to spatially varying earthquake ground motions are compared for the special cases of the earthquake ground motion model. The spatially varying earthquake ground motions are described stochastically based on an empirical coherency loss function and a filtered power spectral density function. The site effect is considered by a transfer function derived from one dimensional wave propagation theory. It is observed that the stationary assumption is reasonable for the considered ground motion duration.

Response of a transmission tower-line system at a canyon site to spatially varying ground motions

Collapses of transmission towers were often observed in previous large earthquakes such as the Chi-Chi earthquake in Taiwan and Wenchuan earthquake in Sichuan, China. These collapses were partially caused by the pulling forces from the transmission lines generated from out-of-phase responses of the adjacent towers owing to spatially varying earthquake ground motions. In this paper, a 3D finite element model of the transmission tower-line system is established considering the geometric nonlinearity of transmission lines. The nonlinear responses of the structural system at a canyon site are analyzed subjected to spatially varying ground motions. The spatial variations of ground motion associated with the wave passage, coherency loss, and local site effects are given. The spatially varying ground motions are simulated stochastically based on an empirical coherency loss function and a filtered Tajimi-Kanai power spectral density function. The site effect is considered by a transfer function derived from 1D wave propagation theory. Compared with structural responses calculated using the uniform ground motion and delayed excitations, numerical results indicate that seismic responses of transmission towers and power lines are amplified when considering spatially varying ground motions including site effects. Each factor of ground motion spatial variations has a significant effect on the seismic response of the structure, especially for the local site effect. Therefore, neglecting the earthquake ground motion spatial variations may lead to a substantial underestimation of the response of transmission tower-line system during strong earthquakes. Each effect of ground motion spatial variations should be incorporated in seismic analysis of the structural system.

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.

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.

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.

Seismic design for steel trussed arch to multi-support excitations

The behavior of steel trussed arch to multi-support excitations is studied. The spatial variation of ground motion is modeled by an empirical coherency loss function. Numerical results indicate that horizontal multi-support excitations have a quite large amplification effect on the seismic responses of the trussed arch. This amplification effect cannot be ignored in the seismic design of such structures. Vertical multi-support excitations reduce the seismic responses of the trussed arch. Therefore the assumption that vertical free-field ground motions are spatially uniform is available to assure the degree of seismic safety reliability of the trussed arch. An average response spectrum method is subsequently introduced to calculate the arch response to multi-support excitations. The advantage of the method is that the linear peak seismic response of the arch to multi-support excitations can be obtained as conveniently as the conventional response spectrum method does. The good agreement of results between the time-history method and the average response spectrum method shows the validity of the latter method.

Analysis of Coupled Lateral-Torsional-Pounding Responses of One-Storey Asymmetric Adjacent Structures Subjected to Bi-Directional Ground Motions Part II: Spatially Varying Ground Motion Input

This is the second paper presenting numerical results of a parametric study of seismic induced lateral-torsional-pounding responses of an asymmetric and a symmetric one-storey adjacent structure. The accompany paper (Part I) (Gong and Hao 2004) assumed ground motion input at all structural supports as uniform. Torsional responses are generated because of inherent structural eccentricity and eccentric pounding. In reality, seismic ground motion at different structural supports inevitably varies owing to wave propagation. Spatially varying ground motion will induce torsional responses of structures, and generate out-of-phase responses between adjacent structures. Thus it might have a significant effect on coupled lateral-torsional-pounding responses. This paper studies the ground motion spatial variation effect. For comparison purpose, same adjacent structure models and impact element used in Part I of this study are adopted here again. 20 sets of spatially varying ground motion time histories are stochastically simulated. All the time histories are compatible with the Newmark-Hall design response spectrum with 5% damping and normalized to 0.5g. The spatial variation of any two simulated time histories is compatible with an empirical coherency loss function. Coupled lateral-torsional-pounding responses of the two structures to the simulated ground motions are calculated. Discussions on the ground motion spatial variation effects are made.

Study of SSI and non-uniform ground motion effect on pounding between bridge girders

Abstracts This paper addresses the effect of spatial variations of ground motion with different wave propagation apparent velocities in soft and medium soil, and the influence of soil–structure interaction (SSI) on the pounding response of two adjacent bridge frames. Spatial ground motion time histories are simulated according to the Japanese design spectra and an empirical coherency loss function. In order to obtain a more reliable conclusion, three sets of spatial ground motions are independently simulated for each considered case. The ensemble mean girder responses obtained from the three independent time history analyses are used for the evaluation of the gap size required to avoid pounding between the bridge girders. The pounding behaviour of girders is analysed by using a combined finite element and boundary element method. The study reveals that both the ground motion spatial variation and SSI should be considered in the analysis of pounding responses of bridge girders.

Response of two-way eccentric building to nonuniform base excitations

This paper studies the combined effects of structural eccentricities and nonuniform base excitations on the coupled torsional-lateral responses of two way eccentric building structures. The structural model used is a single-storey rigid diaphragm supported by four columns. The spatially varying multiple base excitations in the two horizontal directions are considered. Linear elastic structural responses are calculated by time history analysis. Spatially varying ground motion time histories are simulated for the analysis. The simulated time histories are individually compatible with the Newmark-Hall design response spectrum with 5% damping and normalized to 0.5 g, and are compatible with an empirical coherency loss function between each other. Analyses are carried out on the coupled torsional-lateral responses of torsionally flexible and torsionally stiff structures. Results are presented in terms of nondimensional parameters. It is found that nonuniform ground excitations reduce base shear, but induce torque in a building structure. Their effect is more significant than the structural eccentricity effect to torsionally flexible structure, but structural eccentricity effect is more pronounced to torsionally stiff structure.

Seismic Response of Asymmetric Structures to Multiple Ground Motions

If ground motion is not uniform over a building's base, or if the building is asymmetric, torsional response occurs. This paper investigates the effect of torsional coupling induced by both multiple ground excitations and building asymmetry on earthquake forces. The system studied is an idealized single-story two-degrees-of-freedom building model with four supports. Spatially varying ground excitations at the supports are used. Thirty sets of spatially correlated ground-motion time histories are simulated for the analysis. Each set of the simulated time histories are compatible with an empirical coherency loss function of recorded motions, and they are also individually compatible with the Newmark-Hall response spectrum with 5% damping and normalized to 0.5 g . The mean and standard deviations of base shear and torque corresponding to the 30 sets of simulated time histories are calculated. Results are presented in terms of nondimensional parameters, accounting for both the eccentricity and multiple-ground...