Article

Assessment of the seismic behavior of short-to-medium overall length girder bridges under asynchronous ground motions

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Abstract

Proper seismic analysis and design of bridges are critical, especially in locations prone to high seismic activities where critical infrastructure is at a high risk of seismic damage leading to direct and indirect losses. The seismic performance of bridges has been widely investigated in the literature, but the effect of asynchronous ground motions for short-to-medium overall length girder bridges is a phenomenon that has not been adequately addressed by bridge codes and thus it warrants further research. For such bridges, the often-employed envelope response spectrum is not generally applicable for asynchronous ground motions as this is a multiple-support excitation problem where potential local demand concentrations are critical. This study investigates the effects of asynchronous ground motion on the seismic response of short-to-medium overall length girder bridges with reinforced concrete columns considering crustal, subcrustal and subduction earthquakes. The main source of spatial variability of ground motions considered was the variation in the local soil conditions at the foundation of 3-span (short) and 7-span (medium) overall length prototype girder bridges. Soil classes A (rocky soil) and E (softer soil) were considered to establish different combinations of soil distribution in the foundation and then compared to baseline models where site class C was applied to all the supports of the structure to study the effects of asynchronous ground motions. It was found that the variation of site class in the foundations for such structures could produce detrimental effects on the dynamic response of the structure. The presence of softer soil in most of the structure's foundations elongated the vibration period of the structure and resulted in higher displacement demands. Results also showed that critical demands are concentrated at locations where the soil conditions change, indicating increased sensitivity to seismic effects at certain locations, which would not be captured by the typical code-prescribed procedure in the presence of asynchronous ground motion effects.

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SUMMARYA method is presented for simulating arrays of spatially varying ground motions, incorporating the effects of incoherence, wave passage, and differential site response. Non-stationarity is accounted for by considering the motions as consisting of stationary segments. Two approaches are developed. In the first, simulated motions are consistent with the power spectral densities of a segmented recorded motion and are characterized by uniform variability at all locations. Uniform variability in the array of ground motions is essential when synthetic motions are used for statistical analysis of the response of multiply-supported structures. In the second approach, simulated motions are conditioned on the segmented record itself and exhibit increasing variance with distance from the site of the observation. For both approaches, example simulated motions are presented for an existing bridge model employing two alternatives for modeling the local soil response: i) idealizing each soil-column as a single-degree-of-freedom oscillator, and ii) employing the theory of vertical wave propagation in a single soil layer over bedrock. The selection of parameters in the simulation procedure and their effects on the characteristics of the generated motions are discussed. The method is validated by comparing statistical characteristics of the synthetic motions with target theoretical models. Response spectra of the simulated motions at each support are also examined. Copyright © 2011 John Wiley & Sons, Ltd.
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The effects of the spatial variability of the ground motion on the response of bridge structures are investigated in this study. Following a well-established convention, the phenomenon is represented as the combined effect of three causes: the loss of coherence of the motion with distance, the wave-passage, and the local site conditions. Since the nature and amount of non-synchronism vary within ample limits a statistical approach is adopted. A parametric study is carried out on a representative set of bridges subjected to carefully selected combinations of the factors inducing spatial variability. The investigation has shown that the phenomenon affects the response considerably and, hence, the level of protection of these structures. It is observed that for all bridge types considered, the ductility demands at the base of the piers in the presence of spatial variability increase in the majority of cases. Further, for a given bridge type, the probabilities of failure vary by more than one order of magnitude depending on the combination of the parameters. Attention has been focused on a parameter representing the ratio between the maximum curvature ductility demand and the same quantity for the case of fully synchronous motion. This parameter has been used to correct the conventional synchronous design procedure by increasing the available ductility. The re-analysis of all the cases with a modified ductility capacity shows that the procedure is effective in reducing the fragilities to the values corresponding to synchronous input. Copyright
Article
A theoretical model for the coherency function describing spatial variability of earthquake ground motions is developed. The model consists of three components characterizing three distinct effects of spatial variability, namely, the incoherence effect that arises from scattering of waves in the heterogeneous medium of the ground and their differential superpositioning when arriving from an extended source, the wave-passage effect that arises from difference in the arrival times of waves at different stations, and the site-response effect that arises from difference in the local soil conditions at different stations. Attenuation of waves, which also gives rise to spatial variability, is shown to have little influence on the coherency function. It is shown that the incoherence component of the coherency function is a real-valued, non-negative, decaying function of frequency and interstation distance, whereas the wave-passage and site-response components are complex functions of unit modulus that characterize the phasing of the wave components. A parametric study reveals that the site-response effect can be more significant for short- or medium-span structures situated in regions with rapidly varying local soil conditions, whereas the wave-passage effect can be more significant for long-span, flexible structures.
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The performance-based design of lifeline systems requires spatially variable seismic excitations at the structures' supports that are consistent with prescribed seismic ground motion characteristics and an appropriate spatial variability model—such motions can be obtained through conditional simulation. This work revisits the concept of conditional simulation and critically examines the conformity of the generated motions with the characteristics of the target random field and observations from data recorded at dense instrument arrays. Baseline adjustment processing techniques for recorded earthquake accelerograms are extended to fit the requirements of simulated and conditionally simulated spatially variable ground motions. Emphasis is placed on the use of causal vs acausal filtering in the data processing. Acceleration, velocity and displacement time histories are evaluated in two example applications of the approach. The first application deals with a prescribed synthetic time history that incorporates nonstationarity in the amplitude and frequency content of the motions and depends on earthquake magnitude, source–site distance and local soil conditions; this example results in zero residual displacements. The second application considers as prescribed time history a recording in the vicinity of a fault and yields nonzero residual displacements. It is shown that the conditionally simulated time histories preserve the characteristics of the prescribed ones and are consistent with the target random field. The results of this analysis suggest that the presented methodology provides a useful tool for the generation of spatially variable ground motions to be used in the performance-based design of lifeline systems. Copyright
Article
A method to obtain the dynamic response of an extended rigid foundation supported on an elastic half-space when subjected to a spatially varying ground motion including both random and deterministic effects is presented. The method relies on an integral representation of the response of the foundation in terms of the free-field ground motion. Numerical results for a rigid square foundation and for a ground motion characterized by a particular spatial coherence function are described. The results obtained indicate that the spatial randomness of the ground motion produces effects similar to the deterministic effects of wave passage including reduction of the translational components of the response at high frequencies and creation of rocking and torsional response components. The possibility of defining an effective apparent horizontal velocity which produces effects equivalent to those from a given spatial randomness is explored.
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The methodology for dealing with spatial variability of ground motion, site effects and soil–structure interaction phenomena in the context of inelastic dynamic analysis of bridge structures, and the associated analytical tools established and validated in a companion paper are used herein for a detailed parametric analysis, aiming to evaluate the importance of the above effects in seismic design. For a total of 20 bridge structures differing in terms of structural type (fundamental period, symmetry, regularity, abutment conditions, pier-to-deck connections), dimensions (span and overall length), and ground motion characteristics (earthquake frequency content and direction of excitation), the dynamic response corresponding to nine levels of increasing analysis complexity was calculated and compared with the ‘standard’ case of a fixed base, uniformly excited, elastic structure for which site effects were totally ignored. It is concluded that the dynamic response of RC bridges is indeed strongly affected by the coupling of the above phenomena that may adversely affect displacements and/or action effects under certain circumstances. Evidence is also presented that some bridge types are relatively more sensitive to the above phenomena, hence a more refined analysis approach should be considered in their case. Copyright @ 2003 John Wiley & Sons, Ltd.
Article
This paper presents a study of the influence of spatially variable ground motions on the longitudinal seismic response of a short, three-span, 30-degree skewed, reinforced concrete highway bridge. Linear and nonlinear finite element models are created for the bridge and linear elastic and nonlinear inelastic time history analyses conducted. Three different types of illustrative excitations are considered: The first utilizes spatially variable ground motions incorporating the effects of variable soil conditions, loss of coherency and wave passage as input motions at the structures' supports. The time history with the smallest peak displacement and the one with the largest peak displacement from the spatially variable ones are then used as uniform input motions at all bridge supports. The comparative analysis of the bridge model shows that the uniform ground motion input with the largest peak displacement cannot provide conservative seismic demands for all structural components—in a number of cases it results in lower response than that predicted by spatially variable motions. The present results indicate that there is difficulty in establishing uniform input motions that would have the same effect on the response of bridge models as spatially variable ones. Consequently, spatially variable input motions need to be applied as excitations at the bridge supports.
Article
The effect of the spatial variation of earthquake ground motion on the dynamic response of multiple-support structures may be important. The relative performance of two simple analytical methods to model multiple-support seismic analysis of large structures is investigated. These are the relative motion method (RMM), which divides the structural response into a dynamic response component and a pseudo-static response component, and the large mass method (LMM), which attributes fictitious large mass values at each driven nodal degree of freedom (DOF) to obtain the total response of the structure. The seismic response of a four-span bridge using the traveling wave assumption is used to illustrate the practical application of the methods. It is found that the LMM is able to yield results that are almost identical to those of the RMM using large mass values equal to approximately 107 times the total mass of the bridge. Parametric analyses where the travel wave speed is systematically varied show that the structural response tends to increase as the wave velocity decreases and can become significantly larger than the response obtained from synchronous excitation.
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