Traveling Wave Effect Research Articles

Dynamic Response of Lining Structure in a Long Tunnel with Different Adverse Geological Structure Zone Subjected to Non-Uniform Seismic Load

The damage of a long tunnel is found in parts with an adverse geological structure zone under an earthquake. The phenomenon is normally the consequence of a non-uniform seismic load. Thus, to reveal the mechanism of the phenomenon, the dynamic response of the lining structure in a long tunnel passing through an adverse geological structure zone subjected to a non-uniform seismic load is mainly studied in this paper. Firstly, based on the random ground motion synthesis theory, the non-uniform ground motion acceleration–time history curves that reflect local site effects, such as traveling wave effects and attenuation effects, are generated. Secondly, the behavior of the tunnel with a different adverse geological structure zone (including different inclinations, thicknesses, and lithologies) under non-uniform seismic input is studied. Then, the impact of the different adverse geological structure zone on the internal force and safety factor of the tunnel lining is analyzed. Finally, the failure characteristics of the lining structure in the tunnel crossing through the adverse geological structure zone subjected to a non-uniform seismic load are revealed. The results show that the seismic dynamic responses significantly increase under non-uniform seismic input compared with the results under uniform seismic input, and the dynamic responses distribution along the tunnel axial is distinctly different under non-uniform seismic input. The inclination and thickness of the adverse geological structure zone have a significant influence on the internal force and safety factor of the tunnel lining, while the lithology mainly acts around the adverse geological structure zone. When the inclination angle of the adverse geological structure zone is 45°, a large number of compression-bending cracks appear in the entrance and exit sections of the tunnel, and the tunnel is in the most dangerous state.

Dynamic Response Analysis of Buried Drainage Pipes for Polymer Grouting Trenchless Rehabilitation under the Traveling Wave Effect

The polymer grouting nonexcavation repair technology has been widely used in the repair of underground pipeline leaks, but the seismic response to the polymer repair pipeline is currently using a consistent excitation of seismic input without considering the influence of the traveling wave effect. This paper establishes the longitudinal and transverse vibration models of the polymer grout repair pipeline considering the traveling wave effect based on the elastic foundation beam theory. The seismic input uses artificially generated random seismic waves and solves the differential equations for pipeline vibration to carry out seismic response analysis of long‐buried pipelines under three conditions: normal, vacant, and polymer grouting repair. The results show that after considering the traveling wave effect, the reaction of each measuring point on the pipeline has obvious phase characteristics, and the waveform of the distant measuring point has an obvious hysteresis phenomenon; the seismic wave velocity has a great influence on the deformation of the pipeline, and the displacement amplitude of the pipeline increases with the increase of the seismic wave velocity. The peak of pipeline displacement after vacancy will increase by 100%∼300% more than normal, while the difference in pipeline deformation after high polymer grouting is about 25% compared with normal, which means that the bottom vacant will have a great influence on pipeline deformation, and high polymer repair can restore the pipeline mechanical properties to normal levels.

Investigation on Seismic Response of Long‐Span Special Steel Truss Cable‐Stayed Bridge

Due to the small self‐weight of the steel truss cable‐stayed bridge with a single tower and a single cable plane, the torsional stiffness and wind stability of the structure are reduced. The arrangement of the deck type makes the mechanical properties of the cable‐stayed bridge more complicated while reducing the cost and increasing the aesthetics. The effects of structural parameter variations and traveling wave effects on the seismic response of this steel truss cable‐stayed bridge with a single tower and a single cable plane were investigated by the nonlinear time‐history analysis method and nonuniform seismic analysis method. The results show that the displacement of the floating system under seismic action is larger than the other three systems, but its internal force is significantly smaller than the other three systems. The spectral characteristics and the duration of ground shaking have a greater influence on the maximum bending moment values corresponding to the height of the cable tower and the maximum axial force values of the main girder bars corresponding to the length of the bridge under earthquake action. The effect of steel truss girder stiffness parameter variations on structural internal forces of bridges and the effect of traveling wave effects on structural displacements of bridges in specific apparent wave velocity intervals do not exist universally.

Dynamic failure evolution of surrounding rock in a long tunnel with different unfavorable geological structure zones under non-uniform seismic input

Earthquake damage investigations show that damage often occurs in complex geological sections with unfavorable geological structures along a long tunnel. And the unique earthquake damage phenomena are the result of non-uniform ground motion generally. In order to study dynamic failure evolution of surrounding rock in a long tunnel with different unfavorable geological structure zones under earthquake. Therefore, a variety of schemes for dynamic analysis of a long tunnel with different lithology and thickness unfavorable geological structure zones is carried out through non-uniform ground motion input. Firstly, based on stochastic process theory, multiple time history curves of different ground motions that can reflect the traveling wave effect and attenuation effect for long tunnels are generated. Then, the dynamic response of the surrounding rock in the tunnel is analyzed through inputting these non-uniform ground motions. By analyzing the variation of shear plastic strain increment and plastic volume in surrounding rock, the characteristics of the potential failure surface with the earthquake time history in the surrounding rock of the tunnel with different unfavorable geological structure zones are studied. On this basis, the main influencing factors and the degree of influence on the dynamic damage of the surrounding rock of the long tunnel with unfavorable geological structure zone under non-uniform ground motions are evaluated. The results show that the unfavorable geological structure zone has a controlling effect on the seismic dynamic response and destruction of the surrounding rock of the tunnel. Further, the lithology of unfavorable geological structures and the time history of ground motions have a significant impact on the response and damage of surrounding rock.

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.

Traveling Wave Effects in Microwave Quantum Photonics

Traveling wave effects are increasingly exploited in microwave and terahertz quantum devices to implement novel functionalities and obtain improved performance. A suitable quantum circuit modeling approach is discussed for Josephson and bulk-material kinetic inductance traveling-wave parametric amplifiers enabling broadband, quantum-limited amplification. As another example, a multi-domain simulation approach for novel terahertz quantum cascade laser structures exploiting microwave and optical co-propagation effects is presented.

Analytical solutions for seismic responses of shaft-tunnel junction under travelling SH-wave

When the shaft-tunnel junction is subjected to vertically propagating SH-waves, the dominant factor is the discrepant responses between the shaft and the tunnel. However, in the case of inclined SH-waves, the travelling wave effect also has a significant influence, especially on the tunnel. To address this issue in an analytical fashion, the displacement field of the ground under travelling SH-wave is described by the stiffness matrix method and then incorporated into the solutions for the shaft and the tunnel. Some of the major assumptions include: 1) the SH-wave is a plane wave with a given incident angle; 2) the shaft is regarded as a rigid body; and 3) the tunnel is simplified into a massless Euler-Bernoulli beam. Two scenarios are considered according to the direction of the tunnel axis. When the tunnel axis is parallel to the shaking direction of the ground, the travelling wave effect is rather irrelevant, and the solutions for shaft-tunnel junction under uniform longitudinal excitations are still valid with some minor modifications. Therefore, this scenario is only briefly discussed. In the second scenario, when the tunnel axis is parallel to the horizontal propagation of the SH-wave, the travelling wave effect is no longer negligible, and a new set of solutions are offered. Validation of the solutions is made by comparison with finite element method. As demonstrated by the solutions, the displacements of the shaft and the tunnel are both affected by the travelling wave effect. The seismic distortions originate from the nonuniformities of the structure and the seismic excitation at the same time. Great internal forces at the intersection point are inevitable regardless of the direction of wave propagation, but the influence of the shaft on the tunnel diminishes exponentially with increasing distance to the shaft. Beyond the scope of the shaft influence, the responses of the tunnel are dominated by the travelling wave effect. In the case of vertically propagating SH-wave, the internal forces of the tunnel would approach to zero towards the free end of the tunnel. However, under travelling SH-wave, even at a great distance to the shaft, the tunnel would still have significant internal forces due to the travelling wave effect.

철로의 파동 전파특성 분석을 통한 무한 레일의 등가 동적물성 예측

In this study, an experimental method is proposed to measure rail properties in discretely supported tracks. The variations in the dynamic characteristics of the rail pad according to the excitation were estimated. To simulate the equivalent stiffness of the fastening system due to the single fast clip (SFC) device and the rail pad, a modeling of the clamping system was proposed. The discretely supported track was analyzed using the transfer function method. The vibration responses of the track were analyzed to determine the transfer function. As the length of the track increases, the influence of the reflected wave from the joints decreases, and the traveling wave effect becomes dominant. The characteristics of the infinite track were observed. A model with 36.5 m (50 sleepers) railway track was applied to predict the equivalent properties of the rail on discrete supports for each frequency using Newton-raphson method.

Spectral Correlation Between the Non-uniform Input Ground Motion and the Dynamic Response of the Surrounding Rocks of a Long Tunnel

To generate several different time-history curves of ground motion, which have the ability to reflect local site effects, such as the traveling-wave effect and attenuation effect, for long circular tunnels, a random method for the synthesis of ground motion is employed. The dynamic response of the surrounding rocks of a long tunnel under the uniform and non-uniform input ground motions is analyzed using the vertical input method. Based on this, the spectral correlation between the input ground motion and the dynamic response of the surrounding rocks is investigated through the coherence function. Unlike the results under the uniform input ground motion, the transmission coefficient of the surrounding rock monitoring points of each section along the axial direction of the tunnel under the non-uniform input ground motion varies in the main frequency band. In addition, at the same frequency, the transmission coefficient of the monitoring points gradually increases along the tunnel’s axial direction, but the increasing magnitude is variable. The correlation function of each monitoring point along the tunnel axis under the non-uniform input ground motion generally decreases with frequency. Moreover, the further the distance from the tunnel entrance, the faster the attenuation of correlation. The maximum coherence coefficient and the axial distance of the tunnel are basically in conformity with the quadratic polynomial relationship. However, the maximum coherence coefficient of the non-uniform input ground motion is considerably greater than that of the uniform input ground motion. The gap increases with the distance, and the maximum gap is about 0.15.

Testing and Numerical Studies on Transverse Responses of Cable-stayed Bridge Full Model under Transverse Non-uniform Excitations

ABSTRACT A cable-stayed bridge full model was tested to study the travelling wave effects on the transverse acceleration frequency spectra, seismic responses, and pile-soil interactions under transverse non-uniform excitations. The results indicate that the non-uniform excitations affect the transverse acceleration frequency spectra of the girder. The non-uniform excitations increase the displacement at 3/4-span of the girder but decrease the displacements at 1/2- and 1/4-span of the girder. The pile-soil interaction effects of one tower increase, whereas those of another tower decrease due to the non-uniform excitations. The numerical model could generally capture the seismic response changes caused by the non-uniform excitations.

Seismic Response and Vibration Reduction Analysis of Suspended Structure under Wave Passage Excitation

In order to study the influence of traveling wave effect on the seismic response and damping effect of suspended structure, a series of shaking table tests of the 1 : 20 suspended structure have been carried out to compare and analyze the dynamic responses of suspended structures under two points and a consistent input. The vibration damping effect and vibration reduction law of suspended structure are discussed at different apparent wave velocity and in the different connection. The research shows that the damping suspended structure has a good damping effect, and the amplitude reduction of the top displacement peak response is up to 15%, which corresponds to smaller apparent velocities. Moreover, the upper bound of the maximum acceleration response at the structures’ top under nonuniform input motions equals that of the uniform motion. However, there is a hysteresis in the acceleration response under wave travelling excitations, and the smaller the apparent wave velocity, the more obvious the hysteresis.

Assessment of the historic seismic performance of the New Zealand highway bridge stock

This paper presents the assessment of historic seismic bridge performance of the New Zealand highway bridge stock from the 1968 Inangahua earthquake through to the 2016 Kaikōura earthquake. Spatial ground motion details based on recorded and observed ground motion intensities were used to estimate the peak ground acceleration (PGA), as a measure of the seismic demand at each bridge location. Across all events, a PGA of 0.05 g or higher was experienced on over 800 occasions across bridge sites. Damage characteristics were collated from available literature, with the majority of the highway bridges experiencing either no damage or only minor damage across all the events. At PGAs greater than 0.5 g, the number of bridges with moderate and major damage was still relatively small. There were also no apparent differences between the performance of bridges across the different design eras, despite the varied design and construction practices. Some shorter bridges may have performed better than expected due to the effect of abutment stiffness and damping, while some longer bridges may have performed well due to travelling wave effects. These findings will inform future assessment methods and design, and the accuracy of analytical modelling of the bridge stock.

Shaking table test verification of traveling wave resonance in seismic response of pile-soil-cable-stayed bridge under non-uniform sine wave excitation

The traveling wave resonance phenomenon exhibits in the seismic response of the symmetric bridge structure. However, there is a scarcity of shaking table tests validating the traveling wave resonance. A 1/70-scale pile-soil-cable-stayed bridge model was fabricated following the preliminary design of a cable-stayed bridge with a main span of 1400 m. Shaking table tests were performed to verify the traveling wave and mode shape resonances in the seismic response of the bridge model when separately subjected to two specific sine waves longitudinally. The vertical acceleration frequency spectra and seismic response of the bridge model were compared between uniform and non-uniform sine wave excitation. The results showed that the traveling wave and mode shape resonances were examined in the seismic response of the pile-soil-cable-stayed bridge model under non-uniform excitation of the specific sine waves. The traveling wave excitation increased the symmetric response at the symmetric girder location but decreased the antisymmetric responses of the towers and girder, compared to the uniform excitation regarded as antisymmetric input. Finally, a finite element model was developed in OpenSees that could capture the seismic response changes caused by the traveling wave effects of the specific sine waves and proximately reproduce the experimental results. Therefore, the traveling wave and mode shape resonances were verified by the numerical simulations.

Simulation of the In Situ Spatially Varying Ground Motions and Nonlinear Seismic Response Analysis of the Cable-Stayed Bridge

To study the nonlinear seismic behavior and seismic resistance of the long-span cable-stayed bridges subjected to earthquakes, the multidimensional and multisupported artificial ground motions are synthesized first based on the in situ site conditions of the bridge considering the coherent and traveling wave effects. Then, considering the material nonlinearity of the cable-stayed bridge, a 3D finite element model is established based on the OpenSees platform, and the nonlinear seismic response analysis of the bridge is carried out under the synthetic artificial ground motions. The nonlinear seismic response of main bridge components such as piers, towers, bearings, and cables is analyzed, and key conclusions and observations are drawn.

A Method to Calculate Short-Circuit Faults in High-Voltage DC Grids

Accurate fault calculation is vital for the parameter design and protection research of high-voltage DC (HVDC) grids. This paper proposes a general method to calculate short-circuit faults in HVDC grids, and the method is based on the premise that the modular multilevel converter (MMC) blocking and the current interruption have not occurred. The MMC is based on the average value model, and the MMC current source can reflect the impacts of the AC system and MMC control mode. The fault calculations based on variable and constant MMC current sources are presented. The numerical inversion of the Laplace transform is used to obtain the voltages and currents in the time domain. The proposed method has the following merits: 1) it can accurately calculate voltages and currents while considering the fault-generated traveling wave effect and impacts of the AC system and MMC control mode; 2) it is more time efficient than the electromagnetic transient simulation; and 3) it is applicable to HVDC grids with different configurations, such as symmetrical bipolar and asymmetrical monopolar. The proposed method is validated by comparisons with previous calculation methods and PSCAD/EMTDC simulation.

Seismic Analysis of Hybrid System Bridge of Multi-Span Continuous Girder and Arches

The Chengdong Hanjiang Bridge in Ankang City is a multi-span continuous beam-arch combination system bridge of (75+2×125+160+2×125+75) m, and its site is located in the earthquake zone. Calculation model based on Midas / Civil finite element software process analysis method is applied to seismic response analysis using power. At the same time, in order to influence the travelling wave effect and the seismic isolation system on the internal force of the bridge structure, corresponding finite element models were established and calculated with time history analysis. The finite element model under non-uniform excitation uses the “Large Mass Method” (LMM) for analysis and calculation under different wave velocity multi-point excitations. The results show that after considering the traveling wave effect, the displacement and bending moment of the control section of each hole increase, and the internal force of the fixed pier increases. When the wave velocity is 600m/s, the traveling wave effect strengthens the seismic response of the structure the most. With the increase of the wave velocity, the seismic response of the structure gradually approaches the seismic response under uniform excitation. After the friction pendulum seismic isolation support is used, it is fixed. The bending moment of Pier No.32 has been reduced by 80%, the stiffness of the whole bridge is more balanced, the forces of each pier are relatively close, and the isolation effect is good.

Nonlinear control model and operational support system for the Kainji Hydroelectric Power System

Over the past years, hydropower model and control were largely based on classical and linear transfer function, this was motivated by the available control system design techniques that were available and the desire to simplify the design procedure. Such a model is inadequate for dynamic study and design of hydropower station in the presence of uncertainties in the water head, discharge rate, elastic water effect, traveling wave effect, large variation power output and frequency. This research, therefore, focuses on developing a nonlinear model for the Kainji hydroelectric power station. The model relies on the energy conversion principles, inflows, discharge, evaporation rate and number of units on busbar. The parameters of the model were also estimated, and the model validated with an error within +1.4% to -3.6%. The model is expected to be used to determine the optimal control policies for the operation of the station and the release of water to the downstream. Keywords: Hydroelectric Power, Inflow, Model, Operating Head, Turbo-alternator

Effect of seismic wave velocity on the dynamic response of multi-story structures on elastic foundation

Traveling wave effects are generally considered with three main cases: (i) Wave passage effect that results with time delay in earthquake motion. (ii) incoherence effect which is defined as loss of coherency in the ground motion due to the reflection and refraction of waves, and (iii) local site effects. For multi-story structures whose supports are close to each other, the incoherence and local site effect may be omitted. In this case, traveling waves result only in a pure time delay in the earthquake motion (wave passage effect). Due to the wave passage effect of vertical and/or horizontal ground motion, the superstructure needs to be analyzed by multi-support excitation. Raft foundations cannot constrain vertical deformations and/or rotations, but they cause a diaphragm effect in the horizontal direction which results in uniform excitation. In this study, the effect of vertical earthquake motions onto multi-story buildings on elastic soil is investigated. Multi support excitation is considered by using displacement loading, which defines the equivalent seismic loads in terms of the ground displacement. According to the performed simulations of the selected structures, it is shown that structural height has a direct influence that results in member force magnifications with slow traveling wave effect. Among these, the ground floor column axial forces are most affected.

Global concurrent cross-scale nonlinear analysis approach of complex CFRD systems considering dynamic impervious panel-rockfill material-foundation interactions

Evaluating the seismic security of enormous structures is extremely vital, and this concern has continually motivated the trends of refined numerical simulations for years. However, the ability to perform a concurrent global refinement analysis of large-scale projects with complex spatial geometries and spanning huge scales has remained a formidable challenge in settings such as high concrete-faced rockfill dams. In this paper, a global concurrent cross-scale nonlinear analysis approach (GCCNA) benefitting from an efficient hybrid octree-based discretization technique is presented. Significantly, a polygon interface is constructed to automatically connect the cross-scale element and solve the interactions between the concrete-faced rockfill and foundation. A viscoelasticity polygonal artificial boundary element is subsequently developed to render the influence of radiation damping on an infinite foundation so that the travelling wave effect on the dynamic response and stabilization can be captured. A high-efficiency and economically time-consuming solution strategy is adopted, wherein the scaled boundary finite element is introduced to manage the minority polyhedrons in the generated octree model, and the numerous hexahedrons are assigned to the isoparametric element. The features of rapid discretization, high flexibility, extraordinary grid reconstruction and coupling with the conventional finite element are contained perfectly, which are demonstrated via the comprehensive elasto-plastic dynamic simulation of an extremely complicated practical constructed highest rockfill dam. The proposed approach has attractive potential and practicability for the efficient refinement analysis of complicated enormous engineering structures and can be readily extended to subterranean structures, nuclear plants, and architectural and aviation structures.

Study on Seismic Response of Single-layer Cylindrical Reticulated Shell Due to Horizontal One-dimensional Earthquake

A single-layer cylindrical reticulated shell structure model was established by selecting real seismic waves and using ANSYS structural analysis module, and the structural model was subjected to multi-point earthquake input and consistent input time history response calculations. The result shows that in the seismic design of large-span space structures, the traveling wave effect must be considered. When the traveling wave effect is studied, if we only pay attention to the maximum axial force of the structural member, horizontal one-dimensional input can be performed.