Effects of interface material on the performance of free rocking blocks

This paper presents the results of an experimental investigation on the rocking behavior of rigid blocks. Two types of test specimens have been tested, namely M and C types. Nine blocks of the M type and two blocks of the C type with different aspect ratios were tested with varying initial rotational amplitudes and with different materials at the contact interface, namely concrete, timber, steel, and rubber. The results showed that the interface material has significant influence on the free rocking performance of the blocks. Blocks tested on rubber had the fastest energy dissipation followed by concrete and timber bases, respectively. Analysis of the test results has shown that the energy dissipation in the case of tests on a rubber base is a continuous mechanism whereas in the case of tests on rigid bases, i.e. timber and concrete, energy dissipation is a discrete function. Finally, the rocking characteristics of the blocks were calculated using piecewise equations of motion and numerical analysis. It was possible to predict the correct free rocking amplitude response when a reliable value for the coefficient of restitution was used. Copyright © 2010 John Wiley & Sons, Ltd.     

An experimental study on the rocking response of bridge piers with spread footing foundations

Some spread footing foundations from real retrofitting practices in Taiwan were extended to be uneconomically large due to the restriction of foundation uplift regulated in the design code. Although rocking mode of spread footings induced from foundation uplift is not favorable in current design code, recent studies have shown that the rocking of a spread footing may have a beneficial effect on the dynamic performance of piers by reducing the earthquake forces that can be transmitted to the pier base. This implies that the plastic deformation that occurs at the pier's plastic zone can be decreased and as a result the ductility demand of piers can possibly be reduced. In order to gain a better understanding of the structural behavior related to rocking and to clarify that if the widening and strengthening of the foundations to limit the rocking mechanism of spread footing is necessary for the retrofitting work, a series of preliminary rocking experiments were performed. A total of three circular reinforced concrete columns with spread footing foundations were tested. Using pseudo‐dynamic tests and a cyclic loading test, these columns were subjected to different levels of earthquake accelerations, including a near field ground motion. The results of the tests and the rocking behavior of the footings are discussed in this paper. From the benchmark test, the difference between the response behavior of a rocking base and a fixed base foundation was highlighted. By comparing the experimental responses of the retrofitted column with the responses of the original one, the effect of the rocking mechanism on the ductility demand and strength demand of the columns was also identified. Copyright © 2010 John Wiley & Sons, Ltd.     

Biaxial testing of unbonded post‐tensioned rocking bridge piers with external replacable dissipaters

The biaxial response of two bridge piers is experimentally investigated. A post‐tensioned precast bridge pier with external replaceable mild‐steel dissipaters is tested under biaxial loading. The performance of the post‐tensioned bridge pier is compared with a conventionally reinforced monolithic bridge pier. The experimental biaxial response is then compared with previous uniaxial experimental testing of identical bridge piers to understand the influence of biaxial loading, specifically concerning post‐tensioned rocking sections. A 3‐dimensional moment–curvature and moment–rotation analysis program is created to generate the monotonic section response of a conventional and post‐tensioned bridge pier. After comparing the accuracy of the section analysis program to the experimental testing of the monolithic pier, the program is validated against the experimental testing of the post‐tensioned bridge pier. This section analysis program is then used in the calibration of a macro‐model to capture the entire cyclic response of the post‐tensioned bridge pier. The macro‐model adopts multiple linear‐elastic compression‐only springs at the rocking interface, combined with non‐linear inelastic springs for each of the mild‐steel dissipaters and returns encouraging results at both local and global levels. The paper concludes with a number of biaxial moment‐interaction design charts for monolithic and post‐tensioned bridge piers as a function of mechanical and geometric section properties. The design charts define the biaxial yield surface at nominal yield and at the design section capacity defined by one of three material limit states. Copyright © 2011 John Wiley & Sons, Ltd.     

Characterization of rocking shallow foundations using centrifuge model tests

This paper presents new results of centrifuge model tests exploring the behavior of rocking shallow foundations embedded in dry sand, which provides a variety of factors of safety for vertical bearing. The results of slow (quasi‐static) cyclic tests of rocking shear walls and dynamic shaking tests of single‐column rocking bridge models are presented. The moment–rotation and settlement–rotation relationships of rocking footings are investigated. Concrete pads were placed in the ground soil to support some models with the objective of reducing the settlement induced by rocking. The behavior of rocking foundation was shown to be sensitive to the geometric factor of safety with respect to bearing failure, L_f/L_c, where L_f was the footing length, and the L_c was the critical soil‐footing contact length that would be required to support pure axial loading. Settlements were shown to be small if L_f/L_c was reasonably large. Placement of concrete pads under the edges of the footing was shown to be a promising approach to reduce settlements resulting from rocking, if settlements were deemed to be excessive and also had impacts on the energy dissipation and rocking moment capacity. A general discussion of the tradeoffs between energy dissipation and re‐centering of rocking foundations and other devices is included. Copyright © 2011 John Wiley & Sons, Ltd.     

Modeling of rocking frames under seismic loading

A novel modeling approach for the seismic response assessment of rocking frames is presented. Rocking frames are systems with columns that are allowed to fully, or partially, uplift. Despite the apparent lack of a mechanism to resist lateral forces, they have a remarkable capacity against earthquake loading. Rocking frames are found in old structures, for example, ancient monuments, but it is also a promising design concept for modern structures such as bridges or buildings. The proposed modeling can be implemented in a general-purpose structural analysis software, avoiding the difficulties that come with the need of formulating and solving specifically tailored differential equations, or the use of detailed computational models. Different configurations of a rocking portal frame problem are examined. The model is based on rigid, or flexible, beam elements that describe the members of the frame. Negative-stiffness rotational springs are smartly positioned at the rocking interfaces in order to simulate the rocking restoring moment, while the mass and the rotational moment of inertia are considered either lumped or distributed. Both the cases of rigid and flexible piers/columns are discussed, while it is shown that frames with restrained columns can be considered in a straightforward manner. A simple alternative based on an equivalent oscillator that follows the generalized rocking equation of motion is also investigated. The efficiency and the accuracy of the proposed modeling is demonstrated with the aid of carefully chosen case studies.     

Analysis of tubular steel bridge piers

A one‐dimensional model is proposed for the static and dynamic analysis of tubular steel bridge piers subjected to strong ground motions. The present formulation does not require experimental results nor shell analysis to obtain the constitutive equation of the model, which shows strength deterioration. The material properties and dimensions of bridge piers are required for static and dynamic analysis of the present model. The present analysis consists of two steps. The first step is to obtain the stress and strain relationship of the base plastic‐hinge region, where local inelastic buckling is observed. The modified Shanley's model and fiber elements are used to establish the compressive skeleton curve. The strength deterioration is taken into account in the resulting constitutive model. The second step is to analyze static and dynamic responses of tubular steel bridge piers. For overall analysis, the base plastic‐hinge region is discretized in the circumferential direction by using fiber elements whose constitutive equation was obtained in the first step. The validity of the present model has been confirmed through comparisons with existing experimental results. Copyright © 2005 John Wiley & Sons, Ltd.     

Analysis of the rocking response of rigid blocks standing free on a seismically isolated base

This paper examines the rocking response and stability of rigid blocks standing free on an isolated base supported: (a) on linear viscoelastic bearings, (b) on single concave and (c) on double concave spherical sliding bearings. The investigation concludes that seismic isolation is beneficial to improve the stability only of small blocks. This happens because while seismic isolation increase the ‘static’ value of the minimum overturning acceleration, this value remains nearly constant as we move to larger blocks or higher frequency pulses; therefore, seismic isolation removes appreciably from the dynamics of rocking blocks the beneficial property of increasing stability as their size increases or as the excitation pulse period decreases. This remarkable result suggests that free‐ standing ancient classical columns exhibit superior stability as they are built (standing free on a rigid foundation) rather than if they were seismically isolated even with isolation system with long isolation periods. The study further confirms this finding by examining the seismic response of the columns from the peristyle of two ancient Greek temples when subjected to historic records. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic performance of buildings with structural and foundation rocking in centrifuge testing

Rocking motion, established in either the superstructure in the form of a 2‐point stepping mechanism (structural rocking) or resulting from rotational motion of the foundation on the soil (foundation rocking), is considered an effective, low‐cost base isolation technique. This paper unifies for the first time the 2 types of rocking motion under a common experimental campaign, so that on the one hand, structural rocking can be examined under the influence of soil and on the other, foundation rocking can be examined under the influence of a linear elastic superstructure. Two building models, designed to rock above or below their foundation level so that they can reproduce structural and foundation rocking respectively, were tested side by side in a centrifuge. The models were placed on a dry sandbed and subjected to a sequence of earthquake motions. The range of rocking amplitude that is required for base isolation was quantified. Overall, it is shown that the relative density of sand does not influence structural rocking, while for foundation rocking, the change from dense to loose sand can affect the time‐frequency response significantly and lead to a more predictable behaviour.     

Modeling and cyclic behavior of segmental bridge column connected with shape memory alloy bars

This paper examines the quasi-static cyclic behavior,lateral strength and equivalent damping capacities of a system of post-tensioned segmental bridge columns tied with large diameter martensitic Shape Memory Alloy(SMA) link-bars.Moment-curvature constitutive relationships are formulated and analysis tools are developed for the PT column,including a modified four-spring model prepared for the SMA bars.The suggested system is exemplified using a column with an aspect ratio of 7.5 and twelve 36.5 mm diameter NiTi martensitic SMA bars.A post-tensioning force of 40% to 60% of the tendon yield strength is applied in order to obtain a self re-centering system,considering the residual stress of the martensitic SMA bars.The cyclic response results show that the lateral strength remains consistently around 10% of the total vertical load and the equivalent viscous damping ratios reach 10%-12% of critical.When large diameter NiTi superelastic SMA bars are incorporated into the column system,the cyclic response varies substantially.The creep behavior of the superelastic SMA bar is accounted for since it affects the re-centering capability of the column.Two examples are presented to emphasize the modeling sensitivities for these special bars and quantify their cyclic behavior effects within the column assembly.     

Bidirectional loading hybrid tests of square cross‐sections of steel bridge piers

Steel rectangular section columns with stiffened plates are commonly used for elevated highway bridges in the urban areas of Japan. The seismic design of bridge piers is usually performed by dynamic analysis in the horizontal direction using various independent directional seismic acceleration data. However, this simple treatment does not reflect the effect of bilateral loading as a structural response to inelastic interaction. In this study, unidirectional and bidirectional loading hybrid tests were conducted to examine the seismic response and performance of square cross‐sections of steel bridge piers subjected to bidirectional seismic accelerations. Comparison of the results of unidirectional and bidirectional loading tests revealed that the maximum load is the same as the average of unidirectional loading in the NS and EW directions; however, the maximum response displacement and residual displacement increase in proportion with hard to soft ground types. Moreover, a modified seismic design is proposed considering these bidirectional loading effects. Copyright © 2012 John Wiley & Sons, Ltd.     

渡槽结构隔震耗能减振控制的试验研究

本文在理论分析的基础上，对设计中的南水北调中线工程北京段南泉河水大型渡槽工程结构，按几何相似比1：10研制了结构模型及多组隔震耗能混合减振支座，在振动台上成功地进行了多工况的地震模拟试验。试验结果表明：将由隔震器与阻尼器组成的隔震耗能混合减振支座应用于渡槽结构，可以有效地减小渡槽结构的地震响应。此外，所研制的隔震耗能混合减振支座，在实际结构工程中的施工简单可行。     

Rapid repair of severely earthquake-damaged bridge piers with flexural-shear failure mode

An experimental study was conducted to investigate the feasibility of a proposed rapid repair technique for severely earthquake-damaged bridge piers with flexural-shear failure mode. Six circular pier specimens were first tested to severe damage in flexural-shear mode and repaired using early-strength concrete with high-fluidity and carbon fiber reinforced polymers (CFRP). After about four days, the repaired specimens were tested to failure again. The seismic behavior of the repaired specimens was evaluated and compared to the original specimens. Test results indicate that the proposed repair technique is highly effective. Both shear strength and lateral displacement of the repaired piers increased when compared to the original specimens, and the failure mechanism of the piers shifted from flexural-shear failure to ductile flexural failure. Finally, a simple design model based on the Seible formulation for post-earthquake repair design was compared to the experimental results. It is concluded that the design equation for bridge pier strengthening before an earthquake could be applicable to seismic repairs after an earthquake if the shear strength contribution of the spiral bars in the repaired piers is disregarded and 1.5 times more FRP sheets is provided.     

Shaking table tests of a resilient bridge system with precast reinforced concrete columns equipped with springs

This paper presents the shake table test results of a novel system for the design of precast reinforced concrete bridges. The specimen comprises a slab and four precast columns. The connections are dry and the columns are connected to the slab by an ungrouted tendon. One of the tendon ends is anchored above the slab, in series with a stack of washer springs, while the other end is anchored at the bottom of the column. The addition of such a flexible restraining system increases the stability of the system, while keeping it relatively flexible allowing it to experience negative post-uplift stiffness. It is a form of seismic isolation. Anchoring the tendon within the column, caps the design moment of the foundation, and reduces its size. One hundred and eighty-one shake table tests were performed. The first 180 caused negligible damage to the specimen, mainly abrasion at the perimeter of the column top ends. Hence, the system proved resilient. The 181^st excitation caused collapse, because the tendons unexpectedly failed at a load less than 50% of their capacity (provided by the manufacturer), due to the failure of their end socket. This highlights the importance of properly designing the tendons. The tests were used to statistically validate a rigid body model. The model performed reasonably well never underestimating the median displacement response of the center of mass of the slab by more than 30%. However, the model cannot predict the torsion rotation of the slab that was observed in the tests and is due to imperfections.     

涡激振动下管桥段的模糊动力可靠性研究

本文首先给出了管道在流体作用下的力学模型，并对风力作用下管道产生涡激振动的机理进行了分析，从而建立了管桥在风力作用下的力学模型和相应的振动微分方程，同时给出了管桥的固有特性和动力响应分析结果，然后，在此基础上，提出了首超模糊失效、模糊疲劳失效和混合失效等三类模糊失效准则，并依据这些准则分析给出了动力可靠性的计算公式，最后，给出了具体的算例。     

Seismic response of bridge piers on pile groups for different soil damping models and lumped parameter representations of the foundation

This paper presents a wide parametric study aimed at elucidating the influence, on the computed seismic response of bridge piers, of two related aspects of the model: (1) the adoption of the classical hysteretic or the causal Biot's damping models for the soil and (2) the use of two different lumped parameter models of different complexity and accuracy to approximate the impedances of the pile foundation. A total of 2072 cases, including different superstructures, pile foundations, soil deposits, and seismic input signals, are studied. The results are presented so that the influence of the different parameters involved in the analysis can be assessed. From an engineering point of view, both lumped parameter models provide, in general, sufficiently low errors. The choice of the most adequate model for each case will depend not only on the configuration of the structure and the soil-foundation system but also on the assumed soil damping model, whose influence on the computed seismic responses is relevant in many cases. The nonphysical behaviour provided by the classical hysteretic damping model for the soil at zero frequency generates issues in the process of fitting the impedance functions. It is also found that larger deck displacements are predicted by Biot's model due to the higher damping at low frequencies provided by the classical hysteretic damping model.     

基于OpenSees的钢筋混凝土桥墩拟静力试验数值分析

以4个呈弯曲破坏形态的圆形钢筋混凝土桥墩的拟静力试验结果为依据,基于OpenSees中的Beamwith Hinges Element单元,建立了相应的桥墩滞回分析纤维单元模型。由模拟结果与试验结果对比可知,所建立的纤维单元模型对桥墩的骨架曲线及滞回曲线都有良好的模拟效果,且能体现桥墩在反复加载过程中刚度、强度退化现象,表明了模型的有效性。     

Quasi‐static and pseudo‐dynamic testing of unbonded post‐tensioned rocking bridge piers with external replaceable dissipaters

It has been well documented that following a major earthquake a substantial percentage of economic loss results from downtime of essential lifelines in and out of major urban centres. This has thus led to an improvement of both performance‐based seismic design philosophies and to the development of cost‐effective seismic structural systems capable of guaranteeing a high level of protection, low structural damage and reduced downtime after a design‐level seismic event. An example of such technology is the development of unbonded post‐tensioned techniques in combination with rocking–dissipating connections. In this contribution, further advances in the development of high‐performance seismic‐resistant bridge piers are achieved through the experimental validation of unbonded post‐tensioned bridge piers with external, fully replaceable, mild steel hysteretic dissipaters. The experimental response of three 1 : 3 scale unbonded, post‐tensioned cantilever bridge piers, subjected to quasi‐static and pseudo‐dynamic loading protocols, are presented and compared with an equivalently reinforced monolithic benchmark. Minimal physical damage is observed for the post‐tensioned systems, which exhibit very stable energy dissipation and re‐centring properties. Furthermore, the external dissipaters can be easily replaced if severely damaged under a major (higher than expected) earthquake event. Thus, negligible residual deformations, limited repair costs and downtime can be achieved for critical lifeline components. Satisfactory analytical–experimental comparisons are also presented as a further confirmation of the reliability of the design procedure and of the modelling techniques. Copyright © 2008 John Wiley & Sons, Ltd.     

青藏铁路多年冻土区桥墩随机地震反应分析

利用随机振动理论和动力分析的有限元方法,将场地地震动考虑为均值为零的高斯平稳随机过程,对青藏铁路多年冻土区典型桥墩进行了随机地震反应分析,计算了9度地震作用下桥墩随机地震响应的统计特性,分析了冻土层对桥墩地震反应的影响。研究结果表明,冻土层对桥墩地震反应具有显著影响。     

近断层地震动下摇摆-自复位桥墩连续梁地震反应

为讨论近断层地震动下摇摆-自复位(Rocking Self-Centering, RSC)桥墩连续梁的地震反应及其抗震优缺点。基于OpenSees有限元分析平台讨论了RSC桥墩三维建模方法,通过对6个试验构件的模拟,比较模拟与试验桥墩滞回曲线、预应力筋最大应力等指标,验证了模型准确性。建立设置RSC桥墩和普通钢筋混凝土(Reinforced Concrete, RC)桥墩的上部结构相同的两座连续梁桥,输入3组含有强速度脉冲的近断层地震波进行非线性动力时程分析,对比其抗震性能。结果表明：在0.4 g近断层地震动下,RSC桥墩与普通RC桥墩相比,RSC桥墩的最大位移角为普通RC桥墩的78.1%～97.6%,墩底曲率延性系数仅为普通RC桥墩的24.0%～34.0%,减小了桥墩的最大变形,也减轻了桥墩地震损伤,不利的一点是使用RSC桥墩会导致支座位移增大。RSC桥墩震后的残余位移较小,且预应力筋处于弹性受力阶段,为实现震后桥梁功能的快速恢复提供了条件。     

Experimental study of hollow rectangular bridge column performance under vertical and cyclically bilateral loads

To investigate the seismic performance of hollow reinforced concrete(RC) bridge columns of rectangular cross section under constant axial load and cyclically biaxial bending,five specimens were tested.A parametric study is carried out for different axial load ratios,longitudinal reinforcement ratios and lateral reinforcement ratios.The experimental results showed that all tested specimens failed in the flexural failure mode and their ultimate performance was dominated by flexural capacity,which is represented by the rupture/buckling of tensile longitudinal rebars at the bottom of the bridge columns.Biaxial force and displacement hysteresis loops showed significant stiffness and strength degradations,and the pinching effect and coupling interaction effect of both directions severely decrease the structural seismic resistance.However,the measured ductility coefficient varying from 3.5 to 5.7 and the equivalent viscous damping ratio varying from 0.19 and 0.26 can meet the requirements of the seismic design.The hollow RC rectangular bridge columns with configurations of lateral reinforcement in this study have excellent performance under bidirectional earthquake excitations,and may be considered as a substitute for current hollow RC rectangular section configurations described in the Guideline for Seismic Design of Highway Bridges(JTG/T B02-01-2008).The length of the plastic hinge region was found to approach one sixth of the hollow RC rectangular bridge column height for all specimen columns,and it was much less than those specified in the current JTG/T.Thus,the length of the plastic hinge region is more concentrated for RC rectangular hollow bridge columns.