Condition assessment of seismically isolated multi-span highway bridge bearings using recorded and simulated seismic responses

Abstract

This paper describes a study on the responses analyses of a seismically isolated multi-span highway bridge recorded during the 2011 Great East Japan (Tohoku) earthquake and assessment of isolation bearing condition based on the responses. During the earthquake, lateral pounding and locking between the side-stoppers and the upper steel plate of the isolation bearings were observed of several piers. Finite element model was employed to analyze the problem and scenarios of locked bearing on the piers were simulated. The study also presents a wavelet-based technique to detect the presence and location of locked bearing. Instantaneous frequency of continuous wavelet transform of girder and piers accelerations were employed to evaluate isolation bearing condition by identifying the occurrence of high-frequency filtering effect. Afterwards, bearing condition was characterized via statistical clustering technique. Accuracy and efficacy of the technique were verified in simulations using three-dimensional finite element model of the bridge. Results of simulations demonstrate that wavelet-based features can effectively characterize isolation bearings condition directly from seismic responses of girder and piers.

Keywords

highway bridge seismic response 2011 great East Japan (Tohoku) earthquake isolation bearing bearing malfunction detection

Introduction

It has been more than thirty years since the first seismically isolated bridge is constructed in Japan. The first seismically isolated bridge in Japan is the Miyagawa bridge, a three-span continuous non-composite steel girder with length of 105.8m located in Haruno-cho, Shizuoka prefecture. The bridge was opened in March,1991 and was one of eight bridges selected in the country as the pilot construction project for base-isolation system. Lead Rubber Bearing (LRB) was adopted as a seismic isolation device at that time. To examine the earthquake response characteristic of the seismic isolation, strong-motion seismographs (accelerometers) were installed on the bridge. A magnitude 4.9 earthquake occurred on April 25, 1992, with epicenter in Shizuoka area about 30km northeast from the bridge. This is the first ever seismic records from monitoring system of seismically isolated bridge in Japan. Analysis of the records helped confirming some important aspects adopted in the design of base-isolated bridge (Kawashima et al. 1994).

Construction of seismically isolated bridges has increased significantly especially since the 1995 Hyogoken-Nanbu (Kobe) earthquake. Notable examples are the Ohito Viaduct, a 29-span continuous prestressed concrete girder bridge with a total length of 725 m and Tenryu-River Bridge, a 23-span continuous prestressed concrete girder bridge with a total length of 1585 m. The isolation system improves seismic performance of the bridges and makes multi-span continuation of superstructure easier because the horizontal force which acts on bridge piers by temperature change can be reduced using elastic seismic bearings (Unjoh 2014).

Performance of bridges using base-isolation as well as vibration-control technologies have often been validated through responses to actual earthquakes. During large earthquakes such as the 1995 Kobe and 2011 Tohoku earthquakes many of the bridges and buildings that use seismic isolation and control technologies experienced the strong shaking and this provided an opportunity to evaluate performance of the installed control technologies and obtain lessons learned from the monitoring experiences. Detailed investigations (Chaudary et al. 2000) on the performance of base-isolated bridges during a large earthquake was conducted on the Matsunohama Viaduct, an elevated bridge located on the Hanshin Expressway Bayshore Route in the Kansai area, west Japan. The 211.5 m long bridge was opened to traffic in 1994 and was the first application of base-isolated bridges within the Hanshin Expressway. It was located about 35 km southeast from the epicenter of the 1995 Great Hanshin (Kobe area) Earthquake. The study showed that it was possible to capture the overall behavior of the base-isolated Matsunohama Viaduct with simple equivalent linear, two degrees-of-freedom (2-DOF) lumped mass models. The study demonstrated that the base-isolation system performed satisfactorily because it effectively decoupled the superstructure from the substructure, such that the spectra of the girder contained only the dominant superstructure frequency and filtered out other high frequencies especially from the piers. The phenomenon known as the high-frequency filtering effect can be used as an indicator to evaluate effectiveness of seismically isolation system. During the 2011 Great East Japan (Tohoku) earthquake, bridges with seismic isolation generally performed well and better than the conventional non-isolated ones even under extreme ground motions. Only very few of them were damaged by the earthquake (Kawashima and Buckle 2013; Kitahara et al. 2012).

With the advancement of sensing and monitoring technologies, structural health monitoring systems have been implemented in the long-term deployments to assess seismic performance of important long-span bridges, bridges with seismic isolation, and bridges with control systems (Xu & Xia 2011; Xu & He 2017; Xu 2018; Fujino et al., 2010, 2019; Limongelli & Celebi 2019). In the case of seismically isolated bridges in Japan, previous studies using data from seismic monitoring systems of Matsunohama bridge, Yamaage bridge, and Onneto bridge revealed that structural details of isolation bearing such as steel bearing, side stoppers, and upper or lower bearing plates significantly affect overall behavior of seismically isolated bridges (Chaudhary et al., 2002a; Fujino et al., 2016). In the case of Onneto bridge, the steel plate girders became locked with the lateral side-stopper on several bearings causing the deck not isolated completely from the pier (Chaudhary et al., 2002b; Fujino et al. 2016). The locking of isolation bearings at one or more pier during a large earthquake would result in unexpected load redistribution to the substructure because significant inertia force of superstructure will be transmitted to the substructure. This phenomenon is not yet anticipated in design, and therefore should be identified as early as possible and mitigated to avoid further malfunction of the isolation bearings at larger earthquake (Kataoka et al. 2012).

To detect performance of a seismically isolated structure during an earthquake including the case of locked bearing, evaluations based on comparison of identified global parameters such as structural or modal parameters using system identification methods are normally conducted (Derkovian et al. 2014, Limongelli & Celebi 2019). Most of the methods are based on modal analysis in time-domain using piecewise linear approach or in the frequency domain by spectral analysis. In the case of Onneto bridge, for example the locked bearing condition was identified from modal-based information and structural analysis with known structural and soil properties (Chaudhary et al., 2002b). However, since isolation system is expected to behave nonlinearly, characterization of the time-varying property of the structures must account for both temporal evolution of the frequency and amplitude contents of vibration. Neither time analysis nor frequency analysis method alone can entirely describe these characteristics. In addition, locking of isolation bearing is a local phenomenon and detecting such phenomenon based on structural global parameter such as modal parameters can be challenging. Therefore, it is more desirable to have a detection method directly from analysis of the vibration signal without the need for performing a complete process of modal analysis.

In this paper, we describe a case study where unexpected locking of isolation bearing on a continuous multi-span highway bridge is observed during the 2011 Great East Japan (Tohoku) earthquake. There are two main objectives of the paper. The first objective is to present a case study on the occurrence of locked bearing on multi-span seismically isolated girder bridge. Based on the observation of scratch marks on the lateral side-stopper of isolation bearings, detailed investigation on seismic responses of the bridge was conducted using finite element model and seismic responses analyses. The second objective is to propose a technique for detecting the locking of isolation bearing directly from seismic records of the bridge. The technique allows us to monitor the behavior of isolation bearing and detect any changes related to the locking phenomenon directly from seismic records of the bridge without the need for structural model or a reference state. Simulation on effectiveness of the method is presented using finite element model of the bridge.

Organization of the paper is such that the description of the bridge and seismic responses recorded during the 2011 Great East Japan (Tohoku) earthquake is firstly described. Next, the paper describes the responses analysis using three-dimensional finite element model and system identification. Afterwards, simulations by finite element model of a multi-span continuous bridge with numerous scenarios of the locked bearing are presented. A wavelet-based technique for detecting locked bearing directly from seismic records of the structure is proposed and implemented in the finite element simulation. Finally, the paper concludes with discussion on results of simulations.

Description of object bridge

The object of this study is the Yamada highway viaduct bridge on the National Highway No. 45 (hereinafter referred to as the Yamada bridge) located in Iioka, Yamada-cho, Shimohei-gun, Iwate Prefecture, north Japan. The bridge total length is 471m, and the superstructure composes of two 4-span continuous steel box girders with open lower bracing. Figures 1 shows the photo and basic dimension of the Yamada bridge. Table 1 lists the details on the bridge basic structural information. The part from abutment A1 to pier P4 is regarded as one system with a continuous girder, and the other part from pier P4 to abutment A2 is regarded as another system. In the section between abutment A1 and pier P4, the piers are supported by shallow foundation except for abutment A1 which is on a deep pile foundation. On the other part of the section between pier P4 and abutment A2, piers P4 and P5 are supported by direct shallow foundations, and the other piers are on deep pile foundations. The piers are made of hollow reinforced concrete with pedestal cross-sectional dimensions of 4m in bridge axis bridge direction (longitudinal) and 7 m in the direction perpendicular to the bridge axis (lateral), and heights vary between 24m and 35m.

Table 1.

Basic properties of Yamada bridge.

Substructure
Abutment	Inverted T-type of abutment
Pier	Hollow type Reinforced concrete, dimension 4 $\times$ 7 m, heights 2635 m
Foundation	Direct shallow type, deep pile foundation type
Basic plan dimension	Abutment & crossing part: 65 $\times$ 100 cm, Pier 117 $\times$ 122 cm
Superstructure
Girder length	54.4+60+60+59.1m, 54.4+60+60+59.1 m
Girder width	10.5m, 10.5m
Girder Material	Steel box +lower plan bracing
Properties of LRB
Total rubber thickness	Abutment & crossing part: 17mm $\times$ 16 layer $=$ 272 mm, Pier; 222mm
Shear modulus	Abutment & crossing part: 0.6MPa, Pier: 1.2MPa
Primary shape factor	Abutment & crossing part: 11.3, pier: 7.9, 7.5
Secondary shape factor	Abutment & crossing part: 2.3, pier: 5.2, 5.0

The bridge girder is supported by two units of laminated rubber bearing (LRB) on each pier. The size of each LRB unit is 65×100 cm with total rubber thickness 27.2cm on the abutments and 117 x 122 cm with total rubber thickness 22.2cm on the piers. In longitudinal direction, seismic force displaces the bearing allowing movement of the girder relative to the pier during an earthquake. In lateral direction, displacement of LRB is tolerated only for limited length before being restrained by the side-stopper. In this bridge a 5mm gap exists between the isolation bearing and the two side-stoppers. The side-stopper is made of two stiffened angle or welded steel plates located on both sides of the isolation bearing.

The first part of the bridge from A1 and P4 is equipped with strong motion sensor network as shown in Figure 1(d). Strong motion accelerometers are installed at three locations: on the girder, on the top of pier P3, and on the ground around P3 to observe the bridge responses during an earthquake.

Description of seismic records and observation of structure condition in the March 11, 2011 Tohoku Earthquake

The bridge is located about 132km away from epicenter of the 2011 Tohoku earthquake. Figure 2 shows the time-history of ground motion accelerations and the response spectrum obtained from the 2011 Tohoku Earthquake (M9.0). There are two major tremors corresponding to the two major ruptures that occurred off the coast of Miyagi prefecture. In addition, because the sensor was installed on hard ground classified as Class I ground, the ground motion is dominated by the short period components below 0.3s as shown in the response spectra (Figure 2(b)). The maximum value of the acceleration response spectrum in the short period region is about 950 cm/s² in both horizontal directions and about 500cm/s² in the vertical direction. The spectrum figure shows that for period range of 1.9s or 0.52Hz which is the natural frequency of the bridge's fundamental mode in longitudinal direction and for period 0.8s or 1.25Hz, which is the bridge's fundamental mode in lateral direction the horizontal acceleration response spectrum is in the range of 50 to 100 cm/s².

Figure 3 shows acceleration time-histories recorded on the bridge girder and pier P3. On the girder, the peak acceleration was 547 cm/s² recorded on the vertical direction. In horizontal direction, the bridge vibration in lateral or perpendicular to bridge axis was larger than that in longitudinal direction. Meanwhile on the pier P3, the lateral acceleration which is in the strong axis of bridge pier had larger peak acceleration (i.e., 502.6 cm/s²) compared to the peak acceleration in longitudinal direction (pier’s weak axis) which was 312 cm/s². The largest part of the pier lateral direction is related to the spikes in the responses caused by lateral pounding between pier and girder.

Post-earthquake field survey was conducted after the earthquake and the observation show there was no signs of damage on the reinforced concrete piers, abutment, and steel girder. However, scratch marks were found on the upper steel flange of the laminated rubber bearing on several piers as shown in Figure 4. The scratch mark corresponds to the amount of deformation of the bearing or the relative displacement of the bridge girder and pier. As for abutment A1 and A2, which are visually observed from the road, no trace of the expansion or contraction device moving significantly had been confirmed (Kataoka et al. 2012). The scraped paint and scratch marks observed on the surface of bearing’s upper steel flange of the bearing suggest that the side blocks have been in contact with the bearing’s upper steel flange and lateral pounding have occurred. In other words, the relative lateral displacement between pier and girder had exceeded the 5mm gap between side block and bearing’s upper steel flange.

It should be mentioned that such scratch marks would have not appeared had the girder move purely in longitudinal direction without contact or locking in lateral direction. Such lateral pounding incident could occur due to combination of excessive transverse and vertical motion of girder and pier. It is a common practice that the bridge is visually inspected after a large earthquake and finding on bridge condition is reported. The appearance of scratch marks observed after the 2011 Tohoku earthquake is the first time on the bridge.

The indication of isolation bearing locking and appearance of scratch marks have led to decision taken by bridge operator to conduct more extensive investigation on the bridge including detailed analyses of seismic responses during the earthquake. The main concern is that when one or more piers have locked bearings, the force distribution among piers will be different than the case when all piers do not have locked bearings. From a force-based perspective, like the case of bridge with all fixed bearings, the shorter piers that have higher stiffness are subjected to increased seismic force more than the taller piers are. In the case of locked bearing, the same condition could occur since the locked bearing condition on one or more piers changes not only distribution of seismic force but also results in more concentrated seismic force on the said pier. Consequently, damage tends to localize in the relatively stiff (shorter) piers at the locked bearing condition.

System identification method was implemented to the seismic records using input-output state-space system identification method. Recorded ground motions were used and the inputs, while seismic responses on pier P3 and girder were used as the outputs. Using the segment of seismic responses during peak excitation (t=30s-120s), the SRIM system identification (Juang 1997) was implemented, and fundamental modes of the bridge were estimated. In longitudinal direction the first mode was identified at 0.632Hz and damping ratio 3.7%. Whereas in lateral direction the first mode was identified as 1.34 Hz and damping ratio 2.4%.

Description of finite element model of the bridge

To investigate seismic behavior of the bridge more comprehensively, finite element model (FEM) was used in this study. The FEM analysis was conducted as the first step in investigating seismic responses of the bridge. With the availability of seismic records on the bridge pier and girder, and availability of finite element model of the structure, simulation was conducted to find the basic characteristic of seismic responses and explanation for the observed locked bearing as indicated by scratch marks. The fish-bone model was employed in FEM where the girder was modeled as a single beam member and the reinforced concrete piers as well as abutments were modeled with linear beam element. To model the bridge foundations, linear springs were used to connect foundation structures and the ground. The linear spring constants were calculated from the standard penetration test of the soil provided by design document and soil tests. Figure 5 (a) shows the finite element model of the bridge used for seismic response analysis. The model was constructed using structural parameters at the design stage (Table 1). The structural damping constants were assigned as follows: 2% for the superstructure, 5% for reinforced-concrete piers and abutments, and 10% for the foundation-ground system, which are commonly used in seismic design of highway road bridges in Japan. The LRB behavior was modeled using hysteresis bilinear curve in longitudinal and lateral direction. On each pier, there are two units of LRB and their detailed properties for all piers and abutment are given in Table 2.

Table 2.

Characteristics of bilinear shear spring used to represent the LRB in the FE simulation.

Location	Primary Stiffness (kN/m)	Secondary Stiffness (kN/m)	Yield strain (%)	Yield load (kN)
Abutment A1	1889.406	1275.300	0.0212	40.055
Pier P1	15027.939	6450.067	0.0128	192.358
Pier P2	15027.939	6450.067	0.0128	192.358
Pier P3	15027.939	6450.067	0.0128	192.358
Pier P4	1889.406	1275.300	0.0212	40.055
Pier P5	16333.65	6808.140	0.00694	113.356
Pier P6	16333.65	6808.140	0.00694	113.356
Pier P7	16333.65	6808.140	0.00694	113.356
Abutment A2	1889.406	1275.300	0.0212	40.055

The finite element model of the bridge was constructed using TDAP structural analysis software (TDAP 2008). As the first step, the original model was constructed and the resulted dynamic responses under recorded ground motions were compared with the recorded seismic responses. Effect of pounding was not included in this original model, which means that additional stiffness due to side stopper in lateral direction and effect of friction force in longitudinal direction were not considered when assigning the LRB stiffness. To obtain seismic response of the bridge, non-linear time-history analysis was conducted. Structural elements other than the LRBs were assumed to be linear, and their structural damping constants were assigned as in design. In this analysis, structural members other than LRB were assumed to behave linearly. This assumption is considered reasonable since the post-earthquake observation show there was no damage such as cracks on the RC piers and steel girder. It should be mentioned however that option for nonlinear analysis is available once the stress or strain on the bridge elements exceed the linear range, which was not the case in this analysis.

For the linear range of calculation, the proportional damping method was used and the result of eigenvalue analysis, namely the fundamental modes in two principal directions are shown in Figure 6. The first natural frequency in bridge axis (longitudinal) and lateral directions are 0.53Hz and 1.25Hz, respectively. The FEM results are compared with modal parameters estimated from seismic records using system identification. Note that natural frequencies of the fundamental modes derived by finite element model are lower than the corresponding frequencies estimated from seismic records which means that the bridge model is more flexible than the actual one. One possible reason is because in the finite element model, effect of pounding and friction in both lateral and longitudinal directions were not included.

Figure 7 shows the comparisons of simulated and recorded seismic responses and their frequency spectra, at the pier P3 and girder. The figure demonstrates that in terms of amplitude of acceleration, the simulated girder acceleration is smaller than the measured ones, while peaks of spectra occur at lower frequencies than the measured ones. This means the damping assumed in the simulation is different with the actual values and the stiffness of structure assumed in finite element model is generally lower than the actual ones. In the pier responses, the acceleration amplitude is not so different while peaks of spectra also occur at lower frequencies compared to the measured ones. In a related study by Kataoka et al. (2012), the finite element model was adjusted by considering the two effects above, and by tuning bearing stiffness in lateral and longitudinal directions stiffness to six times of the design value to obtain the closest responses with recorded ones.

Figure 8 shows the relative displacement between girder and pier P3 resulted from finite element simulation. It is evident from the figure that the peak relative displacement in longitudinal between the girder and pier at pier P3 is about 17mm which results in the maximum shear strain of the isolation bearing about 6%. In lateral direction, (Figure 8(b), show that the amount of deformation of the bearing has exceeded the clearance of 5 mm, so the contact and locking between the upper flange and the side-stopper during the earthquake as observed from the scratch marks can be confirmed.

Simulations of locked bearings using finite element model

The abovementioned explanation demonstrates that the actual seismic behavior is quite different from the one simulated in finite element model. The locking is preceded by sticking and slipping of the bearing with side stopper. Such condition can be inferred from the records by higher frequency of the fundamental modes when compared to the corresponding ones generated by finite element model. Also, field observation confirmed occurrence of bearing sticking and slipping from scratch marks on the bearing’s upper flange. It should be mentioned however that the occurrence of bearing locking at this earthquake is not very severe as noted by the scratch mark’s length that was only 6cm on pier P3 and the absence of large impulse force on the seismic records of the pier and girder, only relatively small spikes appear on the responses. Unfortunately, only one pier and one location on the girder were equipped with sensors during the earthquake. This means possible occurrence and the extent of locked bearing on the other piers cannot be confirmed.

In this section, we shall describe simulations of locked bearing at arbitrary piers and observe the seismic records of piers and girder to find indication of locked bearing directly from the responses. In this scenario, the bridge is assumed to have seismic monitoring system with at least one sensor on each pier cap and at least one sensor on the girder since the girder is a continuous span. Figure 5(b) and (c) exhibit the condition leading to bearing locking. Longitudinal movement of the girder relative to the pier occurs because of seismic force and it initiates LRB’s longitudinal deformation. Meanwhile in transverse direction, displacement of LRB is tolerated only for limited length before being restrained by the side stopper. Due to large excitation, pounding occurred and gap in one or both sides of the isolator is closed, causing the side stopper locked with the bearing’s upper steel plate. Once the gap is closed, the friction from the contacting surfaces obstructs the movement of the upper steel plate, and in an extreme case, the deck may become completely locked with the pier. The isolation system does not function properly until the actual seismic force exceeds the friction force and girder becomes unlocked from the pier (Figure 5(c)).

The process of bearing locking is simulated in the finite element model by changing the stiffness at the pier-girder connection. The original fishbone model of Yamada bridge is modified by changing the stiffness of LRB at the piers and abutment. In the locked bearing condition, the side-stopper’s stiffness will engage together with the friction force (Fs) resulting in a significant increase of initial stiffness of the deck-pier connection since the stiffness of the side-stopper is larger than that of the elastomeric bearing. In such condition the primary stiffness and secondary stiffness of the locked bearing are assumed to be 196133kN/m and 49000kN/m, respectively. These values were estimated from the stiffness of the side-stopper and the friction force (Fs) between side-stopper and isolator’s upper steel flange. Whereas the yield strain and yield load become 0.2% and 39226.6kN, respectively.

Thirtytwo finite element models were analyzed in the simulations. The thirty-two scenarios include all possible combinations of bearing scenarios, namely: all functioning bearing, locked bearing at one pier, locked bearings at two piers, locked bearing at three piers, locked bearing at four piers and locked bearings at all four piers and abutment. Details of scenarios in the simulations are given in Table 3. In all cases, the triaxial recorded ground motions during 2011 Tohoku earthquake were used as the input excitations. Other components of finite element model were kept the same except for the pier with simulated locked bearing. Note that there are two LRBs on each pier, and in each scenario of locked bearing mentioned in Table 3, both LRBs are assumed to be locked. In addition to this locked bearing condition, the other LRBs that are assumed to function normally and having the LRB properties as described in Table 2. Note that since the bridge has similar two parts of continuous girder, simulation was conducted only on the first part of the bridge girder, namely the part from A1 to P4.

Table 3.

Scenarios of locked bearing in the finite element simulations.

No locked bearing	One locked bearing	Two locked bearings	Three locked bearings	Four locked bearings	Five locked bearings
NL	A1	A1,P1	A1,P1,P2	A1,P1,P2,P3	A1,P1,P2,P3,P4
—	P1	A1,P2	A1,P1,P3	A1,P1,P2,P4
	P2	A1,P3	A1,P1,P4	A1,P1,P3,P4
	P3	A1,P4	A1,P2,P3	A1,P2,P3,P4
	P4	P1,P2	A1,P2,P4	P1,P2,P3,P4
		P1,P3	A1,P3,P4
		P1,P4	P1,P2,P3
		P2,P3	P1,P2,P4
		P2,P4	P1,P3,P4
		P3,P4	P2,P3,P4

In the conventional non-isolated bridge, seismic responses of the girder normally contain high-frequency components transmitted from the piers because piers and girder are rigidly connected. In a functioning seismically isolated bridge, however, the high-frequency components will be filtered out from the girder’s seismic response by the isolation bearing that decouples piers and girder at the connection. This phenomenon is known as the high-frequency filtering effect, and it can be used as an indicator of functioning isolation bearing condition.

To evaluate isolation bearing condition directly from seismic records, time-frequency analysis of the girder and pier's seismic response is conducted using continuous wavelet transform (CWT). In this study, we utilize one of the most popular and widely used wavelet that is the complex Morlet wavelet (Grossmann & Morlet 1984). Properties of continuous wavelet transform, namely the ridge and skeleton are commonly used to track evolution of the signal. The ridge of wavelet transform is related to instantaneous frequency of the signal. To provide definition and derivation of wavelet ridges, consider equation (1) of the continuous wavelet transform represented as the scalar product (Tchamitchian & Torresani 1990):

W (a, b) ≅ \frac{1}{2 a} \int_{- \infty}^{\infty} Λ_{x} (t) Λ_{ψ} (\frac{t - b}{a}) e^{i [ϕ_{x} (t) - ϕ_{ψ} (\frac{t - b}{a})]} d t

(1)

in which

Λ

and

ϕ

are the envelope and instantaneous phase of the asymptotic signal x(t) and wavelet

ψ (t)

, respectively. Note that as pointed out by Tchamitchian & Torresani (1990) and Staszewski & Wallace (2014), the essential contribution to equation (1) is provided by a set of stationary points t=t_s of the function:

Φ (a, b) (t) = ϕ_{x} (t) - ϕ_{ψ} (\frac{t - b}{a})

(2)

where the stationary points can be determined from equation:

\dot{Φ} (a, b) (t_{s}) = \frac{1}{a} {\dot{ϕ}}_{ψ} (\frac{t_{s} - b}{a})

(3)

The stationary points t_s are the set of points in time-scale (a,b) domain for which the t_s (a,b) equals b. The curve that is a function of b (e.g., a = f(b)) is the ridge of the wavelet transform.

The ridge of wavelet transform can be interpreted as the location where the main energy of vibration response is localized among the distributed energy density over the time-scale plane (a,b). Therefore, the ridge can be considered as the governing or dominating vibration characteristics at a specific time duration. One can obtain the ridge of wavelet from time-scale plane (a,b) by employing amplitude-based or phase-based algorithms. In this paper, the amplitude-based ridge extraction is employed. The ridge is obtained by solving the optimization problem of finding the local maxima of wavelet transform magnitude along the scale axis for an individual time. Results of the wavelet ridge is considered as the instantaneous frequency of the signal and utilized to trace time-varying characteristics of the response.

Based on the pattern of instantaneous frequency of piers and girder’s seismic responses, one can categorize them into two clusters, the normal bearing, and the locked bearing. In the first category, the instantaneous frequencies at the peak of acceleration are closer to the pier’s fundamental frequency, whereas for the second category they are closer to the girder’s frequency. To provide a systematic classification of the clusters of instantaneous frequencies as either locked or movable bearing, a classification by k-means clustering (Arthur and Vassilvitskii, 2007) is employed. By this method, the distance between two clusters of instantaneous frequencies during the peak excitation is normalized with the absolute difference between the pier and girder frequency. The normalized distance index (NDI) between the clusters is defined as:

N D I (U_{c 1}, U_{c 2}) = | \frac{(\bar{U_{c 1}} - \bar{U_{c 2}})}{ω_{p} - ω_{g}} |

(4)

In this equation, $\bar{U_{c 1}}$ and $\bar{U_{c 2}}$ are the centroid of cluster 1 and cluster 2 respectively, whereas $ω_{p}$ and $ω_{g}$ are the theoretical natural frequencies of pier and girder, respectively. In the case of a normal bearing, the NDI value will be close to one since the distance between the centroids of the two clusters will approximately equals to the difference between natural frequency of piers and girder. On contrary, for a locked bearing, the NDI value will be closer to zero since the distance between centroids of the two clusters is much smaller than the difference between natural frequencies of pier and girder.

Results of finite element simulations of locked bearings

As the first case, all bearings are assumed to function properly. This means that during the peak excitation, all isolators behave normally, and the force-displacement relationships of all isolators follow the bilinear curves model described in Table 2. This case is investigated to provide a reference for the other cases of locked bearing. Figure 9 shows characteristics of acceleration time-histories, the time-frequency maps, and the corresponding instantaneous frequencies. Note that because the two major tremors occur within the first 120s of the responses, only the first 120s are shown in the figure. The largest peak in the time-frequency map occurs during the peak excitation period t=40–90s. At this time, the girder response is dominated by a single low frequency response at 0.7Hz, which corresponds to the girder longitudinal mode. Based on the instantaneous frequency, it is confirmed that the single frequency girder longitudinal mode remains the dominating frequency until the end of excitation.

Meanwhile, all accelerations on the piers have the same characteristics. One can clearly observe nonstationary characteristics of the acceleration time history which can be verified by the time-frequency map and instantaneous frequency. In the beginning of the response (t=<10s), the piers responses are dominated by a single low frequency response at 0.7Hz similar to the girder. After the arrival main seismic wave, the responses were characterized by higher instantaneous frequencies, within 2–3Hz for all piers and 3–4 Hz for abutment A1. The frequency ranges of 2–3Hz and 3–4Hz correspond to the pier longitudinal frequency at 2.4Hz and abutment A1 at 3.2 Hz, respectively. The results demonstrate that in a normal or moveable bearing condition, the pier and girder accelerations were dominated by their own respective frequencies during the peak excitation suggesting that they behave as uncoupled separate systems. In this condition, the piers are isolated from the girder and the high frequency contents of the pier responses are not transferred to the girder. This condition is expected from a functioning isolation bearing.

In the second simulation, the case of single locked bearing at the middle pier (P2) is considered. Figure 10 reveals the acceleration time-histories, time-frequency maps, and the instantaneous frequencies of girder and all piers. It is evident from the figure that the accelerations of all normal piers are dominated by frequency components associated with the piers’ main frequency during the peak excitation (t=40–90s). Meanwhile, acceleration of the pier with locked bearing (P2) is mainly dominated by the girder frequency at around 0.8Hz. One can observe the similarity of time-frequency characteristics of accelerations on the girder and the pier with locked bearing. For the other piers that function normally, the instantaneous frequency range are in the range of 2–3Hz for piers and 3–4Hz for abutment which corresponds to the longitudinal frequencies at 2.4Hz and 3.2 Hz for pier and abutment A1, respectively. The results demonstrate that in a normal isolation bearing, the pier and girder accelerations were dominated by their own respective frequency suggesting the uncoupled separate systems. The similarity of dominating frequency in a locked bearing indicates that both girder and pier move together as a coupled system. The same phenomenon was observed when single locked bearing occurs at different piers (refer to the scenarios in Table 3), which is not shown here because of space limitation.

The third simulation is for a case of multiple locked bearings, namely at two piers: pier P1 and pier P3. Figure 11 describes the acceleration time-histories, time-frequency maps and the instantaneous frequencies of girder and all piers. The figure shows that characteristics of time-frequency maps of the piers with locked bearing are very similar to that of the girder. During the peak acceleration at the time t=40–90s, the main frequency content of these piers accelerations is 0.85Hz which is the frequency of girder’s longitudinal mode. Note that this frequency is slightly higher than the corresponding frequency in the first two cases due to stiffness increase caused by the two locked bearings. This trend continues until the end of excitation indicating that girder with pier P1, and girder with P3 move together as coupled system. On contrary, the piers with the normal movable bearings are characterized by high frequency components at 2–3Hz at the peak of excitation between t=40–90s. This is the time when the girder becomes isolated from the piers and the isolation bearings start to function.

The fourth simulation is the case of multiple locked bearings at three piers, namely at pier P1, P2 and P3. The acceleration time-histories, time-frequency maps and the instantaneous frequencies of girder and all piers are illustrated in Figure 12. Again, the figure shows that characteristics of time-frequency maps of the piers with locked bearings are very similar to that of the girder where the main frequency content of these piers accelerations is around 1Hz. It is the frequency of girder’s longitudinal mode that is again slightly higher than the corresponding frequency in the previous cases due to stiffness increase because of the three locked bearings. This trend indicates that girder with the locked piers move together as coupled system. On contrary, the piers with the normal movable bearings were characterized by high frequency component at 2–3Hz at the peak of excitation between t=40–90s

Figure 13 shows the results of the fifth simulation where bearings on three piers and an abutment are locked, namely at abutment A1, pier P2, P3 and P4. Note that the characteristics of time-frequency maps and instantaneous frequencies are very similar with that of previous simulation. The time-frequency maps of abutment and piers with locked bearings are dominated by single frequency component with frequency like the girder frequency at 1.2Hz. Only the instantaneous frequencies of pier P1 whose bearing is not locked appear at higher frequency at 2.6Hz. Note that the dominating frequencies of girder and piers with locked bearings are higher than the previous cases because the stiffness of the bridge in longitudinal direction is now higher due to locked bearing condition.

Finally, the results of simulation for the case of all bearings at abutment and piers are locked during the earthquake are shown in Figure 14. It is evident from the figure that time-frequency maps of abutment and all piers are dominated by single frequency component with frequency similar to the girder frequency at 1.5Hz. Once again, the dominating frequency of girder and piers are higher than in the previous cases because now bearings in all piers and abutment are locked causing the stiffness of the bridge in longitudinal direction increased significantly compared to the case when all bearings function normally (i.e., 0.7Hz). In contrast to the condition where all bearings function normally, there is no case of pier with high frequency component appear on their time-frequency maps. Therefore, the results where all piers have a dominating single frequency response which is similar to the girder’s dominating frequency can be noted as an indicator of locking condition in all bearings.

All examples explained above demonstrate the consequence of locked bearing condition on the time-frequency maps of seismic responses. The frequency contents of the piers with locked bearings are dominated by single low frequency component that corresponds to the girder mode. This frequency is higher than the frequency of the girder in the normal (unlocked) bearing because of higher initial stiffness. The physical condition of locked and normal (unlocked) bearing can be inferred from the normalized distance indices denoted by equation (4). The clusters of instantaneous frequencies will have centroids of data that represent the dominant instantaneous frequency in both girder and pier’s accelerations for each scenario. The centroids of data clusters were determined by k-means clustering algorithm as explained in equation (4). When the isolator bearing of a specific pier functions normally, the values of $\bar{U_{c 1}}$ in equation (4) will be close to the girder’s natural frequency and $\bar{U_{c 2}}$ will be close to pier’s natural frequency. On the other hand, the values of $\bar{U_{c 1}}$ and $\bar{U_{c 2}}$ become closer to each other when the bearing is locked because the girder and pier move together as a coupled system. To normalize the distance between centroids of the clusters, they are divided by the distance between the known natural frequencies of girder and pier or abutment. In this case, since the seismic responses of pier and girder in longitudinal direction are dominated by the first mode, the first frequency of girder $ω_{g}$ =0.7Hz is used, while for pier and abutment the first frequency of $ω_{p}$ =2.4Hz and $ω_{p}$ =3.2 Hz are used, respectively.

The summary of cluster classification using instantaneous frequencies obtained via CWT for the thirty-two cases of finite element models is shown in Figure 15 in a form of heat map table. The abscissa in each case describes the pier number with locked bearing and the ordinate describes the identified normalized distance (ND) indices computed by equation (4). It is evident from the results that piers with locked bearing can be identified based on ND indices closer to zero, while piers with normal (movable) bearings were identified with ND indices close to one. The method accurately classifies all cases of pier with locked bearing from the relative indices of ND. Using the comparative indices of ND, one can accurately characterizes the bearing condition. There were some differences in the ND indices for the same bearing condition. The differences, however, do not significantly change the classification, since the comparative indices of ND in one case still clearly provide indicator on the bearing condition of that pier.

Note that in the present condition, the Yamada bridge only has one pier instrumented with sensor in addition to the girder, therefore the location and extent of locked bearing cannot be confirmed directly from the recorded seismic responses. However, in the case where a multi-span isolated bridge has at least one sensor on each pier and one sensor on the girder, then the occurrence of locked bearing and their extent can be predicted directly using the recorded seismic responses by employing the technique explained above. Examples of implementations the method explained in this paper on actual seismic records of seismic monitoring records of multi-span bridges can be found in (Siringoringo et al. 2022; Siringoringo & Fujino 2021).

Conclusions

This paper describes a study on observation and analysis of seismic responses of a multi-span seismically isolated highway bridge. Based on seismic records and visual inspection, the occurrence of locking of isolator bearings was confirmed on the Yamada bridge. Using finite element model, seismic responses of the bridge were analyzed, and numerous scenarios of locked bearing were simulated. A wavelet-based technique for detecting locked bearing directly from seismic records of the structure is explained and implemented in the finite element simulations. The techniques consist of 1) employing continuous wavelet transform to identify instantaneous frequency based on which stiffness changes associated with isolation bearing condition is traced, and 2) classifying bearing condition using k-means cluster classification method. Results of simulations using three-dimensional finite element model of Yamada bridge have demonstrated the effectiveness and accuracy of the technique to characterize behavior of isolation bearing and detect changes related to bearing locking phenomenon directly from seismic records. This technique works well when the multi-span isolated bridge has at least one sensor on each pier and one sensor on the girder.

Structural health monitoring system now has become more common on the major important bridges. In the case of large and important seismically isolated bridge as the bridge in this study, one of the main objectives of structural monitoring is to investigate whether the seismic isolation system function properly after large earthquake. This includes detecting abnormality of the bearing such as the locking of bearing. With the availability of advanced of sensing system such as wireless sensors at reasonable cost, such monitoring system may no longer be far from realization in the near future.

Footnotes

Acknowledgement

The authors gratefully acknowledge Earthquake Disaster Management Division, National Institute of Land and Infrastructure Management, Ministry of Land, Infrastructure, Transport and Tourism, Government of Japan for providing the seismic response records of the 2011 Great East Japan (Tohoku) Earthquake. The authors also gratefully appreciate Dr. Masaaki Yabe from Shutoko Technology Center for his great assistance in providing information on the bridge structural details and model. The first author greatly acknowledges scholarship from Ministry of Education, Culture, Sports, Science, and Technology of Japan (MEXT) and JASSO during the study at Yokohama National University.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

JSPS Grant-in-Aid Kakenhi C No. 18K04320 to the second author.

ORCID iD

Dionysius M Siringoringo

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