Multiple shaking tables tests of seismic pounding effect of reinforced concrete bridge model

2.1. Bridge model

The prototype high pier bridge (overall length is 160 m) with hollow section consists of a continuous rigid frame bridge (spans length is 35 m + 60 m + 35 m) and a simply supported girder bridge (span length is 30 m). In view of the shaking table capacity, a 1/10 scaled prototype high pier bridge was conducted based on the prototype bridge.

The detailed descriptions of the bridge model are shown in Figure 2. To satisfy the mass demand of superstructures with concrete box girder, the additional mass is uniformly distributed on the decks. All piers of the RC bridge have length of 3.0 m. The transverse and longitudinal width of the hollow section is 0.4 m and 0.3 m, respectively; the wall thickness is 0.1 m.

Fig. 2The 1/10 scaled bridge model

One of the principle methods for pounding mitigation is to adopt supplemental damping under strong earthquake. Three orifice-type viscous dampers were installed between a deck and a pier, and the maximum output force is 30 kN. Parameters of the viscous dampers are shown in Table 1. In addition, a tension-compression sensor was added to each piston to monitor the output force.

The initial separation distance between adjacent girders was approximately 6 mm, as suggested by Chinese code for design of highway bridges. A steel tube with diameter of 50 mm was equipped in the center of the section for the continuous rigid frame bridge, and a steel hemisphere with diameter of 10 mm facing towards the steel pipe was installed in the identical position for the simply-supported bridge. More details for the two components are shown in Figure 3.

Fig. 3Model bridges and the upper structure and interface form of bridge pier

Fig. 4Selected accelerograms for the tests

Fig. 5Fourier spectrum

2.2. Selection of earthquake motion input

The tests were conducted on five sub-shaking tables at the Key Laboratory of Urban Security and Disaster Engineering of Beijing University of Technology. As shown in Figure 4, three actual acceleration records are selected for tests: El-Centro wave, Wenchuan wave and Beijing wave. The peak acceleration of the ground motion is 1.1 g (g is gravity acceleration). The specified input acceleration values are shown in Table 2. The excitations are imposed in longitudinal direction of the bridge.

The Fourier spectrum of the three ground motions are shown in Figure 5. Considering the scaling factor of the bridge model, the accelerograms are compressed by a factor of 3.6 to meet the similitude requirements. Simultaneously, peak ground acceleration is modified to 1.1 g.

To verify the traveling wave effect, time lags of the ground motion between the different locations are considered. Time lags of the piers from No. 2 to No. 5 are in sequence 1 s, 1.5 s, 1 s and 1 s than previous piers.

3.1. Pounding effect with isolation bearings

The peak accelerations at the top of piers equipped with lead rubber bearing (LRB) and rubber bearing (RB) are shown in Figure 6. It can be concluded that the peak acceleration responses of bridge model are relatively smaller with LRB compared with RB, and the maximum values reduce by 45 % and 33 % for the excitations of Wenchuan wave and Beijing wave, respectively.

The peak relative displacements between adjacent girders and the strain values of the steel tube are shown in Table 3 and Table 4. The relative displacements of the superstructures and the tube strains are relatively smaller with LRB than RB under uniform excitations. Focusing the attention on the traveling wave excitations, the relative displacement reduces by 24.79 % and the steel tube strain reduced by 61.18 % for Wenchuan wave. Also, the reductions of the relative displacement and the tube strains are 25.00 % and 50.70 % for Beijing wave, respectively.

As compared to RB, equipped with LRB can significantly reduce the seismic pounding effect of the bridge superstructures under both traveling wave excitations and uniform wave excitations.

Fig. 6Peak acceleration at the top of piers with LRB and RB

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b)

Time history of the relative displacement and the tube strain are shown in Figure 7 and Figure 8. Clearly, the relative displacement and the tube stain have significant reductions, when the bridge equipped with LRB. The pounding times for LRB and RB are 7 and 19 under the Wenchuan earthquake motion, also 6 and 29 under Beijing earthquake motion, respectively. Thus, few fierce pounding times are changed into extensive slight poundings when the LRB is equipped. Meanwhile, the pounding effects are mitigated, and the start of pounding is earlier.

It is obvious that laminated rubber bearing with a cylinder of lead, providing damping energy dissipation which can significantly mitigate the pounding response. Hence the appropriate isolation device has the ability to reduce pounding damage even avoid it.

Fig. 7Time history of the relative displacement

Fig. 8Time history of the tube strain

3.2. Pounding effect with dampers

The bar graphs of the peak acceleration at the top of piers with and without dampers are shown in Figure 9. It is found that the peak accelerations are smaller with dampers than without them. When additional dampers are equipped, the reduction rates of the acceleration at pier top are 83.31 %, 35.35 %, 44.92 % for the El-Centro earthquake, Wenchuan earthquake and Beijing earthquake, respectively. The bridge seismic response will reduce with additional damping increases.

The maximum relative displacements between adjacent girders and the tube strains, shown in Table 5 and Table 6, which shows that both parameters have significant reductions, when the bridge equipped with dampers. Conversely, comparing the bridge without damper, it should be noted that the increase of the maximum relative displacement is 4.31 % under uniform excitations for Wenchuan earthquake and the maximum tube strain is increased by as much as 14.39 % under travel wave excitations for Wenchuan earthquake.

The results illustrate that the mitigation for pounding effect of dampers is closely related to the earthquake excitation and spatial variation of ground motions.

Fig. 9Peak acceleration at the top of piers

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Fig. 10Time history the tube strain

Fig. 11Time history of the relative displacement

The time history of the tube strain shown in Figure 10, reveals that the pounding time for the bridge without dampers is 14 times, which is 1.4 times more than equipped with dampers. It is demonstrated that the pounding times and force are both significantly decreased when the damper is equipped. The relative displacement reduced by 50 % with dampers, while the displacement decay is deferred, as shown in Figure 11.

The damping effect of the damper is concerned with not only the input excitations but also the characteristics of bridge structures. Therefore, selected damper should be considered the sit conditions and the optimize parameters of the damper.

3.3. Influence of traveling wave excitation on pounding effect

Peak accelerations of the cap beam under various earthquake excitations is shown in Figure 12. From Figure 12 we can see that the peak acceleration at cap beam under traveling wave excitations is greater than uniform excitations for Whenchuan earthquake and Beijing earthquake. Conversely, for the EI-Centro earthquake, the peak acceleration is decreased by 163 % under travelling wave excitations.

The maximum relative displacements between adjacent girders and the tube strains under various earthquake excitations are shown in Table 7 and Table 8. When compared to the uniform excitations, the relative displacements between adjacent girders under traveling wave excitation are larger, while the degree of influence is varied with the characteristic of ground motion.

Fig. 12Peak acceleration of the cap beam under different earthquake excitations

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Fig. 13The time history curve of steel tube strain

Fig. 14The time history curve of relative displacement

Time history of the tube strain and the relative displacement between adjacent girders under uniform excitations and traveling wave excitations for Beijing earthquake are shown in Figure 13 and Figure 14. Under traveling wave excitation, the duration of the pounding is nearly double as uniform excitations, and the pounding force is also much larger than the uniform excitations. The maximum relative displacement between adjacent girders under traveling-wave excitations is doubled as compared with uniform excitations.

Evidently, the traveling wave excitation has significant influence on seismic pounding responses of bridge superstructures, but the seismic pounding responses under traveling wave excitation are complex and indeterminate.

3.4. Influence of seismic spectra characteristics on pounding effect

As shown in Figure 15, seismic responses of the bridge model under Beijing earthquake including peak accelerations, relative displacement and tube strains is the largest. The reason is that the natural period of the bridge model is 0.246 s using the results of the white noise excitations. The Fourier spectra of the three earthquakes are shown in Figure 5. It is clearly evident that the natural period of the bridge model is close to the predominant period (0.15 s-0.4 s) of the Beijing earthquake. Namely, the dominant frequency of Beijing earthquake covers the natural frequency of the bridge model.

Fig. 15Peak acceleration at the top of piers

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The maximum relative displacements between adjacent girders and the tube strains under various earthquake excitations are shown in Table 9 and Table 10. When the LRB and the dampers are both equipped, the largest maximum tube strain of the pounding effect is for Beijing earthquake, which is equal to 125 times for El-Centro earthquake. Evidently, the pounding effects of the bridge model with isolation bearings and additional dampers are different under various earthquake motions, which are closely related to spectra characteristics of the ground motion. When the dominant frequency of the earthquake motion covers the basic frequency of bridge structures, seismic pounding responses of the bridge structures will increase significantly.

In order to avoid the unfavorable earthquake responses, adopting isolation and dissipation technologies, such as isolation bearing and additional damper, have the ability to reduce the basic frequency of the structural vibration and dissipate the seismic energy input.