Non-uniform Seismic Excitation Research Articles

Seismic responses of deep buried pipeline under non-uniform excitations from large scale shaking table test

The seismic response of long deep buried pipeline under non-uniform excitation is very important for suitable seismic design. However, due to restriction by excitation devices, few model tests have been carried out. In this study, a large-scale shaking table model test for a long deep buried pipeline was carried out, where two controlled-independent tables were used to excite two model containers and the excitations for the two tables are in the three directions and non-uniform. From the model test, the strains and deformations of the pipeline and the accelerations of the soil in containers were measured and evaluated. Some results were achieved: (1) non-uniform seismic excitation has great influence on the acceleration amplification in soil and the strain and displacement of the pipeline; (2) the deep buried pipe in ground has few impact on ground surface acceleration response, but has greater impact on the acceleration response of the soil surrounding the pipe; (3) the bending stain and permanent displacement under uniform excitation are negligible, but not neglected for non-uniform excitation; (4) the model test proves that there is obvious rotation of the pipeline in addition to horizontal and vertical displacements under non-uniform excitation.

Seismic input methods in coupled system of train-track-bridge

To research the influence of seismic input method on the seismic response of traintrack-bridge system, four methods are adopted to input non-uniform seismic excitation, including direct solving method, relative motion method, large mass method and large stiffness method. Train-track-bridge dynamic analysis models under different seismic input methods are established. Taking rigid frame-continuous composite beam bridge with the span of (48+5×80+48) m as an example, the seismic responses of coupled system of train-track-bridge under different seismic input methods are compared. The results show that the seismic responses of vehicle and bridge system from large stiffness method and direct solving method are the same, derailment coefficients and the rates of wheel load reduction from large mass method are bigger than that from direct solving method, the maximum deviation reaches 44.0% and 26.4%; the derailment coefficients, the rates of wheel load reduction and bridge displacements from relative motion method are smaller than that from direct solving method with maximum deviation of 32.5%, 12.8% and 51.9% respectively. As large stiffness method only requires the input of dynamic displacement time-history, so it is more convenient than direct soling method.

Multi-point shaking table test of a long tunnel subjected to non-uniform seismic loadings

A 40-m long test was conducted to estimate the seismic performance of the tunnel of the Hong Kong–Zhuhai–Macau Bridge project under non-uniform earthquake loadings. The test used twelve connected model boxes, a synthetic model soil and a scaled model tunnel. The model boxes included four “active” boxes, which were fixed to four isolated shaking tables that worked as excitation sources, and eight “inactive” boxes, which were passively excited by the active boxes through connections. The soil at the tunnel location was simulated with a mixture of sawdust and sand with mass proportion 1:2.5, that yielded dynamic properties analogous to those of the in situ soil. The tunnel model, at a 1/60 scale, was composed of 98 sections, each with dimensions 600 × 375 × 170 mm, that were made of aluminum, which best approximated the target response of the actual tunnel, given the size of the model, geometry and scaled engineering properties required. In the tests, a non-uniform seismic excitation was provided by imposing the seismic wave to the active model boxes with a time lag equal to the time that would take a seismic wave to travel from one active box to the next along the axis of the tunnel. The test started with the assembly of the tunnel sections and installation of transducers on the tunnel at critical locations. After placement of the soil and the tunnel, the seismic loadings were applied through the active boxes. The test results showed that the acceleration response of the tunnel was larger than that of the surrounding soil. It was also found that the deformation of the tunnel joints under non-uniform excitation was larger than under uniform excitation, to the extent that it could jeopardize the safety of the tunnel had it been designed solely using the uniform excitation. The results of the experiments clearly showed that the effects of non-uniform seismic excitation should be considered for the seismic design of long tunnels.

Analytical Seismic Assessment of a Tall Long-Span Curved Reinforced-Concrete Bridge. Part I: Numerical Modeling and Input Excitation

The seismic response of bridges is affected by a number of modeling considerations, such as pier embedment, buried pile caps, seat-type abutments, pounding, bond slip and architecturally flared part of piers, and loading considerations, such as non-uniform ground excitations and orientation of ground motion components, which are not readily addressed by design codes. This article addresses a methodology for the nonlinear static and dynamic analysis of a tall, long-span, curved, reinforced-concrete bridge, the Mogollon Rim Viaduct. Various modeling scenarios are considered for the bridge components, soil-structure interaction system, and materials, i.e., concrete and reinforcing steel, covering all its geotechnical and structural aspects based on recent advances in bridge engineering. Various analysis methodologies (nonlinear static pushover, time history response to uniform and spatially variable seismic excitations, and incremental dynamic analyses) are performed. For the dynamic analyses, a suite of nine earthquake accelerograms are selected and their characteristics are investigated using seismic intensity parameters. A recently developed approach for the generation of non-uniform seismic excitations, i.e., spatially variable simulations conditioned on the recorded time series, is used. Methods for the evaluation of structural performance are discussed and their limitations addressed. The numerical results of the seismic assessment of the Mogollon Rim Viaduct are presented in the companion article (Part II). The sensitivity of the bridge response to the adopted modeling, loading and analyzing strategies, as well as the correlation between structural damage and seismic intensity parameters are examined in detail.

Multi-point shaking table test for long tunnels subjected to non-uniform seismic loadings - part II: Application to the HZM immersed tunnel

A series of multi-point shaking table tests are conducted on a long immersed tunnel designed for the Hongkong-Zhuhai-Macau linkage (HMZ linkage) under non-uniform seismic excitations. Details of experimental setup are first presented with particular focuses on: shaking table array of the four independent shaking tables; dynamic similitude design between scale model of soil and tunnel structure and prototype model; design and fabrication of the scaled model tunnel and model soil; and procedure for simulation of non-uniform seismic waves. A series of testing cases of the shaking tables are carried out on the model tunnel using input motions with different seismic amplitudes. Dynamic responses measured from the experiment include acceleration of soil stratum and model tunnel, as well as extension and closure of immersion joints. Acceleration and deformation responses in the tunnel segments and their connecting joints are investigated and analyzed in the test cases under both uniform and non-uniform seismic loadings, and the capacity of critical structural components, such as extension of joints is evaluated. Results show that the non-uniform seismic excitation significantly aggravates the extension of immersion joints compared to the uniform excitation, and thus the non-uniform seismic effect should be considered in the design of immersed tunnels.

Multi-point shaking table test for long tunnels subjected to non-uniform seismic loadings – Part I: Theory and validation

The spatially varying ground motions can significantly influence the dynamic response of extended structures such as tunnels. However, current knowledge on the effects of non-uniform seismic excitations on long tunnels is limited to analytical or numerical methods and lack of experimental or field data. This paper presents a confirmatory experimental method for long tunnels subjected to non-uniform excitations, using four independent shaking tables worked in coordination as a large linear shaking table array. The discrete multi-point input mechanism is deemed critical to accomplish a continuous and coordinated excitation over a long tunnel. A 40m-long segmental model container is developed to realize the equivalent transformation from the four independent shaking tables into continuous excitations. The dimension of the segmental model container as well as the connection between each of its components is determined after significant analytical and numerical simulations. A series of tests are conducted to investigate the wave passage effect along the length of the segmental model container. Results show that the wave passage effect is accurately reproduced with the test setup and the acceleration input scheme, and thus the validation of the design of the multi-point test system is approved.

Influence of Spatial Variability of Seismic Shock on Steel Hall with Experimentally Determined Elasto-Plastic Parameters of Steel Material

In the paper the influence of spatial variability of a seismic shock on an industrial steel hall was examined. Different models of seismic excitation were introduced. Firstly, a uniform seismic excitation model was applied, assuming identical motion of all supports of the hall. Then, a non-uniform excitation model was implemented. In that model subsequent points of the ground in the direction of wave propagation repeat the same motion with a certain time delay dependent on the wave velocity. Two direction of the wave passage were assumed: longitudinal (along the longer side of the hall) and transverse (along the shorter side of the hall). To guarantee proper nonlinear elasto-plastic behavior of the structure, the material parameters of the steel were determined experimentally. The dynamic analyses revealed that the response of the hall to the seismic shock was reported beyond the elastic range. Plastic effects appeared in some zones of the primary as well as the secondary structural members of the object, regardless of the excitation model. The model of non-uniform seismic excitation with transverse wave passage turned out to have the greatest impact on the dynamic response of the hall; the plastic strains obtained for that model were much greater than those obtained for other models. The transverse non-uniform excitation generated irreversible strains almost 3 times greater than the uniform excitation. The evolution of significant plastic effects was observed mainly for non-uniform excitations in the lower parts (girts and columns) of the hall, which were strongly affected by the different motions of the ground.

Evaluation on Impact Interaction between Abutment and Steel Girder Subjected to Nonuniform Seismic Excitation

This paper aims to evaluate the impact interaction between the abutment and the girder subjected to nonuniform seismic excitation. An impact model based on tests is presented by taking material properties of the backfill of the abutment into consideration. The conditional simulation is performed to investigate the spatial variation of earthquake ground motions. A two-span continuous steel box girder bridge is taken as the example to analyze and assess the pounding interaction between the abutment and the girder. The detailed nonlinear finite element (FE) model is established and the steel girder and the reinforced concrete piers are modeled by nonlinear fiber elements. The pounding element of the abutment is simulated by using a trilinear compression gap element. The elastic-perfectly plastic element is used to model the nonlinear rubber bearings. The comparisons of the pounding forces, the shear forces of the nonlinear bearings, the moments of reinforced concrete piers, and the axial pounding stresses of the steel girder are studied. The made observations indicate that the nonuniform excitation for multisupport bridge is imperative in the analysis and evaluation of the pounding effects of the bridges.

Seismic analysis of a long tunnel based on multi-scale method

Seismic analysis of long tunnels is difficult due to the lack of available computing power. In this paper, a multi-scale method is used to simulate dynamic responses of a long tunnel, which involves the concurrent discretization of the entire domain with both coarse- and fine-scale finite element meshes. The method can not only capture seismic responses along the full tunnel length, but also the detail structural responses of the segment linings and joints. Both material and contact nonlinearities are considered in the multi-scale model. Effects of buried depths, spectrum characteristics of input seismic waves, non-uniform seismic excitation and flexible joints, are thoroughly investigated on seismic responses of the tunnel. Results show: (1) the seismically induced stress of the tunnel is strongly correlated with the depth and is significantly amplified when the depth is one quarter of the incident wavelength; (2) the spectrum characteristics of the given seismic input waves do affect the amplitude and distribution of tunnel ovaling deformations as well as stresses; (3) the non-uniform seismic excitation will greatly aggravate the tunnel responses compared to the uniform excitation, and the effect of spatial distribution of earthquake excitation should be considered in the design of long tunnels; and (4) it is proved that the flexible joints can slightly mitigate the stress concentration, however, especial attention should be paid to the water proof capability of the flexible joints due to the expected additional deformation. Furthermore, stress and deformation response in lining segments and their connecting bolts are investigated and analyzed within the fine-scale model, and the capacity of critical structural components such as bolts and joints is evaluated.

Nonlinear Response of High Arch Dams to Nonuniform Seismic Excitation Considering Joint Effects

Nonuniform excitation due to spatially varying ground motions on nonlinear responses of concrete arch dams is investigated. A high arch dam was selected as numerical example, reservoir was modelled as incompressible material, foundation was assumed as mass-less medium, and all contraction and peripheral joints were modelled considering the ability of opening/closing. This study used Monte-Carlo simulation approach for generating spatially nonuniform ground motion. In this approach, random seismic characteristics due to incoherence and wave passage effects were investigated and finally their effects on structural response were compared with uniform excitation at design base level earthquake. Based on the results, nonuniform input leads to some differences than uniform input. Moreover using nonuniform excitation increase, stresses on dam body.

Numerical analysis of the Nanjing Dashengguan Yangtze River Bridge subjected to non-uniform seismic excitations

The Nanjing Dashengguan Yangtze River Bridge is a 108 + 192 + 336 + 336 + 192 + 108 m six-span continuous trussed-arch bridge on the Beijing-Shanghai High-speed Railway. As a feature of the long span structure, the response of the main bridge considering the traveling earthquake wave effect should be calculated. Thus, a finite element method (FEM) model is established. The natural frequencies and mode shapes are acquired by the eigen-parameter analysis. By inputting the El Centro earthquake accelerations to the bridge system in association with the Ex+0.3Ey+0.3Ez and 0.3Ex+Ey+0.3Ez components according to the Europe Code, the dynamic responses of the bridge, including the displacement and accelerations of the main nodes of the structure as well as the seismic forces of the key members, are calculated by the structural analysis program. Based on these responses, the main laws of the seismic responses of the bridge are summarized, and the safety of the structure is evaluated. The displacement and the internal force response of the main bridge excited by the El Centro earthquake, with the traveling speed of 300, 500, 1,000 and 2,000 m/s, respectively, are compared with the final results obtained by the spectrum analysis and the common time history analysis.

Effect of Asynchronous Earthquake Motion on Complex Bridges. II: Results and Implications on Assessment

Nonuniform seismic excitation has been shown through previous analytical studies to adversely affect the response of long-span bridge structures. To further understand this phenomenon, this study investigates the response of complex straight and curved long-span bridges under the effect of parametrically varying asynchronous motion. The generation process and modeling procedures are presented in a companion paper. A wide-ranging parametric study is performed aimed at isolating the effect of both bridge curvature and the two main sources of asynchronous strong motion: geometric incoherence and the wave-passage effect. Results from this study indicate that response for the 344m study structure is amplified significantly by nonsynchronous excitation, with displacement amplification factors between 1.6 and 3.4 for all levels of incoherence. This amplification was not constant or easily predicable, demonstrating the importance of inelastic dynamic analysis using asynchronous motion for assessment and design of this class of structure. Additionally, deck stiffness is shown to significantly affect response amplification, through response comparison between the curved and an equivalent straight bridge. Study results are used to suggest an appropriate domain for consideration of asynchronous excitation, as well as an efficient methodology for analysis.

Dynamic analysis of train–bridge system subjected to non-uniform seismic excitations

Based on the theory of dynamic wheel–rail interactions, a dynamic model of coupled train–bridge system subjected to earthquakes is established, in which the non-uniform characteristics of the seismic wave input from different foundations are considered. The bridge model is based on the modal comprehension analysis technique. Each vehicle is modelled with 31 degrees of freedom. The seismic loads are imposed on the bridge by using the influence matrix and exerted on the vehicles through the dynamic wheel–rail interaction relationships. The normal wheel–rail interaction is tackled by using the Hertzian contact theory, and the tangent wheel–rail interaction by the Kalker linear theory and the Shen–Hedrick–Elkins theory. A computer code is developed. A case study is performed to a continuous bridge on the planned Beijing–Shanghai high-speed railway in China. Through input of typical seismic waves with different propagation velocities to the train–bridge system, the histories of the train running through the bridge are simulated and the dynamic responses of the bridge and the vehicles are calculated. The influences of train speed and seismic wave propagation velocity on the dynamic responses of the bridge–vehicle system are studied. The critical train speeds are proposed for running safety on high-speed railway bridges under earthquakes of various intensities. Copyright © 2006 John Wiley & Sons, Ltd.

Simplified Modeling of Bridge Response on Soft Soil to Nonuniform Seismic Excitation

Simple modeling is developed for the response of bridges on soft soil to spatially nonuniform seismic excitation. The bridges are modeled as single- and multispan elastic frames founded on a homogeneous soil layer over rigid rock. Three different excitation types are considered: (1) general harmonic excitation with different amplitude and phase at each support; (2) oblique harmonic SH waves traveling within the soil layer (“wave-passage effect”); and (3) vertically propagating SH waves in conjunction with different soil conditions at the supports (“site-response effect”). Response of a single-span symmetric bridge is obtained by decomposing the excitation into symmetric and antisymmetric components. The analysis is then extended to a multispan integral bridge subjected to translational and rotational input. Harmonic and transient responses are considered and analytical expressions for various response parameters are obtained. Soil-structure interaction (SSI) effects are studied by considering long, drilled shaft foundations. To compare the effects of uniform and nonuniform input, pertinent response ratios are introduced. It is shown that when the amplitude of ground motion varies among the supports, defining a reference uniform excitation is not straightforward.

Nonlinear Dynamic Analysis of a Structure Subjected to Multiple Support Motions

A modal superposition method for the nonlinear dynamic analysis of a structure subjected to multiple support motions is presented. The nonlinearities are due to clearances between the components and their supports. The finite element method is used to derive the equations of motion with the nonlinearities represented by a pseudo force vector. The displacement response may be divided into two parts: elastic deformation and rigid body motion. The presence of rigid body motion necessitates the inclusion of the higher modes in the transient analysis. The modal superposition method is used to analyze the dynamic response of one loop of the nuclear steam supply system. This loop has nonlinear supports and is subjected to nonuniform seismic excitations at the supports. It is shown that the computational cost of the modal superposition method is lower than that of the direct integration.