Seismic performance of an existing bridge with scoured caisson foundation

This paper presents in-situ seismic performance tests of a bridge before its demolition due to accumulated scouring problem. The tests were conducted on three single columns and one caisson-type foundation. The three single columns were 1.8 m in diameter,reinforced by 30-D32 longitudinal reinforcements and laterally hooped by D16 reinforcements with spacing of 20 cm. The column height is 9.54 m,10.59 m and 10.37 m for Column P2,P3,and P4,respectively. Column P2 had no exposed foundation and was subjected to pseudo-dynamic tests with peak ground acceleration of 0.32 g first,followed by one cyclic loading test. Column P3 was the benchmark specimen with exposed length of 1.2 m on its foundation. The exposed length for Column P4 was excavated to 4 m,approximately 1/3 of the foundation length,to study the effect of the scouring problem to the column performance. Both Column P3 and Column P4 were subjected to cyclic loading tests. Based on the test results,due to the large dimension of the caisson foundation and the well graded gravel soil type that provided large lateral resistance,the seismic performance among the three columns had only minor differences. Lateral push tests were also conducted on the caisson foundation at Column P5. The caisson was 12 m long and had circular cross-sections whose diameters were 5 m in the upper portion and 4 m in the lower portion. An analytical model to simulate the test results was developed in the OpenSees platform. The analytical model comprised nonlinear flexural elements as well as nonlinear soil springs. The analytical results closely followed the experimental test results. A parametric study to predict the behavior of the bridge column with different ground motions and different levels of scouring on the foundation are also discussed.     

Seismic response of rocking frames with top support eccentricity

The seismic response of rocking frames that consist of a rigid beam freely supported on rigid freestanding rectangular piers has received recent attention in the literature. Past studies have investigated the special case where, upon planar rocking motion, the beam maintains contact with the piers at their extreme edges. However, in many real scenarios, the beam‐to‐pier contact lies closer to the center of the pier, affecting the overall stability of the system. This paper investigates the seismic response of rocking frames under the more general case which allows the contact edge to reside anywhere in‐between the center of the pier and its extreme edge. The study introduces a rocking block model that is dynamically equivalent to a rocking frame with vertically symmetric piers of any geometry. The impact of top eccentricity (ie, the distance of the contact edge from the pier's vertical axis of symmetry) on the seismic response of rocking frames is investigated under pulse excitations and earthquake records. It is concluded that the stability of a top‐heavy rocking frame is highly influenced by the top eccentricity. For instance, a rocking frame with contacts at the extreme edges of the piers can be more seismically stable than a solitary block that is identical to one of the frame's piers, while a rocking frame with contacts closer to the centers of the piers can be less stable. The concept of critical eccentricity is introduced, beyond which the coefficient of restitution contributes to a greater reduction in the response of a frame than of a solitary pier.     

Semiactive control of rigid blocks under earthquake excitation

This paper investigates the usefulness of a semiactive control to reduce the overturning vulnerability of a rigid block on a rigid plane under earthquake excitation. The proposed feedback law is used to set the stiffness of restraints placed at the 2 lower corners of the block. The performance of the semiactive control is numerically validated by subjecting the block to 100 recorded accelerograms. Specific simulations are performed to study the effect of different anchorage design parameters on the utility of the control. Finally, the robustness of the proposed control is addressed with respect to typical issues of the real‐world implementation.     

Controlled overturning of unanchored rigid bodies

Typical small hospital and laboratory equipment and general supplies cannot be anchored to resist earthquake motions. In order to protect these non‐structural components, a common procedure is to provide barriers to restrain overturning of objects on shelves and other furniture. In many cases this option is not available, especially for hospital equipment, because of other functional requirements. This work presents an alternative approach. The method proposed here does not avoid overturning, but controls the direction of overturning by providing an inclination to the support base so that the overturning occurs in a preferential direction towards a safe area. For example, objects on shelves, could overturn towards the inside or a wall, and equipment on tables could overturn away from the edge. In both cases this would not only reduce the damage to the particular items, but reduce the amount of debris on the floor. In order to determine the proper inclination of the base, specific rigid bodies are analytically evaluated for bi‐directional excitation obtained from 314 earthquake records, in approximately 7500 cases. For each case, several inclination angles are evaluated. Finally, a parametric curve is adjusted to the data, given a relation between angle of inclination and percentage of controlled overturning cases. In all cases a 7° angle gives more than 98% confidence of controlled overturning. The design expressions were later compared with experimental results obtained on a six‐degree‐of‐freedom shake table; confirming the analytical expressions. Copyright © 2006 John Wiley & Sons, Ltd.     

On the seismic performances of rigid block‐like structures coupled with an oscillating mass working as a TMD

In this paper, the effects of a mass damper on the rocking motion of a non‐symmetric rigid block‐like structure, subject to different seismic excitation, are investigated. The damper is modelled as a single degree of freedom oscillating mass, running at the top of the block and connected to it by a linear visco‐elastic device. The equations of rocking motion, the uplift and the impact conditions are derived. A nondimensionalisation of the governing equations is performed with the aim to obtain an extensive parametric analysis. The results are achieved by numerical integration of these equations. The slenderness and the base of the rigid block, and the eccentricity of the centre of mass are taken as variable parameters in the analyses. The main objective of the study is to check the performance of the damper versus the spectral characteristics of the seismic input. Three earthquake registrations with different frequency contents are used in the analyses. The results show that the presence of the mass damper leads to different levels of improvement of the response of the system, depending on the spectral characteristics of the seismic input. Curves providing the overturning slenderness of blocks of specific sizes versus the characteristics of the TMD are obtained. Copyright © 2017 John Wiley & Sons, Ltd.     

Behavior of rigid blocks with geometrical defects under seismic motion: an experimental and numerical study

The present work investigates the influence of small geometrical defects on the behavior of slender rigid blocks. A comprehensive experimental campaign was carried out on one of the shake tables of CEA/Saclay in France. The tested model was a massive steel block with standard manufacturing quality. Release, free oscillations tests as well as shake table tests revealed a non‐negligible out‐of‐plane motion even in the case of apparently plane initial conditions or excitations. This motion exhibits a highly reproducible part for a short duration that was used to calibrate a numerical geometrically asymmetrical model. The stability of this model when subjected to 2000 artificial seismic horizontal bidirectional signals was compared with the stability of a symmetrical one. This study showed that the geometrical imperfections slightly increase the rocking and overturning probabilities for earthquake signals in a narrow range of peak ground acceleration. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental investigation on seismic behavior of scoured bridge pier with pile foundation

This study investigated the seismic performance and soil‐structure interaction of a scoured bridge models with pile foundation by shaking table tests using a biaxial laminar shear box. The bridge pier model with pile foundation comprised a lumped mass representing the superstructure, a steel pier, and a footing supported by a single aluminum pile within dry silica sand. End of the pile was fixed at the bottom of the shear box to simulate the scenario that the pile was embedded in a firm stratum of rock. The bridge pier model was subjected to one‐directional shakes, including white noise and earthquake records. The performance of the bridge pier model with pile foundation was discussed for different scoured conditions. It is found that the moment demand of pile increases with the increase of scoured depth whereas the moment demand of the bridge pier decreases, and this transition may induce the bridge failure mechanism transform from pier to pile. The seismic demand on scoured pile foundations may be underestimated and misinterpreted to a certain degree. When evaluating the system damping ratio with SSI, the system response may not be significantly changed even if the soil viscous damping contribution is varied. Copyright © 2014 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.     

Response analysis of rigid structures rocking on viscoelastic foundation

In this paper the rocking response of slender/rigid structures stepping on a viscoelastic foundation is revisited. The study examines in depth the motion of the system with a non‐linear analysis that complements the linear analysis presented in the past by other investigators. The non‐linear formulation combines the fully non‐linear equations of motion together with the impulse‐momentum equations during impacts. The study shows that the response of the rocking block depends on the size, shape and slenderness of the block, the stiffness and damping of the foundation and the energy loss during impact. The effect of the stiffness and damping of the foundation system along with the influence of the coefficient of restitution during impact is presented in rocking spectra in which the peak values of the response are compared with those of the rigid block rocking on a monolithic base. Various trends of the response are identified. For instance, less slender and smaller blocks have a tendency to separate easier, whereas the smaller the angle of slenderness, the less sensitive the response to the flexibility, damping and coefficient of restitution of the foundation. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic response of bridge pier on rigid caisson foundation in soil stratum

An analytical method to study the seismic response of a bridge pier supported on a rigid caisson foundation embedded in a deep soil stratum underlain by a homogeneous half space is developed. The method reproduces the kinematic and inertial responses, using translational and rotational distributed Winkler springs and dashpots to simulate the soil-caisson interaction. Closed-form solutions are given in the frequency domain for vertical harmonic S-wave excitation. Comparison with results from finite element （FE） analysis and other available solutions demonstrates the reliability of the model. Results from parametric studies are given for the kinematic and inertial responses. The modification of the fundamental period and damping ratio of the bridge due to soil-structure interaction is graphically illustrated.     

桥梁沉井基础抗震性能研究现状及展望

随着国内外大跨桥梁特别是跨海桥梁建设的迅速发展,沉井基础在桥梁基础中所占的比例越来越大。虽然沉井基础作为1种刚性基础具有良好的力学性能,然而震害实践表明沉井基础在地震作用下也并非万无一失。通过分析国内外典型桥梁沉井基础的震害特征发现,沉井基础的地震破坏与桩基础有显著差异,且与埋置深度有直接关系;研究表明:地震作用下沉井基础的破坏机理及地基承载力与静力作用下明显不同,但目前在该方面的研究还较为欠缺;总结和对比了现有几种沉井基础-土相互作用研究方法,并分析了几种研究方法的优缺点和适用场合;同时也归纳和对比了各国抗震规范对桥梁沉井基础的基本规定、适用范围、计算方法和构造规定等方面的内容。最后结合现有的研究现状对沉井基础抗震性能研究的发展方向进行了展望,此外,随着我国跨海、跨江及跨库区大跨桥梁建设的发展,地震力和波浪力等多灾害因素共同作用下深水沉井基础桥梁破坏机理及设计方法的研究势在必行。     

Seismic response assessment of rocking systems using single degree-of-freedom oscillators

A new modeling for the seismic response assessment of free-standing, rigid or flexible, pure rocking systems is presented. The proposed modeling is based on equivalent single degree-of-freedom (SDOF) oscillators that can be implemented with common engineering software or user-made structural analysis codes. The SDOF models adopted use beam elements that are connected to a nonlinear rotational spring with negative stiffness that describes the self-centering capacity of the rocking member. The loss of energy at impact is treated with an “event-based” approach consistent with Housner's theory. Different variations pertinent to rigid blocks are first presented, and then the concept is extended to the flexible case. The implementation of the method requires some minor programming skills, while thanks to the versatility of the finite element method, it is capable to handle a variety of rocking problems. This is demonstrated with two applications: (a) a vertically restrained block equipped with an elastic tendon and (b) a rigid block coupled with an elastic SDOF oscillator. The accuracy and the efficiency of the proposed modeling is demonstrated using simple wavelets and historical ground motion records.     

Seismic response analysis of continuous rigid frame bridge considering canyon topography effects under incident SV waves

To evaluate the importance of the canyon topography effects on large structures, based on a rigid frame bridge across a 137-m-deep and 600-m-wide canyon, the seismic response of the canyon site is analyzed using a two-dimensional finite element model under different seismic SV waves with the assumptions of vertical incidence and oblique incidence to obtain the ground motions, which are used as the excitation input on the pier foundations of the bridge with improved large mass method. The results indicate th...     

Seismic fragilities of single-column highway bridges with rocking column-footing

Rocking isolation has been increasingly studied as a promising design concept to limit the earthquake damage of civil structures. Despite the difficulties and uncertainties of predicting the rocking response under individual earthquake excitations (due to negative rotational stiffness and complex impact energy loss), in a statistical sense, the seismic performance of rocking structures has been shown to be generally consistent with the experimental outcomes. To this end, this study assesses, in a probabilistic manner, the effectiveness of using rocking isolation as a retrofit strategy for single-column concrete box-girder highway bridges in California. Under earthquake excitation, the rocking bridge could experience multi-class responses (eg, full contacted or uplifting foundation) and multi-mode damage (eg, overturning, uplift impact, and column nonlinearity). A multi-step machine learning framework is developed to estimate the damage probability associated with each damage scenario. The framework consists of the dimensionally consistent generalized linear model for regression of seismic demand, the logistic regression for classification of distinct response classes, and the stepwise regression for feature selection of significant ground motion and structural parameters. Fragility curves are derived to predict the response class probabilities of rocking uplift and overturning, and the conditional damage probabilities such as column vibrational damage and rocking uplift impact damage. The fragility estimates of rocking bridges are compared with those for as-built bridges, indicating that rocking isolation is capable of reducing column damage potential. Additionally, there exists an optimal slenderness angle range that enables the studied bridges to experience much lower overturning tendencies and significantly reduced column damage probabilities at the same time.     

Experimental assessment of the seismic performance of hospital cabinets using shake table testing

An experimental investigation of hospital building equipment is presented. Dynamic properties and seismic performance of typical ambulatory freestanding cabinets are assessed by unidirectional and bidirectional shake table tests, also considering the presence of internal partitions and cabinet contents. Vulnerability analysis is performed according to the most recent and reliable assessment methods, evaluating the influence of different parameters of the sample cabinets. The performance criteria referred within this research are the limit states reached by the specimens (ie, rocking and overturning) and by their contents (ie, overturning and breaking). Fragility curves are evaluated for the components and the contents, considering both acceleration and velocity intensity measures, and also using dimensionless intensity measures developed in recent studies. The outcomes of the present study confirm the findings of previous laboratory tests and numerical simulations carried out by the same authors and provide a further insight for the reliable seismic performance assessment of hospital cabinets and their contents.     

大跨径钢筋混凝土拱桥抗震性能分析

结合跨径220米的许沟大桥结构设计,通过对全桥有限元模型动力分析和通车动载试验,对钢筋混凝土拱桥全桥动力特性进行分析,并选用50年超越概率为3%的人工地震波和E l Centro波(调整至7度)进行时程分析。根据抗震分析的结果分析控制截面地震内力,并结合通车动载试验结论,对许沟大桥抗震性能做出综合评价,对大跨径钢筋混凝土拱桥抗震设计提出合理建议。     

Dynamics of a sliding-rocking block considering impact with an adjacent wall

A freestanding rigid block subjected to base excitation can exhibit complicated motion described by five response modes: rest, pure rocking, pure sliding, combined sliding-rocking, and free flight. Previous studies on the dynamics of a rocking block have assumed that the block does not interact with neighboring objects. However, there are many applications in which the block may start or come in contact with an adjacent boundary during its motion, for example, a bookcase or cabinet colliding with a partition wall in an earthquake. This paper investigates the dynamics of a sliding-rocking block considering impact with an adjacent wall. A model is developed in which the base and wall are assumed rigid, and impact is treated using the classical impulse and momentum principle. The model is verified by comparing its predictions in numerical simulations against those of an existing general-purpose rigid-body model in which impact is treated using a viscoelastic impact model. The developed model is used to investigate the effects of different parameters on the stability of a block subjected to analytical pulse excitations. It is found that wall placement (left or right) has a dominant effect on the shape of the overturning acceleration spectra for pulse excitations. In general, decreasing the gap distance, base friction coefficient, and wall coefficient of restitution enhance the stability of the block. Similar observations are made when evaluating the overturning probability of a block using earthquake floor motions.     

Investigations into the benefits of base isolation for non‐symmetric rigid blocks

In this paper the influence of base isolation on the behaviour of a work of art has been analysed. To make things more realistic, the work of art has been modelled with a non‐symmetrical rigid body, sitting on a base that is connected to a visco‐elastic device, which represents the passive control system. To prevent the breaking of the isolation device, security stops have been introduced to limit the displacement of the oscillating base to a maximum safety value. All analyses have been carried out comparing the behaviour of the non‐isolated and the isolated non‐symmetric rigid body subject to impulsive and seismic excitations. The analysis is particularly focused on the effects of the eccentricity of the rigid body and on the presence of the security stops. Generally, base isolation improves the behaviour of the system while the presence of an eccentricity makes the performance of the system worse with respect to the symmetric rigid body. Moreover the security stops, although they preserve the isolator devices, cause a worsening in the performance of the systems. Copyright © 2008 John Wiley & Sons, Ltd.     

SV波入射下地形条件对大跨刚构桥地震响应的影响

计算了SV波在3种角度入射下两座山峰及其间自由场地的时程响应, 并以此作为两座山峰之间大跨桥的桥台及桥墩基础处的多点地震输入.这种地震输入考虑了行波传播效应和地形效应的综合影响. 然后基于多点激励下桥梁地震响应分析方法, 计算了地形条件下总长440 m的高墩连续刚构桥的墩顶位移及墩底内力, 并与忽略地形条件仅考虑行波效应时结构的响应进行了对比分析. 该结果可为建于复杂地形条件下结构的抗震设计提供参考.      

Linearization and first‐order expansion of the rocking motion of rigid blocks stepping on viscoelastic foundation

In structural mechanics there are several occasions where a linearized formulation of the original non‐linear problem reduces considerably the computational effort for the response analysis. In a broader sense, a linearized formulation can be viewed as a first‐order expansion of the dynamic equilibrium of the system about a ‘static’ configuration; yet caution should be exercised when identifying the ‘correct’ static configuration. This paper uses as a case study the rocking response of a rigid block stepping on viscoelastic supports, whose non‐linear dynamics is the subject of the companion paper, and elaborates on the challenge of identifying the most appropriate static configuration around which a first‐order expansion will produce the most dependable results in each regime of motion. For the regime when the heel of the block separates, a revised set of linearized equations is presented, which is an improvement to the unconservative equations published previously in the literature. The associated eigenvalues demonstrate that the characteristics of the foundation do not affect the rocking motion of the block once the heel separates. Copyright © 2008 John Wiley & Sons, Ltd.