Akashi Kaikyo Bridge Research Articles

Explicit solution framework and new insights of 3-DOF linear flutter considering various frequency relationships

Different engineering structures, e.g., long-span bridges, bundled conductors, and cable-supported photovoltaic modules, exhibit various frequency relationships among different degrees of freedom (DOFs). Despite extensive research, the initiation mechanisms of flutter remain somewhat ambiguous for a 3-DOF system considering heaving-lateral-torsional motions, especially when frequencies are close among different DOFs. This study introduced an explicit eigenvalue solution framework for tackling the 3-DOF linear flutter problem by utilizing matrix perturbation methods, enabling the extraction of modal damping and frequency solutions for all possible frequency scenarios. These solutions explicitly clarified the influence mechanism of all flutter derivatives (aerodynamic damping and stiffness), structural frequencies, and mechanical dampings. Important flutter derivatives, flutter risk level, and sensitivity level to mechanical damping and to frequency detuning were summarized in a table for all frequency scenarios, providing a panoramic perspective on flutter instability and the coupling mechanism. Numerical studies were conducted on a thin plate, the Akashi Kaikyo Bridge, and an eight-bundled conductor to examine the proposed explicit solutions. The results showed that approaching frequencies can amplify the coupling effect among different DOFs by half an order, but this does not necessarily mean the system is more prone to flutter. A system where the torsional frequency approximates the heaving/lateral frequency is expected to face a higher flutter risk if given significant torsional-related aerodynamic stiffness (H3*, P3*). Evidently, this high risk exhibits insensitivity to mechanical damping and small frequency-detuning. Though usually ignored in bridge flutter analysis, drag force and lateral motion could exert noticeable influence in a minority of cases, e.g., more than 10 m/s decrease of critical wind speed for the Akashi Kaikyo Bridge at large angles of attack. The proposed explicit solution framework provides a systematic view and new insights into the flutter initiation mechanism, serving as a reference in the design and studies of various engineering structures with different frequencies and coupling features.

Super-long-span bridges: wind-resistant design developments and open issues

Suspension bridges with spans exceeding 1500 m were only achieved in 1998 with completion of the Akashi Kaikyo Bridge in Japan and the Great Belt Bridge in Denmark. The most recent record is the 1915 Çanakkale Bridge in Turkey, with a main span of 2023 m. A slightly longer bridge is currently under construction in China and significantly greater spans are in planning, such as the Messina Strait Bridge, aiming for an impressive 3300 m span connecting Sicily with mainland Italy. Three critical challenges associated with such ambitious designs are addressed in this article. The first challenge centres on the significance of vortex-induced vibrations, particularly in multi-box girders. The prediction of these vibrations before construction relies on wind tunnel tests with scaled-down models characterised by inherent uncertainties. The second issue involves non-synoptic winds, such as downbursts. Although these events are relatively small and short-lived, they have a non-negligible probability of occurrence on large structures and may induce damage and loss of serviceability due to their intensity and the presence of vertical velocity components. Finally, the importance of robust design practices is underlined, emphasising the potential risks of relying solely on aerodynamic cross-section optimisation without providing additional structural stiffness and damping resources in these critical structures.

Monitoring System of Akashi Kaikyo Bridge and a Monitoring Case in Strong Wind

Monitoring System of Akashi Kaikyo Bridge and a Monitoring Case in Strong Wind

Application of dehumidification as anti-corrosion technology on suspension bridges: A review

• Dehumidification is a proactive corrosion protection for suspension bridges’ main cable. • A review on different dehumidification systems on suspension bridges. • Discussion on limitations and adaptations for main cable anti-corrosion application. • Identifying future scenarios and challenges of dehumidification on suspension bridges. The moisture from residual droplets during construction and infiltration of wet air during operation can cause metal corrosion of main cables on suspension bridges. Main cable dehumidification, emerged as a prospective corrosion protection approach, which provides an internal environment of relative humidity below 60%, would significantly mitigate the corrosion. This paper presents a state-of-the-art listicle review of existing dehumidification systems implemented on 47 suspension bridges (e.g., the Akashi Kaikyo Bridge, the Runyang Yangtze River Bridge). Dehumidification methods adopted in suspension bridges, including solid desiccant dehumidification, condensing dehumidification and integrated dehumidification, are elaborated. Based on that, crucial limitations and adaptations of various systems for main cable applications are discussed. Then, technical suggestions concerning the moisture load matching, sensor configurations, full-bridge sealings, dehumidification equipment placement and system division, are given to realize system sustainability and energy efficiency. Finally, this paper examined one potential development of a multi-stage dehumidification system that uses condensing dehumidification and solid desiccant dehumidification, which facilitates cascade utilization of the waste energy and enhances the system efficiency.

Long-span Suspension Bridge Flutter Analysis with Drag Force Effects

The paper investigates the influence of the drag force onto the flutter velocity and frequency of the Akashi Kaikyo Bridge. Finite element analyses were run in ANSYS by combining unsteady lift and moment actions with: (a) unsteady drag, (b) steady drag, (c) no drag. The finite element results are compared to those obtained by an in-house MATLAB code based on a semi-analytic continuum model and with others from the literature. The continuum model includes flexural-torsional second-order effects induced by steady drag force into the bridge’s equations of motion, in addition to unsteady lift and moment actions. The results show that good predictions of the flutter velocity can be obtained by combining steady drag with unsteady lift and moment.

Analytical formulas of thermal deformation of suspension bridges

Deformation of a long-span suspension bridge is mainly caused by ambient temperature changes. The temperature-induced deformation of a bridge is usually calculated using complex three-dimensional finite element analysis, the mechanism of which is often unclear. In this study, we derive general, succinct analytical formulas of the thermal deformation of three-span suspension bridges. The deformation of different components is unified into a one-dimensional thermal expansion formula (δL=LEθ·δT) by introducing an equivalent length LE. The sag effect of side-span cables is characterized by the modification coefficients, which demonstrate that the neglect of the sag effect overestimates the thermal deformation. Furthermore, the thermal deformation of the main- and side-span cables and towers is found to interact with each other as a result of the cable tension changes with varying temperature. The analytical formulas are validated using eight long-span suspension bridges including the Akashi Kaikyo bridge, the longest main-span suspension bridge in the world. The closed-form solutions herein also apply to the self-anchored suspension bridges.

25-1 明石海峡大橋によるテレビ電波障害のシミュレーションと検証

25-1 明石海峡大橋によるテレビ電波障害のシミュレーションと検証

Advances in Steel Materials for Innovative and Elegant Steel Structures in Japan–A Review

Over the course of the past 150 years, since the first iron- and steel-based bridge was constructed in 1868, Japan has become one of the most advanced countries in the construction of steel structures. Various innovative and elegant steel structures were constructed in the past such as the world’s longest suspension bridge called the Akashi Kaikyo Bridge. The advances of steel structures were attributed to a significant extent to the development of high-performance steels. Such materials developed in Japan were characterized by three types of versatilities: strength, functional, and sectional. Some examples of such materials include fairly high and low strength steels, high-bridge performance steel, seismic-resistant steel, fire-resistant steel, and size-flexible H-shaped beam. In Japan, these steel material innovations enabled the progress in steel structures to leap forward and in turn challenging new structures gave birth to further advancements in steel materials. In this paper, the advancements of steel structures and materials were reviewed, focusing largely on the steel materials and their contributions to the construction of steel structures. In addition, in light of recently developed innovative steels and their strength-increasing potential, the further advancements of steel materials were suggested for the future innovations of steel structures.

Practical Diagrammatical Technique for 3-DOF Bridge Flutter Analysis

For long bridges with bluff deck sections, the influence of lateral wind loads on flutter performance needs to be carefully investigated. In this paper, an advanced three-degree-of-freedom (3-DOF) analytical framework considering lateral aeroelastic effects is developed to refine bridge flutter analysis. This approach uses high-order nonlinear equations to determine twin critical flutter parameters, i.e., velocity and frequency. An optimization model to determine the critical flutter parameters is developed. A practical diagrammatical technique is proposed to solve this problem, which is an improvement over the traditional optimization techniques. The intuitiveness and effectiveness of the diagrammatical technique is fully verified using a numerical example. The optimization model and diagrammatical technique are applied to the 3-DOF flutter analyses of two bridges with bluff deck sections. It is revealed that the flutter derivatives H5∗, H6∗, A5∗, A6∗, and Pi∗ (i=1,2,…,6) play an insignificant role in flutter performance of both bridges. If H5∗=H6∗=A5∗=A6∗=0, the Pi∗ (i=1,2,…,6) will be paralyzed, and the influence of only the conventional eight flutter derivatives, those related to the heaving and torsional motions, can be considered. On the other hand, if Pi∗=0 (i=1,2,…,4), H5,6∗, A5,6∗, and P5,6∗ will also lose efficacies. These novel findings are first presented, which can be steadily proved by the explicit expression of the optimization model. This study presents a valuable insight into the flutter characteristics of both bridges and explores the roles in the flutter onset played by various parameters. Further, even with bluff deck sections of both bridges, the analytical results of 2-DOF vertical-torsional coupled flutter for the Akashi Kaikyo Bridge and the 1-DOF torsional flutter for the Suramadu Bridge are coincident with the experimental observations. Thus, the effectiveness of analytical framework is again verified.

비선형 FEM 해석을 이용한 기존 강재 주탑기부 설계의 개선방안 연구

본 연구에서는 강주탑 기부와 기초콘크리트 연결 구조에 대해서 국내에서 특수교량의 강주탑 기부 설계에 보편적으로 적용하고 있는 명석해협대교(明石海峽大橋) 시방기준과 비선형 FEM 해석결과를 비교하였다. 명석해협대교(明石海峽大橋) 시방기준은 1970년도에 만들어진 일본 기준으로 주탑 기부와 PS 강봉 및 기초콘크리트를 스프링으로 선형 모델링하여 설계하는 방법으로서 43년이 지난 지금까지도 간편성을 이유로 이 기준을 적용하고 있다. 그러나 비선형 FEM 해석결과의 비교를 통해 특수 장대교의 강주탑 기부의 해석 및 설계에 이 기준을 적용하는 것은 여러 가지 문제점이 있음을 알 수 있었으며, 풍하중, 지진하중에 주요하게 저항하면서도 다양한 부재들로 복잡하게 연결된 강주탑 기부에 대해서는 한계상태설계법으로 발전하려는 현 시대에 맞추어 실제 거동을 반영하는 비선형 FEM해석을 적용해야 할 것이다. In this study nonlinear FEM analysis for steel pylon base of a cable supported bridge is performed in order to compare the results of Akashi-Kaikyo bridge's design specification established in 1970. Due to convenience of its application, the Akashi grand bridge's design specification has been applied to the base design of cable stayed bridges. It has been using linear spring in order to model prestressed high tensioned bars between steel pylon bottom plates and the base concrete. However, the results of nonlinear FEM analysis revealed that the Akashi-Kaikyo bridge's design specification has various problems in the analysis of the steel pylon base. And the steel pylon base has various complex members connecting with each other, and it is main member to resist against the wind load or the earthquake load. Therefore, the nonlinear FEM analysis has to be conducted in order to predict the behavior of steel pylon base exactly. Also, the nonlinear FEM analysis is more reasonable for the load and resistant factor design.

Modelling and Control of a Suspended-Span Bridge Section

We study the modelling and flutter suppression of a suspended-span bridge section using aerodynamic control means. The aerodynamic actuators are controllable leading- and trailing-edge flaps fitted to both edges of the bridge deck. The modelling is based on thin aerofoil theory which describes the bridge deck - air stream interactions. The model also consider the mass and inertia effects of the flaps. Passive mechanical controllers are proposed that sense the vertical velocity of the leading- and trailing-edge flap pivots and use these signals to produce control torques and adjust the flap angles accordingly. The control system is insensitive to the wind direction in the case of identical leading- and trailing-edge mechanical controllers. The Akashi-Kaikyo bridge is used as a working example for the numerical simulation evaluation of the control system performance.

Vibration Control of Bridge Tower (Akashi-Kaikyo Bridge and Tatara Bridge)

Vibration Control of Bridge Tower (Akashi-Kaikyo Bridge and Tatara Bridge)

Flutter and its application—Flutter mode and ship navigation

Based on the aerodynamic interaction between the heaving vortex-induced vibration and the torsional flutter, another explanation of the drastic change of the vibrational mode from the 5th symmetrical heaving mode to the 1st asymmetrical torsional mode is introduced. Some fundamental characteristics of the coupled flutter of a thin plate and a plate like structure, such as the flutter modes, the flutter branches, are explained by use of the “Step-by-Step flutter analysis”. The flutter properties obtained by the 3DOF multi-modes-flutter analysis are compared with the ones by the 2DOF 2modes- flutter analysis t. 3DOF multi-modes flutter analysis is recommended to use for more accurate verification of the flutter property as the lessons from the aerodynamic behavior of the full-scale elastic model of Akashi Kaikyo Bridge. The reduction of the key equivalent aerodynamic derivatives, by suitable span-wise arrangement of the girders with different girder-shapes, is significantly effective to stabilize the flutter instability of a long spanned suspension bridge. Furthermore, the significantly similar formula with the Selberg formula can be derived under the simple assumptions. As an application of the coupled flutter, the generation mechanism of the propulsion force by use of coupled flutter motion is introduced. Finally, it is confirmed that the H-90 mode can produce the propulsion force by the test of the ship-navigation with the flapping plate controlled in the particular flutter mode is shown.

Development of a Nonlinear Model for Soft Rock and its Applications

A phenomenological model has been developed for soft rock based on the results of a series of triaxial compression (TC) tests conducted on Kobe sandstone with a very high precision measurement. From the analysis and interpretation of the test results, it has been found that small strain Young’s modulus (Ee) was a function of the major principal stress. Ee for elastic strains of soft rock was assumed to be cross-anisotropic. A damage function has been used to derive the appropriate elastic Young’s modulus when subjected to shear loading. As the basic stress–strain relation, the relationship between the tangent modulus and the shear stress level was used. The differential form of which was subsequently integrated by a 4th order Runge–Kutta solver to obtain the stress–strain relation. The model of soft rock is based on an isotropic strain hardening elasto-plastic framework which takes into account the pressure sensitivity, cross-anisotropy, degradation of Young’s modulus with the degree of mobilized shear stress and the nonlinearity of the shear stress-shear strain relationship. Although the model was developed from the analysis of the TC tests results of Kobe sandstone, it was also applied to the other types of soft rock or stiff geomaterials. Plate loading tests were conducted at a level of 61 m below the ground level at the bottom of a large excavated shaft at four locations. Finally, the model was used to simulate the plate loading test results successfully. This model was successfully calibrated with Akashi sandstone and applied in the simulation for the settlement of Akashi-Kaikyo Bridge piers. The simulations were carried out for both drained and undrained condition by changing the Poisson’s ratio. The layering information beneath the foundations were used in the FEM simulation. The use of very accurate Young’s modulus from the field shear wave velocity test was the key to the successful simulation of the settlement under bridge pier foundations.

明石海峡大橋並列ハンガーロープのウェイク振動対策

明石海峡大橋並列ハンガーロープのウェイク振動対策

Measures against Wind - Induced Vibration of the Towers of the Akashi Kaikyo Bridge

Measures against Wind - Induced Vibration of the Towers of the Akashi Kaikyo Bridge

Several Geotechnical Design and Construction Issues with Akashi Strait Bridge

The Akashi Kaikyo (Strait) Bridge, one of the major bridges of the Honshu-Shikoku bridge network connecting the main island and the Shikoku island, is the world's longest suspension bridge with a center span of about 2,000 m. The bridge was constructed over the Akashi Strait and opened to traffic in 1998 after a construction period of about 10 years. The granite stratum in the Akashi Strait was very deep, while the granite stratum provides the foundations for the other long span bridges which have been constructed in Japan. Three of the four foundations had to be constructed on either a weakly cemented gravelly soil deposit or a sedimentary soft rock layer. The geological structure was carefully investigated and the geotechnical properties, in particular the strength and deformation characteristics of these geomaterial types, were carefully evaluated. To this end, a comprehensive series of advanced triaxial compression (TC) tests were performed on rotary core tube samples of sedimentary soft rock after it was found that the due design was not possible based on unconfined compression tests. Both CD and CU TC tests and cyclic undrained triaxial tests were performed on rotary core tube samples (30 cm in dia.) of the gravelly soil. Based on the data, the long-term and seismic stabilities of the foundations were evaluated. The importance of strain- and pressure-dependent nonlinear stress-strain behaviour at small strains, as well as accurate strain measurements in the laboratory stress-strain tests, was confirmed by analyzing the full-scale behaviour of the foundation during and after construction and comparing the back-calculated stiffness values with those obtained from laboratory stress-strain tests, pressure-meter tests, plate loading tests and field shear wave velocity measurements.

New consideration on flutter properties based on step-by-step analysis

This paper studies the coupled flutter mechanism of plate and long span bridges based on step-by-step analysis (SBS). Fundamental flutter modes are defined based on amplitude ratio and phase difference between heaving and torsional motions. Furthermore, a formula remarkably similar to the Selberg formula can be derived by use of the particular simplified flutter-onset condition. In the process of SBS analysis, some torsional divergent velocities where the torsional rigidity becomes zero can be defined. Finally, the flutter-behavior of an elastic model of the complete Akashi-Kaikyo Bridge, which is the longest suspension bridge in the world, is studied from the point of view of flutter in 2 degrees of freedom, namely heaving and torsional motion, taking into account the structural coupling effect of additional torsional displacement induced by horizontal displacement as a structural coupling property.

Seismic design and seismic performance retrofit study for the Akashi Kaikyo Bridge

This paper presents the original seismic design and seismic performance retrofit study against large-scale earthquakes of the Akashi Kaikyo Bridge. The Akashi Kaikyo Bridge is the world's longest suspension bridge and was completed in 1998. In the original seismic design, an inland near-field earthquake with large magnitude was not considered for the seismic design force. Although the bridge encountered the Hyogo-ken Nanbu Earthquake in 1995, it was not seriously damaged since the earthquake occurred during its construction. Therefore, a seismic performance retrofit study against large-scale earthquakes has been started. In the seismic performance retrofit study, site-specific large-scale earthquakes including inland near-field earthquakes were defined based on the latest seismological information. As a result, it was found that target seismic performance was ensured by taking some minor countermeasures.

Effects of approximation of self-excited forces by rational function on wind-induced response of a long-span bridge

In this paper, time-domain modeling of bridge deck flutter is first developed. The frequency dependent self-excited forces acting on a bridge deck are approximated in the Laplace transform domain by rational functions. The least-square matrix formulation of the rational function approximation is applied to flutter derivatives of the Akashi Kaikyo Bridge and airfoil. Besides, numerical analyses of the wind-induced response of the Akashi Kaikyo Bridge were conducted to facilitate the discussion. After that, the vertical deflection and torsion at the span center of the Akashi Kaikyo Bridge caused by buffeting and self-excited forces using the results of approximated flutter derivatives are examined to investigate the sensitivity of the approximation to the wind-induced response.