Earthquake response of submerged gravity foundation on soft rock

A gravity foundation submerged in the water is subject to the buoyancy force and is hence vulnerable to sliding at the base when it is subjected to a large lateral load. The effects of sliding on the earthquake response were investigated for this type of foundation on soft rock, considering the friction characteristics at the contact between concrete and soft rock. Shake table tests were conducted to observe the behavior of a submerged foundation on soft rock which slid during the excitation. Large-scale cyclic direct shear tests were conducted to examine in detail the friction characteristics at the contact between the concrete and soft rocks. Based on the results obtained in shake table and cyclic shear tests, a numerical model was established for simulating the earthquake response behavior of a submerged gravity foundation on soft rock. Numerical parametric studies were conducted by using this model and selected earthquake ground motion records. Various important features were observed in the earthquake response of this foundation.     

On the Effects of Non-planar Geometry for Blind Thrust Faults on Strong Ground Motion

— We quantify the effects of complex fault geometry on low-frequency (<1 Hz) strong ground motion using numerical modeling of dynamic rupture. Our tests include the computation of synthetic seismograms for several simple rupture scenarios with planar and curved fault approximations of the 1994 Northridge earthquake. We use the boundary integral equation method (BIEM) to compute the dynamic rupture process, which includes the normal stress effects along the curved fault geometries. The wave propagation and computation of synthetic seismograms are modeled using a fourth-order finite-difference method (FDM). The near-field ground motion is significantly affected by the acceleration, deceleration and arrest of rupture due to the curvature of the faults, as well as the variation in directivity of the rupture. For example, a 6-km-long hanging-wall or footwall splay with a maximum offset of 1 km can change 1-Hz peak velocities by up to a factor of 2-3 near the fault. Our tests suggest that the differences in waveform are larger on the hanging wall compared to those on the footwall, although the differences in amplitude are larger in the forward rupture direction (footwall). The results imply that kinematic ground motion estimates may be biased by the omission of dynamic rupture effects and even relatively gentle variation in fault geometry, and even for long-period waves.     

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.     

The rocking response of large flexible structures to earthquakes

The rocking response of structures subjected to strong ground motions is a problem of ‘several scales’. While small structures are sensitive to acceleration pulses acting successively, large structures are more significantly affected by coherent low frequency components of ground motion. As a result, the rocking response of large structures is more stable and orderly, allowing effective isolation from the ground without imminent danger of overturning. This paper aims to characterize and predict the maximum rocking response of large and flexible structures to earthquakes using an idealized structural model. To achieve this, the maximum rocking demand caused by different earthquake records was evaluated using several ground motion intensity measures. Pulse-type records which typically have high peak ground velocity and lower frequency content caused large rocking amplitudes, whereas non-pulse type records caused random rocking motion confined to small rocking amplitudes. Coherent velocity pulses were therefore identified as the primary cause of significant rocking motion. Using a suite of pulse-type ground motions, it was observed that idealized wavelets fitted to velocity pulses can adequately describe the rocking response of large structures. Further, a parametric analysis demonstrates that pulse shape parameters affect the maximum rocking response significantly. Based on these two findings, a probabilistic analysis method is proposed for estimating the maximum rocking demand to pulse-type earthquakes. The dimensionless demand maps, produced using these methods, have predictive power in the near-field provided that pulse period and amplitude can be estimated a priori. Use of this method within a probabilistic seismic demand analysis framework is briefly discussed.     

An analytical model of a deformable cantilever structure rocking on a rigid surface: experimental validation

This paper describes an experimental program to examine the dynamic response of deformable cantilevers rocking on a rigid surface. The primary goal of the tests is to verify and validate a dynamic rocking model that describes the behavior of these structures. The benchmark response data was obtained from shaking‐table tests on deformable rocking specimens with different natural vibration frequencies and different aspect ratios excited by analytical pulses and recorded ground motions. The responses computed using the model are found to be in good agreement with the benchmark test results. Widely used impact, restitution and damping assumptions are revisited based on the experiment results and the analytical model findings. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of floor response spectra in shake table experiments

Among several different experimental techniques, used to test the response of structures and to verify their seismic performance, the shake table testing allows to reproduce the conditions of true effects of earthquake ground motions in order to challenge complex model structures and systems. However, the reproduction of dynamic signals, due to the dynamics of the shake table and of the specimen, is usually imperfect even though closed‐loop control in a shake table system is used to reduce these errors and obtain the best fidelity reproduction. Furthermore, because of the dynamic amplifications in the specimen, the signal recorded at desired locations could be completely different from the expected effect of shake table motion. This paper focuses on the development of practical shake table simulations using additional ‘open loop’ feedforward compensation in form of inverse transfer functions (i.e. the ratio of the output structural response to an input base motion in the frequency domain) in order to obtain an acceptable reproduction of desired acceleration histories at specific locations in the specimen. As the first step, a well‐known global feedforward procedure is reformulated for the compensation of the table motion distortions due to the servo‐hydraulic system. Subsequently, the same concept is extended to the table‐structure system to adjust the shake table input in order to achieve a desired response spectrum at any floor of the specimen. Implementations show how such a method can be used in any experimental facility. Copyright © 2010 John Wiley & Sons, Ltd.     

Mechanisms to limit higher mode effects in a controlled rocking steel frame. 1: Concept,modelling, and low‐amplitude shake table testing

Controlled rocking steel frames have been proposed as an efficient way to avoid the structural damage and residual deformations that are expected in conventional seismic force resisting systems. Although the base rocking response is intended to limit the force demands, higher mode effects can amplify member design forces, reducing the viability of the system. This paper suggests that seismic forces may be limited more effectively by providing multiple force‐limiting mechanisms. Two techniques are proposed: detailing one or more rocking joints above the base rocking joint and providing a self‐centring energy dissipative (SCED) brace at one or more levels. These concepts are applied to the design of an eight‐storey prototype structure and a shake table model at 30% scale. A simple numerical model that was used as a design tool is in good agreement with frequency characterization and low‐amplitude seismic tests of the shake table model, particularly when multiple force‐limiting mechanisms are active. These results suggest that the proposed mechanisms can enable better capacity design by reducing the variability of peak seismic force demands without causing excessive displacements. Similar results are expected for other systems that rely on a single location of concentrated nonlinearity to limit peak seismic loads. Copyright © 2012 John Wiley & Sons, Ltd.     

Hybrid simulation testing of a self‐centering rocking steel braced frame system

The self‐centering rocking steel frame is a seismic force resisting system in which a gap is allowed to form between a concentrically braced steel frame and the foundation. Downward vertical force applied to the rocking frame by post‐tensioning acts to close the uplifting gap and thus produces a restoring force. A key feature of the system is replaceable energy‐dissipating devices that act as structural fuses by producing high initial system stiffness and then yielding to dissipate energy from the input loading and protect the remaining portions of the structure from damage. In this research, a series of large‐scale hybrid simulation tests were performed to investigate the seismic performance of the self‐centering rocking steel frame and in particular, the ability of the controlled rocking system to self‐center the entire building. The hybrid simulation experiments were conducted in conjunction with computational modules, one that simulated the destabilizing P‐Δ effect and another module that simulated the hysteretic behavior of the rest of the building including simple composite steel/concrete shear beam‐to‐column connections and partition walls. These tests complement a series of quasi‐static cyclic and dynamic shake table tests that have been conducted on this system in prior work. The hybrid simulation tests validated the expected seismic performance as the system was subjected to ground motions in excess of the maximum considered earthquake, produced virtually no residual drift after every ground motion, did not produce inelasticity in the steel frame or post‐tensioning, and concentrated the inelasticity in fuse elements that were easily replaced. Copyright © 2014 John Wiley & Sons, Ltd.     

自复位高墩振动台模型试验

为探讨自复位桥墩的地震反应,以某简支梁桥为工程背景,设计并制作了一个缩尺的模型桥梁。通过白噪声扫频获得了自复位桥墩的动力特性及其变化规律,选取El-Centro、Mexico和Chi-Chi强震记录作为地震动输入,进行振动台模型试验。试验记录了墩顶的加速度和位移反应,考查了地震动强度、频谱特性及预应力钢筋及其初始预加力对模型桥墩动力特性及摇摆反应的影响。试验结果表明:墩顶水平加速度反应随地震动强度及初始预加力的提高而增大,墩顶位移反应受地震动的强度、频谱特性及初始预加力大小影响较大。墩底提离面轻微损伤会明显降低体系的整体水平刚度,初始预加力则能提高体系整体水平刚度,桥墩的阻尼比随体系的水平刚度增大而减小。强震下自复位桥墩发生了预期的提离摇摆,震后墩底提离面出现轻微损伤,墩身无裂缝产生,结构具有良好的抗震及自复位性能。振动台试验结果验证已有文献的数值分析结论,振动台试验数据可用于数值模型校核或修正。     

Seismic response of rocking isolated railway bridge piers with sacrificial components

In this study, sacrificial components were incorporated into self-centering railway bridge piers to improve the lateral stiffness. The seismic response of this new detail was investigated. First, the method to compute the initial uplift moment of the self-centering pier is given. In addition, shaking table tests were conducted on a free-rocking pier without sacrificial components, which was used to validate a two-spring numerical model. Good agreement was obtained between the numerical results and experimental data. Furthermore, the validated model was employed to investigate the influence of sacrificial components on the seismic response of rocking piers. For this purpose, two models were developed, with and without sacrificial components. Nonlinear response history analysis was then performed on both models under three historical motions. The results showed that compared to the one without sacrificial components, the rocking pier with sacrificial components has comparable displacement at the top of the pier, and maximum uplift moment at high amplitude motion. Therefore, incorporating sacrificial components into the rocking pier can increase the lateral stiffness at service load and low amplitude frequent earthquakes but can produce comparable response at high seismic excitation. These results provide support for performance-based seismic design of self-centering rocking piers.

     

Rotation of vertically oriented objects during earthquakes

Vertically oriented objects, such as tombstones, monuments, columns, and stone lanterns, are often observed to shift and rotate during earthquake ground motion. Such observations are usually limited to the mesoseismal zone. Whether near-field rotational ground motion components are necessary in addition to pure translational movements to explain the observed rotations is an open question. We summarize rotation data from seven earthquakes between 1925 and 2009 and perform analog and numeric rotation testing with vertically oriented objects. The free-rocking motion of a marble block on a sliding table is disturbed by a pulse in the direction orthogonal to the rocking motion. When the impulse is sufficiently strong and occurs at the ‘right’ moment, it induces significant rotation of the block. Numeric experiments of a free-rocking block show that the initiation of vertical block rotation by a cycloidal acceleration pulse applied orthogonal to the rocking axis depends on the amplitude of the pulse and its phase relation to the rocking cycle. Rotation occurs when the pulse acceleration exceeds the threshold necessary to provoke rocking of a resting block, and the rocking block approaches its equilibrium position. Experiments with blocks subjected to full 3D strong motion signals measured during the 2009 L’Aquila earthquake confirm the observations from the tests with analytic ground motions. Significant differences in the rotational behavior of a monolithic block and two stacked blocks exist.     

Rocking bodies with arbitrary interface defects: Analytical development and experimental verification

The rocking response of a rigid, freestanding block in two dimensions typically assumes perfect contact at the base of the block with instantaneous impacts at two distinct, symmetric rocking points. This paper extends the classical two‐dimensional rocking model to account for an arbitrary number of rocking points at the base representing geometric interface defects. The equations of motion of this modified rocking system are derived and presented in general terms. Energy dissipation is modeled assuming instantaneous point impacts, yielding a discrete angular velocity adjustment. Whereas this factor is always less than unity in the classical model, it is possible for this factor to exceed unity in the presented model, yielding a finite increase in the angular velocity at impact and a markedly different rotational response than the classical model predicts. The derived model and the classical model are numerically integrated and compared to the results of recent shake table tests. These comparisons show that the new model significantly enhances agreement in both peak angular displacement and motion decay. The equations of motion and the energy dissipation of the presented model are further investigated parametrically considering the size of the defect, the number of rocking points, and the aspect ratio and size of the block.     

西南交通大学8m×10m地震模拟振动台运行对场地振动的影响分析

西南交通大学建成的8m×10m/160t振动台是目前国内规模最大的振动台,对其运行质量和振动影响进行评价具有示范效应。探讨该振动台振动影响的现场实验于2017年初展开,实测结果表明:该振动台在工作频段内受控性能很好,对地震动信号重现度很高;台面满载满负荷运行时实验室建筑基础10m以内地面振动加速度实测值不超过6.6gal,振动速度小于2mm/s,不会对实验室厂房及附属办公建筑的安全、使用舒适性及人们正常工作、生活造成不利影响。     

Tall building performance‐based seismic design using SCEC broadband platform site‐specific ground motion simulations

The scarcity of strong ground motion records presents a challenge for making reliable performance assessments of tall buildings whose seismic design is controlled by large‐magnitude and close‐distance earthquakes. This challenge can be addressed using broadband ground‐motion simulation methods to generate records with site‐specific characteristics of large‐magnitude events. In this paper, simulated site‐specific earthquake seismograms, developed through a related project that was organized through the Southern California Earthquake Center (SCEC) Ground Motion Simulation Validation (GMSV) Technical Activity Group, are used for nonlinear response history analyses of two archetype tall buildings for sites in San Francisco, Los Angeles, and San Bernardino. The SCEC GMSV team created the seismograms using the Broadband Platform (BBP) simulations for five site‐specific earthquake scenarios. The two buildings are evaluated using nonlinear dynamic analyses under comparable record suites selected from the simulated BBP catalog and recorded motions from the NGA‐West database. The collapse risks and structural response demands (maximum story drift ratio, peak floor acceleration, and maximum story shear) under the BBP and NGA suites are compared. In general, this study finds that use of the BBP simulations resolves concerns about estimation biases in structural response analysis which are caused by ground motion scaling, unrealistic spectral shapes, and overconservative spectral variations. While there are remaining concerns that strong coherence in some kinematic fault rupture models may lead to an overestimation of velocity pulse effects in the BBP simulations, the simulations are shown to generally yield realistic pulse‐like features of near‐fault ground motion records.     

Rocking response of rigid blocks to earthquakes

This investigation deals with the rocking response of rigid blocks subjected to earthquake ground motion. A numerical procedure and computer program are developed to solve the non-linear equations of motion governing the rocking motion of rigid blocks on a rigid base subjected to horizontal and vertical ground motion. The response results presented show that the response of the block is very sensitive to small changes in its size and slenderness ratio and to the details of ground motion. Systematic trends are not apparent: The stability of a block subjected to a particular ground motion does not necessarily increase monotonically with increasing size or decreasing slenderness ratio. Overturning of a block by a ground motion of particular intensity does not imply that the block will necessarily overturn under the action of more intense ground motion. In contrast, systematic trends are observed when the problem is studied from a probabilistic point of view with the ground motion modelled as a random process. The probability of a block exceeding any response level, as well as the probability that a block overturns, increases with increase in ground motion intensity, increase in slenderness ratio of the block and decrease in its size. It is concluded that probabilistic estimates of the intensity of ground shaking may be obtained from its observed effects on monuments, minarets, tombstones and other similar objects provided suitable data in sufficient quantity is available, and the estimates are based on probabilistic analyses of the rocking response of rigid blocks, considering their non-linear dynamic behaviour.     

Is rocking motion predictable?

An argument of engineers and researchers against the use of rocking as a seismic response modification technique is that the rocking motion of a structure is chaotic and the existing models are incapable of predicting it well. This argument is supported by the documented inability of rocking models to predict the motion of a specimen excited by a single ground motion. A statistical comparison of the experimental and the numerical responses of a rigid rocking oscillator not to a specific ground motion, but to ensembles of ground motions that have the same statistical properties, is presented. It is shown that the simple analytical model proposed by Housner in 1963 is capable of predicting the statistics of seismic response of a rigid rocking oscillator.     

Shake‐table tests of a three‐story reinforced concrete frame with masonry infill walls

This paper presents the shake‐table tests of a 2/3‐scale, three‐story, two‐bay, reinforced concrete frame infilled with unreinforced masonry walls. The specimen is representative of the construction practice in California in the 1920s. The reinforced concrete frame had nonductile reinforcement details and it was infilled with solid masonry walls in one bay and infill walls with window openings in the other bay. The structure was subjected to a sequence of dynamic tests including white‐noise base excitations and 14 scaled historical earthquake ground motion records of increasing intensity. The performance of the structure was satisfactory considering the seismic loads it was subjected to. The paper summarizes the design of the specimen and the major findings from the shake‐table tests, including the dynamic response, the load resistance, the evolution of damage, and the final failure mechanism. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental and analytical studies on the response of 1/4-scale models of freestanding laboratory equipment subjected to strong earthquake shaking

This paper investigates the seismic response of freestanding equipment when subjected to strong earthquake motions (2% probability of being exceeded in 50 years). A two-step approach is followed because the displacement limitations of the shake table do not permit full-scale experiments. First, shake table tests are conducted on quarter-scale wooden block models of the equipment. The results are used to validate the commercially available dynamic simulation software Working Model 2D. Working Model is then used to compute the response of the full-scale freestanding equipment when subjected to strong, 2% in 50 years hazard motions. The response is dominated by sliding, with sliding displacements reaching up to 70 cm. A physically motivated dimensionless intensity measure and the associated engineering demand parameter are identified with the help of dimensional analysis, and the results of the numerical simulations are used to obtain a relationship between the two that leads to ready-to-use fragility curves.     

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.     

Seismic responses of bridges with rocking column-foundation: A dimensionless regression analysis

Rocking column-foundation system is a new design concept for bridges that can reduce overall seismic damage, minimize construction and repair time, and achieve lower cost in general. However, such system involves complex dynamic responses due to impacts and highly nonlinear rocking behavior. This study presents a dimensionless regression analysis to estimate the rocking and shaking responses of the flexible column-foundation system under near-fault ground motions. First, the transient drift and rocking responses of the system are solved numerically using previously established analytical models. Subsequently, the peak column drifts and uplift angles are derived as functions of ground motion characteristics and the geometric and dynamic parameters of column-foundation system in regressed dimensionless forms. The proposed response models are further examined by validating against the numerical simulations for several as-built bridge cases. It is shown that the proposed model not only physically quantifies the influences of prominent parameters, but also consistently reflects the complex dynamics of the system. The seismic demands of rocking column-foundation system can be realistically predicted directly from structural and ground motion characteristics. This can significantly benefit the design of bridges incorporating this new design concept.