This study presents the experimental results on a scaled bridge model with a newly proposed unidirectional rocking isolation bearing system (referred to as Uni-RIBS) on a shaking table. The bridge model features one superstruc- ture girder and four bearings. The experimental input encompassed a variety of recorded, design, and harmonic ground motions, characterized by differing peak accelerations, with or without vertical components, and time-scaled attributes. The superstructure girder’s mass was altered for two conditions (full and half). The test results validate the rocking mechanism inherent in the Uni-RIBS and demonstrate the analytical model’s accuracy in predicting the system’s dynamics, including its negative stiffness, mass-independent, and energy dissipation characteristics during bearing rotation reversals. Additionally, this study examines the effectiveness of a simplified numerical model in varying complexities for predicting the seismic responses of the bridge model.

The objective of this study is to examine the feasibility of estimating the parameters of various devices in seismic control systems and evaluating the maximum responses of the quantities of interest. The observability condition was applied to determine the sensor layout and modeling assumptions of the structure for the joint estimation problem and to eliminate unsuitable layouts. To estimate the parameters of multiple members at the isolation layer, including laminated rubber bearings, oil dampers, and elastic sliding bearings, and to evaluate the maximum response, an adaptive unscented Kalman filter was utilized. Moreover, the study investigated the influence of partially unmeasured inputs on the observability of the established system through a case study involving the base layer of the building model colliding with the retaining walls. Experimental data from a full-scale shaking table test on a seismic isolation building was used as an example for validation purposes. The results demonstrated that even under varying initial estimates, varying sensor layouts, and the occurrence of unmeasured impact forces, the parameters and maximum responses of interest can be estimated with acceptable accuracy when the observability condition is met.

A bidirectional rocking isolation bearing system (Bi-RIBS) is proposed to provide seismic protection for bridge structures. By using the 3-D rocking motion of the Bi-RIBS, this system acts as a mechanical fuse to limit the maximum force transmitted to the bridge piers and as a restoring component to control an excessive girder response. Possible applications in bridge structures were discussed. A simple analytical model was established to characterize the dynamics of an example bridge featuring such a Bi-RIBS. A series of dynamic analyses were performed by using the proposed model to investigate the effects of several factors on controlling the seismic responses of the bridge, for example, the design parameters of Bi-RIBS including inclined angle and size, the damping property at the support interface, and the mass ratio. The peak ground accelerations of the bidirectional ground motion record were scaled to various levels to evaluate the maximum performance indices of the bridge structure and the response control effectiveness of the Bi-RIBS compared to the uncontrolled counterparts. The simulation results demonstrated that the proposed Bi-RIBS could effectively control the maximum pier displacement while keeping the bearing from overturning if suitable parameters were selected. In particular, the control effectiveness on the maximum pier response becomes more significant as the seismic intensity increases, due to its distinctive negative stiffness property.

In this study, the effects of the degree of directionality on critical seismic performance assessment are investigated from two aspects: the bidirectional seismic demand represented by maximum-direction spectrum and the performance indices obtained from nonlinear time-history analysis. Firstly, typical representations of the bidirectional demand of ground motions are reviewed and compared, in seismic design practices (e.g., ASCE 7-16, Eurocode8, and JRA). Statistical analysis using 83 ground motions underlines the implication of the spectrum-compatible condition that has not been fully considered in past studies investigating the bidirectional effects. In the second part, a series of spectrum-compatible bidirectional ground motions with various degrees of directionality are generated as inputs. The corresponding seismic performance assessment results of a base isolation building with the friction pendulum system are investigated. According to the simulation results, the current design practices could introduce unconservative assessment on the maximum bearing displacement due to the omission of the directionality effect included in the design ground motions, particularly, when the directionality parameter is at a large value (less directionality). The cases with nondirectionality always tend to result in a nearly constant envelope of the maximum interstory drift and the maximum floor acceleration assessment for the full directionality case, over all incident directions. For the critical seismic performance assessment, the two extreme cases, namely the full directionality and nondirectionality cases, are recommended to be considered.

Rocking structures are recognized as an effective seismic response modification technique due to their peculiar dynamic characteristics. Meanwhile, in bridge structures, strong ground motions have frequently caused a rocking motion of pin bearings around their two toes, resulting in the pulling-out of anchor bolts. This study, motivated by the promising features of rocking behaviors, seeks to develop a rocking isolation bearing system (RIBS) to control excessive response in bridges. An example bridge featuring such a RIBS, consisting of the pin bearings removing anchor bolts to release the rocking motion, the girder-type superstructure, and an array of bridge piers, is characterized by a simplified model. Two coefficients of restitution (COR) models are used to investigate the effects of energy dissipation during impact: the Housner model, and a model which simultaneously modifies the velocities of the superstructure and substructures. The dynamic characteristics of RIBS and its control effectiveness on the bridge structure are discussed through a series of dynamic analyses, under both observed ground motions and the design ground motions specified in the Japan Road Association (JRA) design specifications for highway bridges. The simulation results demonstrate that the seismic performance of the bridge structure can be substantially improved, with decreased pier displacement at an allowable bearing rotation level.

近年，既設橋梁の耐震補強において，既設鋼製支承から変形性能に優れた免震支承への更新が進められている．その中で，一般的な積層ゴム系免震支承よりも構造高が低く，設置スペースの制約を受けにくい球面すべり支承が注目されている．球面すべり支承の免震効果の決定要因は長周期化とエネルギー吸収性能であり，これらは球面の形状によって定まる剛性と球面とスライダー間の摩擦係数に依存する．本研究ではデータ同化手法であるアンセンテッドカルマンフィルタを橋梁模型実験で得られた動的データに適用し，球面すべり支承の剛性と摩擦係数を含む橋梁のシステム状態推定を試みた．

This study proposes a novel online data forecasting strategy for dynamic measurements in structural health monitoring applications, which excels in both time and frequency domain, based on a spectral-temporal deep learning network integrated with signal decomposition and filtering techniques in moving windows. For complex structural dynamic measurements from bridges or buildings, the varying time–frequency features within moving windows are difficult to capture for conventional deep learning networks, e.g., CNN or GNN, resulting in spectral bias or other related issues. To address this challenge, in this study, signal decomposition is adopted to simplify the frequency domain features, i.e., variational mode decomposition (VMD), into multiple intrinsic mode functions (IMFs), each of which has limited bandwidth frequency and regular time domain pattern. The decomposed signals are then fed into a spectral-temporal deep learning network for data forecasting step by step, and the predicted datasets are further finetuned by associated bandpass filters, respectively, to selectively remove the unwanted frequency components to enhance the accuracy. The performance of proposed method is validated on both numerical simulation data and field test data, and the results demonstrate that the predicted datasets match well with ground truth values in both time and frequency domains. Compared to the state-of-the-art solution, the proposed method can achieve much higher forecasting accuracy. In addition, the effects of hyperparameters and VMD are investigated, and the result shows that the introduction of signal decomposition plays a critical role to improve the state-of-the-art solution for data forecasting. The proposed solution can efficiently help to reconstruct dynamic measurements from data anomalies (e.g., missing, bias, and drifts) or to detect structural anomalies (e.g., rare events and damages) in long-term structural health monitoring systems.

As the dynamics of modern infrastructures grow increasingly complex, the application of structural health monitoring (SHM) techniques to these dynamic systems presents a crucial challenge—how to derive maximal system information from limited sensor deployments. This study addresses this challenge by applying Lie symmetry analysis on nonlinear input-output (I-O) mappings, formed by dynamic systems and sensor layouts. Specifically, we focus on systems characterized by Bouc-Wen type hysteresis behaviors, under minimal sensor deployments. We introduce differentiable unidirectional and bidirectional Bouc-Wen models to enhance the maximum inferable capability of I-O mappings in these systems and extend their application to other nonlinear hysteresis models. The utility of the proposed differentiable hysteresis models is demonstrated through three Bayesian estimation scenarios under the limit of minimal sensor, involving numerical and experimental data from a typical dynamic example with unidirectional hysteresis behavior, as well as a hybrid simulation test and a shaking table test example with bidirectional hysteresis behavior.

Ground motions compatible with the maximum-direction response spectrum (RotD100) condition are emphasized in performance-based design and seismic risk assessment of civil structures in different regions. Due to the complex nature and uncertainty of earthquakes, the comprehensive inclusion of essential characteristics of ground motions is crucial. Recently, the directionality effect of horizontal bi-directional ground motions, representing the variation of the response spectral ordinate amplitude along various directions, on the seismic performance assessment of certain structures or key structural elements has received increasing attention in seismic analysis. However, from the seismic design perspective, there is still a lack of a method that can generate bi-directional ground motions comprehensively reflecting the directionality effect. This study focuses on the correction of ground motion directionality when generating synthetic bi-directional ground motions for a given target response spectrum. An efficient and integrated algorithm is proposed. To demonstrate the applicability of the proposed algorithm, three different target RotD100 response spectra are determined according to modern seismic design codes, and 20 pairs of bi-directional ground motions are generated using the proposed algorithm for each target spectrum. It is shown that with the proposed algorithm, the generated motions present a close match to the target RotD100 response spectrum and meet the specific directionality requirement. In addition, due to the iterative modification of the envelope function, the energy of the generated ground motion is also consistent with the scaled natural records.

This study presents an innovative approach to the realization of an isolation bearing system in bridge structures, termed as the Rocking Isolation Bearing System (RIBS). Period elongation is achieved by the bearing's rocking motion, while energy dissipation is realized through the impact force at the boundary interface. The inception of the rocking motion can be easily designed based on the bearing's geometry to satisfy seismic protection requirements at various earthquake levels. Emphasis is accorded to the following aspects: the damage-free design concept in the bearing system, potential applications and structural designs for bridge structures, illustration of designing the bearing system for a specific bridge and analyzing the corresponding seismic response characteristics, and the progression of an ongoing experimental validation test for a representative bridge model.

Although seismic isolation techniques have been widely recognized as effective in modifying the seismic response of protected structures, clearance parts to accommodate the large relative displacement anticipated in seismic design are likely to encounter pounding problems. In most cases, the pounding is unpredictable and unmeasurable and can compromise the accuracy of system identification approaches. To decide whether an isolation structure could continue to be used after strong earthquakes, parameter estimation based on earthquake monitoring systems should identify the variation of structural parameters related to damage, under uncertain pounding problems. The Kalman filter is a versatile system identification method for dealing with modeling and measurement uncertainties. The present study investigates the effectiveness of the unscented Kalman filter under such situations for the measured data from the shaking table (E-defense) test of an isolation building. Specifically, the base layer of the building was designed to collide with the retaining walls to evaluate the influence of pounding. The results show that the parameters related to the isolation layer can be estimated with acceptable accuracy when the proper conditions are met.

Although the friction pendulum bearing system (FPS) has been widely used in the construction of buildings, bridges, and other structures to enhance their seismic performance, the FPS was adopted in bridge construction in Japan for the first time in 2020 on the Tokai-Hokuriku expressway. To validate the design hypotheses of the real bridge with FPS, a series of static and dynamic tests were performed, and the parameters of the FPSs were estimated. The girder of the bridge supported by four FPSs was pushed to various specified displacements considered in a maximum considered earthquake event in a quasi-static manner by hydraulic jacks equipped with large-caliber valves to enable quick pressure release. The load of the jacks was then suddenly released so that the bridge entered free vibration. The bearings in the site static tests are found to undergo a noncontinuous sliding motion (stick–slip) because a small loading rate of jacks is applied. This stick–slip phenomenon is confirmed in both the site and laboratory tests in cases where the sliding velocity either approached 0 or departed from 0, i.e., at every velocity reversal. The friction coefficient is estimated from the force and displacement data at the sliding points, and good agreement is observed between the site static tests and the laboratory tests. The friction coefficient model for dynamic analysis, accounting for the stick–slip effect and several dependencies, is calibrated by these test results. The free-vibration test results, including measured displacements and accelerations, show agreement with the simulation results based on a simplified model of the bridge with the FPSs. Finally, the unscented Kalman filter and its adaptive variant are applied to estimate the design parameters of the FPSs.

After a strong earthquake, it is crucial to evaluate accurately the health of structures in order to decide whether they can continue to be used. Isolation techniques are well known for enhancing the seismic performance of structures; however, a large response displacement anticipated in the design will likely impact the expansion joints. The occurrence of any damage or impact involves a large disturbance in the system or measurement equations. The Kalman filter (KF) is effective and reliable under proper conditions, but a simple simulation may show disrupted stability conditions after a large disturbance, causing a temporary filter divergence. If the filter design cannot be rapidly adjusted, an overall filter divergence may occur, preventing an accurate evaluation of structural health. This study proposes a performance recovery strategy for the unscented KF (UKF). Rather than identifying optimal parameter estimates at the current instant, the filter meets the stability conditions and asymptotically approaches the true estimates. The measurement noise is adaptively adjusted to bound the true noise covariance. Once the filter divergence is identified based on the expected measurement residual error, the state covariance is adjusted by a covariance-matching technique to bound the true error covariance. After sufficient measurements are obtained, the state covariance is reduced to a low level, indicating filter convergence and a reliable estimation. The effectiveness of the proposed approach is numerically validated for an isolation bridge and building under several scenarios, and two existing UKF variants, which adaptively estimate the system and measurement noise covariances, are compared.

When the earthquake intensity exceeds the design expectation, the conventional rubber-type isolation bearings could generate a higher reaction force transmitted to the substructure with the increase of the bearing displacement, implying difficulties in controlling the maximum response displacement of the substructure. According to past earthquake damage investigation reports, when the rocking motion of the conventional pin bearings, followed by the pulling-out of their anchor bolts, was observed, the damages to the substructure and to the flange of the girder were significantly mitigated. Motivated by this so-called seismic isolation effect, a new rocking isolation bearing system (RIBS) was proposed, in which the maximum horizontal reaction force is adjusted by the height and width of the bearing and the energy is absorbed by the collision at the bottom of the bearing during its rocking vibration. In this study, the dynamic characteristics and the maximum response control effectiveness of an example bridge featuring such RIBS were analytically investigated. Eighteen ground motions corresponding to the maximum considered earthquake (MCE) in design specifications in Japan and a set of harmonic ground motions with various amplitudes and periods were used as inputs. As for the maximum displacement of the piers, nearly 30~40% reduction under MCE and no obvious resonance peak under the harmonic inputs were observed. The isolation effect of RIBS becomes more significant as the ground condition be- comes stiffer. At the moment of the peak pier displacement, a phase difference of nearly 90 degrees between the bearing and pier vibrations was found, implying desirable seismic response control effectiveness.

In general, bridge structures are designed to resist the maximum considered earthquake (MCE) specified in design specifications. Given the threat of the occurrence of unanticipated earthquakes, the development of the bridge with anti-catastrophic or damage-free capability becomes essential. An innovative rocking isolation bearing system (RIBS) was proposed to control the excessive pier displacement as well as girder displacement under unanticipated earthquakes. The rocking motion of RIBS is activated to provide seismic isolation effect when the seismic action exceeds a specified level. The seismic energy is dissipated by the collision between the bottom plate of RIBS and the top of the bridge pier. The dynamics of an example bridge featuring such RIBS were characterized as a simplified model. Two coefficient of restitution (COR) models were used to investigate the effects of energy dissipation during the impact: the Housner model and a model derived from the conservation of the angular momentum and the linear momentum in the horizontal direction. A series of nonlinear time-history analyses were performed for the example bridge under varying intensities of the design ground motions corresponding to MCE in Japan. When an appropriate selection of the design parameters of RIBS is achieved, the maximum pier displacement shows insensitive against varying intensities of ground motions, since the mechanical fuse of RIBS limits the maximum reaction force acting on the piers; the rocking bearing is not overturned until the design ground motion is scaled over several times its original intensity, implying its anti-catastrophic or damage-free capability.

In the process of seismic performance-based design of bridges with slide bearings, there exist intrinsic tradeoffs between minimization of bearing displacement and that of the pier response in selecting bearing parameters for strong earthquake events. However, difficulty in determining the optimal parameters of the bearings that satisfy the two objectives arises, in conjunction with considerable computational resource requirement for nonlinear time-history analysis. In order to find the solutions of the multi-objective optimization problem that reduce the computational cost, a procedure that utilizes the stochastic structural response of equivalent linear systems is proposed. To obtain the performance indices, seismic load is modeled as a stationary random process, whose characteristics are determined for the standard design ground motions specified by the Japanese design code, and the nonlinear behavior of the slide bearings is modeled as equivalent-linear elements using the stochastic linearization technique. As the result, a set of optimal parameter candidates is obtained as the Pareto-front solutions in the multi-objective function space. As the next step, the search of the optimal parameters is conducted by performing nonlinear time-history analysis only for the Pareto-front solution parameter sets to save the computational requirement. As a numerical example, the proposed method is applied to bridges with two types of slide bearings: the uplifting sliding shoe (UPSS) consisting of multiple sliding surfaces, and functionally discrete bearings (FDB) in which friction bearings and elastomeric bearings set in parallel are combined. It is demonstrated that the seismic performance of the bridge for the case of the design parameters obtained by the proposed procedure is almost equivalent to the one with the optimal parameters found by the conventional exhaustive search approach.

The bridge bearings with seismic functionality, namely the aseismic bearings, have been adopted in bridge construction to satisfy the sufficient seismic performance requirements of bridges as well as to support the superstructure subjected to various environmental actions. Appropriate performance assessment and efficient design approach for bridges with these bearings under seismic excitations are the key issues in performance-based design. The seismic performance assessment of bridges by means of nonlinear time history analysis using unidirectional spectrum-matched seismic loads is generally adopted in the design specifications of bridges in Japan. However, there has been of long-term concern that the bi-directional performance of bridges may not be accurately evaluated by using the unidirectional approach. On the other hand, the bearing parameter selection to satisfy the seismic performance requirements of bridges is fraught with several difficulties in the process of performance-based design. The main scope of the study presented in this dissertation is to explore the seismic performance of girder bridges with aseismic bearings subjected to bi-directional ground motions and the efficient bearing design parameter. Three main parts are included in this study. In part I, the seismic performance of girder bridges with the bi-directional uplifting slide shoe (UPSS) bearing subjected to bi-directional ground motions is investigated. The UPSS is a new type of bearing which has been proposed to achieve reduced displacement under strong earthquakes without losing the advantage of the slide bearing to deal with the thermal effect on bridge girders. The bi-directional UPSS, implementing multiple UPSS devices in a combination of the longitudinal and transverse directions of the bridge girder, was proposed to achieve an improved seismic performance of girder bridges under bi-directional ground motions. A multi-spring model of the bi-directional UPSS based on a past study, considering the coupling effect of the friction mechanism and the geometric contact condition of the slider, is adopted to assess the bi-directional bridge response including the integrated coupling effects between the longitudinal and transverse components. The results show that the bi-directional UPSS is effective in controlling the bi-directional seismic response of the example bridge compared with the conventionally proposed unidirectional UPSS, and it is superior to the functionality discrete bearing (FDB) system in effectively reducing both the bearing displacement and the pier response ductility factor. Moreover, the impact effect of the bi-directional UPSS during the transition between two sliding surfaces on the seismic performance assessment of girder bridges is investigated. To consider various impact conditions due to the inherent uncertainties of the pounding process, the impact force is modeled in two manners: 1) a simplified model where the impact force is introduced as the centrifugal force of a tubular arc superimposed in the boundary areas; 2) the multi-spring model where the impact force is introduced by an overlapped fictitious sliding surface element. The results show that the impact force does not evidently change the distribution of the most efficient bearing design in which both the bearing and pier response are reduced. In part II, the study focuses on the influence of the directionality of bi-directional ground motions on the seismic performance assessment of a girder bridge with two types of bearings, namely the high damping rubber (HDR) bearings and the FDB in their bi-directional application. Artificially generated spectrum-compatible bi-directional ground motions are used as the input to specify the directionality effect in terms of the degree of elliptic property. The results show that the maximum bearing displacement response of HDR tends to decrease when subjected to bi-directional ground motions in particular with less directionality, while an opposite tendency is presented for FDB. In addition, the energy dissipation capacity of the bearings and the phase lag angle of the bi-directional hysteretic restoring force under a series of quasi-statically bi-directional displacement loads are investigated. Furthermore, a method without performing bi-directional nonlinear time-history analysis to assess the bi-directional displacement demand for bridge bearings subjected to ground motions with a specified directionality effect is proposed. For structures with azimuth-independent properties, the bi-directional bearing displacement demand is approximated as the unidirectional demand multiplying an increase/decrease coefficient, which considers the bi-directional interaction of the bearings. The accuracy of the proposed method is validated by the analysis using the synthesized bi-directional ground motions and the actual strong ground motions. In part III, a stochastic-deterministic approach is proposed to determine the efficient bearing design parameters based on the concept of multi-objective optimization that minimizes the bearing displacement as well as the pier response. The search of the optimal bearing parameters is conducted by performing the nonlinear time-history analysis only for the candidate parameter sets found from the Pareto-front solution of stochastic analysis results to save the computational requirement. As a numerical example, the proposed method is applied to the optimal parameter selection of UPSS and FDB in a girder bridge. It is demonstrated that the seismic performance of the bridge for the case of the design parameters obtained by the proposed procedure is almost equivalent to the one with the optimal parameters found by the conventional exhaustive search approach. In addition, an extended search algorithm is incorporated with the proposed procedure to significantly improve the assessment error by slightly increasing the cases of performing the nonlinear time-history analysis.

The Uplifting Sliding Shoe (UPSS) bearing is a type of friction bearing proposed to ensure a sufficient seismic performance and to provide a cost saving solution for the thermal expansion and contraction of the multi-span continuous girder bridges. The use of multiple sliding surfaces of specific geometric shape is the main feature of UPSS to effectively provide restoring force in the event of strong earthquakes. Since impact force caused by the boundary region between two sliding surfaces is one of the critical factor in the design, the influence of the impact force on the seismic response of the bridge is investigated for the bidirectional application of UPSS in the bridge system in the present study. A two-phase analysis procedure is introduced to provide a reasonable discussion of the impact effect. In the first step, a rigorous modelling of UPSS based on the dynamic equilibrium analysis with a tubular arc in the boundary areas of the sliding surfaces is shown to control the intensity of impact. In the second step, a multiple spring model with various boundary properties is used to confirm the results of the first step and to investigate the impact effect in a quantitative manner. The study indicates that the bearing displacement response of the bidirectional UPSS is relatively robust so that the influence of the assumed boundary conditions is regarded as minor, while the simplified model is likely to overestimate the bearing displacement response compared with the multiple springs model. Furthermore, the potential impact effect can result in uncertainty to the pier response ductility factor.