Evaluation of horizontal stiffness of fibre‐reinforced elastomeric isolators

Unbonded fibre‐reinforced elastomeric isolator (U‐FREI) is relatively new seismic base isolator in which fibre layers are used as reinforcement to replace steel shims as are normally used in conventional isolators. Further, the top and bottom end steel connector plates of conventional isolators are also removed. In general, the horizontal response of U‐FREI is nonlinear because of reduction in contact area due to rollover deformation and reduction in shear modulus of isolator under large deformation. Thus, evaluation of horizontal stiffness of U‐FREI is a challenging problem. Most previous studies were focused on the investigation of horizontal response of scaled models of U‐FREIs with low shape factors. A few analytical approaches were suggested for predicting the horizontal response of U‐FREI; but their results were not in good agreement with experimental observations. In the present study, the horizontal responses of prototype U‐FREIs are evaluated under a constant vertical pressure and cyclic loading using both experiments and finite element analysis. Prototype U‐FREIs with different shear moduli and with different shape factors are considered. Finite element simulations of corresponding bonded FREIs are also performed under the same loadings as in U‐FREIs. A rational analytical approach including the influence of rollover deformation and simultaneous reduction in shear modulus is proposed as a basic analytical tool for predicting the horizontal stiffness of FREIs (both bonded and unbonded). It is in reasonably good agreement with the results obtained from experiments and numerical analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

Inelastic seismic response of stiffening systems and development of demand spectrum: Application to MSSS bridges

A stiffening system is a system that increases its stiffness as it goes under large displacements. Such behavioural characteristic can result from constitutive behaviour or at the structural level often from closure of gaps between various components (sub‐systems) of the structure. An example of the latter situation is multi‐span simply supported (MSSS) bridges under horizontal earthquake ground motion. Unlike softening systems, stiffening systems have not been studied. In addition to the need for more understanding of the seismic response of stiffening systems, there is a need to develop response spectrum that can be used in design. Several parameters including gap size and ratios of sub‐systems stiffness, strength, and mass control the behaviour of a stiffening system. In this study, a simplified stiffening model is developed and over 367 000 cases are analysed to investigate the nonlinear stiffening behaviour and pounding. Parameters considered also include ground motion characteristic. Results are evaluated and compared in terms of displacement and dissipated hysteretic energy. Parameter study results show that, on average, the displacement response is lower for stiffening systems, however, they dissipates higher hysteretic energy, due to higher yield cycles and yield excursions, and can possibly sustain more damage than a bilinear, elastic–plastic system. Using parameter study database, design response spectrum for stiffening systems is also proposed and its practical application is demonstrated through its application to an MSSS bridge. Results of this study goes beyond MSSS bridges and will have application for many structural systems where response is characterized by a stiffening behaviour. Copyright © 2007 John Wiley & Sons, Ltd.     

Shake table study on an ordinary low‐rise building seismically isolated with SU‐FREIs (stable unbonded‐fiber reinforced elastomeric isolators)

This paper reports on the investigation of novel fiber reinforced elastomeric isolator (FREI) bearings, which do not have thick end plates, and are used in an unbonded application. Owing to the stable lateral load‐displacement response exhibited by the unbonded FREI bearings, the proposed bearings are referred to as stable unbonded (SU)‐FREIs. A shake table test program was conducted on a two‐story test‐structure having well‐defined elastic response characteristics. Compared with the results for the corresponding fixed base (FB) structure, the peak response values, distribution of lateral response throughout the height of the structure, and response time histories of the tested base isolated (BI) structure indicate that significantly improved response can be achieved. This study clearly indicates that SU‐FREI bearings can provide an effective seismic isolation system. Copyright © 2009 John Wiley & Sons, Ltd.     

A simple procedure to approximate slip displacement of freestanding rigid body subjected to earthquake motions

A simple calculation procedure for estimating absolute maximum slip displacement of a freestanding rigid body placed on the ground or floor of linear/nonlinear multi‐storey building during an earthquake is developed. The proposed procedure uses the displacement induced by the horizontal sinusoidal acceleration to approximate the absolute maximum slip displacement, i.e. the basic slip displacement. The amplitude of this horizontal sinusoidal acceleration is identical to either the peak horizontal ground acceleration or peak horizontal floor response acceleration. Its period meets the predominant period of the horizontal acceleration employed. The effects of vertical acceleration are considered to reduce the friction force monotonously. The root mean square value of the vertical acceleration at the peak horizontal acceleration is used. A mathematical solution of the basic slip displacement is presented. Employing over one hundred accelerograms, the absolute maximum slip displacements are computed and compared with the corresponding basic slip displacements. Their discrepancies are modelled by the logarithmic normal distribution regardless of the analytical conditions. The modification factor to the basic slip displacement is quantified based on the probability of the non‐exceedence of a certain threshold. Therefore, the product of the modification factor and the basic slip displacement gives the design slip displacement of the body as the maximum expected value. Since the place of the body and linear/nonlinear state of building make the modification factor slightly vary, ensuring it to suit the problem is essential to secure prediction accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

Shake table testing of un‐reinforced brick masonry building test model isolated by U‐FREI

This paper presents a detailed study on feasibility of un‐bonded fiber reinforced elastomeric isolator (U‐FREI) as an alternative to steel reinforced elastomeric isolator (SREI) for seismic isolation of un‐reinforced masonry buildings. Un‐reinforced masonry buildings are inherently vulnerable under seismic excitation, and U‐FREIs are used for seismic isolation of such buildings in the present study. Shake table testing of a base isolated two storey un‐reinforced masonry building model subjected to four prescribed input excitations is carried out to ascertain its effectiveness in controlling seismic response. To compare the performance of U‐FREI, same building is placed directly on the shake table without isolator, and fixed base (FB) condition is simulated by restraining the base of the building with the shake table. Dynamic response characteristic of base isolated (BI) masonry building subjected to different intensities of input earthquakes is compared with the response of the same building without base isolation system. Acceleration response amplification and peak response values of test model with and without base isolation system are compared for different intensities of table acceleration. Distribution of shear forces and moment along the height of the structure and response time histories indicates significant reduction of dynamic responses of the structure with U‐FREI system. This study clearly demonstrates the improved seismic performance of un‐reinforced masonry building model supported on U‐FREIs under the action of considered ground motions. Copyright © 2015 John Wiley & Sons, Ltd.     

Kinematic transformations for planar multi‐directional pseudodynamic testing

The pseudodynamic (PSD) test method imposes command displacements to a test structure for a given time step. The measured restoring forces and displaced position achieved in the test structure are then used to integrate the equations of motion to determine the command displacements for the next time step. Multi‐directional displacements of the test structure can introduce error in the measured restoring forces and displaced position. The subsequently determined command displacements will not be correct unless the effects of the multi‐directional displacements are considered. This paper presents two approaches for correcting kinematic errors in planar multi‐directional PSD testing, where the test structure is loaded through a rigid loading block. The first approach, referred to as the incremental kinematic transformation method, employs linear displacement transformations within each time step. The second method, referred to as the total kinematic transformation method, is based on accurate nonlinear displacement transformations. Using three displacement sensors and the trigonometric law of cosines, this second method enables the simultaneous nonlinear equations that express the motion of the loading block to be solved without using iteration. The formulation and example applications for each method are given. Results from numerical simulations and laboratory experiments show that the total transformation method maintains accuracy, while the incremental transformation method may accumulate error if the incremental rotation of the loading block is not small over the time step. A procedure for estimating the incremental error in the incremental kinematic transformation method is presented as a means to predict and possibly control the error. Copyright © 2009 John Wiley & Sons, Ltd.     

Residual displacements of RC structures as SDOF systems

Residual displacements are sensitive to ground motion details, hence more random than peak inelastic displacements. Among the factors with systematic impact on residual displacements, the post‐yield‐stiffness‐ratio has been studied thoroughly; its effects are not investigated further. Concerning another important factor, the hysteresis law, past studies have focused on the bilinear model, which does not represent concrete structures. Residual displacements from nonlinear response‐history analyses of bilinear systems are compared to those from models tuned to concrete structures, conforming to modern codes, deficient or intermediate. Deficient‐type structures, with their narrow, almost self‐centering hysteresis loops, develop markedly smaller residual displacements than those with stable energy‐dissipating behavior. A velocity pulse in the motion increases peak inelastic and residual displacements by about the same proportion. As a fraction of the peak inelastic or spectral displacement, residual displacements are on average almost independent of the period and increase when the lateral strength ratio increases, reaching a limit at a lateral strength ratio of 2 to 5. Peak inelastic displacements are a better basis for estimation of residual displacements than spectral ones: the ratio of the two is almost independent of the period, the lateral strength ratio (beyond values of 2 to 3) and velocity pulses. The spectrum of the ratio of residual displacement to peak inelastic or spectral displacement is considered as a random process of period; its mean and variance functions, marginal probability distributions and autocorrelation functions are given in terms of the lateral strength ratio, the hysteresis model and the presence of a velocity pulse. Copyright © 2014 John Wiley & Sons, Ltd.     

Inelastic displacement demand of bridge columns considering shear–flexure interaction

Reinforced concrete bridge columns exhibit complex hysteretic behavior owing to combined action of shear, bending moment, and axial force under multi‐directional seismic shakings. The inelastic displacement of columns can be increased by shear–flexure interaction (SFI). This paper develops a simple yet reliable demand model for estimating the inelastic displacement and ductility based on the nonlinear time history analyses of 24 full‐size columns subject to a suite of near‐fault ground motions. A coupled hysteretic model is used to simulate the shear‐flexure interactive (SFI) behavior of columns and the accumulated material damage during loading reversals, including pinching, strength deterioration, and stiffness softening. Guided by rigorous dimensional analysis, the inelastic displacement responses of bridge columns are presented in dimensionless form showing remarkable order. A dimensionless nonlinearity index is derived taking into account of the column strength, ground motion amplitude, and softening or hardening post‐yield behavior. Strong correlation is revealed between the normalized inelastic displacement and the dimensionless structure‐to‐pulse frequency, the dimensionless nonlinearity index as well as the aspect ratio. Two regressive equations for displacement and ductility demands are proposed and validated against the simulation results. The SFI effects are discussed and included explicitly through the aspect ratio in the proposed model. This study offers a new way to realistically predict the inelastic displacement of columns directly from structural and ground motion characteristics. Copyright © 2010 John Wiley & Sons, Ltd.     

Further development of a multimodal pushover analysis procedure for seismic assessment of bridges

An improvement is first suggested to the modal pushover analysis (MPA) procedure for bridges initially proposed by the writers (Earthquake Engng Struct. Dyn. 2006; 35 (11):1269–1293), the key idea being that the deformed shape of the structure responding inelastically to the considered earthquake level is used in lieu of the elastic mode shape. The proposed MPA procedure is then verified by applying it to two actual bridges. The first structure is the Krystallopigi bridge, a 638 m‐long multi‐span bridge, with significant curvature in plan, unequal pier heights, and different types of pier‐to‐deck connections. The second structure is a 100 m‐long three‐span overpass bridge, typical in modern motorway construction in Europe, which, although ostensibly a regular structure, is found to exhibit a rather unsymmetric response in the transverse direction, mainly due to torsional irregularity. The bridges are assessed using response spectrum, ‘standard’ pushover (SPA), and MPA, and finally using non‐linear response history analysis (NL‐RHA) for a number of spectrum‐compatible motions. The MPA provided a good estimate of the maximum inelastic deck displacement for several earthquake intensities. The SPA on the other hand could not predict well the inelastic deck displacements of bridges wherever the contribution of the first mode to the response of the bridge was relatively low. Copyright © 2009 John Wiley & Sons, Ltd.     

Predictive active control of MDOF structures

This paper presents a theoretical study of a predictive active control system used to improve the response of multi‐degree‐of‐freedom (MDOF) structures to earthquakes. As an example a building frame equipped with electrorheological (ER) dampers is considered. The aim of the design is to find a combination of forces that are produced by the ER dampers in order to obtain an optimal structural response. The mechanical response of ER fluid dampers is regulated by an electric field. Linear auto‐regressive model with exogenous input (ARX) is used to predict the displacements and the velocities of the frame in order to overcome the time‐delay problem in the control system. The control forces in the ER devices are calculated at every time step by the optimal control theory (OCT) according to the values of the displacements and of the velocities that are predicted at the next time step at each storey of the structure. A numerical analysis of a seven‐storey ER damped structure is presented as an example. It shows a significant improvement of the structural response when the predictive active control system is applied compared to that of an uncontrolled structure or that of a structure with controlled damping forces with time delay. The structure's displacements and velocities that were used to obtain the optimal control forces were predicted according to an ‘occurring’ earthquake by the ARX model (predictive control). The response was similar to that of the structure with control forces that were calculated from a ‘known’ complete history of the earthquake's displacement and velocity values, and were applied without delay (instantaneous control). Copyright © 2000 John Wiley & Sons, Ltd.     

Numerical simulations of a highway bridge structure employing passive negative stiffness device for seismic protection

A new passive seismic response control device has been developed, fabricated, and tested by the authors and shown to be capable of producing negative stiffness via a purely mechanical mechanism, thus representing a new generation of seismic protection devices. Although the concept of negative stiffness may appear to be a reversal on the desired relationship between the force and displacement in structures (the desired relationship being that the product of restoring force and displacement is nonnegative), when implemented in parallel with a structure having positive stiffness, the combined system appears to have substantially reduced stiffness while remaining stable. Thus, there is an ‘apparent weakening and softening’ of the structure that results in reduced forces and increased displacements (where the weakening and softening is of a non‐damaging nature in that it occurs in a seismic protection device rather than within the structural framing system). Any excessive displacement response can then be limited by incorporating a damping device in parallel with the negative stiffness device. The combination of negative stiffness and passive damping provides a large degree of control over the expected performance of the structure. In this paper, a numerical study is presented on the performance of a seismically isolated highway bridge model that is subjected to various strong earthquake ground motions. The Negative Stiffness Devices (NSDs) are described along with their hysteretic behavior as obtained from a series of cyclic tests wherein the tests were conducted using a modified design of the NSDs (modified for testing within the bridge model). Using the results from the cyclic tests, numerical simulations of the seismic response of the isolated bridge model were conducted for various configurations (with/without negative stiffness devices and/or viscous dampers). The results demonstrate that the addition of negative stiffness devices reduces the base shear substantially, while the deck displacement is limited to acceptable values. This assessment was conducted as part of a NEES (Network for Earthquake Engineering Simulation) project which included shaking table tests of a quarter‐scale highway bridge model. Copyright © 2014 John Wiley & Sons, Ltd.     

水合物分解对桩基础应力和变形影响的研究

赋存于海底沉积物中的天然气水合物与固体颗粒相互胶结,增加了沉积物的强度,一旦水合物分解,会引起沉积物剪切强度降低,如果在含有水合物层上面或附近存在桩基础,必然影响其稳定性。本文采用应力释放法,通过数值计算,分别讨论了桩基础底部位于含水合物地层不同深度时,水合物分解对桩基础应力和变形的影响规律。计算结果表明,随着水合物分解过程中的模量软化和强度衰减,桩基础的水平和竖向位移增大,由于地基水平,土体没有驱动剪应力,水平位移增加不大,地基和桩基础主要表现为竖向沉降;桩底部位于水合物层中间的桩基础的沉降变形,比桩底穿过水合物层的桩基础大,在桩基础及其附近的土体产生较大的应力。     

Experimental and analytical studies on the response of freestanding laboratory equipment to earthquake shaking

This paper presents results of a comprehensive experimental program on the seismic response of full‐scale freestanding laboratory equipment. First, quasi‐static experiments are conducted to examine the mechanical behavior of the contact interface between the laboratory equipment and floors. Based on the experimental results, the response analysis that follows adopts two idealized contact friction models: the elastoplastic model and the classical Coulomb friction model. Subsequently, the paper presents shake table test results of full‐scale freestanding equipment subjected to ground and floor motions of hazard levels with corresponding displacements that can be accommodated by the shake table at the UC Berkeley Earthquake Engineering Research Center. For the equipment tested, although some rocking is observed, sliding is the predominant mode of response, with sliding displacements reaching up to 60 cm. Numerical simulations with the proposed models are performed. Finally, the paper identifies a physically motivated intensity measure and the associated engineering demand parameter with the help of dimensional analysis and presents ready‐to‐use fragility curves. Copyright © 2008 John Wiley & Sons, Ltd.     

The Influence of Thrust Fault Structure on Cross-fault Short-leveling Survey

Aiming at different variation patterns of cross-fault short-leveling before earthquakes, the paper establishes the 2-D finite-element models with different crustal stratification and fault occurrence perpendicular to Longmenshan fault zone. By contact analysis and viscoelastic finite element method, the influence of fault structure on cross-fault short-leveling is obtained under the same constraint conditions, the results show that:with the increase of the horizontal projection distance of fault, the cumulative displacements of surface increase gradually in the models with fixed dip angles of the fault plane (model 1). However, when the horizontal projection distance exceeds 20km, the influence of fault''s dip angle on the cumulative displacements of surface short-leveling will decrease significantly, and the cumulative displacements are maintained at about 1.5m. However, in the listric fault models (model 2),when the projection distance is less than 20km, the listric fault structure impedes the sliding of fault. The short-leveling variation rate is only half of model 1; as a result, the ability to reflect the regional stress enhancement by cross-fault short-leveling is further weakened. But when the horizontal projection distance exceeds 25km, the cumulative displacements significantly increase, with the maximum displacement reaching 1.75m. The results of equivalent stress show that the listric fault structure causes a sudden increasement in equivalent stress when the horizontal projection distance is 10km, higher equivalent stress values are accumulated between the projection distance of 5-20km, and then high-low stress difference zones are formed at the bottom of the fault plane and near the transition zone of low-high dip angle.     

Accounting for directionality as a function of structural typology in performance‐based earthquake engineering design

For the seismic design of a structure, horizontal ground shaking is usually considered in two perpendicular directions, even though real horizontal ground motions are complex two‐dimensional phenomena that impose different demands at different orientations. While the issue of ground motion dependence on the orientation of the recording devices has been the focus of many significant developments during the last decade, the effects of directionality on the characteristics of the structure have received less attention. This work presents a proposal to calculate the probability of exceedance of elastic spectral displacements accounting for structural typology and illustrates its relevance by means of its application to two case‐study buildings. In order to ease its implementation in seismic design codes, a simplification is developed by means of a detailed statistical analysis of the results obtained using four sets of real hazard curves. The framework presented herein is considered to represent an important contribution to the field of performance‐based earthquake engineering, permitting improved treatment of directionality effects within seismic risk design and assessment. Copyright © 2016 John Wiley & Sons, Ltd.     

A friction damped base isolation system with fail-safe characteristics

An experimental study of a Coulomb friction damped aseismic base isolation system with fail-safe characteristics is described in this paper. The base isolation system utilized commercially made natural rubber bearings and a skid system which comes into operation at preset-levels of relative horizontal displacement between the structure and the foundation. The fail-safe skid provides hysteretic damping and prevents failure of the isolation system in the event of displacements larger than those assumed in the original design. The isolation system can be designed for an earthquake which can be reasonably expected within the lifetime of the structure; in the event of an earthquake of unanticipated intensity the failsafe system will prevent collapse of the structure. The testing of the system involved an 80,000lb model, approximately 1/3 scale to a real structure mounted on the 20′ × 20′ shaking table at EERC and subject to a variety of earthquake inputs. The results show that the hysteretic effect of the fail-safe system does not greatly increase the accelerations experienced by the structure but considerably reduces the relative displacements at the isolation bearings. The action of the fail-safe system was tested by using an earthquake input that produced a resonant response in the isolated mode of the model. The stability limit of the isolation system was exceeded and the bearings failed but complete failure of the isolation system and thus collapse of the model was prevented by the fail-safe system. The implementation of the system in full scale structures poses no technical or construction problems. An equivalent linearization technique was developed for this system for design purposes using response spectra. The accuracy of this approach was verified by comparison with the experimental results.     

近断层双向水平地震作用下隔震结构地震反应

近断层地震动脉冲特性在2个水平分量上具有差异,采用平方和开方法分析了近断层脉冲地震动双向地震作用下基础隔震结构和组合隔震结构的隔震层位移,并与近断层脉冲单向地震作用进行了对比分析,结果表明:若仅地震动加速度峰值大的分量或2个方向分量均存在明显速度脉冲,则产生的隔震层位移大于单向地震动;若仅地震动加速度峰值小的分量存在明...     

Performance of a real‐time pseudodynamic test system considering nonlinear structural response

This paper presents the implementation details of a real‐time pseudodynamic test system that adopts an implicit time integration scheme. The basic configuration of the system is presented. Physical tests were conducted to evaluate the performance of the system and validate a theoretical system model that incorporates the dynamics and nonlinearity of a test structure and servo‐hydraulic actuators, control algorithm, actuator delay compensation methods, and the flexibility of an actuator reaction system. The robustness and accuracy of the computational scheme under displacement control errors and severe structural softening are examined with numerical simulations using the model. Different delay compensation schemes have been implemented and compared. One of the schemes also compensates for the deformation of an actuator reaction system. It has been shown that the test method is able to attain a good performance in terms of numerical stability and accuracy. However, it has been shown that test results obtained with this method can underestimate the inelastic displacement drift when severe strain softening develops in a test structure. This can be attributed to the fact that the numerical damping effect introduced by convergence errors becomes more significant as a structure softens. In a real‐time test, a significant portion of the convergence errors is caused by the time delay in actuator response. Hence, a softening structure demands higher precision in displacement control. Copyright © 2007 John Wiley & Sons, Ltd.     

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.