Multi-support Excitation Research Articles

Analysis of Depth Spatial Variations of Accelerograms Recorded from the Center for Engineering Strong Motion Data: Numerical Simulation for Multipoint Ground Motions

Studies on depth spatial variations are rare because of the limited number of measured recordings of the subsurface along the depth direction from the ground surface. However, these depth variations can directly influence the seismic dynamic response of underground structures or the foundations of space structures through multi-support excitation. In this study, depth spatial variations, including phase and amplitude, are analyzed to describe ground motions along different depths based on surface-earthquake time histories. The observed recordings from the Center for Engineering Strong Motion Data are used to investigate the spatial variation characteristics of the phase and amplitude in the depth direction, represented by the lagged coherence and Fourier amplitude spectrum ratio, respectively. A corresponding model is established under various site conditions to simulate multipoint correlated ground motions along the depth from the surface. Finally, a numerical simulation of multipoint ground motions is conducted to verify the application of the established models. This study provides an effective tool for describing spatial variations in both phase and amplitude, which are crucial for simulating ground motions at various depths.

Investigation of seismic response amplification effects of diverse multi-support earthquake excitations on cable-stayed bridges

This study addresses the critical need to understand the seismic behavior of cable-stayed bridges under Multi-Support Excitation (MSE) in order to mitigate earthquake-induced damage to these structures. The primary focus is on the investigation of response amplification phenomena and their seismic implications for cable-stayed bridges. Through a detailed comparative analysis of MSE and Synchronous Excitation (SE) across various structural locations, the study evaluates the impact of site-specific recorded ground motions of different earthquake categories. A pragmatic framework is developed to simulate realistic MSE ground motions for diverse earthquake scenarios, emphasizing the necessity of considering MSE in bridge design. The findings reveal a significant amplification of the design requirements due to antisymmetric mode excitation and increased tower and pier motions. The study also identified the need for in-depth analysis of cable-stayed bridges to address the increased vulnerability of tower-adjacent areas and to devise targeted reinforcement strategies of vulnerable components. These insights are critical for advancing seismic design practices and improving the resilience of cable-stayed bridges, contributing to safer urban infrastructure.

Seismic fragility and vulnerability assessment of a multi-span irregular curved bridge under spatially varying ground motions

Multi-span reinforced concrete (RC) curved box-girder bridges are commonly designed to facilitate traffic flow at highway interchanges. The Aksemsettin Viaduct (henceforth, A Viaduct for brevity) in Istanbul, Turkey, is an eleven-span interchange bridge with a total length of 596.8 m. Located in a high seismicity zone, the A Viaduct is designed with a curved deck, multiple bearings that have different isolation mechanisms at different bents and directions, ten rectangular columns with unequal heights, and a mix of pile foundations and spread footings. The significant length of the viaduct crossed by eleven spans also makes it susceptible to varying ground motion excitations at different foundations. To evaluate the effects of the degree of modeling detail and analysis complexity on the estimated seismic performance, the present study conducts a comprehensive fragility assessment of the specimen viaduct under various ground motion excitation schemes. First, a three-dimensional finite element model is developed with detailed simulations for the deck, columns, bearings, foundations, and abutment components. To enable different ground motion excitations at each foundation, 57 sets of spatially varying ground motions are simulated by considering the realistic surface topography and soil stratigraphy at the bridge site. Cyclic pushover analyses are performed along multiple loading directions to develop the direction-dependent capacity limit state models for hollow rectangular columns. Subsequently, a demand-capacity ratio method is utilized to develop reliable fragility models for bridge columns. Component- and system-level fragilities of the A Viaduct are then assessed under uniform versus multi-support excitations, vertical motions, and ground motions with varying incidence angles. To further capture the seismic damage discrepancies of the same components at different locations, seismic repair cost ratios of the A Viaduct are assessed when subjected to uniform and multi-support excitations. This study highlights the significance of considering multi-support excitations to achieve more realistic seismic fragility and loss estimates for multi-span long curved highway bridges.

Time history analysis of structures under multi-support excitation by state-space method

Because of the variety of methods to simulate the dynamic behaviors of the structure under earthquake loading trying to approach the reality. This paper provides a contribution to simulate this behavior using three methods, mainly starting with state space. Secondly, we compare it with the finite element method (Duhamel integral and direct method of Newmark), taking into consideration the effect of Non-uniform excitation in the supports. The obtained results proves the three methods are efficient and very close to each other for simple structures but in term the computing time, the state space method is faster than the others. At the end, add a big structure to test the limits of each method.

Analysis of the Seismic Response of a High Voltage Transmission Tower-line System under Multi-support Excitation

Analysis of the Seismic Response of a High Voltage Transmission Tower-line System under Multi-support Excitation

Seismic behavior of cable-stayed bridges under strong ground motions

Seismic behavior analysis of the long-span cable-stayed bridge is a complex process involving different uncertainties. This paper performs a sensitivity analysis of cable-stayed bridges using the finite element method on Midas/Civil. They include different types of ground motions scaled to different peak ground acceleration (PGA) levels, the effect of the multi-support excitations due to time-lag propagation or nonsynchronous excitations, and the effect of the angle of the incidence of the earthquake is determined. To evaluate the optimum initial cable prestress forces in cables unknown load factors method is used. The response quantities of interest include the displacement of the tower and deck, variation in prestress force in cables, torsional in the deck, shear force, and bending moment at the supports. Results show that the effect of the PGA variation and angle of incidence of the earthquake is moderate. In contrast, the synchronous and nonsynchronous seismic excitation effect on the response quantities is significant.

Wavelet packets-based simulation of non-stationary multivariate ground motions

This study proposes a novel approach to simulate non-stationary multivariate earthquake accelerograms for the seismic analysis of extended structures. This approach is based on an extension of the traditional stochastic decomposition technique applied to the wavelet packet theory using the spectral representation method. Using the advantages of a wavelet packet to identify the time and frequency characteristics of ground motion effectively, the generated recordings successfully reflected the non-stationarity in both the time and frequency domains. Accordingly, the spatial correlation trend was consistent with the selected coherence function. Compared to the ground motions observed using the traditional method, the proposed approach was exemplified by simulating ensembles of ground motions at three points spaced 200 m apart. The multivariate ground motions simulated by different methods were applied as multi-support excitations for the dynamic time–history analysis of a 190 m continuous rigid-frame box girder bridge. Notable variations in structural response were observed when considering the non-stationarity of the frequency domain, contrasting with the cases where it was not taken into account. This study provides an effective approach for generating non-stationary multivariate earthquake accelerograms, which is of great significance for structural response analysis in engineering applications.

Seismic response of a single-layer reticulated dome: Fault-to-structure simulation

Seismic response of large-span spatial structures is particularly susceptible to soil-structure interaction and spatial variability of ground motions. Yet existing seismic analysis fail to properly account for the foundation soil, and the ground motions are commonly determined based on empirical formulas. Physics-based 3D seismic simulation has recently been developed to provide site-specific ground motions, and the fault-to-structure simulation facilitates the incorporation of seismic wave field and soil-structure interaction into the analysis of engineering structures. This article innovatively implements the fault-to-structure simulation on a single-layer reticulated dome. Structural response of fault-to-structure model and two commonly used models is compared and discussed. Results show that the damping of soil reduces the stress and horizontal acceleration of the reticulated dome, while the soil movement leads to an increase in displacement. Noticeably, the seismic propagation characteristics increase vertical acceleration of the inner rings. Compared with fault-to-structure model, the multi-support excitation model and uniform excitation model reduce the vertical displacement of 29.1% and 50.1%, respectively, and reduce the vertical acceleration of the inner rings of 59.9% and 69.0%, respectively.

Random analysis of train-bridge coupled system under non-uniform ground motion

The increasing prevalence of simply supported bridges in high-speed railway (HSR) lines has raised concerns about the safety of trains crossing these bridges during an earthquake. As these bridges are typically continuous and long, it is essential to consider the effects of traveling seismic waves on the random vibration of the train-bridge coupled (TBC) system. To address this issue, the new point estimate method (NPEM) is used to analyze the dynamic response and parametric sensitivity of a three-dimensional TBC system subjected to non-uniform ground motion with multiple random parameters. The motion equations of the TBC system are derived using bridge seismic theory under multi-support excitations. The analysis incorporates random variables such as the damping ratio, density, Young’s modulus, and seismic magnitude to capture the influence of traveling seismic waves on the random vibration of the TBC system. Simulation results show that the traveling seismic wave effect can cause changes in the first vibration frequencies of the train and bridge, potentially leading to the first few frequencies reordering. Additionally, considering the traveling wave effect will make the TBC system’s response less apparent than without considering the traveling wave effect. The uncertainty of bridge and seismic parameters can seriously affect the train’s running safety. The sensitivity of the bridge density and seismic magnitude is particularly prominent for bridge responses when the traveling seismic waves effect is strong. This methodology can be used for random and sensitivity analysis of a train running over a long bridge under non-uniform earthquake conditions. Overall, the NPEM can provide valuable insights into the dynamic behavior and safety of TBC systems, enabling more effective design and maintenance of HSR bridges.

Nonlinear static analysis of extreme structural behavior: Overcoming convergence issues via an unconditionally stable explicit dynamic approach

Simulating extreme structural behavior is of vital importance as it is a major means to study the damage and failure mechanism of engineering structures. However, convergence issues frequently occur when simulating structural response under extreme loading using traditional nonlinear solution strategies, e.g., the Newton–Raphson family of methods. Though commercial finite element software provides explicit dynamic methods to overcome this issue, they are only conditionally stable and require a small time step size. In this paper, a new explicit dynamic approach to simulate static problems involving extreme structural behavior is presented. The multi-support excitation pattern is employed to apply a nodal displacement history of the problem in a dynamic way, then the unconditionally stable explicit KR-α method is used to eliminate the convergence issues. Three examples are presented to illustrate the effectiveness of the proposed dynamic approach, and a parametric study is conducted to investigate the influence of the algorithmic parameters. The results indicate that the proposed method provides the same accuracy as the traditional static method without any convergence issues.

Seismic Response of Long-Span Staggered Storey Isolated Structure Under Multi-support Excitation

Seismic Response of Long-Span Staggered Storey Isolated Structure Under Multi-support Excitation

Simplified procedure for simulating artificial non-stationary multi-point earthquake accelerograms

A simplified procedure is proposed to generate artificial non-stationary multi-point ground motion inputs for the dynamic seismic analysis of long span or large scale structures. The probability distribution parameters for the phase difference were fitted using 438 recordings selected from Center for Engineering Strong Motion Data. Then the time curve of the number of zero crossings were fitted using the same dataset. By implementation of the empirical coherency function, we simulated the non-stationary multi-point artificial ground motions given design earthquake scenario (i.e. magnitude and epicentral distance) of the target site. The generated artificial recordings successfully account for non-stationarity in both the time domain and frequency domain, and the trend of spatial correlation is consistent with the utilized coherency function. The generated artificial ground motions were then applied as multi-support excitations for dynamic time-history analysis of the 190 m continuous rigid-frame box girder bridge. Approximately 15%–30% structural response difference was observed between using multi-support excitations and uniform excitations. The vertical displacement amplitude regarding mid-span of the bridge using multi-support excitations is significantly larger than the results using the uniform excitations. For both uniform input and non-uniform input cases, it is also found that the structural response of studied bridge using fitted mean ± standard deviation time curves of number of zero crossings are smaller than the results using fitted mean time curve. The difference is largely caused by the various energy content of generated recordings that are indicated by Arias intensity. This study provides an efficient procedure to generate artificial non-stationary multi-point earthquake accelerograms without cumbersome computation cost, and could be easily implemented in engineering applications.

Spatial Coherency Model Considering Focal Mechanism Based on Simulated Ground Motions

The spatial coherencies of ground motions are the key to establishing multi-support excitation for large-dimension structures. Most of the existing models were established based on ground motions recorded at dense observation arrays which barely show any detailed information on the focal mechanism. However, in the near field, ground motions are dominated by the source, and so are the spatial coherencies of ground motions. In this paper, a deterministic physics-based method was used to simulate ground motions in the near field for various focal mechanism scenarios. The coherencies of the simulated ground motions were calculated. The Loh coherency model was used to fit the variation in the calculated coherencies for each scenario. The results show that the focal mechanism has a significant effect on the spatial coherencies of simulated ground motions. Finally, the probability density distributions of the parameters, a and b, of the Loh coherency model were obtained, and a coherency model was proposed, based on the Loh coherency model, in which the parameters are taken to be dependent on the focal mechanism.

배관계 시간이력 다지점 가진 해석의 입력 방법에 관한 연구

The finite element analysis (FEA) of the nuclear power plant (NPP) system is generally excited by a single representative acceleration data as the supporting points have similar elevations. However, NPP pipes have multiple supporting points so that the multi-support excitation methodology which applies excitation on each support is generally considered to obtain the exact seismic responses. In this research, we study input methods for conducting multi-support excitations in FEA, and all the methods are constructed under time history analysis considered more precise than floor response spectrum analysis. Three types of input methods, namely large mass method, mode superposition transient, and displacement input transient analysis, were considered in this research. As a result, we conclude that all the methods generate similar motion parameters to the reference acceleration data on each supporting point. In addition, it is considered whether there is an appropriate input method to simulate another type of supports by changing the boundary condition on the support area.

Study of seismic-responses and semi-active control of Taizhou Bridge under multi-support excitation

PurposeIn order to make sure of the safety of a long-span suspension bridge under earthquake action, this paper aims to study the traveling wave effect of the bridge under multi-support excitation and optimize the semi-active control schemes based on magneto-rheological (MR) dampers considering reference index as well as economical efficiency.Design/methodology/approachThe finite element model of the long-span suspension bridge is established in MATLAB and ANSYS software, which includes different input currents and semi-active control conditions. Six apparent wave velocities are used to conduct non-linear time history analysis in order to consider the seismic response influence in primary members under traveling wave effect. The parameters α and β, which are key parameters of classical linear optimal control algorithm, are optimized and analyzed taking into account five different combinations to obtain the optimal control scheme.FindingsWhen the apparent wave velocity is relatively small, the influence on the structural response is oscillatory. Along with the increase of the apparent wave velocity, the structural response is gradually approaching the response under uniform excitation. Semi-active control strategy based on MR dampers not only restrains the top displacement of main towers and relative displacement between towers and girders, but also affects the control effect of internal forces. For classical linear optimal control algorithm, the values of two parameters (α and β) are 100 and 8 × 10–6 considering the optimal control effect and economical efficiency.Originality/valueThe emphasis of this study is the traveling wave effect of the triple-tower suspension bridge under multi-support excitation. Meanwhile, the optimized parameters of semi-active control schemes using MR dampers have been obtained, providing relevant references in improving the seismic performance of three-tower suspension bridge.

Inelastic response of cable-stayed bridges subjected to non-uniform motions

This paper studies for the first time the effect of the spatial variability of ground motions (SVGM) with large intensities on the inelastic seismic response of the pylons which are responsible for the overall structural integrity of cable-stayed bridges. The svgm is defined by the time delay of the earthquake at different supports, the loss of coherency of the seismic waves and the incidence angle of the ground motion. An extensive study is conducted on cable-stayed bridges with ‘H’- and inverted ‘Y’-shaped pylons and with main spans of 200, 400 and 600 m. The svgm is most detrimental to the pylon of the 200-m span bridge owing to the large stiffness of this bridge compared to its longer counterparts. The stiff configuration of the inverted ‘Y’-shaped pylon makes it more susceptible against the multi-support excitation than the flexible ‘H’-shaped pylon, especially in the transverse direction of the response. Finally, the earthquake incidence angle is strongly linked with the svgm and should be included in the seismic design of cable-stayed bridges.

Seismic Performance of a Long-Span Cable-Stayed Bridge under Spatially Varying Bidirectional Spectrum-Compatible Ground Motions

Considering the socioeconomic prominence of long-span cable-stayed bridges, it is important to ensure their normal operation after strong earthquake events. To this end, their seismic performance must be based on a proper understanding of the relationship between structural capacity and seismic demand. However, evaluating the seismic demands on cable-stayed bridges is challenging due to relatively long distances between supports and the complex composition of various structural elements. The large dimension in the horizontal direction inevitably leads to incoherent input ground motions at supports, while various structural components such as cables, decks, and pylons make it difficult to define the system’s performance limit-state or capacity using a single index or function. This work presents three main contributions to properly assess the seismic performance of a long-span cable-stayed bridge. First, an algorithm was proposed to generate a set of bidirectional spectrum-compatible ground motions for the multiple supports of a bridge. Second, two performance measures were proposed to quantitatively assess the seismic demands and capacity of a cable-stayed bridge: probabilistic comparison index and axial force-bending moment (PM) safety factor. Third, the impacts of the seismic motions on the long-span cable-stayed bridge were thoroughly examined using eight different scenarios in terms of the three aspects: (1) multisupport excitation, (2) assumed soil class, and (3) wave passage effect. For this purpose, the Incheon Grand Bridge was chosen as a reference structure. This bridge has a central span of 800 m and a total length of 1,480 m. The results demonstrate that the seismic demands of the long-span cable-stayed bridge vary along with different conditions of seismic motions, and the proposed performance measures and ground motion-generating algorithm enable quantitative investigation of the impact of different conditions on the long-span cable-stayed bridge.

Spatiotemporal seismic excitation of bridges with an anti-symmetrical first mode

This study uses a generalized and parametrized reduced-order model in the frequency-domain to evaluate the effects of asynchronous excitation on the lateral response of bridge structures. Bridge geometry parametric regions, corresponding conceptually to valley profile shapes, are explored. Both modal and bounding analyses, that are dependent on bridge geometry alone, are employed to highlight regions where the first mode is anti-symmetrical and the likely error between identical support excitation (ISE) and multi-support excitation (MSE) analyses is large. Numerical time history analyses, using a heuristic bridge case and spatiotemporal ground motion from the SMART-1 array, are employed. These analyses confirm that in parametric configurations where the first mode is anti-symmetrical the error between MSE and ISE is often larger. This confirms the utility of geometry only modal and bounding analyses in identifying critical regions. These critical parametric cases of a first mode that is anti-symmetrical correspond to shallow valleys with a central rise. In these cases it is recommended that both ISE and MSE analyses should be employed to be conservative.

Exploring a generalized nonlinear multi-span bridge system subject to multi-support excitation using a Bouc-Wen hysteretic model

This paper presents a generalized reduced-order nonlinear model subjected to multi-support seismic excitation. The hysteretic, nonlinear, relationship of piers is phenomenologically captured by a calibrated Bouc-Wen model. This generalized reduced-order model is benchmarked against legacy physical experimental tests performed at the University of Bristol.A deterministic approach using real spatiotemporal ground motions recorded at the SMART-1 array, Taiwan, is employed as an alternative to a stochastic methodology used in current provision codes. This is so that the influence of nonlinearity and ground motion aleatory and epistemic effects are fully captured. Incremental Dynamic Analysis (IDA) is then performed to identify the performance levels at which this system transitions from elastic to inelastic behaviour. A parametric study is then performed to explore the effect of the spatial variability of the ground motion while bridge alignment, valley profile and ground motion intensity are modified. Results indicate that bridges over shallow valleys with a central rise are prone to significant analysis errors if multi-support excitation is not employed.

A theoretical and experimental exploration of the seismic dynamics of multi-span bridges

A generalized reduced-order model of a multi-span continuous bridge, on flexible discrete supports, that is subjected to multi-support seismic excitation is presented. This model highlights the key non-dimensional system parameters. Real spatiotemporal ground motion time-series (from the SMART-1 array, Taiwan) are used, as an alternative to employing artificial ground motion based on some spatial incoherence kernels. Benchmark experimental test data, using the multiple support excitation rig of a four-span bridge and SMART-1 array excitation, is used to validate/calibrate the proposed reduced-order model. An operational modal analysis is conducted to obtain least-square estimates of these key dynamic parameters using a Levenberg–Marquardt algorithm. The computationally efficient reduced-order model is then employed for a parametric study that explores the effect of spatial incoherence, bridge alignment and archetypal symmetrical and asymmetrical bridge geometries. A comparison of identical and multi-support excitation cases indicate the likely range of beneficial/adverse errors in neglecting the spatiotemporal nature of ground motions in design analyses.