Bi-directional Earthquake Excitations Research Articles

Effect of Lead Core Heating on Residual Displacements of Lead Rubber Bearings Under Bi-Directional Earthquake Excitations

ABSTRACT This paper investigates the variation in residual displacements (RDs) of lead rubber bearings (LRBs) subjected to bi-directional earthquake excitations when lead core heating effect is of concern. Accordingly, several dynamic analyses were conducted considering isolator response with and without lead core heating effect. A wide range of isolation system properties, several characteristic strength to weight ratios, isolation periods and yield displacements were considered to construct the bi-linear force-displacement relations of LRBs. Ground motions were selected to represent different magnitudes and pulse characteristics. Results were also used to assess the efficacy of code suggested equations to estimate RDs of seismic isolators.

In-plan distribution of peak floor acceleration demands in torsionally irregular buildings

The precise estimation of peak floor acceleration demands is essential to ensure the seismic safety of building contents and attachments. The present study aims to investigate the distribution of the peak floor acceleration demands across the floor plan in torsionally irregular buildings. To achieve this objective, 28 mid-rise reinforced concrete buildings with torsional irregularities are analyzed under 5600 bidirectional earthquake excitations, considering various strength ratios in buildings. A total of 2,59,200 in-structure amplification factors are estimated at multiple locations within the building plan and also at different floors. It is observed that current seismic design codes tend to underestimate the in-structure amplification factor for torsionally irregular buildings, particularly at locations distant from the center of rigidity (towards flexible frames), by up to 137 % for elastic buildings, and up to 54 % for moderately inelastic buildings. Even in the case of frames closer to the stiff frames, the seismic design codes underestimated the in-structure amplification factor by up to 68 % for elastic buildings. It is observed that a strong relationship exists between the torsional amplification of the peak floor acceleration and displacement amplification due to building torsion at the floor of interest. The torsional amplification of peak floor acceleration is found to be approximately equal to torsional displacement amplification for the flexible frames at the floor of interest. Simplified equations are developed for their integration with existing building codes to precisely estimate the in-plan distribution of peak floor acceleration demands in torsionally irregular buildings.

Bidirectional performance assessment of UFREI-isolated structures with single and multiple tuned mass dampers under earthquakes and winds

An innovative hybrid vibration controller (HVC) composed of unbonded fiber-reinforced elastomeric isolators (UFREIs) and tuned mass dampers (TMDs) is utilized for the vibration control of an existing hospital building under the multi-hazard scenario of earthquakes and (nonconcurrent) winds. A 3-dimensional nonlinear model of the considered hospital building is analyzed. Four configurations of the HVC are investigated, wherein single or multiple TMDs are utilized, having various tuning properties and locations along the height of the building. All the various controlled and uncontrolled structures are subjected to site-specific bidirectional earthquake and wind excitations. Results reveal that the HVC with two TMDs, having favorable tuning conditions for both earthquakes and winds, are the most efficient under the multi-hazard scenario. Interestingly, the increase in the TMD mass ratio always improves the performance of the HVC under wind excitations, however under earthquakes, it may also result in enhanced deterioration of HVC performance in detuned conditions.

Seismic multi-objective stochastic parameters optimization of multiple tuned mass damper system for a large podium twin towers structure

The lateral-torsional coupled dynamic response under earthquake excitation is a critical problem for eccentric building structures. To control the hazardous coupled seismic response, a tuned mass damper (TMD) is an attractive vibration control device. A multiple TMD (MTMD) system, which is composed by several TMDs with different frequencies and damping ratios, has a better structural control effect under stochastic excitation with a wide frequency range such as earthquake. To improve the lateral-torsional coupled seismic mitigation performance of MTMD for eccentric structures, a multi-objective stochastic parameters optimization method is proposed, and a building with a large podium and twin towers is proposed as the case study. Considering the randomness of earthquakes, a stationary white noise stochastic process based on the Kanai-Tajimi spectrum is used as the input in the optimization. According to structural modal shapes, three TMDs are distributed in the podium, left tower and right tower respectively in the X direction, and two TMDs are in the left tower and right tower respectively in the Y direction, while both the maximum and root mean square (RMS) displacements of top stories of the podium, left tower and right tower are all considered in the optimization. Artificial fish swarm algorithm (AFSA) is used to search optimized parameters of MTMD in this study. For comparison, a MTMD system designed based on the traditional method is presented. Numerical results show that under bi-directional earthquake excitations, the proposed MTMD system has the best seismic mitigation effect generally, in both displacement and acceleration responses. Though the proposed MTMD system is aimed at X- and Y- directional translational responses, it can control torsional responses effectively as well.

Peak floor acceleration demands in torsionally irregular buildings

AbstractAccurate estimation of the peak floor acceleration (PFA) plays a crucial role in ensuring the seismic safety of a building, its contents, and attachments. This study investigates amplification in PFA due to building torsion. Torsionally irregular reinforced‐concrete moment‐resisting frame buildings are analyzed under bidirectional earthquake excitations for five levels of ductility demands. A total of 5600 nonlinear dynamic analyses are conducted on the considered buildings while subjected to the far‐field ground motions suite. It is shown that the existing code provisions significantly underpredict the PFA demands at the flexible edge of elastic and moderately inelastic torsionally irregular buildings. The torsional amplification factors for PFA demands depend on the building's torsional and strength characteristics. Further, these torsional amplification factors are correlated well with the building's elastic floor displacement‐based torsional irregularity indices. Practice‐oriented equations are proposed to predict the torsional amplification factors for PFA demands in torsionally irregular buildings. The proposed equations can be easily used after estimating the elastic floor displacement‐based torsional irregularity indices using the modal superposition method. When applied with the latest ASCE 7 provisions, the proposed equations provide reasonably accurate estimates of the PFA demands in torsionally irregular buildings.

Bi-directional semi-active tuned mass damper for torsional asymmetric structural seismic response control

Tuned mass damper (TMD) is a popular vibration absorber. To improve the seismic protection performance of a bi-directional passive TMD, a bi-directional semi-active TMD (BSTMD) with adaptive stiffness, variable mass and semi-active damping is proposed in this study. The BSTMD can adapt to structural X- and Y-directional instantaneous frequencies at the same time under bi-directional ground motions, which are identified through wavelet transform (WT), and the instantaneous angle of a diamond spring device is adjusted according to the instantaneous frequency ratio of two directions, which means that the stiffness ratio of two directions is retuned first. Then, the mass is retuned to match the exact instantaneous frequency. At last, the semi-active damping is realized according to an extended output signals-based control algorithm. A two-directional asymmetric torsional benchmark model is proposed as a case study. For comparison, two optimal passive TMDs implemented in X and Y directions separately and two unidirectional STMDs with variable stiffness and damping implemented in X and Y directions separately are investigated as well. Numerical results show that under bi-directional earthquake excitations in the benchmark problem, the two optimal passive TMDs have a good control effect. Two unidirectional STMDs have the best aseismic mitigation effect generally, in both lateral and torsional dynamic responses; while the BSTMD has a comparable control effect with less electromechanical devices, and can reduce the stroke of unidirectional STMD to a great degree. Though the BSTMD is aimed at X- and Y- directional dynamic responses, it can control torsional responses effectively as well, and when the eccentricity is enlarged to double, it remains effective for seismic mitigation.

Floor displacement-based torsional amplification factors for seismic design of acceleration-sensitive non-structural components in torsionally irregular RC buildings

In this study, the effects of inherent building torsion on the seismic response of acceleration-sensitive non-structural components are investigated. To achieve this objective, a group of elastic torsionally irregular step-back reinforced concrete moment-resisting frame buildings are analyzed under bi-directional earthquake excitations. The floor torsional amplification factors, defined as the ratio between the floor spectral ordinate at the flexible/stiff edge to the floor spectral ordinate at the center of rigidity, are obtained as a function of the tuning ratio for varying damping ratios of non-structural components. The correlations of the peak torsional amplification factors at different floors for the rigid and flexible non-structural components are studied with their floor displacement-based torsional irregularity indices, recommended in the national building codes of the United States and India. It is observed that the torsional amplification factors are building characteristics and tuning ratio-dependent. These torsional amplification factors are further observed to be well-correlated with the corresponding floor displacement-based torsional irregularity indices for both the rigid and flexible non-structural components. Contrarily, the torsional amplification factors for the very flexible non-structural components tend to unity and are thereby observed to be independent of the characteristics of both the building and the non-structural components. Simplified and numerically validated, floor displacement-based models are proposed to compute the torsional amplification factors, which can be used in aggregation with the existing codes to design acceleration-sensitive non-structural components in torsionally irregular buildings.

Seismic performance assessment of reinforced concrete hilly buildings with open story

This study focuses on investigating the effect of one or more open stories in reinforced concrete hilly buildings. Two building configurations, i.e., (i) stepback and (ii) split-foundation, with three different story ratios, are considered. Open stories are provided at different levels in a building according to the prospective location of the approach road level. These buildings are subjected to bi-directional earthquake excitation, and non-linear dynamic analyses are performed under a suite of 22 ground motion records. Dynamic characteristics and seismic responses such as peak inter-story drift ratio, peak floor acceleration, peak roof displacement, and maximum story shear of the buildings are investigated. A probabilistic performance assessment of these buildings with different probable locations of the open story is presented. In general, the probabilistic assessment reveals that the presence of the open story significantly reduces the seismic performance of these buildings. Moreover, the buildings with the open story at the uppermost foundation level are found to be the most vulnerable under earthquake excitation.

Attaining Optimum Passive Control in Liquid-Storage Tank by Using Multiple Vertical Baffles

AbstractThe effect of vertical baffles as the passive control in liquid storage tanks (LSTs) on the reduction of seismic responses was investigated for bidirectional earthquake excitations. Various...

Comparative Study of Cyclic and Shake Table Tests for Simple for Dead Load and Continuous for Live Load Steel Bridge System in Seismic Area

A new superstructure to pier connection for simple for dead load and continuous for live load (SDCL) steel bridge system in seismic areas was developed. As proof of concept, component level and system level tests were carried out on scale models. The component test was conducted under cyclic loading and the results showed satisfactory performance conforming to design standards. The same detail was incorporated in a system level shake table testing which was subjected to bidirectional earthquake excitations. The results showed that the connection behaved well under high levels of drift and acceleration. The capacity protected elements sustained minimal damage and the plastic hinge was limited to a predefined location in the column. In this paper, a summary of results from both tests is presented and compared. The results showed that the SDCL components remained within the elastic range. It was concluded that the dowel bars in the cap beam are the main load-carrying elements under excitations in the longitudinal direction of the bridge and the provisions of current design codes are adequate for the design of these reinforcing bars. Both test protocols showed similar behavior despite the differences in construction methods and material properties.

Performance improvement of base isolation systems by incorporating eddy current damping and magnetic spring under earthquakes

An innovative subsystem with the incorporation of eddy current (EC) damping and magnetic negative stiffness spring (MNSS) is proposed to develop feasible strategies for performance improvement of existing base isolation techniques. The concept of integrating the eddy current damping mechanism and the nonlinear negative stiffness spring is firstly introduced for better energy transition behavior under earthquake excitations. The analytical expressions of the force characteristics of the EC and the MNSS components are presented accordingly, and a parametric study is conducted to evaluate the inherent properties of the integrated magnetic subsystem. To demonstrate the advantages of the EC–MNSS subsystem, an illustrative example of a two-DOF model simulating both the superstructure and the isolation layer is numerically investigated by adopting two representative isolators and the proposed subsystem. The EC–MNSS subsystem is illustrated to significantly and simultaneously improve the isolation performances in terms of base drift and structural acceleration. The energy exchange and dissipation behavior are further revealed by employing time history analysis and energy-displacement-velocity plots. Furthermore, the proposed EC–MNSS subsystem is implemented in a benchmark isolation problem adopting an eight-story frame structure subjected to bidirectional earthquake excitations. The simulation results indicate the superior and the comparable performances of the integrated isolation system as compared to those of the passive and the control-augmented isolations, respectively.

Shaking table tests of bridge model with friction sliding bearings under bi-directional earthquake excitations

The widespread use of seismic isolation to protect structures from damage has already been proven as an effective and economical method. In order to investigate the seismic performance and isolation effect of isolated bridge with the traditional friction pendulum bearing (FPB) and the novel triple friction pendulum bearing (TFPB), the force–displacement hysteretic relationships of FPB and TFPB were validated by the displacement-controlled tests, and the shaking table tests were carried out on a 1/10 scaled simple-supported bridge model with FPBs and TFPBs under bi-directional earthquake excitations. The effects of the friction coefficients and the radius of the TFPB on the seismic responses were analysed using the extensive experimental results. The experimental data and the numerical results show that the TFPB can be reliably used for the passive device to control the seismic response of the bridge, which could satisfy the demand of performance-based seismic design philosophy in high seismicity regions. In addition, the results illustrate that the bi-directional interaction of the TFPB has effects on the dynamic responses of the bridge. If the bi-directional interaction is ignored, the deck displacements are underestimated, which can be crucial from the design point of view.

Modeling of high damping rubber bearings under bidirectional shear loading

The behavior of high damping rubber bearings is highly complex. The models that are currently available are generally limited to unidirectional motion and, in most cases, difficult to extend to general bidirectional loading. One of the major limitations is their inability to characterize the behavior of the bearings at different levels of shear deformation. In the present work, a set of bidirectional models are presented, obtained by combining relatively simple bi-dimensional formulations. The models are calibrated over a set of unidirectional test data and are shown to accurately describe the response of the bearings at low, intermediate and high strain levels using a single set of parameters. Validation is carried out using bidirectional displacement-controlled tests available in the literature and numerical simulations are performed of a base-isolated building subjected to free vibration and bidirectional earthquake excitation.

Evaluation of ASCE 61-14 NSPs for the estimation of seismic demands in marginal wharves

The Standard ASCE 61-14 proposes the Substitute Structure Method (SSM) as a Nonlinear Static Procedure (NSP) to estimate nonlinear displacement demands at the center of mass of piers or wharves under seismic actions. To account for bidirectional earthquake excitation according to the Standard, results from independent pushover analyses in each orthogonal direction should be combined using either a 100/30 directional approach or a procedure referred to as the Dynamic Magnification Factor, DMF. The main purpose of this paper is to present an evaluation of these NSPs in relation to four wharf model structures on soil conditions ranging from soft to medium dense clay. Results from nonlinear static analyses were compared against benchmark values of relevant Engineering Design Parameters, EDPs. The latter are defined as the geometric mean demands that are obtained from nonlinear dynamic analyses using a set of 30 two-component ground motion records. It was found that SSM provides close estimates of the benchmark displacement demands at the center of mass of the wharf structures. Furthermore, for the most critical pile connection at a landside corner of the wharf the 100/30 and DMF approaches produced displacement, curvature, and force demands that were reasonably comparable to corresponding benchmark values.

Earthquake response of continuous girder bridge for high-speed railway: A shaking table test study

Continuous girder bridges for high-speed railway (HSR) are increasingly used to overcome undulating terrain and to provide a flat surface for high-speed travel. Only a few dynamic experiments have been applied to such bridges, none of them focusing on HSR continuous girder bridges. The aim of this paper is to use experimental results to investigate the earthquake response of bridges of this type constructed in China. To address this aim, a 1/12-scale typical Chinese HSR continuous girder bridge specimen was constructed and the experimental procedures were detailed. From the experimental results it was found that the first natural frequency of piers was obviously decreased after the specimen was subjected to the peak ground acceleration of 0.38 g earthquake excitation. The acceleration response observed at the top of piers increased with the increase of earthquake intensity, and the concrete at the bottom of piers was cracked when the peak ground acceleration exceeded 0.20 g. The results also showed that a fixed bearing installed on the HSR bridge was damaged under 0.32 g earthquake excitation, whereas no damage was found in a girder for all test scenarios (i.e., from 0.15 g to 0.38 g). In addition, compared to unidirectional earthquake excitation, the earthquake response increased under bidirectional earthquake excitation. The experimental procedures and findings can be used as benchmarks for practical applications or for further similar experiments.

Seismic capacity estimation of a reinforced concrete containment building considering bidirectional cyclic effect

This study serves to estimate the seismic capacity of the reinforced concrete containment building considering its bidirectional cyclic effect and variations of energy. The implementation of the capacity estimation has been performed by extending two well-known methods: nonlinear static pushover and incremental dynamic analysis. The displacement and dissipated energy demands are obtained from the static pushover analysis considering bidirectional cyclic effect. In total, 18 bidirectional earthquake intensity parameters are developed to perform the incremental dynamic analysis for the reinforced concrete containment building. Results show that the bidirectional static pushover analysis tends to decrease the capacity of the reinforced concrete containment building in comparison with unidirectional static pushover analysis. The 5% damped first-mode geometric mean spectral acceleration strongly correlates with the maximum top displacement of the containment building. The comparison of the incremental dynamic analysis and static pushover curves is employed to determine the seismic capacity of the reinforced concrete containment building. It is concluded that bidirectional static pushover and incremental dynamic analysis studies can be used in performance evaluation and capacity estimation of reinforced concrete containment buildings under bidirectional earthquake excitations.

Performance comparison of Kalman−based filters for nonlinear structural finite element model updating

Finite element (FE) model updating has emerged as a powerful technique for structural health monitoring and damage identification of civil structures. Updating mechanics-based nonlinear FE models allows for a complete and comprehensive damage diagnosis of large and complex structures, but it is computationally demanding. This paper first introduces an Iterated Extended Kalman filter (IEKF) to update mechanics-based nonlinear FE models of civil structures. Different model updating techniques using the Extended Kalman filter (EKF), Unscented Kalman Filter (UKF) and IEKF, are then compared for their performance in terms of convergence, accuracy, robustness, and computational demand. Finally, a non-recursive estimation procedure is presented and its effectiveness in reducing the computational cost, while maintaining accuracy and robustness, is demonstrated. An application example is presented based on numerically simulated response data for a three-dimensional 5-story 2-by-1 bay reinforced concrete (RC) frame building subjected to bi-directional earthquake excitation. Excellent estimation results are obtained with the EKF, UKF, and IEKF used in conjunction with the proposed non-recursive estimation approach. Because of the analytical linearization used in the EKF and IEKF, abrupt and large jumps in the estimates of the model parameters are observed with these filters, which may lead to divergence of the nonlinear FE model solution procedure. The UKF slightly outperforms the EKF and IEKF, but at a higher computational cost.

Nonlinear seismic response of a base isolated single pylon cable-stayed bridge

The vulnerability of single pylon cable-stayed bridges under strong ground motions are of great concern to both researchers and engineers. This paper investigates the seismic performance of reinforced concrete (RC) single pylon cable-stayed bridge equipped with friction sliding bearings under bi-directional earthquake excitations. Three-dimensional numerical models, consisting of the dynamic p-y elements, the fiber elements and the multi-layer shell elements, were developed in this study based on the prototype of a single pylon cable-stayed bridge in Guizhou Province, China, to investigate its seismic response. Three different types of friction sliding bearings were implemented between the base of the RC pier and the pile foundation to mitigate the dynamic response of the bridge superstructure under strong ground motions. The results of the nonlinear time history analyses indicate that friction sliding bearings can effectively reduce the base shear and the bending moment of the RC pier, as well as the seismic responses of substructure, at the cost of increasing the absolute displacement of the deck. To reduce the deck displacement, viscous dampers were implemented in parallel to the friction sliding bearings. Parametric studies and optimization analyses were performed on the critical parameters of the viscous dampers with the target of minimizing the absolute displacement of the deck and reducing the base shear of the RC pier to an acceptable level. The numerical results show that implementation of friction sliding bearings together with the viscous dampers is an effective seismic control approach to mitigate the seismic damage of the single pylon cable-stayed bridge.

Experimental assessment of the cyclic response of friction-based isolators under bidirectional motions

Experimental research on the lateral response of Concave Surface Sliders (CSS) under bi-directional earthquake excitations has shown significant differences in comparison to the uni-directional case. This is mainly due to the stepwise variation of the direction of the frictional force, which is assumed to be parallel to the device trajectory; on the other hand recentering force can still be considered as directed towards the centre of the device. The present endeavor shows results of a wide experimental campaign on a full-scale CSS device, according to a special testing protocol with both uni-directional and bi-directional dynamic tests. Results have shown non-negligible discrepancies in the hysteretic loops of the device between the bi-axial interaction of the directions of motion, in comparison to radial motions: such a behaviour is expected to significantly influence the overall response of a base-isolated structural system, if it is not properly modeled.

Seismic Fragility of a Typical Containment under Bidirectional Earthquake Excitations

Existing research to predict seismic fragility of Reinforced Concrete Containment (RCC) buildings does not take into account the impact of its inelastic bidirectional interaction arising from bidirectional horizontal ground motions. Hence, this study attempts to present a reliable and feasible method for fragility of the RCC subject to bidirectional ground motions. Three bidirectional load histories due to inelastic bidirectional interaction are firstly introduced to determine displacement-based failure limits for this structure. Nine bidirectional earthquake Intensity Measures (IMs) are developed to perform the bidirectional Incremental Dynamic Analysis (IDA). For the selection of an optimum method for fragility under bidirectional earthquake excitations, three fragility analysis methods are conducted and their results are compared. Results show that the maximum likelihood method yields better fragility results than the other two methods. The safety factor method for fragility cannot get the aleatory randomness properly. Besides, the first-mode geometric mean spectral acceleration SaGM (T1) is found to strongly correlate with the demand measure for the RCC and is suggested for deriving fragility curves for such structures under bidirectional earthquake excitations.