Effect of torsional stiffness of prestressed concrete box girders and uplift of abutment bearings on seismic performance of bridges

Uplift of certain abutment bearings during earthquake may be utilized as a safety mechanism for the protection of the bridge against excessive stress. For this reason design codes such as Eurocode 8 permit the uplift of such bearings under certain conditions. Uplift of an abutment bearing occurs when the torque at the deck end exceeds a critical value. Therefore the torsional stiffness of the deck, before or after concrete cracking, is an important factor. In this work realistic values for the cracked torsional stiffness of the bridge deck are estimated from a parametric study of typical thin-walled prestressed box girders, based on non-linear analysis of softened space truss models proposed in the literature. Moreover the interaction between bearing uplift and pier flexural response is investigated and recommendations for the seismic design of bridges are proposed, taking into account the possibility of uplift of abutment bearings before or after yielding of the piers.     

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.     

Seismic response of isolated bridges with soil–structure interaction

The modern transportation facilities demand that the bridges are to be constructed across the gorges that are located in seismically active areas and at the same time the site conditions compel the engineers to rest the pier foundation on soil. The purpose of this study is to assess the effects of soil–structure interaction (SSI) on the peak responses of three-span continuous deck bridge seismically isolated by the elastomeric bearings. The emphasis has been placed on gauging the significance of physical parameters that affect the response of the system and identify the circumstances under which it is necessary to include the SSI effects in the design of seismically isolated bridges. The soil surrounding the foundation of pier is modelled by frequency independent coefficients and the complete dynamic analysis is carried out in time domain using complex modal analysis method. In order to quantify the effects of SSI, the peak responses of isolated and non-isolated bridge (i.e. bridge without isolation device) are compared with the corresponding bridge ignoring these effects. A parametric study is also conducted to investigate the effects of soil flexibility and bearing parameters (such as stiffness and damping) on the response of isolated bridge system. It is observed that the soil surrounding the pier has significant effects on the response of the isolated bridges and under certain circumstances the bearing displacements at abutment locations may be underestimated if the SSI effects are not considered in the response analysis of the system.     

Implications of seismic pounding on the longitudinal response of multi-span bridges-an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach, Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is essential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Implications of seismic pounding on the longitudinal response of multi-span bridges - an analytical perspective

Seismic pounding between adjacent frames in multiple-frame bridges and girder ends in multi-span simply supported bridges has been commonly observed in several recent earthquakes. The consequences of pounding include damage to piers, abutments, shear keys, bearings and restrainers, and possible collapse of deck spans. This paper investigates pounding in bridges from an analytical perspective. A simplified nonlinear model of a multiple-frame bridge is developed including the effects of inelastic frame action and nonlinear hinge behavior, to study the seismic response to longitudinal ground motion. Pounding is implemented using the contact force-based Kelvin model, as well as the momentum-based stereomechanical approach. Parameter studies are conducted to determine the effects of frame period ratio, column hysteretic behavior, energy dissipation during impact and near source ground motions on the pounding response of the bridge. The results indicate that pounding is most critical for highly out-of-phase frames and is not significant for frame period ratios greater than 0.7. Impact models without energy dissipation overestimate the displacement and acceleration amplifications due to impact, especially for elastic behavior of the frames. Representation of stiffness degradation in bridge columns is cssential in capturing the accurate response of pounding frames subjected to far field ground motion. Finally, it is shown that strength degradation and pounding can result in significant damage to the stiffer frames of the bridge when subjected to large acceleration pulses from near field ground motion records.     

Restrain of a seismically isolated bridge by external stoppers

The current design of seismically isolated bridges usually combines the use of bearings and stoppers, as a second line of defence. The stoppers allow the development of the in-service movements of the bridge deck, without transmitting significant loads to the piers and their foundations, while during earthquake they transmit the entire seismic action. Despite the fact that stoppers, which restrain the transverse seismic movements of the deck, are used frequently in seismically isolated bridges, the use of longitudinal stoppers is relatively rare, mainly due to the large in-service constraint movements of bridges. The present paper proposes a new type of external longitudinal stoppers, which are installed in stiff sub-structures-boundaries, aiming at limiting the bridge seismic movements. The parametric investigation, which was conducted in order to identify the seismic efficiency of the external stoppers, showed that the interaction of the bridge with the stiff boundaries can lead to significant reductions in the seismic movements of the bridge. Serviceability is appropriately arranged in the paper by expansion joints and approach slabs.     

A simplified design method for metallic dampers used in the transverse direction of cable-stayed bridges

The aseismic design of cable-stayed bridges in the transverse direction with newly proposed metallic dampers that can accommodate both longitudinal and transverse movement of the deck has recently been considered. This work focuses on developing a simplified method to design an appropriate metallic damper. The seismic performance of cablestayed bridges with different damper stiffness, main span lengths, tower shapes and types of deck in the transverse direction are investigated. The transverse displacement of the deck of a cable-stayed bridge increases significantly with the increment of the damper stiffness, which proves that the design of the damper stiffness is crucial. A simplified model considering the damper stiffness, cable system and tower in the transverse direction is developed to evaluate the period and lateral displacement of a complicated cable-stayed bridge. Based on the simplified model, a design method is proposed and assessed using two cable-stayed bridges as examples. The results show that metallic dampers can be designed with high efficiency, and the optimal ductility of the damper can be selected.     

The eigenvalues of isolated bridges with transverse restraints at the end abutments

This paper examines the eigenvalues of multi‐span seismically isolated bridges in which the transverse displacement of the deck at the end abutments is restricted. With this constraint the deck is fully isolated along the longitudinal direction, whereas along the transverse direction the deck is a simple‐supported beam at the end abutments which enjoys concentrated restoring forces from the isolation bearings at the center piers. For moderate long bridges, the first natural period of the bridge is the first longitudinal period, while the first transverse period is the second period, given that the flexural rigidity of the deck along the transverse direction shortens the isolation period offered by the bearings in that direction. This paper shows that for isolated bridges longer than a certain critical length, the first transverse period becomes longer than the first longitudinal period despite the presence of the flexural rigidity of the deck. This critical length depends on whether the bridge is isolated on elastomeric bearings or on spherical sliding bearings. This result is also predicted with established commercially available numerical codes only when several additional nodes are added along the beam elements which are modeling the deck in‐between the bridge piers. On the other hand, this result cannot be captured with the limiting idealization of a beam on continuous distributed springs (beam on Wrinkler foundation)—a finding that has practical significance in design and system identification studies. Finally, the paper shows that the normalized transverse eigenperiods of any finite‐span deck are self‐similar solutions that can be represented by a single master curve and are independent of the longitudinal isolation period or on whether the deck is supported on elastomeric or spherical sliding bearings. Copyright © 2009 John Wiley & Sons, Ltd.     

不同约束方式对匝道桥动力特性的影响研究

近年来,地震作用下的匝道桥表现出较高的地震易损性。为建立匝道桥的有效约束方式,以减小其地震损伤,本文基于汶川地震中连续梁桥约束方式的调研结果,建立了4种不同匝道桥支座约束方式,并以石家庄石环线某匝道桥为例,对比分析了不同约束方式下匝道桥的自振特性及地震响应。结果表明:板式橡胶支座具有一定的剪切变形能力,可降低桥墩与支座组成的体系刚度,有效分散了上部结构的地震惯性力,保护了下部结构,但应注意其引起的较大主梁位移;固定支座或墩梁固结形式会放大桥墩受力,增加下部结构的损坏,不宜设置在高度较矮、刚度较大的桥墩上;双层挡块和垫石凹槽分级限位支座具有较好的限位能力,并可耗散部分地震能量。     

板式橡胶支座对斜交连续梁桥地震反应的影响

为充分了解板式橡胶支座对斜交连续梁桥地震反应的影响,利用OpenSees软件建立简化的斜交桥计算模型进行时程分析,研究板式橡胶支座摩擦滑移效应,以及支座动摩擦系数、剪切刚度、局部脱空等参数对斜交桥地震反应的影响。结果表明:板式橡胶支座考虑摩擦滑移后,不仅桥面位移和转角显著增大,而且出现残余位移和残余转角;随着支座剪切刚度的增大,桥面位移和转角均明显减小;随着桥墩处支座动摩擦系数的增大,桥面位移、转角均呈增长趋势,然而桥台处支座动摩擦系数的影响与之相反;桥墩处局部支座脱空对斜交桥的影响明显大于桥台支座。     

考虑上部结构影响的山区桥梁支座刚度设计方法研究

为了合理计算山区桥梁支座刚度,针对桥墩高度不相同的特点,考虑上部结构对桥墩顶部的转动约束作用,提出在横桥向可将墩顶视为自由约束,而在纵桥向将墩顶视为定向约束。分别按照地震作用下各墩底剪力和弯矩相等的原则,推导桥梁支座纵、横桥向的刚度设计公式,并给出各桥墩支座的设计方法。为验证方法的正确性,以墩底剪力相等的原则为例,利用OpenSees建立一座墩高不等的5跨连续梁桥模型,并依支座刚度取值不同分三种工况:工况一各桥墩支座刚度相同;工况二按墩顶自由计算各支座的纵、横桥向刚度;工况三按墩顶定向约束计算各支座的纵、横桥向刚度。分别对三种工况下的桥梁结构输入三条地震动记录进行时程分析,考察各桥墩的底部剪力。分析结果表明:工况一各桥墩纵、横桥向的底部剪力均不相同;工况二各桥墩横桥向的底部剪力相同而纵桥向的底部剪力不同;工况三各桥墩纵桥向的底部剪力相同而横桥向的底部剪力不同。上述结果表明在桥梁支座设计时,横桥向桥墩的抗推刚度应按墩顶自由计算,而纵桥向桥墩的抗推刚度应按墩顶为定向约束计算。     

Seismic response of base isolated buildings including p-Δ effects of isolation bearings

In order to achieve a low isolation frequency, elastomeric bearings used for base isolation of buildings usually have low shear rigidity which leads to a significant reduction in the buckling load. The effects of compression load on the bearing behaviour are therefore an important consideration. A study of seismic response of base isolated buildings is presented in this paper, fully accounting for the P-Δ effects of isolation bearings. An analytical procedure is formulated that treats separately the superstructure and the supporting bearings and assembles the governing equations via the interaction forces at the base deck. The resulting equations are then solved step-by-step numerically. Numerical results obtained for a base isolated five-storey shear building show that neglecting the P-Δ effects can lead to considerable errors in the computed seismic response when the buckling safety factor of bearings is low.     

Inertial interaction effects on deck isolated bridges

This work investigates the influence of a flexible foundation on the nonlinear dynamic response of a group of representative deck isolated bridges (24 cases) located on two different soil types. The bridges were analyzed with full 3D models. Inertial soil structure interaction (SSI) effects were studied modeling the flexibility of the foundations with constant springs and dashpots defined at a particular frequency. Kinematic SSI effects were not included. The study was conducted in three stages: first the seismic response of the bridges without deck isolation on rigid supports was obtained, next the response of the bridges with deck isolation, but still on rigid supports was considered; finally analyses were conducted of the bridges with deck isolation and SSI. The results from the three cases were compared. They indicated that for bridges and foundations designed according to the Mexican design criteria inertial interaction effects were not significant. To assess by how much the stiffness of the foundation would have to be reduced (due perhaps to nonlinear soil behavior) a simplified model with 2DOF was used to conduct more parametric studies. The main conclusion is that the reduction in the stiffness would have to be considerable.     

Effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings

A finite element model is constructed for a sliding friction bearing in a seismically isolated bridge under vertical excitation with contact/friction elements. The effects of vertical excitation on the seismic performance of a seismically isolated bridge with sliding friction bearings and different bearing friction coefficients and different stiffness levels (pier diameter) are discussed using example calculations, and the effects of excitation direction for vertical excitation on the analysis results are explored. The analysis results shows that vertical excitation has a relatively large impact on seismic performance for a seismically isolated bridge with sliding friction bearings, which should be considered when designing a seismically isolated bridge with sliding friction bearings where vertical excitation dominates.     

Seismic performance of highway bridges with fusing bearing components for quasi‐isolation

Modern highway bridges in Illinois are often installed with economical elastomeric bearings that allow for thermal movement of the superstructure, and steel fixed bearings and transverse retainers that prevent excessive movement from service‐level loadings. In the event of an earthquake, the bearing system has the potential to provide a quasi‐isolated response where failure of sacrificial elements and sliding of the bearings can cause a period elongation and reduce or cap the force demands on the substructure. A computational model that has been calibrated for the expected nonlinear behaviors is used to carry out a parametric study to evaluate quasi‐isolated bridge behavior. The study investigates different superstructure types, substructure types, substructure heights, foundation types, and elastomeric bearing types. Overall, only a few bridge variants were noted to unseat for design‐level seismic input in the New Madrid Seismic Zone, indicating that most structures in Illinois would not experience severe damage during their typical design life. However, Type II bearing systems, which consist of an elastomeric bearing and a flat PTFE slider, would in some cases result in critical damage from unseating at moderate and high seismic input. The sequence of damage for many bridge cases indicates yielding of piers at low‐level seismic input. This is caused by the high strength of the fixed bearing element, which justifies further calibration of the quasi‐isolation design approach. Finally, the type of ground motion, pier height, and bearing type were noted to have significant influence on the global bridge response. Copyright © 2013 John Wiley & Sons, Ltd.     

Extending the application of integral frame abutment bridges in earthquake‐prone areas by using novel isolators of recycled materials

Integral abutment bridges (IABs) are jointless structures without bearings or expansion joints which require minimum or zero maintenance. The barrier to the application of long‐span integral abutment bridges is the interaction of the abutment with the backfill soil during the thermal expansion and contraction of the bridge deck, that is, serviceability, or when the bridge is subjected to dynamic loads, such as earthquakes. The interaction of the bridge with the backfill leads to settlements and ratcheting of the soil behind the abutment and, as a result, the soil pressures acting on the abutment build up in the long term. This paper provides a solution for the aforementioned challenges by introducing a novel isolator that is a compressible inclusion of reused tyre‐derived aggregates placed between the bridge abutment and the backfill. The compressibility of typical tyre‐derived aggregates was measured by laboratory tests, and the compressible inclusion was designed accordingly. The compressible inclusion was then applied to a typical integral frame abutment model, which was subjected to static and dynamic loads representing in‐service and seismic loads correspondingly. The response of both the conventional and the isolated abutment was assessed based on the settlements of the backfill, the soil pressures and the actions of the abutment. The study of the isolated abutment showed that the achieved decoupling of the abutment from the backfill soil results in significant reductions of the settlements of the backfill and of the pressures acting on the abutment. Hence, the proposed research enables extending the length limits of integral frame bridges subjected to earthquake excitations. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling of cable vibration effects of cable-stayed bridges

The analysis of dynamic responses of cable-stayed bridges subjected to wind and earthquake loads generally considers only the motions of the bridge deck and pylons. The influence of the stay cable vibration on the responses of the bridge is either ignored or considered by approximate procedures. The transverse vibration of the stay cables, which can be significant in some cases, are usually neglected in previous research. In the present study, a new three-node cable element has been developed to model the transverse motions of the cables. The interactions between the cable behavior and the other parts of the bridge superstructure are considered by the concept of dynamic stiffness. The nonlinear effect of the cable caused by its self-weight is included in the formulation. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed model. The impact of cable vibration behavior on the dynamic characteristics of cable-stayed bridges is discussed. Supported by: Natural Science and Engineering Research Council of Canada     

Seismic energy dissipation for cable-stayed bridges using passive devices

This study assesses analytically the effectiveness, feasibility and limitations of elastic and hysteretic damping augmentation devices, such as elastomeric and lead–rubber bearings, with respect to the dynamic and seismic performance of cable-stayed bridges. This type of bridge, which has relatively greater flexibility, is more susceptible to undesirable vibrations due to service and environmental loadings than are conventional bridges. Therefore, damping is a very important property. Supplementary damping devices based on the plastic deformation of lead and steel are proposed at critical zones, such as the deck–abutment and deck–tower connections, to concentrate hysteretic behaviour in these specially designed energy absorbers. Inelastic behaviour in primary structural elements of the bridge can therefore be avoided, assuring the serviceability of these cable-supported bridges. Analytically, three-dimensional modelling is developed for the bridge and the damping devices, including the bridge geometrical large-displacement non-linearity and the local material and geometric non-linearities of the energy dissipation devices. The effects of various modelling and design parameters of the bridge response are also studied, including the properties, modelling accuracy and location of the devices along the bridge superstructure. It is shown that an optimum model of the seismic performance of the bridges with these passive control devices can be obtained by balancing the reduction in forces along the bridge against tolerable displacements. Appropriate locations and hysteretic energy dissipation properties of the devices can achieve a significant reduction in seismic-induced forces, as compared to the case with no dampers added, and relatively better control of displacements. In addition, proper selection of the location of the passive control systems can help redistribute forces along the structure which may provide solutions for retrofitting some existing bridges. However, caution should be exercised in simulating the device response for a reliable bridge structural performance. Moreover, while seismic response of the bridge can be significantly improved with added dampers, their degree of effectiveness also depends on the energy absorption characteristics of the dampers.     

寒区环境温度对板式橡胶支座连续梁桥地震易损性影响研究

针对现行规范对寒区桥梁减隔震设计中仅考虑橡胶支座力学特性受环境温度作用影响,而忽略桥墩混凝土材料特性受温度影响的不足,以高寒地区一座两联3×30 m混凝土连续梁桥为背景,开展不同环境温度下桥墩混凝土材料抗压性能试验,确定温度对其力学参数的影响,基于试验结果对不同环境温度下的桥墩混凝土力学参数进行修正,从而建立不同环境温度下的全桥精细化非线性有限元模型,并基于增量动力分析(IDA)法探究不同环境温度下该桥的地震易损性。结果表明:极端温度引起桥墩混凝土材料参数和支座刚度的改变,使得该桥自振频率随着温度的升高而降低;地震作用下,极端低温时桥墩墩顶位移较常温增大了26.8%,而极端高温时支座位移增大了19.4%;根据现行规范计算的极端低温时支座和桥梁系统的损伤概率偏小,极端高温时结构和构件的损伤概率偏大,在设计中应予以重视;极端低温下桥墩、支座及桥梁系统的损伤概率,较常温分别增大45.0%、35.2%和27.5%,对于高寒地区该类桥梁设计时需考虑低温对其抗震性能的影响。