Specific to severe damage to curved bridges in earthquakes caused by the excessive force of the fixed bearings and piers, a new seismic design method on curved bridges considering bearing friction sliding isolation is proposed in this paper. Seismic model bridge and isolation model bridge with similarity ratio of 1/20 were made and the shaking table comparison test was conducted. The experimental results show that the isolation model curved bridge suffered less seismic damage than the seismic model curved bridge. The fundamental frequencies of the seismic model bridge and isolation model bridge decreased and the damping ratio increased with the increase of seismic intensity. Compared with seismic curved bridge, the maximum reduction rates of peak acceleration along the radial and tangential directions on the top of pier of the isolation model curved bridge were 47.3% and 55.5%, respectively, and the maximum reduction rate of the peak strain on the bottom of pier of the isolation model curved bridge was 43.4%. For the isolation model curved bridge, the maximum reduction rate of peak acceleration on the top of pier was 24.6% compared with that on the bottom of pier. The study results can provide experimental basis for the seismic design of curved bridges.
The frequent earthquake disasters in recent years resulted in severe damage to bridge structures, while the damage to the curved bridges was more serious [
Up to date, many scholars have carried out theoretical studies on the application of the isolation device in the highway bridge. Ozbulut and Hurlebaus [
In recent years, much progress has been made in the research of isolated curved bridges. Ates and Constantinou [
The shaking table tests, as an effective means of reappearance of the earthquake process, have been widely adopted at present. On the basis of theoretical research, the scholars have also carried out some shaking table tests on isolated bridges [
Based on the dynamic test theory [
Similar constants.
Properties | Physical quantity | Similitude relation | Similitude parameter |
---|---|---|---|
Geometric properties | Length |
|
0.05 |
Strain |
|
1 | |
Material properties | Stress |
|
0.6377 |
Mass |
|
6.377 × | |
Load | Force |
|
1.592 × |
Cycle |
|
0.1414 | |
Dynamic properties | Acceleration |
|
2.5 |
Gravity | 1 | 1 |
As the model materials used in shaking table tests directly affect the visibility and accuracy of test results, the selection of model materials is very important. HRB335 ribbed bars (nominal yield strength is 335 MPa) with the diameter of Φ6 mm were used for the longitudinal reinforcement of model pier and girder; HRB335 plain round bars with the diameter of Φ6 mm were used for stirrup, with the stirrup spacing being Φ6 cm. The pier-girder reinforcement skeleton is shown in Figure
Reinforcement skeleton.
Girder
Pier
Loading and measurement of block.
Load
Measurement
Two laminated rubber bearings in size of 6 cm × 6 cm × 1.5 cm were installed above each pier in the isolation model. Upon testing, the horizontal shear stiffness of rubber bearings was
In this paper, S-shaped curved bridge is taken as study object and model bridge is designed based on the similarity ratio of 1/20. The model bridge consists of four parts: circular curve, transition curve, transition curve, and circular curve; and the length of each part is 0.933 m, 1 m, 1 m, and 0.933 m, respectively. The full-bridge span combination is 2 × 1.785 m; the length of curve is 3.86 m. The superstructure of the model is box girder with uniform cross section and the piers are in rectangular single pier cross section, with the height of 1.55 m. The correspondences between the prototype and the bridge model are shown in Table
Correspondences between the prototype and the bridge model.
Items | Prototype | Bridge model |
---|---|---|
Span length (m) | 35.7 | 1.785 |
Curved span length (m) | 38.6 | 1.93 |
Deck width (m) | 7 | 0.35 |
Pier height (m) | 31 | 1.55 |
Girder mass (kg) | 1175737 | 155.3 |
Pier mass (kg) | 1437012 | 189.6 |
Two curved bridge models are designed based on the parameters shown in Table
Design of model (unit: cm).
Plan view
Elevation of seismic model
Elevation of isolation model
Bearing arrangement
The main design dimensions and the reinforcement assembly of section of the model bridge are shown in Figures
Reinforcement assembly of section (unit: cm).
Girder
Pier
The model tests must meet the criterion for dynamical mass similarity. Upon calculation, the total weight of counterweight required was 1321.4 kg and the actual weight of counterweight was 1040 kg. The counterweight rate could be up to 80%, so the requirements of shaking table test were satisfied. The two models applied with the counterweight are shown in Figure
Model weights.
Seismic model
Isolation model
In this test, the layouts of measuring point of the two models were the same. Nine acceleration sensors measuring points were arranged on the top of shaking table, the tangential direction of the top and bottom of piers #1, #2, and #3, and the radial direction of the bottom and top of pier #3, respectively. Four displacement sensors were arranged in the radial and tangential direction at the top of pier #2 and the girder (bridge deck), respectively. 12 strain gauges were arranged on steel bar at the bottom of the piers.
The PCB type series 380 GFB3G/30AY acceleration sensors were used to measure acceleration response of the models. 891-II type displacement sensors were used to measure the displacement response of the models. The TMR-200 small multichannel dynamic data acquisition instrument was used to measure the strain data of the models.
In this paper, El Centro wave (NS direction) [
Table
Load conditions.
Load condition | Model | The inputted peaks acceleration of shaking table (g) | The measured peaks acceleration of shaking table (g) |
---|---|---|---|
1 | Seismic model | 0.250 | 0.246 |
2 | 0.375 | 0.346 | |
3 | 0.500 | 0.486 | |
4 | 0.750 | 0.736 | |
5 | 1.000 | 0.973 | |
|
|||
6 | Isolation model | 0.250 | 0.237 |
7 | 0.375 | 0.335 | |
8 | 0.500 | 0.472 | |
9 | 0.750 | 0.717 | |
10 | 1.000 | 0.998 |
The damage to seismic model under seismic excitation was mainly in the form of cracks in piers, as shown in Figure
Pier’s crack distribution (unit: cm).
The isolation model suffers less damage to its piers than the seismic model. The bearings were placed directly on the piers without any treatment throughout the test. When the seismic wave was applied with 0.375 g PGA, the outer arc side bearing of pier #1 was found with radial sliding in sliding distance of 3 mm; the outer arc side bearing of pier #3 was found sliding along both tangential and radial directions of the bridge, including tangential sliding of 2 mm and radial sliding of 2 mm. When the seismic wave was applied with 0.5 g PGA, the outer arc side bearings of piers #1 and #3 were found with sliding of 6 mm and 7 mm in addition to the original sliding; the inner arc side bearing of pier #1 was in radial sliding of 2 mm and tangential sliding of 3 mm; the inner arc side bearing of pier #3 was in radial sliding of 2 mm and tangential sliding of 4 mm. When the seismic wave was applied with 0.75 g PGA, the outer arc side bearing of pier #1 partially came off the girder, and all the remainder bearings have greater sliding. When the seismic wave was applied with 1 g PGA, the outer arc side bearing of pier #1 completely came off; the bearing on the north side of pier 2# came off the girder by 1/2; the bearing on the outer arc side of pier #3 came off the girder by 2/3. The typical seismic damage to the bearings was shown in Figure
Damage to bearings.
Bearing sliding
Bearing coming off
Conclusion can be drawn from the above experimental phenomena: The main seismic damage to the seismic model is exhibited as the many cracks due to excessive force at the bottom of pier and the pier-girder connections. Compared with the seismic model, bearings in isolation bridge are placed directly between girder and pier; the bearings in the isolation model slide significantly upon completion of the test and even slide out of the pier top. The contact surfaces of the curved bridge with consideration of bearing friction sliding isolation may have certain slide under seismic excitation. The seismic horizontal forces are transmitted only through friction action of the contact surfaces. Not only will the bearing friction consume part of the seismic energy, but it also will play the role of reducing the effect of transferring the inertia force of the superstructure to the substructure under seismic excitation. Therefore, the dynamic response of the isolation bridge is effectively reduced. Throughout the test, the damage to the isolation model pier is relatively smaller. Thus, the curved bridge with seismic design considering bearing friction sliding isolation has proven to have good seismic performance and can be applied to seismic design of high-intensity earthquake area.
In order to obtain the dynamic characteristics at different stages of the model bridge, the fundamental frequency of each model was tested by hammering before and after the load conditions were applied to each test, while the damping ratio corresponding to the fundamental frequency of the structure was obtained by using the logarithmic decrement method in dynamics of structures [
Dynamic characteristics of the model.
Acceleration amplitude (g) | Seismic model | Isolation model | ||
---|---|---|---|---|
Frequency (HZ) | Damping ratio (%) | Frequency (HZ) | Damping ratio (%) | |
0 | 5.675 | 3.64 | 5.078 | 2.79 |
0.25 | 4.697 | 4.04 | 3.951 | 4.19 |
0.375 | 4.305 | 4.47 | 3.315 | 7.04 |
0.5 | 4.011 | 7.94 | 3.204 | 9.30 |
0.75 | 2.739 | 14.37 | 2.703 | 11.83 |
1 | 2.642 | 20.93 | 2.116 | 20.52 |
Table
With the increase of seismic intensity, the damping ratio of the model increases. When the seismic wave was applied with 1 g PGA, the damping of the seismic model increases to be 475% compared to the original damping ration; and the damping of the isolation model increases to be 636% compared to the original damping ration. Increase of structural damping makes the structure have better capacity of seismic energy dissipation. Change law of damping ration and frequency of isolation bridge indicate better seismic capacity when isolation bridge is in injured working state.
Table
Peak acceleration of measuring points (unit: g).
Measuring point | Load condition | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 6 | 2 | 7 | 3 | 8 | 4 | 9 | 5 | 10 | ||
SM | IM | SM | IM | SM | IM | SM | IM | SM | IM | ||
Bottom of pier #1 | Tangential | 0.256 | 0.242 | 0.379 | 0.319 | 0.397 | 0.460 | 0.764 | 0.694 | 0.800 | 0.962 |
Top of pier #1 | 0.520 | 0.372 | 0.415 | 0.371 | 0.486 | 0.453 | 1.243 | 0.905 | 1872 | 1623 | |
Bottom of pier #2 | Tangential | 0.210 | 0.262 | 0.341 | 0.413 | 0.440 | 0.483 | 0.612 | 0.790 | 0.867 | 1.133 |
Top of pier #2 | 0.479 | 0.275 | 0.353 | 0.340 | 0.472 | 0.371 | 0.753 | 0.669 | 1.986 | 1.345 | |
Bottom of pier #3 | Radial | 0.128 | 0.175 | 0.205 | 0.277 | 0.284 | 0.352 | 0.452 | 0.654 | 0.598 | 0.906 |
Top of pier #3 | 0.446 | 0.411 | 0.501 | 0.385 | 0.594 | 0.415 | 0.660 | 0.604 | 1.473 | 0.776 | |
Bottom of pier #3 | Tangential | 0.206 | 0.198 | 0.241 | 0.275 | 0.311 | 0.357 | 0.490 | 0.552 | 0.713 | 0.395 |
Top of pier #3 | 0.391 | 0.265 | 0.391 | 0.272 | 0.442 | 0.315 | 0.569 | 0.416 | 1.041 | 0.463 |
Note: SM stands for the seismic model; IM stands for the isolation model.
The following can be seen from Table For seismic models, the peak acceleration values at the corresponding positions of the piers top were all magnified compared with the bottom of pier as the effect of acceleration along the height direction of bridge pier is magnified. With the increase in seismic intensity, the bearings of the isolation model start to slide above the pier, and the sliding of bearings reduced the transfer of seismic inertia force of the girder towards the piers, thereby playing effective isolation action. Under load condition 7, the tangential peak acceleration value at the top of pier #2 was reduced to 17.7% compared with the bottom of pier. Under load condition 8, the tangential peak acceleration value at the top of pier #2 was reduced to 23.2% compared with the bottom of pier, and the tangential peak acceleration value at the top of #3 pier is reduced to 11.8% compared with the bottom of pier. Under load condition 9, the peak acceleration value at the top of pier #2 was reduced to 15.4% compared with the bottom of pier, the radial peak acceleration value at the top of pier #3 is reduced to 7.6% compared with the bottom of pier, and the tangential peak acceleration value at the top of pier #3 was reduced to 24.6% compared with the bottom of pier. Under load condition 10, the radial peak acceleration value at the top of pier #3 was reduced to 14.3% compared with the bottom of pier.
Figure
Comparison of time history curves of acceleration. Note: 0.25-1-R stands for the radial acceleration time history curves of the top of pier #1 when the input peak acceleration of seismic wave was 0.25 g PGA; 0.25-1-T stands for the tangential acceleration time history curves of the top of pier #1 when the input peak acceleration of seismic wave was 0.25 g PGA and similar to other circumstances.
0.25-1-T
0.25-2-T
0.25-3-R
0.25-3-T
0.375-1-T
0.375-2-T
0.375-3-R
0.375-3-T
0.5-1-T
0.5-2-T
0.5-3-R
0.5-3-T
0.75-1-T
0.75-2-T
0.75-1-R
0.75-3-T
1-1-T
1-2-T
1-3-R
1-3-T
The following can be seen from Figure The peak acceleration values on top of the piers of the isolation model were reduced to varying degree under earthquake excitation of different seismic intensities compared with the seismic model. When the input peak acceleration of seismic wave was 0.25 g PGA, the reduction rates of tangential peak acceleration at the top of piers #1, #2, and #3 are 28.5%, 42.6%, and 32.2%, respectively, and the reduction rate of radial peak acceleration at the top of pier #3 is 7.8%. When the input peak acceleration of seismic wave was 0.375 g PGA, the reduction rates of tangential peak acceleration at the top of piers #1, #2, and #3 are 10.6%, 3.7%, and 30.4%, respectively, and the reduction rate of radial peak acceleration at the top of pier #3 is 23.2%. When the input peak acceleration of seismic wave was 0.5 g PGA, the reduction rates of tangential peak acceleration at the top of piers #1, #2, and #3 are 6.7%, 21.4%, and 28.7%, respectively, and the reduction rate of radial peak acceleration at the top of pier #3 is 30.1%. When the input peak acceleration of seismic wave was 0.75 g PGA, the reduction rates of tangential peak acceleration at the top of piers #1, #2, and #3 are 27.2%, 11.1%, and 26.9%, respectively, and the reduction rate of radial peak acceleration at the top of pier #3 is 8.5%. When the input peak acceleration of seismic wave was 1 g PGA, the reduction rates of tangential peak acceleration at the top of piers #1, #2, and #3 are 13.3%, 32.3%, and 55.5%, respectively, and the reduction rate of radial peak acceleration at 3# pier top was 47.3%.
From the above analysis, when curved bridge design considering the bearings friction sliding isolation is used, the isolation effects become more remarkable with the increase in seismic intensity; the maximum reduction rates of peak acceleration can be up to 47.3% radially and 55.5% tangentially. The experimental results by Zhong et al. [
Previous study results show that the displacement of the superstructure above the isolation layer will be amplified, which exists in the isolation structures. The displacement time history curve in this paper shows the comparison of the top of pier #2 and its upper girder under effect of El Centro wave at different seismic intensities, as shown in Figure
Comparison of time history curve of displacement. Note: 0.25-R stands for the radial displacement time history curves of pier top and girder when the input peak acceleration of seismic wave was 0.25 g PGA; 0.25-T stands for the tangential displacement time history curves of pier top and girder when the input peak acceleration of seismic wave was 0.25 g PGA and similar to other circumstances.
0.25-R
0.25-T
0.375-R
0.375-T
0.5-R
0.5-T
0.75-R
0.75-T
1-R
1-T
Figure
The experimental results of previous studies [
The destruction due to excessive force carried by the bridge pier is one of the main forms of seismic damage which occurred to curved bridge during earthquake [
Comparison of strain time history curves. Note: 0.25-1 shows the strain time history curve at the bottom of pier #1 when the input peak acceleration of seismic wave was 0.25 g PGA and similar to other circumstances.
0.25-1
0.25-2
0.25-3
0.375-1
0.375-2
0.375-3
0.5-1
0.5-2
0.5-3
0.75-1
0.75-2
0.75-3
1-1
1-2
1-3
The following can be seen from Figure When the input peak acceleration of seismic wave was applied from 0.25 g to 1 g, the strain peak values for the bottom of pier #1 of seismic model were 205 In summary, the peak strain values for the bottom of piers of the isolation model are greatly reduced compared with the seismic model. Basically, the isolation effect increases proportionally with the seismic intensity. The curved bridge considering bearing friction sliding isolation is designed to isolate the girder from the lower part of the bridge structure using bearing, reasonably extend the life cycle of the bridge structure system, and reduce the seismic force transmitted from the bridge superstructure to the pier by dissipating partial seismic energy and avoid or reduce the nonelastic deformation of the bridge pier. The previous experiment result [
In this paper, the shaking table comparison tests of two curved bridges considering or not bearings friction sliding isolation are carried out, respectively; the dynamic characteristics and response of the model structures are studied. The following conclusions can be drawn: With the increase of seismic intensity, the natural frequencies of the two model bridges significantly decrease, while the damping ration increases. The stiffness is degraded for both the seismic model and the isolation model. The stiffness degradation of seismic model is caused by severe damage after cracks appear at piers, and the stiffness degradation of isolation model is caused by the change in boundary condition of bridge due to greater sliding movement of the bearings. For curved bridge considering bearing friction sliding isolation, its maximum reduction rate of peak acceleration at the pier top after earthquake is 24.6% compared with the bottom of pier. Its damping effect is more significant with the increase of seismic intensity in contrast to the curved bridge without considering bearing friction sliding isolation. The maximum reduction rate is 47.3% for radial peak acceleration and 55.5% for tangential peak acceleration. The tangential displacement response of the girder of the isolation curved bridge is basically not magnified compared with the pier, while the maximum radial relative displacement between girder and pier is 13.7 mm. Thus, during seismic design, the radial displacement of the curved bridge should be strictly controlled, and the girder unseating damage can be avoided by measures, for example, the installation of energy-dissipated vibration reduction retainers. The strain values at the bottom of pier of the curved bridge without considering bearing friction sliding isolation become greater with the increase of seismic intensity. In contrast, the strain values on the bottom of pier of the curved bridge considering bearing friction sliding isolation decrease with increase of seismic intensity. Under the same intensity, the strain values at the bottom of pier of isolation model have significantly reduced compared with the seismic model, with maximum reduction rate of 43.4%. Therefore, the curved bridge considering bearing friction sliding isolation has remarkable seismic effect, and it can be applied to the seismic design of high-intensity seismic areas. The curved bridge considering bearing friction sliding isolation adopts clear-cut isolation mechanism. Its friction sliding can be used to dissipate seismic energy under earthquake action and minimize the seismic force transferred to the substructure. In addition, the laminated rubber bearing has advantages of simple construction, low cost, and easy installation, so that the operational capability of bridge can be restored after earthquake through reinstatement or the replacement of the bearings.
The authors declare that there are no competing interests regarding the publication of this paper.
The research presented herein was supported by the Natural Science Foundation of China (Grant no. 51078306) and the Youth Foundation of China (Grant no. 51508453). The writers are grateful for this support.