Bidirectional Earthquake Research Articles

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.

Absolute Instantaneous Optimal Control Performance Index for Active Vibration Control of Structures under Seismic Excitation

In this paper, an instantaneous optimal control performance index for active control of structures under seismic excitation is analytically proposed. Absolute velocity and absolute displacement terms are implemented to the conventional state vector terms and eventually to the resulting performance index expression. The seismic response reduction effectiveness of the proposed performance index is compared with the linear quadratic regulator control (LQR). For numerical verification of the performance index, an eight‐story shear building with a fully active tendon controller system under unidirectional earthquake is considered as the first example. For a more complex model, a three‐dimensional tier building under the effect of bidirectional earthquakes is selected as second numerical example. Unidirectional near fault and bidirectional near fault earthquakes are used in the simulations. The control energy demand of each control method is also considered in the comparison. It is obtained from numerical simulations that the proposed performance index is as effective as LQR in attenuating structural vibrations. However, the resulting performance index does not require a priori knowledge of the seismic excitation like the LQR. The nonlinear Riccati matrix equation solution of the LQR is not required in the proposed performance index as well.

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.

Seismic Response of Base-isolated CRLSS Considering Nonlinear Elasticity of Concrete

The purpose of this paper is to study the seismic response of a base-isolated, concrete rectangular liquid-storage structure (CRLSS) under small-amplitude sloshing. In this study, the three-dimensional FEM of the base isolated CRLSS is established by using ADINA. The concrete material is assumed to be nonlinear and elastic, and the criterion for the small amplitude sloshing is defined to determine the seismic response of a base-isolated CRLSS under different conditions. The results show that when small-amplitude sloshing occurs and the nonlinear elasticity of the concrete material is considered, the displacement of wallboard, the height of liquid sloshing and the equivalent stress are increased with the increase in the earthquake intensity when comparing the same liquid height and different intensities of a bidirectional earthquake. The liquid height is found to affect the seismic response of the base-isolated CRLSS. The lower the liquid height is, the larger the equivalent stress is, and the greater the displacement of the wallboard and the amplitude of the liquid sloshing are.

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.

Modeling and Simulation of Reinforced Concrete Shear Wall under Bidirectional Earthquake Action

Reinforced concrete shear walls under bidirectional earthquake action were taken as research object, and discretized into irregular polygons in plane, which were stretched into prisms along thickness direction of the wall. Multiple concrete spring points were distributed at side edges of the prism, deformation of concrete spring points were separately considered in axial directions and tangential directions, and they were mutually coupled in stiffness and strength. Reinforced spring points were arranged at intersection points between reinforcements and polygon prisms, and dowel action of reinforcements were neglected. Through a comparison between numerical simulation results and model test results, it could be seen that numerical simulation could accord with model test very well in aspects of failure mode and load-displacement curve. Axial compression ratio and out-of-plane deformation were taken as parameters to expand test data. Research found that when axial compression was not large, increase of axial compression ratio improved bearing capacity of the specimen. If in-plane force was conducted after a certain displacement out-of-plane was applied, the greater the out-of-plane displacement above the shear wall was, the more the in-plane bearing capacity reduced, and the more in-plane deformability degraded.

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.

Discrete-time sliding mode for building structure bidirectional active vibration control

In terms of vibrations along bidirectional earthquake forces, several problems are faced when modelling and controlling the structure of a building, such as lateral-torsional vibration, uncertainties surrounding the rigidity and the difficulty of estimating damping forces. In this paper, we use a fuzzy logic model to identify and compensate the uncertainty which does not require an exact model of the building structure. To attenuate bidirectional vibration, a novel discrete-time sliding mode control is proposed. This sliding mode control has time-varying gain and is combined with fuzzy sliding mode control in order to reduce the chattering of the sliding mode control. We prove that the closed-loop system is uniformly stable using Lyapunov stability analysis. We compare our fuzzy sliding mode control with the traditional controllers: proportional–integral–derivative and sliding mode control. Experimental results show significant vibration attenuation with our fuzzy sliding mode control and horizontal-torsional actuators. The proposed control system is the most efficient at mitigating bidirectional and torsional vibrations.

Shake-table testing of a self-centering precast reinforced concrete frame with shear walls

The seismic performance of a self-centering precast reinforced concrete (RC) frame with shear walls was investigated in this paper. The lateral force resistance was provided by self-centering precast RC shear walls (SPCW), which utilize a combination of unbonded prestressed post-tensioned (PT) tendons and mild steel reinforcing bars for flexural resistance across base joints. The structures concentrated deformations at the bottom joints and the unbonded PT tendons provided the self-centering restoring force. A 1/3-scale model of a five-story self-centering RC frame with shear walls was designed and tested on a shake-table under a series of bi-directional earthquake excitations with increasing intensity. The acceleration response, roof displacement, inter-story drifts, residual drifts, shear force ratios, hysteresis curves, and local behaviour of the test specimen were analysed and evaluated. The results demonstrated that seismic performance of the test specimen was satisfactory in the plane of the shear wall; however, the structure sustained inter-story drift levels up to 2.45%. Negligible residual drifts were recorded after all applied earthquake excitations. Based on the shake-table test results, it is feasible to apply and popularize a self-centering precast RC frame with shear walls as a structural system in seismic regions.

Damage Index Distributions in RC Dual Lateral Load-Resistant Multi-Story Buildings Considering SSI Effects Under Bidirectional Earthquakes

Inelastic seismic responses of flexibly supported reinforced concrete (RC) moment-resisting frames representing short-to-tall structures stiffened with ductile RC structural walls were evaluated considering both far-field and near-field ground motions. A dual shear wall-frame resisting system with symmetric reference plan was created by adding shear walls into excitation direction of the three-dimensional frames developed by generic structure algorithm. The current study also aims to take into account soil–structure interaction effects in to damage assessment of multi-story RC buildings in terms of ductility demand, damage index, story shear force and overturning moment, as well as kinetic energy profile over the structure height. In doing so, the developed set of generic frames was considered accounting for different values of story strength, stiffness distribution and number of stories. A realistic modeling of nonlinear ductile behavior of RC elements was developed in combination with the sub-structuring method to consider the foundation flexibility in nonlinear seismic responses. Conducting a parametric study through nonlinear static analyses (pushover) as well as nonlinear response history analyses, the results indicated that the near-field ground motion presents much more damage than the far-field one. Inelastic dynamic responses to near-field records demonstrated that structures with a fundamental period greater than the pulse period respond differently from those that have shorter periods. The results were also presented as charts and tables that provide helpful information for engineering design purposes such as damage assessment of multi-story RC buildings with specific fundamental natural period and base shear strength.

Dynamic Response of a Combined Isolation Based Mega‐Substructure under Bidirectional Near‐Fault Ground Motions

A typical megaframe structure has a high lateral stiffness and is excellent for high‐rise structures. However, this high stiffness can lead to poor seismic response of a structure. Seismic isolation technology is a mature and cheap vibration control method that is used for vibration reduction in megaframes. This paper introduces a megaframe structure based on substructure combined isolation. The structure consists of two parts. The main body is a megaframe, and the substructure is the subframe with the combined isolation layer arranged at the bottom of the subframe. The seismic performance of this structure system was evaluated by performing shaking table tests of two megaframe model structures. The responses of the deformation, acceleration, and shear of the structure were measured. The dynamic behaviors of the structure with or without the combined isolation layer when exposed to single and bidirectional near‐fault and far‐fault ground motions with different peak values were investigated. The results showed that the combined isolation layer can reduce the bidirectional seismic response of the main frame and subframe. The acceleration, base shear, and displacement responses had similar vibration reduction trends for the two model structures, and the structural responses under bidirectional earthquake were generally greater than that under a single directional earthquake. The near‐fault pulse effect increased the seismic response of the structure. The increase of the predominant period of ground motion also increased the seismic response of the structure.

A mixed explicit–implicit time integration approach for nonlinear analysis of base-isolated structures

The paper investigates the accuracy, the stability and the computational efficiency of a mixed explicit–implicit time integration approach proposed for predicting the nonlinear response of base-isolated structures subjected to earthquake excitation. Adopting the central difference method for evaluating the response of the nonlinear base isolation system and the Newmark’s constant average acceleration method for estimating the superstructure linear response, the proposed partitioned solution approach is used to analyze a 3D seismically isolated structure subjected to a bidirectional earthquake excitation. Both isolation systems adopting lead rubber and friction pendulum bearings are considered. Numerical results show that the computational time required by the proposed method, in spite of its conditional stability arising from the use of the central difference method in the explicit integration substep, is clearly reduced in comparison to the widely used implicit time integration method adopted in conjunction with the pseudo-force approach (i.e., pseudo-force method). As a matter of fact, the typical low stiffness of the isolation system leads to a critical time step larger than the one used to define the ground acceleration accurately and the proposed method preserves its computational efficiency even in the case of isolators with very high initial stiffness (i.e., friction pendulum bearings) for which the critical time step size could become smaller.

Dynamic Responses of Sliding Isolation Concrete Rectangular Liquid Storage Structure with Limiting Devices Under Bidirectional Earthquake Actions

There is no lack of destructions of concrete liquid storage structures in the previous earthquake, and concrete rectangular liquid storage structures (RLSSs) are widely used in all kinds of engineering fields, so it is significant to study energy dissipation method aiming at structural responses and wave height. An energy dissipation method combination of sliding isolation and limiting-device is proposed for concrete RLSS, considering fluid– structure interaction, simplified and numerical models of a concrete RLSS with displacement-limiting devices are established. The dynamic responses of sliding isolation concrete RLSS with limiting devices under bidirectional earthquake actions are studied, parameter analysis is conducted, and seismic decrease coefficient is used to evaluate the reduction effect of sliding isolation on concrete RLSS. The results show that damping effect of sliding isolation with limiting devices on concrete RLSS is significant, and the dynamic responses under horizontal bidirectional earthquake actions are obviously higher than that of unidirectional earthquake action. The smaller the friction coefficient is, wall tensile stress and wave height are more reduced; in the premise of keeping the structural displacement within the limit, the limiting-device diameter should be smaller; liquid height mainly affects wall tensile stress and structural displacement. When the friction coefficient and limiting-device diameter are designed reasonably, seismic decrease coefficients corresponding to wall tensile stress and wave height are all large enough. Therefore, the proposed energy dissipation method is of great significance for the prevention and control of the common two types of failure modes (wall cracking and liquid overflow) of concrete RLSSs.

Stability Analysis of a Cross-Sea Tunnel Structure under Seepage and a Bidirectional Earthquake

Stability Analysis of a Cross-Sea Tunnel Structure under Seepage and a Bidirectional Earthquake

Numerical failure analysis of a continuous reinforced concrete bridge under strong earthquakes using multi-scale models

Previous failure analyses of bridges typically focus on substructure failure or superstructure failure separately. However, in an actual bridge, the seismic induced substructure failure and superstructure failure may influence each other. Moreover, previous studies typically use simplified models to analyze the bridge failure; however, there are inherent defects in the calculation accuracy compared with using a detailed three-dimensional (3D) finite element (FE) model. Conversely, a detailed 3D FE model requires more computational costs, and a proper erosion criterion of the 3D elements is necessary. In this paper, a multi-scale FE model, including a corresponding erosion criterion, is proposed and validated that can significantly reduce computational costs with high precision by modelling a pseudo-dynamic test of an reinforced concrete (RC) pier. Numerical simulations of the seismic failures of a continuous RC bridge based on the multi-scale FE modeling method using LS-DYNA are performed. The nonlinear properties of the bridge, various connection strengths and bidirectional excitations are considered. The numerical results demonstrate that the failure of the connections will induce large pounding responses of the girders. The nonlinear deformation of the piers will aggravate the pounding damages. Furthermore, bidirectional earthquakes will induce eccentric poundings to the girders and different failure modes to the adjacent piers.

Effects of nonlinear soil–structure-interaction on seismic damage of 3D buildings on cohesive and frictional soils

The present paper investigates the impact of nonlinear soil–foundation–structure-interaction (NLSFSI) on the damage response of 3D R/C buildings supported on different soil types with varying flexibility. The main goal of the paper is to present a first approach towards the possible quantitative differentiation, with respect to fixed base conditions, on the overall damage level when NLSFSI effects are accounted for. To accomplish this purpose nine buildings with various heights and structural systems are studied. For the foundation of the buildings two different soil types are considered, namely cohesive and frictional ones. Moreover, the soil flexibility is taken into account by using two different values of the soil’s shear wave velocity. The buildings are subjected to 65 bidirectional earthquake records, for which nonlinear time history analyses are conducted. The accelerograms of each record are scaled to two different seismic intensities corresponding to certain performance levels using appropriate scaling factors. The damage state of the buildings is expressed through the maximum interstorey drift ratio. The assessment of the results revealed that the role of soil–foundation–structure-interaction (SFSI) is not necessarily beneficial. In order to assess the SFSI effects a number of parameters are important as the frequency content of the earthquake ground motion, the building’s structural system, the foundation soil flexibility as well as the earthquake intensity.