Uplift‐restraining Friction Pendulum seismic isolation system

This paper extends the scope of seismic isolation by introducing an innovative uplift‐restraining Friction Pendulum system. Termed the XY‐FP isolator, the new isolation device consists of two orthogonal opposing concave beams interconnected through a sliding mechanism that permits tension to develop in the bearing, thereby preventing uplift. Owing to its distinct configuration, the XY‐FP isolator possesses unique properties for a seismic isolator, including uplift restraint, decoupling of the bi‐directional motion along two orthogonal directions, and capability of providing independent stiffness and energy dissipation along the principal horizontal directions of the bearing. The study concentrates on introducing the concept and establishing the underlying principles of operation of the new XY‐FP isolator, formulating the mathematical model for the XY‐FP isolator, and presenting its mechanical behaviour through a displacement‐control testing program on a single XY‐FP isolator. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental and analytical study of the bi‐directional behavior of the triple friction pendulum isolator

This paper presents a non‐linear, kinematic model for triple friction pendulum isolation bearings. The model, which incorporates coupled plasticity and circular restraining surfaces for all sliding surfaces, is capable of capturing bi‐directional behavior and is able to explicitly track the movement of each internal component. The model is general so that no conditions regarding bearing properties, which effect the sequence of sliding stages, are required for the validity of the model. Controlled‐displacement and seismic‐input experiments were conducted using the shake table at the University of California, Berkeley to assess the fidelity of the proposed model under bi‐directional motion. Comparison of the experimental data with the corresponding results of the kinematic model shows good agreement. Additionally, experiments showed that the performance of TFP bearings is reliable over many motions, and the behavior is repeatable even when initial slider offsets are present. Copyright © 2011 John Wiley & Sons, Ltd.     

Bi‐directional coupled tuned mass dampers for the seismic response control of two‐way asymmetric‐plan buildings

This paper proposes bi‐directional coupled tuned mass dampers (BiCTMDs) for the seismic response control of two‐way asymmetric‐plan buildings subjected to bi‐directional ground motions. The proposed BiCTMD was developed from the three‐degree‐of‐freedom modal system, which represents the vibration mode of a two‐way asymmetric‐plan building. The performance of the proposed BiCTMD for the seismic response control of elastic two‐way asymmetric‐plan buildings was verified by investigating the reductions of the amplitudes of the associated frequency response functions. In addition, the investigation showed that the proposed BiCTMD is effective in reducing the seismic damage of inelastic asymmetric‐plan buildings. Therefore, the BiCTMD is an effective approach for the seismic response control of both elastic and inelastic two‐way asymmetric‐plan buildings. Copyright © 2010 John Wiley & Sons, Ltd.     

Development and validation of p‐y modeling approach for seismic response predictions of highway bridges

This study aims to realistically simulate the seismic responses of typical highway bridges in California with considerations of soil–structure interaction effects. The p‐y modeling approaches are developed and validated for embankments and pile foundations of bridges. The p‐y approach models the lateral and vertical foundation flexibility with distributed p‐y springs and associated t‐z and q‐z springs. Building upon the existing p‐y models for pile foundations, the study develops the nonlinear p‐y springs for embankments based on nonlinear 2D and 3D continuum finite element analysis under passive loading condition along both longitudinal and transverse directions. Closed‐form expressions are developed for two key parameters, the ultimate resistant force p_ult and the displacement y₅₀, where 0.5p_ult is reached, of embankment p‐y models as functions of abutment geometry (wall width and height, embankment fill height, etc.) and soil material properties (wall‐soil friction angle, soil friction angle, and cohesion). In order to account for the kinematic and site responses, depth‐varying ground motions are derived and applied at the free‐end of p‐y springs, which reflects the amplified embankment crest motion. The modeling approach is applied to simulate the seismic responses of the Painter Street Bridge and validated through comparisons with the recorded responses during the 1992 Petrolia earthquake. It is demonstrated that the flexibility and motion amplification at end abutments are the most crucial modeling aspects. The developed p‐y models and the modeling approach can effectively predict the seismic responses of highway bridges. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of the angle of seismic incidence on the fragility curves of bridges

This study examines the effect of the angle of seismic incidence θ on the fragility curves of bridges. Although currently, fragility curves of bridges are usually expressed only as a function of intensity measure of ground motion (IM) such as peak ground acceleration, peak ground velocity, or S_a(ω₁), in this study they are expressed as a function of IM with θ as a parameter. Lognormal distribution function is used for this purpose with fragility parameters, median c_m and standard deviation ζ to be estimated for each value of θ chosen from 0 < θ < 360°. A nonlinear 3D finite element dynamic analysis is performed, and key response values are calculated as demand on the bridge under a set of acceleration time histories with different IM values representing the seismic hazard in Los Angeles area. This method is applied to typical straight reinforced concrete bridges located in California. The results are validated with existing empirical damage data from the 1994 Northridge earthquake. Even though the sample bridges are regular and symmetric with respect to the longitudinal axis, the results indicate that the weakest direction is neither longitudinal nor transverse. Therefore, if the angle of seismic incidence is not considered, the damageability of a bridge can be underestimated depending on the incidence angle of seismic wave. Because a regional highway transportation network is composed of hundreds or even thousands of bridges, its vulnerability can also be underestimated. Hence, it is prudent to use fragility curves taking the incident angle of seismic waves into consideration as developed here when the seismic performance of a highway network is to be analyzed. Copyright © 2012 John Wiley & Sons, Ltd.     

Influence of FPS bearing properties on the seismic performance of base‐isolated structures

The paper analyzes the influence of friction pendulum system (FPS) isolator properties on the seismic performance of base‐isolated building frames. The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the FPS isolator behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. The uncertainty in the seismic input is taken into account by considering a set of natural records with different characteristics scaled to increasing intensity levels. The variation of the statistics of the response parameters relevant to the seismic performance is investigated through the nondimensionalization of the motion equation and an extensive parametric study carried out for different isolator and system properties. The proposed approach allows to explore a wide range of situations while limiting the required nonlinear response history analyses. Two case studies consisting of base‐isolated building frames described as shear‐type systems are finally investigated in order to demonstrate the capabilities of the proposed simplified model in unveiling the essential characteristics of the performance of buildings isolated with FPS bearings. Copyright © 2015 John Wiley & Sons, Ltd.     

长联大跨摩擦摆支座隔震连续梁桥多维地震反应分析

结合长联大跨连续梁桥的特点,以1座(65+123+156+123+10×90+55)m长联大跨摩擦摆支座隔震连续梁桥为背景,建立了全桥三维有限元模型,运用非线性时程分析法,分析了地震动输入模式、地震动强度、摩擦摆支座参数对该桥内力、位移和能量响应的影响。研究结果表明:(1)长联大跨连续梁桥布置摩擦摆支座,可有效延滞固定墩顶有效主梁质量效应,实现全桥协同抗震。大部分地震能量可通过支座滞回耗能散耗,大幅降低了该桥固定墩地震能量耗散需求。(2)长联大跨连续梁桥减隔震设计中,建议采用水平单向+竖向地震组合进行内力设计,采用三向地震组合进行位移设计。(3)强震作用下,支座摩擦因数取0.029~0.034时该桥隔震性能最优。     

On the inelastic torsional response of single‐storey structures under bi‐axial excitation

An attempt has been made to explore the general trends in the seismic response of plan‐asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi‐directional excitation were studied. Idealized single‐storey models with bi‐axial eccentricity were employed. The systems were torsionally stiff and, in the majority of cases, mass‐eccentric. The main findings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional effect on the flexible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the stiff side generally strongly depends on the effect of several modes of vibration and on the influence of the ground motion in the transverse direction. These influences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally stiff structures, usually decreases with increasing plastic deformations. As an additional effect of large plastic deformations, a flattening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional effects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Hysteretic models for sliding bearings with varying frictional force

The friction pendulum system is a sliding seismic isolator with self‐centering capabilities. Under severe earthquakes, the movement may be excessive enough to cause the pendulum to hit the side rim of the isolator, which is provided to restrain the sliding. The biaxial behavior of a single friction pendulum, in which the slider contacts the restrainer, is developed using a smooth hysteretic model with nonlinear kinematic hardening. This model is extended to simulate the biaxial response of double and triple friction pendulums with multiple sliding surfaces. The model of a triple friction pendulum is based on the interaction between four sliding interfaces, which in turn is dependent upon the force and displacement conditions prevailing at these interfaces. Each of these surfaces are modeled as nonlinear biaxial springs suitable for a single friction pendulum, using the yield surface, based on the principles of the classical theory of plasticity, and amended for varying frictional yield force, due to variation in vertical load and/or velocity‐dependent friction coefficient. The participation of the nonlinear springs is governed by stick‐slip conditions, dictated by equilibrium and kinematics. The model can simulate the overall force‐deformation behavior, track the displacements in individual sliding surfaces, and account for the ultimate condition when the sliders are in contact with their restrainers. The results of this model are verified by comparison to theoretical calculations and to experiments. The model has been implemented in programs IDARC2D and 3D‐BASIS, and the analytical results are compared with shake table experimental results. Copyright © 2013 John Wiley & Sons, Ltd.     

The three‐dimensional behavior of inverted pendulum cylindrical structures during earthquakes

In order to use rocking as a seismic response modification strategy along both directions of seismic excitation, a three‐dimensional (3D) rocking model should be developed. Since stepping or rolling rocking structural members out of their initial position is not a desirable performance, a rocking design should not involve these modes of motion. To this end, a model that takes the aforementioned constraint into account needs to be developed. This paper examines the 3D motion of a bounded rigid cylinder that is allowed to uplift and sustain rocking and wobbling (unsteady rolling) motion without sliding or rolling out of its initial position (i.e., a 3D inverted pendulum). Thus, the cylinder is constrained to zero residual displacement at the end of its 3D motion. This 3D dynamic model of the rocking rigid cylinder has two DOFs (three when damping is included), making it the simplest 3D extension of Housner's classical two‐dimensional (2D) rocking model. The development of models with and without damping is presented first. They are simple enough to perform extensive parametric analyses. Modes of motion of the cylinder are identified and presented. Then, 3D rocking and wobbling earthquake response spectra are constructed and compared with the classical 2D rocking earthquake response spectra. The 3D bounded rocking earthquake response spectra for the ground motions considered seem to have a very simple linear form. Finally, it is shown that the use of a 2D rocking model may lead to unacceptably unconservative estimates of the 3D rocking and wobbling seismic response. Copyright © 2017 John Wiley & Sons, Ltd.     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic response of three‐dimensional r/c multi‐storey frame building under uni‐ and bi‐directional input ground motion

This paper deals with seismic analysis of plan‐asymmetric r/c frame multi‐storey buildings. Non‐linear numerical analyses are carried out by using a lumped plasticity model for beams and a multi‐spring model for columns, the latter one introduced to account for axial force–biaxial bending moment interaction. A comparison between numerical analyses and experimental test results is reported in order to calibrate the numerical model, showing that the adopted model is very suitable. In order to study the effects of the earthquake orthogonal component, the seismic response of the modelled structure under uni‐directional excitation is compared to the one under bi‐directional excitation. Such comparison shows that the maximum base shear and the top displacement are not very sensitive to the presence of the orthogonal component, which, conversely, leads to large increase in the column plastic excursions. Copyright © 2007 John Wiley & Sons, Ltd.     

Study on the effect of ground motion direction on the response of engineering structure

Due to the randomness of earthquake wave magnitude and direction, and the uncertain direction of strong axis and weak axis in the construction of engineering structures, the effect of the direction of ground motion on a structure are studied herein. Ground motion records usually contain three vertical ground motion data, which are obtained by sensors arranged in accordance with the EW(East-West) direction, NS(South- North) direction and perpendicular to the surface(z) direction, referring to the construction standard of seismic stations. The seismic records in the EW and NS directions are converted to Cartesian coordinates in accordance with the rotation of θ = 0°-180°, and consequently, a countless group of new ground motion time histories are obtained. Then, the characteristics of the ground motion time history and response spectrum of each group were studied, resulting in the following observations:(1) the peak and phase of ground motion are changed with the rotation of direction θ, so that the direction θ of the maximum peak ground motion can be determined;(2) response spectrum values of each group of ground motions change along with the direction θ, and their peak, predominant period and declining curve are also different as the changes occur; then, the angle θ in the direction of the maximum peak value or the widest predominant period can be determined; and(3) the seismic response of structures with different directions of ground motion inputs has been analyzed under the same earthquake record, and the results show the difference. For some ground motion records, such as the Taft seismic wave, these differences are significant. Next, the Lushan middle school gymnasium structure was analyzed and the calculation was checked using the proposed method, where the internal force of the upper space truss varied from 25% to 28%. The research results presented herein can be used for reference in choosing the ground motion when checking the actual damage to structures following earthquakes and explaining the seismic damage. Meanwhile, it also provides a reference value for research into the most severe ground motion.     

Seismic fragility and reliability of structures isolated by friction pendulum devices: seismic reliability‐based design (SRBD)

The paper deals with the seismic reliability of elastic structural systems equipped with friction pendulum isolators (friction pendulum system). The behavior of these systems is analyzed by employing a two‐degree‐of‐freedom model accounting for the superstructure flexibility, whereas the friction pendulum system device behavior is described by adopting a widespread model that considers the variation of the friction coefficient with the velocity. With reference to medium soil condition, the uncertainty in the seismic inputs is taken into account by considering a set of artificial records, obtained through Monte Carlo simulations within the power spectral density method, with different frequency contents and characteristics depending on the soil dynamic parameters and scaled to increasing intensity levels. The sliding friction coefficient at large velocity is also considered as random variable modeled through a uniform probability density function. Incremental dynamic analyses are developed in order to evaluate the probabilities exceeding different limit states related to both r.c. superstructure and isolation level defining the seismic fragility curves through an extensive parametric study carried out for different structural system properties. Finally, considering the seismic hazard curves related to a site near L'Aquila (Italy), the seismic reliability of the r.c. superstructure systems is evaluated, and seismic reliability‐based design abacuses are derived with the aim to define the radius in plan of the friction pendulum devices in function of the structural properties and reliability level expected. Copyright © 2016 John Wiley & Sons, Ltd.     

On the inelastic seismic response of asymmetric buildings under bi‐axial excitation

The elastic and inelastic seismic response of plan‐asymmetric regular multi‐storey steel‐frame buildings has been investigated under bi‐directional horizontal ground motions. Symmetric variants of these buildings were designed according to Eurocodes 3 and 8. Asymmetric buildings were created by assuming a mass eccentricity in each of the two principal directions. The torsional response in the elastic and inelastic range is qualitatively similar with the exception of the stiff edge in the strong direction of torsionally stiff buildings and the stiff edge in the weak direction of torsionally flexible buildings. The response is influenced by the intensity of ground motion, i.e. by the magnitude of plastic deformation. In the limiting case of very strong ground motion, the behaviour of initially torsionally stiff and initially torsionally flexible buildings may become qualitatively similar. A decrease in stiffness due to plastic deformations in one direction may substantially influence the behaviour in the orthogonal direction. The response strongly depends on the detailed characteristics of the ground motion. On average, torsional effects are reduced with increasing plastic deformations, unless the plastic deformations are small. Taking into account also the dispersion of results which is generally larger in the inelastic range than in the elastic one, it can be concluded that (a) the amplification of displacements determined by the elastic analysis can be used as a rough estimate also in the inelastic range and (b) any favourable torsional effect on the stiff side of torsionally stiff buildings, which may arise from elastic analysis, may disappear in the inelastic range. The conclusions are limited to fairly regular buildings and subject to further investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental and analytical studies of structures seismically isolated with an uplift‐restraining friction pendulum system

This paper presents findings from a comprehensive analytical and experimental study on the uplift‐restraining XY‐FP sliding isolation system. To investigate the effectiveness of the XY‐FP isolator and provide a rational basis for evaluating the efficacy of the developed mathematical model, an extensive experimental program was conducted on the earthquake simulator at the University at Buffalo. The experimental program involved a slender, five‐storey, scale‐model frame seismically isolated with four XY‐FP isolators subjected to simulations of historical horizontal and vertical ground motions. The experimental response demonstrates the validity of the concept and provides evidence for the effectiveness of the XY‐FP isolator in preventing uplift. A comprehensive analytical model capable of emulating the mechanical behaviour of the XY‐FP isolator is developed and implemented in program 3D‐BASIS‐ME. The newly enhanced program is used to predict the dynamic response of the seismically‐isolated model structure. Comparison of analytical predictions with experimental results attests to the efficacy of the analytical model for simulating the response of the XY‐FP isolator. With its appealing conceptual simplicity and its proven effectiveness, the new uplift‐restraining isolator has the potential to facilitate the application of seismic isolation even under the most extreme of conditions, including but not limited to near‐fault strong ground motions and uplift‐prone structural systems. Copyright © 2005 John Wiley & Sons, Ltd.     

Earthquake ground motion modeling of induced seismicity in the Groningen gas field

A physics‐based numerical approach is used to characterize earthquake ground motion due to induced seismicity in the Groningen gas field and to improve empirical ground motion models for seismic hazard and risk assessment. To this end, a large‐scale (20 km × 20 km) heterogeneous 3D seismic wave propagation model for the Groningen area is constructed, based on the significant bulk of available geological, geophysical, geotechnical, and seismological data. Results of physics‐based numerical simulations are validated against the ground motion recordings of the January 8, 2018, M_L 3.4 Zeerijp earthquake. Taking advantage of suitable models of slip time functions at the seismic source and of the detailed geophysical model, the numerical simulations are found to reproduce accurately the observed features of ground motions at epicentral distances less than 10 km, in a broad frequency range, up to about 8 Hz. A sensitivity analysis is also addressed to discuss the impact of 3D underground geological features, the stochastic variability of seismic velocities and the frequency dependence of the quality factor. Amongst others, results point out some key features related to 3D seismic wave propagation, such as the magnitude and distance dependence of site amplification functions, that may be relevant to the improvement of the empirical models for earthquake ground motion prediction.     

Polynomial friction pendulum isolators (PFPIs) for seismic performance control of benchmark highway bridge

The seismic response of a benchmark highway bridge isolated with passive polynomial friction pendulum isolators (PFPIs) is investigated and subjected to six bidirectional ground motion records. The benchmark study is based on a lumped mass finite-element model of the 91/5 highway overcrossing located in Southern California. The PFPI system possesses two important parameters; one is horizontal flexibility and the other is energy absorbing capacity through friction. The evaluation criteria of the benchmark bridge are analyzed considering two parameters, time period of the isolator and coefficient of friction of the isolation surface. The results of the numerical study are compared with those obtained from the traditional friction pendulum system (FPS). Dual design performance of the PFPI system suppressed the displacement and acceleration response of the benchmark highway bridge. The dual design hysteresis loop of the PFPI system is the main advantage over the linear hysteresis loop of the FPS. The numerical result indicates that the seismic performance of the PFPI system is better than that of the traditional FPS isolated system. Further, it is observed that variations of the isolation time period and coefficient of friction of the FPS and PFPI systems have a significant effect on the peak responses of the benchmark highway bridge.     

El Niño Impact on Polar Motion Prediction Errors

The polar motion prediction is computed as a least-squares extrapolation of the polar motion data. The least-squares model consists of a Chandler circle with constant or variable amplitude, annual and semiannual ellipses, and a bias. The model with constant amplitude of the Chandler oscillation is fit to the last three years of polar motion data and the model with variable amplitude of the Chandler oscillation is fit to the whole time series ranging from 1973.0 to 2001.1. The variable amplitude of the Chandler oscillation is modeled from the envelope of the Chandler oscillation filtered by the Fourier transform band pass filter from the long-term IERS EOPC01 polar motion series. The accuracy of the polar motion prediction depends mostly on the phase variation of the annual oscillation, which is treated as a constant in the least-squares adjustment. There were two significant changes of the annual oscillation phase of the order of 30° before the two El Niño events in 1982/83 and 1997/98.