An energy approach to sliding of single-span simply supported slab-on-girder steel highway bridges with damaged bearings

This paper investigates the non-linear inelastic seismic response of existing single-span simply supported bridges having bearings which can remain stable and slide after their anchor bolts are ruptured. A simplified equivalent model is developed for the inelastic analysis of these single-span simply supported bridges. Non-linear inelastic time-history analyses are conducted for various acceleration inputs. It is found that narrower bridges with longer spans may have considerable sliding displacements and fall off their supports if adequate seat width is not provided. It is also found that for the same ratio of friction coefficient to peak ground acceleration, the sliding displacement of a structural system is linearly proportional to the amplitude of the peak ground acceleration beyond a certain threshold value. This is also demonstrated analytically from an energy approach point of view. The distribution of the energy content of an earthquake, which is related to its velocity time history, can be an indication of the propensity of an earthquake to cause high sliding displacements. Ground motions with high frequency content or high A_p/V_p ratio may produce smaller sliding displacements than ground motions with relatively lower A_p/V_p ratios.     

Reduction of structural response to near fault earthquakes by seismic isolation columns and variable friction dampers

<正>This paper focuses on the investigation of a hybrid seismic isolation system with passive variable friction dampers for protection of structures against near fault earthquakes.The seismic isolation can be implemented by replacing the conventional columns fixed to the foundations by seismic isolating ones.These columns allow horizontal displacement between the superstructure and the foundations and decouple the building from the damaging earthquake motion.As a result, the forces in the structural elements decrease and damage that may be caused to the building by the earthquake significantly decreases.However,this positive effect is achieved on account of displacements occurring in the isolating columns.These displacements become very large when the structure is subjected to a strong earthquake.In this case,impact may occur between the parts of the isolating column yielding their damage or collapse.In order to limit the displacements in the isolating columns,it is proposed to add variable friction dampers.A method for selecting the dampers' properties is proposed.It is carried out using an artificial ground motion record and optimal active control algorithm.Numerical simulation of a seven-story structure shows that the proposed method allows efficient reduction in structural response and limits the displacements at the seismic isolating columns.     

Scaling of residual displacements in terms of elastic and inelastic spectral displacements for existing SDOF systems

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make them unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given lateral strength ratio. It is observed in the case of a class of ground motions that there are no trends in the dependence of residual displacement on the temporal features of the ground motion, and thus any estimation of residual displacements should be carried out only in the statistical sense. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered, and it is found that normalization with respect to inelastic spectral displacements is preferable. Expressions for residual displacement spectra are proposed for both types of normalizations and for the givenlateral-strength-ratio type oscillators.     

Seismic response of simple structures using spring-assisted sliding slabs with coulomb damping

Coulomb damping can be utilized effectively to reduce the dynamic response of structures subjected to seismic ground motions. To activate this damping, some parts of a vibrating structure are allowed to slide at rough interfaces. The dynamic response of structures provided with sliding interfaces at the base, between a floor slab and frame and in the cross bracings of a frame has been examined recently. In this paper, a simple slab sliding system provided with a spring to introduce a recovery mechanism and to reduce the sliding displacement requirement for low frequency structures has been examined. The equations of motion for this system are developed. An approach is presented to solve these coupled equations for earthquake induced ground motions. Structures with varying frequency and friction characterisics are considered and the numerical results are presented in response spectrum form. It is observed that, in low frequency structures, provision of a rather weak spring can reduce the sliding displacement requirements without significantly increasing the forces in the supporting frame and the acceleration input to supported secondary systems.     

不规则框架结构的组合隔震反应分析

为研究不规则框架隔震结构的地震反应,分别对一个传统抗震结构、一个铅芯叠层橡胶支座隔震结构和四个组合隔震结构(隔震层由铅芯支座和滑板支座组成)进行了弹塑性地震反应时程分析,研究隔震支座参数对隔震效果的影响。结果表明:采用组合隔震技术时,合理选择隔震层的铅芯支座布置位置、滑板支座的摩擦系数和铅芯叠层橡胶支座的型号,可以有效地降低上部结构的扭转效应;对于不规则的建筑隔震结构,为减小地面运动带来的扭转效应,建议采用由铅芯支座和滑板支座组合而成的隔震层,可对上部结构的扭转起到很好的抑制作用。     

Response of sliding structures to harmonic support motion

The problem of response of a single degree of freedom structure supported on a sliding foundation and subjected to harmonic support motions is considered. The non-linear governing equations of motion are derived. It turns out that these equations are linear in each sliding and non-sliding phase and can be solved in closed forms in each phase. The equations for evaluation of the beginning and ending times of different phases are also formulated and solved numerically. The response for different coefficients of friction and various levels of excitation is evaluated and presented graphically. It is concluded that sliding supports can be quite effective in isolating structures from support excitations.     

Computation of sliding displacements of bridge abutments by pseudo-dynamic method

The paper focuses on seismic sliding displacement calculations of gravity wall bridge abutments when subjected to passive condition during earthquakes. Pseudo-dynamic approach has been used for the calculation of the passive seismic earth pressure. A novel element of the present investigation is the computation of seismic passive earth pressure coefficients by considering the composite curved rupture surface behind the abutment wall in the framework of limit equilibrium method. Sliding failure along the wall base is considered in the new pseudo-dynamic method. The critical seismic acceleration coefficient for sliding and sliding component of the displacement, resulting from horizontal and vertical sinusoidal ground accelerations, are computed by using Newmark's sliding block method. The effect of sliding on the response of earth structures is evaluated and comparisons are made between sliding displacements calculated using planar and composite failure mechanisms. Results of the comparative study showed that the assumption of planar failure mechanism for rough soil–wall interfaces significantly overestimates the critical seismic accelerations for sliding and underestimates the sliding displacements.     

Scaling of constant-ductility residual displacement spectrum

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make those unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given ductility ratio. Such oscillators belong to the class of bilinear hysteresis models applicable to steel structures, with post-yield-stiffness ratio taken as zero, and may be used for the conservative estimates of residual displacements when the post-yield-stiffness ratio is unlikely to become negative. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered and expressions are proposed for both types of normalizations. The statistical dependence of residual displacement on the seismological and site parameters and strong motion duration is also studied and a simple scaling model is proposed in terms of earthquake magnitude, epicentral distance, and geologic site condition parameter for the seismic region of western U.S.A. According to this model, the variation of residual displacement with period primarily depends on the site conditions, and the residual displacements are more sensitive to ductility ratio at low ductility ratios.     

摩擦摆基础隔震结构双向地震反应分析

采用双向耦合力学模型模拟摩擦摆支座的双向耦合效应,对摩擦摆基础隔震结构进行了单向和双向地震反应对比分忻,分析表明在双向地震作用下结构各层的加速度反应较小,隔震层的层间位移较大,而上部结构的层间位移较小,并且在双向地震作用下,支座的最大位移明显大于单向地震作用时的支座最大位移,因而应考虑双向地震作用对摩擦摆基础隔震结构地震反应和隔震支座性能的影响。     

结构震后残余位移研究进展

结构在强震作用下进入非线性阶段会产生不可恢复的永久位移或残余变形,结构残余位移是震后结构抗震性能和地震损失评估的重要参数,具有重要的理论意义和工程实用价值。为了深入分析残余位移的研究现状,为面向性态抗震设计和抗震韧性评估的地震动强度指标研究提供参考,全面和系统分析了国内外结构残余位移相关文献,介绍了残余位移的定义,重点论述了影响结构残余位移的主要因素,总结归纳了残余位移计算模型、残余位移控制方法及考虑残余位移的抗震性能评估方法,最后讨论了残余位移研究中存在的问题和建议。     

Deterministic sliding block methods for estimating seismic displacements of earth structures

A review and quantitative comparison of existing deterministic sliding block methods for predicting permanent displacements of earth structures subjected to seismic loading is presented. The reviewed sliding block methods are divided into two main groups based on the characteristic earthquake parameters referenced in each method. One group uses the maximum horizontal ground acceleration and velocity, and the other uses the maximum horizontal ground acceleration and the predominant period of the acceleration spectrum. Displacement functions published by previous authors are reformulated to give common non-dimensionalized displacement functions of the critical acceleration ratio which are then used to compare the different methods for the estimate of permanent seismic displacement of soil structures. The results show that despite the fact that the different methods were formulated using a wide range of earthquake records and different characteristic seismic parameters, permanent displacement values predicted using these methods fall within a reasonably narrow band. Selected acceleration data from three recent earthquakes that occurred in California are used to evaluate and compare the accuracy of the reviewed displacement methods for practical applications.     

A simple procedure to approximate slip displacement of freestanding rigid body subjected to earthquake motions

A simple calculation procedure for estimating absolute maximum slip displacement of a freestanding rigid body placed on the ground or floor of linear/nonlinear multi‐storey building during an earthquake is developed. The proposed procedure uses the displacement induced by the horizontal sinusoidal acceleration to approximate the absolute maximum slip displacement, i.e. the basic slip displacement. The amplitude of this horizontal sinusoidal acceleration is identical to either the peak horizontal ground acceleration or peak horizontal floor response acceleration. Its period meets the predominant period of the horizontal acceleration employed. The effects of vertical acceleration are considered to reduce the friction force monotonously. The root mean square value of the vertical acceleration at the peak horizontal acceleration is used. A mathematical solution of the basic slip displacement is presented. Employing over one hundred accelerograms, the absolute maximum slip displacements are computed and compared with the corresponding basic slip displacements. Their discrepancies are modelled by the logarithmic normal distribution regardless of the analytical conditions. The modification factor to the basic slip displacement is quantified based on the probability of the non‐exceedence of a certain threshold. Therefore, the product of the modification factor and the basic slip displacement gives the design slip displacement of the body as the maximum expected value. Since the place of the body and linear/nonlinear state of building make the modification factor slightly vary, ensuring it to suit the problem is essential to secure prediction accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic response of sliding equipment and contents in base‐isolated buildings subjected to broadband ground motions

Base isolation has been established as the seismic design approach of choice when it comes to protecting nonstructural contents. However, while this protection technology has been widely shown to reduce seismic demands on attached oscillatory equipment and contents (EC), its effectiveness in controlling the response of freestanding EC that are prone to sliding has not been investigated. This study examines the seismic behavior of sliding EC inside base‐isolated buildings subjected to broadband ground motions. The effect of isolation system properties on the response of sliding EC with various friction coefficients is examined. Two widely used isolation models are considered: viscously damped linear elastic and bilinear. The study finds isolation to be generally effective in reducing seismic demands on sliding EC, but it also exposes certain situations where isolation in fact increases demands on EC, most notably for low friction coefficients and high earthquake intensities. Damping at the isolation level is effective in controlling the EC sliding displacements, although damping over about 20% is found to be superfluous. The study identifies a physically motivated dimensionless intensity measure and engineering demand parameter for sliding equipment in base‐isolated buildings subjected to broadband ground motions. Finally, the paper presents easy‐to‐use design fragility curves and an example that illustrates how to use them. Copyright © 2014 John Wiley & Sons, Ltd.     

Seismic performance of cable-sliding friction bearing system for isolated bridges

During past strong earthquakes, highway bridges have sustained severe damage or even collapse due to excessive displacements and/or very large lateral forces. For commonly used isolation bearings with a pure friction sliding surface, seismic forces may be reduced but displacements are often unconstrained. In this paper, an alternative seismic bearing system, called the cable-sliding friction bearing system, is developed by integrating seismic isolation devices with displacement restrainers consisting of cables attached to the upper and lower plates of the bearing. Restoring forces are provided to limit the displacements of the sliding component. Design parameters including the length and stiffness of the cables, friction coefficient, strength of the shear bolt in a fixed-type bearing, and movements under earthquake excitations are discussed. Laboratory testing of a prototype bearing subjected to vertical loads and quasi-static cyclic lateral loads, and corresponding numerical finite element simulation analysis, were carried out. It is shown that the numerical simulation shows good agreement with the experimental force-displacement hysteretic response, indicating the viability of the new bearing system. In addition, practical application of this bearing system to a multi-span bridge in China and its design advantages are discussed.     

Effect of viscous,viscoplastic and friction damping on the response of seismic isolated structures

In this paper the efficiency of various dissipative mechanisms to protect structures from pulse‐type and near‐source ground motions is examined. Physically realizable cycloidal pulses are introduced, and their resemblance to recorded near‐source ground motions is illustrated. The study uncovers the coherent component of some near‐source acceleration records, and the shaking potential of these records is examined. It is found that the response of structures with relatively low isolation periods is substantially affected by the high‐frequency fluctuations that override the long duration pulse. Therefore, the concept of seismic isolation is beneficial even for motions that contain a long duration pulse which generates most of the unusually large recorded displacements and velocities. Dissipation forces of the plastic (friction) type are very efficient in reducing displacement demands although occasionally they are responsible for substantial permanent displacements. It is found that the benefits by hysteretic dissipation are nearly indifferent to the level of the yield displacement of the hysteretic mechanism and that they depend primarily on the level of the plastic (friction) force. The study concludes that a combination of relatively low friction and viscous forces is attractive since base displacements are substantially reduced without appreciably increasing base shears and superstructure accelerations. Copyright © 2000 John Wiley & Sons, Ltd.     

A GLE-based model for seismic displacement analysis of slopes including strength degradation and geometry rearrangement

Seismic performance of natural slopes, earth structures and solid-waste landfills can be evaluated through displacement-based methods in which permanent displacements induced by earthquake loading are assumed to progressively develop along the critical sliding surface as a result of transient activation of plastic mechanisms within the soil mass. For sliding mechanisms of general shape the earthquake-induced displacements should be computed using a model that provides a closer approximation of sliding surface. When large permanent displacement are induced by seismic actions, due to substantial shear strength reduction, and significant changes in ground surface occur, an improved estimate of permanent displacement can be obtained using a model which accounts for shear strength reduction and mass transfer between adjacent portions of the slope resulting from geometry changes of ground surface during the seismic event.In this paper, a GLE-based model is proposed for seismic displacement analysis of slopes that accounts for shear strength degradation and for geometry rearrangement. Model accuracy is validated against experimental results obtained from shaking table tests carried out on small scale model slopes. Comparison of computed and experimental results demonstrates the capability of the proposed approach in capturing the main features of the observed seismic response of the model slopes.     

断层错动引起的上覆土体破裂演化规律研究

断层引起的地面永久大变形是工程特别是生命线工程地震破坏的重要原因之一, 而研究断层错动下上覆土体变形和破裂的发展演化规律, 则是预测地面永久变形状态和分析断层危害性的基础． 本文采用有限元方法对垂直断层错动引起的上覆土体破裂演化规律进行了研究, 建立了垂直断层作用下上覆土体模拟的有限元模型, 对断层错动作用下上覆土体的破裂发展过程进行了模拟分析, 并分析了加载速率、 土体特性及断层倾角等参数对上覆土体的破裂演化发展过程的影响． 结果表明: ① 断层倾角越陡, 地表出现破裂时需要增加的垂直位移越大; ② 由于惯性力的影响, 断层加载速率对地表破裂所需施加位移和土层破裂角产生一定的影响; ③ 断层类型对土层地表破裂角与膨胀角、 摩擦角之间的关系有很大影响． 该分析结果可为新建工程的抗震设计和已建工程结构的抗震加固等工作提供依据．     

Shake table testing on restoring capability of double concave friction pendulum seismic isolation systems

After an earthquake, non‐negligible residual displacements may affect the serviceability of a base isolated structure, if the isolation system does not possess a good restoring capability. The permanent offset does not affect the performance unless the design is problematic for utilities, also considering possible concerns related to the maintenance of the devices. Starting from experimental and analytical results of previous studies, the restoring capability of Double Concave Friction Pendulum bearings is investigated in this paper. A simplified design suggestion for the estimation of maximum expected residual displacements for currently used friction pendulum systems is then validated. The study is based on controlled‐displacement and seismic input experiments, both performed under unidirectional motion. Several shaking table tests have been carried out on a three‐dimensional isolated specimen structure. The same sequence of seismic inputs was applied considering three different conditions of sliding surfaces corresponding to low, medium and high friction. The accumulation of residual displacements is also investigated by means of nonlinear dynamic analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

POST-EARTHQUAKE RESIDUAL DISPLACEMENTS OF BILINEAR OSCILLATORS

Structures subjected to large inelastic deformations during violent ground shaking do not always return to their initial ‘at-rest’ position but may have residual displacements. Even if collapse does not occur, large residual displacements may render them unusable or irreparable. In order to investigate the likely magnitude of residual displacement many bilinear single-degree-of-freedom oscillators with specified ductilities of 2·0, 4·0 and 6·0, stiffness ratios ranging from −0·25 to 1·0 and fundamental periods from 0 to 3·0s were subjected to 11 earthquake records from various ground types. It is shown that bilinear oscillators with positive stiffness ratios generally have small residual displacements, while those with negative stiffness ratios tend to undergo little inelastic reversal of deformation and have larger residual displacements. Reasons for this behaviour were able to be explained by means of a ‘hysteresis centre curve’. A design example for structures able to be modelled as single-degree-of-freedom oscillators is provided. © 1997 John Wiley & Sons, Ltd.     

Sliding fragility of block‐type non‐structural components. Part 1: Unrestrained components

Motivated by the development of performance‐based design guidelines with emphasis on both structural and non‐structural systems, this paper focuses on seismic vulnerability assessment of block‐type unrestrained non‐structural components under sliding response on the basis of seismic inputs specified by current seismic codes. Two sliding‐related failure modes are considered: excessive relative displacement and excessive absolute acceleration. It is shown that an upper bound for the absolute acceleration response can be assessed deterministically, for which a simple yet completely general equation is proposed. In contrast, fragility curves are proposed as an appropriate tool to evaluate the excessive relative displacement failure mode. Sample fragility curves developed through Monte‐Carlo simulations show that fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative, especially for relatively large values of the coefficient of friction. It is also found that reasonable estimates of relative displacement response at stories other than the ground in multistorey buildings cannot in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Failure modes considered in this study are found to be essentially independent of each other, a property that greatly simplifies assessment of conditional limit states. Copyright © 2002 John Wiley & Sons, Ltd.