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## Parameter identification of hysteretic model of rubber-bearing based on sequential nonlinear least-square estimation

### Earthquake Engineering and Engineering Vibration (2010-09-01) 9: 375-383 , September 01, 2010

In order to evaluate the nonlinear performance and the possible damage to rubber-bearings (RBs) during their normal operation or under strong earthquakes, a simplified Bouc-Wen model is used to describe the nonlinear hysteretic behavior of RBs in this paper, which has the advantages of being smooth-varying and physically motivated. Further, based on the results from experimental tests performed by using a particular type of RB (GZN110) under different excitation scenarios, including white noise and several earthquakes, a new system identification method, referred to as the sequential nonlinear least-square estimation (SNLSE), is introduced to identify the model parameters. It is shown that the proposed simplified Bouc-Wen model is capable of describing the nonlinear hysteretic behavior of RBs, and that the SNLSE approach is very effective in identifying the model parameters of RBs.

## Research on seismic performance of shear walls with concrete filled steel tube columns and concealed steel trusses

### Earthquake Engineering and Engineering Vibration (2011-12-01) 10: 535-546 , December 01, 2011

In order to further improve the seismic performance of RC shear walls, a new composite shear wall with concrete filled steel tube (CFT) columns and concealed steel trusses is proposed. This new shear wall is a double composite shear wall; the first composite being the use of three different force systems, CFT, steel truss and shear wall, and the second the use of two different materials, steel and concrete. Three 1/5 scaled experimental specimens: a traditional RC shear wall, a shear wall with CFT columns, and a shear wall with CFT columns and concealed steel trusses, were tested under cyclic loading and the seismic performance indices of the shear walls were comparatively analyzed. Based on the data from these experiments, a thorough elastic-plastic finite element analysis and parametric analysis of the new shear walls were carried out using ABAQUS software. The finite element results of deformation, stress distribution, and the evolution of cracks in each phase were compared with the experimental results and showed good agreement. A mechanical model was also established for calculating the load-carrying capacity of the new composite shear walls. The results show that this new type of shear wall has improved seismic performance over the other two types of shear walls tested.

## Delay-dependent stability and added damping of SDOF real-time dynamic hybrid testing

### Earthquake Engineering and Engineering Vibration (2010-09-01) 9: 425-438 , September 01, 2010

It is well-recognized that a transfer system response delay that reduces the test stability inevitably exists in real-time dynamic hybrid testing (RTDHT). This paper focuses on the delay-dependent stability and added damping of SDOF systems in RTDHT. The exponential delay term is transferred into a rational fraction by the Padé approximation, and the delay-dependent stability conditions and instability mechanism of SDOF RTDHT systems are investigated by the root locus technique. First, the stability conditions are discussed separately for the cases of stiffness, mass, and damping experimental substructure. The use of root locus plots shows that the added damping effect and instability mechanism for mass are different from those for stiffness. For the stiffness experimental substructure case, the instability results from the inherent mode because of an obvious negative damping effect of the delay. For the mass case, the delay introduces an equivalent positive damping into the inherent mode, and instability occurs at an added high frequency mode. Then, the compound stability condition is investigated for a general case and the results show that the mass ratio may have both upper and lower limits to remain stable. Finally, a high-emulational virtual shaking table model is built to validate the stability conclusions.

## Diffraction of plane SV waves by a cavity in poroelastic half-space

### Earthquake Engineering and Engineering Vibration (2009-03-01) 8: 29-46 , March 01, 2009

This paper presents an indirect boundary integration equation method for diffraction of plane SV waves by a 2-D cavity in a poroelastic half-space. The Green’s functions of compressive and shear wave sources are derived based on Biot’s theory. The scattered waves are constructed using fictitious wave sources close to the boundary of the cavity, and their magnitudes are determined by the boundary conditions. Verification of the accuracy is performed by: (1) checking the satisfaction extent of the boundary conditions, (2) comparing the degenerated solutions of a single-phased case with well-known solutions, and (3) examining the numerical stability of the solutions. The nature of diffraction of plane SV waves around a cavity in a poroelastic half-space is investigated by numerical examples.

## New lumped-mass-stick model based on modal characteristics of structures: development and application to a nuclear containment building

### Earthquake Engineering and Engineering Vibration (2013-06-01) 12: 307-317 , June 01, 2013

In this study, a new lumped-mass-stick model (LMSM) is developed based on the modal characteristics of a structure such as eigenvalues and eigenvectors. The simplified model, named the “frequency adaptive lumped-massstick model,” hasonly a small number of stick elements and nodes to provide the same natural frequencies of the structure and is applied to a nuclear containment building. To investigate the numerical performance of the LMSM, a time history analysis is carried out on both the LMSM and the finite element model (FEM) for a nuclear containment building. A comparison of the results shows that the dynamic responses of the LMSM in terms of displacement and acceleration are almost identical to those of the FEM. In addition, the results in terms of fl oor response spectra at certain elevations are also in good agreement.

## 3-D consistency dynamic constitutive model of concrete

### Earthquake Engineering and Engineering Vibration (2010-06-01) 9: 233-246 , June 01, 2010

Based on the consistency-viscoplastic constitutive model, the static William-Warnke model with threeparameters is modified and a consistency-viscoplastic William-Warnke model with three-parameters is developed that considers the effect of strain rates. Then, the tangent modulus of the consistency viscoplastic model is introduced and an implicit backward Elure iterative algorithm is developed. Comparisons between the numerical simulations and experimental data show that the consistency model properly provides the uniaxial and biaxial dynamic behaviors of concrete. To study the effect of strain rates on the dynamic response of concrete structures, the proposed model is used in the analysis of the dynamic response of a simply-supported beam and the results show that the strain rate has a significant effect on the displacement and stress magnitudes and distributions. Finally, the seismic responses of a 278 m high arch dam are obtained and compared by using the linear elastic model, as well as rate-independent and rate-dependent William-Warnke three-parameter models. The results indicate that the strain rate affects the first principal stresses, and the maximal equivalent viscoplastic strain rate of the arch dam. Numerical calculations and analyses reveal that considering the strain rate is important in the safety assessments of arch dams located in seismically active areas.

## Karhunen-Loéve expansion for random earthquake excitations

### Earthquake Engineering and Engineering Vibration (2015-03-01) 14: 77-84 , March 01, 2015

This paper develops a trigonometric-basis-function based Karhunen-Loéve (KL) expansion for simulating random earthquake excitations with known covariance functions. The methods for determining the number of the KL terms and defining the involved random variables are described in detail. The simplified form of the KL expansion is given, whereby the relationship between the KL expansion and the spectral representation method is investigated and revealed. The KL expansion is of high efficiency for simulating long-term earthquake excitations in the sense that it needs a minimum number of random variables, as compared with the spectral representation method. Numerical examples demonstrate the convergence and accuracy of the KL expansion for simulating two commonly-used random earthquake excitation models and estimating linear and nonlinear random responses to the random excitations.

## Research on the random seismic response analysis for multi- and large-span structures to multi-support excitations

### Earthquake Engineering and Engineering Vibration (2015-09-01) 14: 527-538 , September 01, 2015

The pseudo excitation method (PEM) has been improved into a more practical form, on which the analytic formulae of seismic response power spectral density (PSD) of simplified large-span structural models have been derived. The analytic formulae and numerical computing results of seismic response PSD have been derived to study the mechanism of multi-support excitation effects, such as the wave-passage effect and incoherence effect, for the seismic response of multiand large-span structures. By using a multi-span truss as an example, the influence of multi-support excitation effects on the seismic response of such structures is studied.

## Analytical solutions for dynamic pressures of coupling fluid-solid-porous medium due to P wave incidence

### Earthquake Engineering and Engineering Vibration (2004-12-01) 3: 263-271 , December 01, 2004

Wave reflection and refraction in layered media is a topic closely related to seismology, acoustics, geophysics and earthquake engineering. Analytical solutions for wave reflection and refraction coefficients in multi-layered media subjected to P wave incidence from the elastic half-space are derived in terms of displacement potentials. The system is composed of ideal fluid, porous medium, and underlying elastic solid. By numerical examples, the effects of porous medium and the incident wave angle on the dynamic pressures of ideal fluid are analyzed. The results show that the existence of the porous medium, especially in the partially saturated case, may significantly affect the dynamic pressures of the overlying fluid.

## Double deck bridge behavior and failure mechanism under seismic motions using nonlinear analyzes

### Earthquake Engineering and Engineering Vibration (2013-09-01) 12: 447-461 , September 01, 2013

This paper investigates the behavior and the failure mechanism of a double deck bridge constructed in China through nonlinear time history analysis. A parametric study was conducted to evaluate the influence of different structural characteristics on the behavior of the double deck bridge under transverse seismic motions, and to detect the effect of bidirectional loading on the seismic response of this type of bridge. The results showed that some characteristics, such as the variable lateral stiffness, the foundation modelling, and the longitudinal reinforcement ratio of the upper and lower columns of the bridge pier bents have a major impact on the double deck bridge response and its failure mechanism under transverse seismic motions. It was found that the soft story failure mechanism is not unique to the double deck bridge and its occurrence is related to some conditions and structural characteristics of the bridge structure. The analysis also showed that the seismic vulnerability of the double deck bridge under bi-directional loading was severely increased compared to the bridge response under unidirectional transverse loading, and out-of-phase movements were triggered between adjacent girders.

## Ground motion spatial variability effects on seismic response control of cable-stayed bridges

### Earthquake Engineering and Engineering Vibration (2011-03-25) 10: 37-49 , March 25, 2011

The spatial variability of input ground motion at supporting foundations plays a key role in the structural response of cable-stayed bridges (CSBs); therefore, spatial variation effects should be included in the analysis and design of effective vibration control systems. The control of CSBs represents a challenging and unique problem, with many complexities in modeling, control design and implementation, since the control system should be designed not only to mitigate the dynamic component of the structural response but also to counteract the effects of the pseudo-static component of the response. The spatial variability effects on the feasibility and efficiency of seismic control systems for the vibration control of CSBs are investigated in this paper. The assumption of uniform earthquake motion along the entire bridge may result in quantitative and qualitative differences in seismic response as compared with those produced by uniform motion at all supports. A systematic comparison of passive and active system performance in reducing the structural responses is performed, focusing on the effect of the spatially varying earthquake ground motion on the seismic response of a benchmark CSB model with different control strategies, and demonstrates the importance of accounting for the spatial variability of excitations.

## Time-domain identification of dynamic properties of layered soil by using extended Kalman filter and recorded seismic data

### Earthquake Engineering and Engineering Vibration (2004-12-01) 3: 237-247 , December 01, 2004

A novel time-domain identification technique is developed for the seismic response analysis of soil-structure interaction. A two-degree-of-freedom (2DOF) model with eight lumped parameters is adopted to model the frequencydependent behavior of soils. For layered soil, the equivalent eight parameters of the 2DOF model are identified by the extended Kaiman filter (EKF) method using recorded seismic data. The polynomial approximations for derivation of state estimators are applied in the EKF procedure. A realistic identification example is given for the layered-soil of a building site in Anchorage, Alaska in the United States. Results of the example demonstrate the feasibility and practicality of the proposed identification technique. The 2DOF soil model and the identification technique can be used for nonlinear response analysis of soil-structure interaction in the time-domain for layered or complex soil conditions. The identified parameters can be stored in a database for use in other similar soil conditions. If a universal database that covers information related to most soil conditions is developed in the future, engineers could conveniently perform time history analyses of soil-structural interaction.

## Suboptimal Rayleigh damping coefficients in seismic analysis of viscously-damped structures

### Earthquake Engineering and Engineering Vibration (2014-12-01) 13: 653-670 , December 01, 2014

An optimization method for the consistent evaluation of two Rayleigh damping coefficients is proposed. By minimizing an objective function such as an error term of the peak displacement of a structure, the two coefficients can be determined with response spectral analysis. The optimization method degenerates into the conventional method used in current practices when only two modes of vibration are included in the objective function. Therefore, the proposed method with all significant modes included for simplicity in practical applications results in suboptimal damping coefficients. The effects of both spatial distribution and frequency content of excitations as well as structural dynamic characteristics on the evaluation of Rayleigh damping coefficients were investigated with a five-story building structure. Two application examples with a 62-story high-rise building and a 840 m long cable-stayed bridge under ten earthquake excitations demonstrated the accuracy and effectiveness of the proposed method to account for all of the above effects.

## Health monitoring of time-varying stochastic structures by latent components and fuzzy expert system

### Earthquake Engineering and Engineering Vibration (2008-05-01) 7: 91-106 , May 01, 2008

In this paper, a novel parametric model-based decomposition method is proposed for structural health monitoring of time-varying structures. For this purpose, the advanced Functional-Series Time-dependent Auto Regressive Moving Average (FS-TARMA) technique is used to estimate the parameters and innovation variance used in the parametric signal decomposition scheme. Additionally, a unique feature extraction and reduction method based on the decomposed signals, known as Latent Components (LCs), is proposed. To evaluate the efficiency of the proposed method, numerical simulation and an experimental study in the laboratory were conducted on a time-varying structure, where various types of damage were introduced. The Fuzzy Expert System (FES) was used as a classification tool to demonstrate that the proposed method successfully identifies different structural conditions when compared with other methods based on non-reduced and ordinary feature extraction.

## Site effects by generalized inversion technique using strong motion recordings of the 2008 Wenchuan earthquake

### Earthquake Engineering and Engineering Vibration (2013-06-01) 12: 165-184 , June 01, 2013

The generalized inversion of S-wave amplitude spectra from the free-field strong motion recordings of the China National Strong Motion Observation Network System (NSMONS) are used to evaluate the site effects in the Wenchuan area. In this regard, a total of 602 recordings from 96 aftershocks of the Wenchuan earthquake with magnitudes of *M*3.7-*M*6.5 were selected as a dataset. These recordings were obtained from 28 stations at a hypocenter distance ranging from 30 km to 150 km. The inversion results have been verified as reliable by comparing the site response at station 62WUD using the Generalized Inversion Technique (GIT) and the Standard Spectral Ratio method (SSR). For all 28 stations, the site predominant frequency *F*_{p} and the average site amplification in different frequency bands of 1.0–5.0 Hz, 5.0–10.0 Hz and 1.0–10.0 Hz have been calculated based on the inversion results. Compared with the results from the horizontal-to-vertical spectral ratio (HVSR) method, it shows that the HVSR method can reasonably estimate the site predominant frequency but underestimates the site amplification. The linear fitting between the average site amplification for each frequency band and the *V*_{s20} (the average uppermost-20 m shear wave velocity) shows good correlation. A distance measurement called the asperity distance *D*_{Aspt} is proposed to reasonably characterize the source-to-site distance for large earthquakes. Finally, the inversed site response is used to identify the soil nonlinearity in the main shock and aftershocks of Wenchuan earthquake. In ten of the 28 stations analyzed in the main shock, the soil behaved nonlinearly, where the ground motion level is apparently beyond a threshold of PGA > 300 cm/s^{2} or PGV > 20 cm/s, and only one station coded 51SFB has evidence of soil nonlinear behavior in the aftershocks.

## Design spectra including effect of rupture directivity in near-fault region

### Earthquake Engineering and Engineering Vibration (2006-12-01) 5: 159-170 , December 01, 2006

In order to propose a seismic design spectrum that includes the effect of rupture directivity in the near-fault region, this study investigates the application of equivalent pulses to the parameter attenuation relationships developed for near-fault, forward-directivity motions. Near-fault ground motions are represented by equivalent pulses with different waveforms defined by a small number of parameters (peak acceleration, *A*, and velocity *V*; and pulse period, *T*_{v}). Dimensionless ratios between these parameters (e.g., *AT*_{v}/*V*, *VT*_{v}/*D*) and response spectral shapes and amplitudes are examined for different pulses to gain insight on their dependence on basic pulse waveforms. Ratios of *AT*_{v}/*V*, *VT*_{v}/*D*, and the ratio of pulse period to the period for peak spectral velocity (*T*_{v-p}) are utilized to quantify the difference between rock and soil sites for near-fault forward-directivity ground motions. The *AT*_{v}/*V* ratio of recorded near-fault motions is substantially larger for rock sites than that for soil sites, while *T*_{v-p}/*T*_{v} ratios are smaller at rock sites than at soil sites. Furthermore, using simple pulses and available predictive relationships for the pulse parameters, a preliminary model for the design acceleration response spectra for the near-fault region that includes the dependence on magnitude, rupture distance, and local site conditions are developed.

## Earthquake damage potential and critical scour depth of bridges exposed to flood and seismic hazards under lateral seismic loads

### Earthquake Engineering and Engineering Vibration (2015-12-01) 14: 579-594 , December 01, 2015

Many bridges located in seismic hazard regions suffer from serious foundation exposure caused by riverbed scour. Loss of surrounding soil significantly reduces the lateral strength of pile foundations. When the scour depth exceeds a critical level, the strength of the foundation is insufficient to withstand the imposed seismic demand, which induces the potential for unacceptable damage to the piles during an earthquake. This paper presents an analytical approach to assess the earthquake damage potential of bridges with foundation exposure and identify the critical scour depth that causes the seismic performance of a bridge to differ from the original design. The approach employs the well-accepted response spectrum analysis method to determine the maximum seismic response of a bridge. The damage potential of a bridge is assessed by comparing the imposed seismic demand with the strengths of the column and the foundation. The versatility of the analytical approach is illustrated with a numerical example and verified by the nonlinear finite element analysis. The analytical approach is also demonstrated to successfully determine the critical scour depth. Results highlight that relatively shallow scour depths can cause foundation damage during an earthquake, even for bridges designed to provide satisfactory seismic performance.

## Dynamic shear modulus of undisturbed soil under different consolidation ratios and its effects on surface ground motion

### Earthquake Engineering and Engineering Vibration (2013-12-01) 12: 561-568 , December 01, 2013

The dynamic shear modulus for three types of undisturbed soil under different consolidation ratios is presented by using the resonant column test method. Its effects on surface ground motion is illustrated by calculation. The test results indicate that the power function is a suitable form for describing the relationship between the ratio of the maximum dynamic shear modulus due to anisotropic and isotropic consolidations and the increment of the consolidation ratio. When compared to sand, the increment of the maximum dynamic shear modulus for undisturbed soil due to anisotropic consolidation is much larger. Using a one-dimensional equivalent linearization method, the earthquake influence factor and the characteristic period of the surface acceleration are calculated for two soil layers subjected to several typical earthquake waves. The calculated results show that the difference in nonlinear properties due to different consolidation ratios is generally not very notable, but the degree of its influence on the surface acceleration spectrum is remarkable for the occurrence of strong earthquakes. When compared to isotropic consolidation, the consideration of actual anisotropic consolidation causes the characteristic period to decrease and the earthquake influence factor to increase.

## Damage characteristics and seismic capacity of buildings during Nepal M s 8.1 earthquake

### Earthquake Engineering and Engineering Vibration (2015-09-01) 14: 571-578 , September 01, 2015

The extensive damage to buildings caused by the Nepal *M*_{s} 8.1 earthquake has attracted much attention by the international community. After the preliminary scientific investigations on the different affected areas in Nepal, the construction and damage characteristics of five different types of buildings commonly existing in Nepal were discussed and the reasons of their disaster performance were analyzed. Types of buildings investigated include reinforced concrete (RC) frame structures, rubble structures, brick-wood structures, raw soil structures, and brick-wood structures of historic buildings. In addition, the weak links of the seismic design were pointed out, which was very important for the post-earthquake reconstruction and recovery, and gave a preliminary explanations for the damage experienced.

## Control devices incorporated with shape memory alloy

### Earthquake Engineering and Engineering Vibration (2007-06-01) 6: 159-169 , June 01, 2007

Shape Memory Alloy (SMA) is a type of material that offers some unique characteristics for use in devices for vibration control applications. Based on SMA’s material properties, four types of control devices that incorporate NiTiSMA wires are introduced in this paper, which include three types of dampers (SMA damper, SMA-MR damper and SMA-friction damper) and one kind of isolation bearing (SMA-rubber bearing). Mechanical models of these devices and their experimental verifications are presented. To investigate the control performance of these devices, the SMA-MR damper and SMA-rubber bearing are applied to structures. The results show that the control devices could be effective in reducing the seismic response of structures.

## Seismic vulnerability evaluation of axially loaded steel built-up laced members II: evaluations

### Earthquake Engineering and Engineering Vibration (2008-06-01) 7: 125-136 , June 01, 2008

The test results described in Part 1 of this paper (Lee and Bruneau, 2008) on twelve steel built-up laced members (BLMs) subjected to quasi-static loading are analyzed to provide better knowledge on their seismic behavior. Strength capacity of the BLM specimens is correlated with the strength predicted by the AISC LRFD Specifications. Assessments of hysteretic properties such as ductility capacity, energy dissipation capacity, and strength degradation after buckling of the specimen are performed. The compressive strength of BLMs is found to be relatively well predicted by the AISC LRFD Specifications. BLMs with smaller *kl/r* were ductile but failed to reach the target ductility of 3.0 before starting to fracture, while those with larger *kl/r* could meet the ductility demand in most cases. The normalized energy dissipation ratio, *E*_{C}/*E*_{T} and the normalized compressive strength degradation, *C*_{r}″/*C*_{r} of BLMs typically decrease as normalized displacements *δ*/*δ*_{b,exp} increase, and the ratios for specimens with larger *kl/r* dropped more rapidly than for specimens with smaller *kl/r*; similar trends were observed for the monolithic braces. The BLMs with a smaller slenderness ratio, *kl/r*, and width-to-thickness ratio, *b/t*, experienced a larger number of inelastic cycles than those with larger ratios.

## Attenuation characteristics of ground motions in northern China

### Earthquake Engineering and Engineering Vibration (2002-12-01) 1: 161-166 , December 01, 2002

Four recently developed attenuation models are calibrated by using a very limited amount of strong motion data recorded in China. The research shows that the attenuation characteristics of the earthquake shaking in northern China are similar to those in the western US. The supporting evidence includes Q factors, preliminary results of kappa values, stress drop, shear wave velocity profile in the shallow earth crust, areas enclosed by the isoseismals of Modified Mercalli Intensity V. From these comparisons of different attenuation models, it is recommended that the Crouse and McGuire spectral attenuation model could possibly be used for northern China.

## A SPH simulation on large-amplitude sloshing for fluids in a two-dimensional tank

### Earthquake Engineering and Engineering Vibration (2013-03-01) 12: 135-142 , March 01, 2013

Smoothed particle hydrodynamics (SPH) is a mesh-free adaptive Lagrangian particle method with attractive features for dealing with the free surface flow. This paper applies the SPH method to simulate the large-amplitude lateral sloshing both with and without a floating body, and the vertical parametrically-excited sloshing in a two-dimensional tank. The numerical results show that the SPH approach has an obvious advantage over conventional mesh-based methods in handling nonlinear sloshing problems such as violent fluid-solid interaction, and flow separation and wave-breaking on the free fluid surface. The SPH method provides a new alternative and an effective way to solve these special strong nonlinear sloshing problems.

## Improving the seismic torsional behavior of plan-asymmetric, single-storey, concrete moment resisting buildings with fluid viscous dampers

### Earthquake Engineering and Engineering Vibration (2016-03-01) 15: 61-78 , March 01, 2016

The optimal distribution of fluid viscous dampers (FVD) in controlling the seismic response of eccentric, single-storey, moment resisting concrete structures is investigated using the previously defined center of damping constant (CDC). For this purpose, a number of structural models with different one-way stiffness and strength eccentricities are considered. Extensive nonlinear time history analyses are carried out for various arrangements of FVDs. It is shown that the arrangement of FVDs for controlling the torsional behavior due to asymmetry in the concrete structures is very dependent on the intensity of the peak ground acceleration (PGA) and the extent of the structural stiffness and strength eccentricities. The results indicate that, in the linear range of structural behavior the stiffness eccentricity es which is the main parameter in determining the location of optimal CDC, is found to be less or smaller than the optimal damping constant eccentricity *e**_{d}, i.e., |e*_{d}| > |e_{s}|. But, in the nonlinear range of structural behavior where the strength eccentricity er is the dominant factor in determining the location of optimal CDC, |e*_{d}| > |e_{r}|. It is also concluded that for the majority of the plan-asymmetric, concrete structures considered in this study with e_{r} ≠ 0, the optimal CDC approaches the center of mass as e_{r} decreases.

## Parametric study on performance of bridge retrofitted by unseating prevention devices

### Earthquake Engineering and Engineering Vibration (2006-06-01) 5: 111-118 , June 01, 2006

Over the past decade, seismically induced damage to bridges has been widely reported following major earthquakes such as the 1994 Northridge, 1995 Kobe and 1999 Chi-Chi events. Since these earthquakes, restrainers and stoppers have been installed on bridges to prevent unseating and excessive displacements, respectively. Alternatively, column jacketing has also been proven to be effective. However, the enhanced shear strength may result in extra retrofitting works on the footing. For bridges damaged in the Chi-Chi earthquake, investigations revealed that most bridge columns experienced none-to-minor damage in the longitudinal direction. The reason for this unexpected performance was the construction practice of using a rubber bearing, which is an unbolted design that may slide under large lateral forces. In this paper, parametric studies on simply-supported bridges retrofitted by a restrainer or concrete shear key along the longitudinal and transverse axes were carried out. The research focuses on finding suitable combinations of the design force and gap spacing so the restrainer and concrete shear key can be used as an unseating prevention device, with respect to the allowable column damage in terms of displacement ductility under near-facult type earthquakes. A two-lane PCI-girder bridge was selected as the benchmark model. In the longitudinal direction, a total of nine combinations considering yielding strength and gap spacing for the restrainer were analyzed; while parameters for the concrete shear key were divided into three shear force levels and three gap spacings. In the transverse direction, a similar approach was adapted, except smaller gap spacing was used. For each of the above mentioned earthquakes, seven input ground motions were selected and their PGAs were adjusted to 0.36g and 0.45g as the Design earthquake and Maximum Considerable Earthquake, respectively. Based on the results of nonlinear time history analyses, proper parameters to design the restrainers and concrete shear keys are obtained. Responses obtained from numerical simulations under the Chi-Chi earthquake leaded to new implications to design those devices. Restrainer should not exceed its breaking strain and sufficient unseating length will be needed always. Concrete Shear key was determined by considering both displacement demand of the superstructure and displacement ductility of the column at the same time. Further study is needed to provide optimal design parameters for use in performance based bridge design.

## Numerical analysis on seismic response of Shinkansen bridge-train interaction system under moderate earthquakes

### Earthquake Engineering and Engineering Vibration (2011-03-01) 10: 85-97 , March 01, 2011

This study is intended to evaluate the influence of dynamic bridge-train interaction (BTI) on the seismic response of the Shinkansen system in Japan under moderate earthquakes. An analytical approach to simulate the seismic response of the BTI system is developed. In this approach, the behavior of the bridge structure is assumed to be within the elastic range under moderate ground motions. A bullet train car model idealized as a sprung-mass system is established. The viaduct is modeled with 3D finite elements. The BTI analysis algorithm is verified by comparing the analytical and experimental results. The seismic analysis is validated through comparison with a general program. Then, the seismic responses of the BTI system are simulated and evaluated. Some useful conclusions are drawn, indicating the importance of a proper consideration of the dynamic BTI in seismic design.

## On time-step in structural seismic response analysis under ground displacement/acceleration

### Earthquake Engineering and Engineering Vibration (2009-09-01) 8: 341-347 , September 01, 2009

There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model (DIM) and the Acceleration Input Model (AIM). The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.

## Structural health monitoring of long-span suspension bridges using wavelet packet analysis

### Earthquake Engineering and Engineering Vibration (2007-09-01) 6: 289-294 , September 01, 2007

During the service life of civil engineering structures such as long-span bridges, local damage at key positions may continually accumulate, and may finally result in their sudden failure. One core issue of global vibration-based health monitoring methods is to seek some damage indices that are sensitive to structural damage. This paper proposes an online structural health monitoring method for long-span suspension bridges using wavelet packet transform (WPT). The WPT-based method is based on the energy variations of structural ambient vibration responses decomposed using wavelet packet analysis. The main feature of this method is that the proposed wavelet packet energy spectrum (WPES) has the ability to detect structural damage from ambient vibration tests of a long-span suspension bridge. As an example application, the WPES-based health monitoring system is used on the Runyang Suspension Bridge under daily environmental conditions. The analysis reveals that changes in environmental temperature have a long-term influence on the WPES, while the effect of traffic loadings on the measured WPES of the bridge presents instantaneous changes because of the nonstationary properties of the loadings. The condition indication indices *V*_{D} reflect the influences of environmental temperature on the dynamic properties of the Runyang Suspension Bridge. The field tests demonstrate that the proposed WPES-based condition indication index *V*_{D} is a good candidate index for health monitoring of long-span suspension bridges under ambient excitations.

## Pushover analysis procedure for systems considering SSI effects based on capacity spectrum method

### Earthquake Engineering and Engineering Vibration (2007-09-01) 6: 269-279 , September 01, 2007

This paper presents a new procedure to transform an SSI system into an equivalent SDOF system using twice equivalence. A pushover analysis procedure based on the capacity spectrum method for buildings with SSI effects (PASSI) is then established based on the equivalent SDOF system, and the modified response spectrum and equivalent capacity spectrum are obtained. Furthermore, the approximate formulas to obtain the dynamic stiffness of foundations are suggested. Three steel buildings with different story heights (3, 9 and 20) including SSI effects are analyzed under two far-field and two near-field historical records and an artificial seismic time history using the two PASSI procedures and the nonlinear response history analysis (NL-RHA) method. The results are compared and discussed. Finally, combined with seismic design response spectrum, the nonlinear seismic response of a 9-story building with SSI effects is analyzed using the PASSI procedures, and its seismic performance is evaluated according to the Chinese ‘Code for Seismic Design of Buildings.’ The feasibility of the proposed procedure is verified.

## Field testing of stiffened deep cement mixing piles under lateral cyclic loading

### Earthquake Engineering and Engineering Vibration (2013-06-01) 12: 261-265 , June 01, 2013

Construction of seaside and underground wall bracing often uses stiffened deep cement mixed columns (SDCM). This research investigates methods used to improve the level of bearing capacity of these SDCM when subjected to cyclic lateral loading via various types of stiffer cores. Eight piles, two deep cement mixed piles and six stiffened deep cement mixing piles with three different types of cores, H shape cross section prestressed concrete, steel pipe, and H-beam steel, were embedded though soft clay into medium-hard clay on site in Thailand. Cyclic horizontal loading was gradually applied until pile failure and the hysteresis loops of lateral load vs. lateral deformation were recorded. The lateral carrying capacities of the SDCM piles with an H-beam steel core increased by 3–4 times that of the DCM piles. This field research clearly shows that using H-beam steel as a stiffer core for SDCM piles is the best method to improve its lateral carrying capacity, ductility and energy dissipation capacity.

## A disjoint algorithm for seismic reliability analysis of lifeline networks

### Earthquake Engineering and Engineering Vibration (2002-12-01) 1: 207-212 , December 01, 2002

The algorithm is based on constructing a disjoin kg t set of the minimal paths in a network system. In this paper, cubic notation was used to describe the logic function of a network in a well-balanced state, and then the sharp-product operation was used to construct the disjoint minimal path set of the network. A computer program has been developed, and when combined with decomposition technology, the reliability of a general lifeline network can be effectively and automatically calculated.

## Strength and stiffness reduction factors for infilled frames with openings

### Earthquake Engineering and Engineering Vibration (2014-09-01) 13: 437-454 , September 01, 2014

Framed structures are usually infilled with masonry walls. They may cause a significant increase in both stiffness and strength, reducing the deformation demand and increasing the energy dissipation capacity of the system. On the other hand, irregular arrangements of the masonry panels may lead to the concentration of damage in some regions, with negative effects; for example soft story mechanisms and shear failures in short columns. Therefore, the presence of infill walls should not be neglected, especially in regions of moderate and high seismicity. To this aim, simple models are available for solid infills walls, such as the diagonal no-tension strut model, while infilled frames with openings have not been adequately investigated. In this study, the effect of openings on the strength and stiffness of infilled frames is investigated by means of about 150 experimental and numerical tests. The main parameters involved are identified and a simple model to take into account the openings in the infills is developed and compared with other models proposed by different researchers. The model, which is based on the use of strength and stiffness reduction factors, takes into account the opening dimensions and presence of reinforcing elements around the opening. An example of an application of the proposed reduction factors is also presented.

## Neural network analysis of overturning response under near-fault type excitation

### Earthquake Engineering and Engineering Vibration (2005-12-01) 4: 213-228 , December 01, 2005

Under strong seismic excitation, a rigid block will uplift from its support and undergo rocking oscillations which may lead to (complete) overturning. Numerical and analytical solutions to this highly nonlinear vibration problem are first highlighted in the paper and then utilized to demonstrate how sensitive the overturning behavior is not only to the intensity and frequency content of the base motion, but also to the presence of strong pulses, to their detailed sequence, and even to their asymmetry. Five idealised pulses capable of representing “rupture-directivity” and “fling” affected ground motions near the fault, are utilized to this end: the one-cycle sinus, the one-cycle cosinus, the Ricker wavelet, the truncated (T)-Ricker wavelet, and the rectangular pulse “Overturning-Acceleration Amplification” and “Rotation” spectra are introduced and presented. Artificial neural network modeling is then developed as an alternative numerical solution. The neural network analysis leads to closed-form expressions for predicting the overturning failure or survival of a rigid block, as a function of its geometric properties and the characteristics of the excitation time history. The capability of the developed neural network modeling is validated through comparisons with the numerical solution. The derived analytical expressions could also serve as a tool for assessing the destructiveness of near-fault ground motions, for structures sensitive to rocking with foundation uplift.

## From the editors

### Earthquake Engineering and Engineering Vibration (2005-06-01) 4: iii , June 01, 2005

## A method for computing interstory drift spectra with consideration of gravity effects

### Earthquake Engineering and Engineering Vibration (2010-12-01) 9: 513-521 , December 01, 2010

Vertical loads such as gravity may have an important influence on the seismic response of buildings. In this paper, the continuous shear-beam model is extended to study the seismic demand of shear buildings with consideration of the gravity load effect under near-field ground motions. An analytical solution of the free motion equation of as gravity shear beam model is provided in terms of a Bessel series. A method for computing interstory drift spectra is proposed. The interstory drift spectra for two near-field records with distinct pulses are presented to illustrate the effects of gravity and the damping ratio. The interstory drift spectra are also used to analyze the spectral characteristics of near fault ground motion during the 2008 Wenchuan earthquake. The effects of the gravity load ratio, damping ratio and higher modes are investigated and discussed.

## Simulation of large-scale numerical substructure in real-time dynamic hybrid testing

### Earthquake Engineering and Engineering Vibration (2014-12-01) 13: 599-609 , December 01, 2014

A solution scheme is proposed in this paper for an existing RTDHT system to simulate large-scale finite element (FE) numerical substructures. The analysis of the FE numerical substructure is split into response analysis and signal generation tasks, and executed in two different target computers in real-time. One target computer implements the response analysis task, wherein a large time-step is used to solve the FE substructure, and another target computer implements the signal generation task, wherein an interpolation program is used to generate control signals in a small time-step to meet the input demand of the controller. By using this strategy, the scale of the FE numerical substructure simulation may be increased significantly. The proposed scheme is initially verified by two FE numerical substructure models with 98 and 1240 degrees of freedom (DOFs). Thereafter, RTDHTs of a single frame-foundation structure are implemented where the foundation, considered as the numerical substructure, is simulated by the FE model with 1240 DOFs. Good agreements between the results of the RTDHT and those from the FE analysis in ABAQUS are obtained.

## Seismic performance of an existing bridge with scoured caisson foundation

### Earthquake Engineering and Engineering Vibration (2014-08-01) 13: 151-165 , August 01, 2014

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.

## Precise integration method without inverse matrix calculation for structural dynamic equations

### Earthquake Engineering and Engineering Vibration (2007-03-01) 6: 57-64 , March 01, 2007

The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.

## Discussion 1 on “Introspection on improper seismic retrofit of Basilica Santa Maria di Collemaggio after 2009 Italian earthquake” by G.P. Cimellaro, A.M.Reinhorn and A. De Stefano

### Earthquake Engineering and Engineering Vibration (2012-06-01) 11: 281-282 , June 01, 2012

## Identification and imaging of soil and soil-pile deformation in the presence of liquefaction

### Earthquake Engineering and Engineering Vibration (2006-12-01) 5: 171-182 , December 01, 2006

A simple identification technique is developed to visualize the dynamic deformation mechanisms of centrifuge models of saturated soil and soil-pile systems using the measurements provided by sparsely distributed sensors. Cross-correlation analyses are employed first to assess the variation of shear wave velocity profile with time as soil experiences stiffness reduction and degradation during dynamic excitations. The corresponding time-dependent modal configurations are determined using the finite-element technique. These configurations are used along with recorded motions to evaluate optimal time histories of displacement and strain fields based on a spectral motion reconstruction. Visualizations of the response of infinite slope and soil-pile centrifuge models revealed salient and complex multi-dimensional deformation patterns, especially at high pore pressure ratios. The developed technique provides an effective tool to visualize and analyze the dynamic response of centrifuge, shake-table and field soil systems.

## Control strategies and experimental verifications of the electromagnetic mass damper system for structural vibration control

### Earthquake Engineering and Engineering Vibration (2008-06-01) 7: 181-192 , June 01, 2008

The electromagnetic mass damper (EMD) control system, as an innovative active control system to reduce structural vibration, offers many advantages over traditional active mass driver/damper (AMD) control systems. In this paper, studies of several EMD control strategies and bench-scale shaking table tests of a two-story model structure are described. First, two structural models corresponding to uncontrolled and Zeroed cases are developed, and parameters of these models are validated through sinusoidal sweep tests to provide a basis for establishing an accurate mathematical model for further studies. Then, a simplified control strategy for the EMD system based on the pole assignment control algorithm is proposed. Moreover, ideal pole locations are derived and validated through a series of shaking table tests. Finally, three benchmark earthquake ground motions and sinusoidal sweep waves are imposed onto the structure to investigate the effectiveness and feasibility of using this type of innovative active control system for structural vibration control. In addition, the robustness of the EMD system is examined. The test results show that the EMD system is an effective and robust system for the control of structural vibrations.

## Statistical damage detection method for frame structures using a confidence interval

### Earthquake Engineering and Engineering Vibration (2010-03-01) 9: 133-140 , March 01, 2010

A novel damage detection method is applied to a 3-story frame structure, to obtain statistical quantification control criterion of the existence, location and identification of damage. The mean, standard deviation, and exponentially weighted moving average (EWMA) are applied to detect damage information according to statistical process control (SPC) theory. It is concluded that the detection is insignificant with the mean and EWMA because the structural response is not independent and is not a normal distribution. On the other hand, the damage information is detected well with the standard deviation because the influence of the data distribution is not pronounced with this parameter. A suitable moderate confidence level is explored for more significant damage location and quantification detection, and the impact of noise is investigated to illustrate the robustness of the method.

## Assessment of seismic design response factors of concrete wall buildings

### Earthquake Engineering and Engineering Vibration (2011-03-01) 10: 115-127 , March 01, 2011

To verify the seismic design response factors of high-rise buildings, five reference structures, varying in height from 20- to 60-stories, were selected and designed according to modern design codes to represent a wide range of concrete wall structures. Verified fiber-based analytical models for inelastic simulation were developed, considering the geometric nonlinearity and material inelasticity of the structural members. The ground motion uncertainty was accounted for by employing 20 earthquake records representing two seismic scenarios, consistent with the latest understanding of the tectonic setting and seismicity of the selected reference region (UAE). A large number of Inelastic Pushover Analyses (IPAs) and Incremental Dynamic Collapse Analyses (IDCAs) were deployed for the reference structures to estimate the seismic design response factors. It is concluded that the factors adopted by the design code are adequately conservative. The results of this systematic assessment of seismic design response factors apply to a wide variety of contemporary concrete wall buildings with various characteristics.

## Seismic response of underground utility tunnels: shaking table testing and FEM analysis

### Earthquake Engineering and Engineering Vibration (2010-12-01) 9: 555-567 , December 01, 2010

Underground utility tunnels are widely used in urban areas throughout the world for lifeline networks due to their easy maintenance and environmental protection capabilities. However, knowledge about their seismic performance is still quite limited and seismic design procedures are not included in current design codes. This paper describes a series of shaking table tests the authors performed on a scaled utility tunnel model to explore its performance under earthquake excitation. Details of the experimental setup are first presented focusing on aspects such as the design of the soil container, scaled structural model, sensor array arrangement and test procedure. The main observations from the test program, including structural response, soil response, soil-structure interaction and earth pressure, are summarized and discussed. Further, a finite element model (FEM) of the test utility tunnel is established where the nonlinear soil properties are modeled by the Drucker-Prager constitutive model; the master-slave surface mechanism is employed to simulate the soil-structure dynamic interaction; and the confining effect of the laminar shear box to soil is considered by proper boundary modeling. The results from the numerical model are compared with experiment measurements in terms of displacement, acceleration and amplification factor of the structural model and the soil. The comparison shows that the numerical results match the experimental measurements quite well. The validated numerical model can be adopted for further analysis.

## Dynamic finite element model updating of prestressed concrete continuous box-girder bridge

### Earthquake Engineering and Engineering Vibration (2009-09-01) 8: 399-407 , September 01, 2009

The dynamic finite element model (FEM) of a prestressed concrete continuous box-girder bridge, called the Tongyang Canal Bridge, is built and updated based on the results of ambient vibration testing (AVT) using a real-coded accelerating genetic algorithm (RAGA). The objective functions are defined based on natural frequency and modal assurance criterion (MAC) metrics to evaluate the updated FEM. Two objective functions are defined to fully account for the relative errors and standard deviations of the natural frequencies and MAC between the AVT results and the updated FEM predictions. The dynamically updated FEM of the bridge can better represent its structural dynamics and serve as a baseline in long-term health monitoring, condition assessment and damage identification over the service life of the bridge.

## A method for stochastic seismic response analysis of non-classically damped structures

### Earthquake Engineering and Engineering Vibration (2004-06-01) 3: 75-84 , June 01, 2004

A method to calculate the stationary random response of a non-classically damped structure is proposed that features clearly-defined physical meaning and simple expression. The method is developed in the frequency domain. The expression of the proposed method consists of three terms, i.e., modal velocity response, modal displacement response, and coupled (between modal velocity and modal displacement response). Numerical results from the parametric study and three example structures reveal that the modal velocity response term and the coupled term are important to structural response estimates only for a dynamic system with a tuned mass damper. In typical cases, the modal displacement term can provide response estimates with satisfactory accuracy by itself, so that the modal velocity term and coupled term may be ignored without loss of accuracy. This is used to simplify the response computation of non-classically damped structures. For the white noise excitation, three modal correlation coefficients in closed form are derived. To consider the modal velocity response term and the coupled term, a simplified approximation based on white noise excitation is developed for the case when the modal velocity response is important to the structural responses. Numerical results show that the approximate expression based on white noise excitation can provide structural responses with satisfactory accuracy.

## Dynamic performance of angle-steel concrete columns under low cyclic loading-I: Experimental study

### Earthquake Engineering and Engineering Vibration (2008-03-01) 7: 67-75 , March 01, 2008

This paper describes low cyclic loading testing of nine angle-steel concrete column (ASCC) specimens. In the tests, the influence of the shear-span ratio, axial compression ratio and shear steel plate ratio on the hysteretic behavior, energy dissipation, strength degradation, stiffness degradation, skeleton curve and ductility of the ASCCs is studied. Based on the test results, some conclusions are presented. The *P*-*Δ* and sectional *M* — *ϕ* hysteretic models for the ASCCs are presented in a companion paper (Zheng and Ji, 2008).

## Performance evaluation of a novel rotational damper for structural reinforcement steel frames subjected to lateral excitations

### Earthquake Engineering and Engineering Vibration (2014-03-01) 13: 75-84 , March 01, 2014

In this study, a novel rotational damper called a Rotational Friction Viscoelastic Damper (RFVD) is introduced. Some viscoelastic pads are added to the Rotational Friction Damper (RFD) in addition to the friction discs used in this conventional device. Consequently, the amount of energy dissipated by the damper increases in low excitation frequencies. In fact, the input energy to the structure is simultaneously dissipated in the form of friction and heat by frictional discs and viscoelastic pads. In order to compare the performance of this novel damper with the earlier types, a set of experiments were carried out. According to the test results, the RFVD showed a better performance in dissipating input energy to the structure when compared to the RFD. The seismic behavior of steel frames equipped with these dampers was also numerically evaluated based on a nonlinear time history analysis. The numerical results verified the performance of the dampers in increasing the energy dissipation and decreasing the energy input to the structural elements. In order to achieve the maximum dissipated energy, the dampers need to be installed in certain places called critical points in the structure. An appropriate approach is presented to properly find these points. Finally, the performance of the RFVDs installed at these critical points was investigated in comparison to some other configurations and the validity of the suggested method in increasing the energy dissipation was confirmed.

## Simplified seismic fatigue evaluation for rigid steel connections

### Earthquake Engineering and Engineering Vibration (2003-12-01) 2: 245-253 , December 01, 2003

A simplified fatigue-life model is proposed for assessing the seismic inelastic rotational capacity of steel connections. First relations are developed for rigid steel connections under lateral loading. Next this is extended to account for the effects of the welded steel moment frame (WSMF) connections of the so-called pre-Northridge type. The seismic fatigue theory is validated against experimental results. The experiments were conducted under increasing ductility amplitudes until the onset of fracture. Miner’ rule was used to convert the test results to given an equivalent constant amplitude cyclic fatigue life. Satisfactory agreement is obtained when comparing the experimental observations with the theoretical predictions.

## Performance of sand and shredded rubber tire mixture as a natural base isolator for earthquake protection

### Earthquake Engineering and Engineering Vibration (2015-12-01) 14: 683-693 , December 01, 2015

The performance of a well-designed layer of sand, and composites like layer of sand mixed with shredded rubber tire (RSM) as low cost base isolators, is studied in shake table tests in the laboratory. The building foundation is modeled by a 200 mm by 200 mm and 40 mm thick rigid plexi-glass block. The block is placed in the middle of a 1m by 1m tank filled with sand. The selected base isolator is placed between the block and the sand foundation. Accelerometers are placed on top of the footing and foundation sand layer. The displacement of the footing is also measured by LVDT. The whole setup is mounted on a shake table and subjected to sinusoidal motions with varying amplitude and frequency. Sand is found to be effective only at very high amplitude (> 0.65 g) of motions. The performance of a composite consisting of sand and 50% shredded rubber tire placed under the footing is found to be most promising as a low-cost effective base isolator.