Published: 28 December 2022

Time history analysis of seismic response of through CFST non isolated and isolated arch bridges

Zhonghu Gao1
Weigang Sun2
1School of Civil Engineering, Northwest Minzu University, Lanzhou, China
2School of Civil Engineering, Shijiazhuang Tiedao University, Shijiazhuang, China
Corresponding Author:
Zhonghu Gao
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Abstract

To explore the difference in the impact of transverse bracing on the seismic effect of through concrete-filled steel tube arch bridges with non-isolated and earthquake-isolated, nine non-isolated and earthquake-isolated structural models under different cross-bracing arrangements were established, and Elcentro seismic waves were selected. The internal force, displacement, velocity, absolute acceleration, relative acceleration, and separation of arch ribs of each model were compared and analyzed under uniform excitation along the bridge, transverse and vertical directions, multi-dimensional combined excitation, and multipoint excitation considering the traveling wave effect. Based on the shear force and displacement of the earthquake support, it is concluded that the internal force response of different excitations of various models is more complicated. The installation of transverse bracing on the upper part of the arch rib can reduce the vertical displacement of the arch rib of the nonseismic structure. The “X”-shaped cross brace at the top of the arch rib and the “K”-shaped cross brace at the lower part help to reduce the transverse acceleration of the arch rib. The absolute acceleration and relative acceleration of the seismic structure arch ribs are significantly reduced.

Time history analysis of seismic response of through CFST non isolated and isolated arch bridges

Highlights

  • Time-history response of arch foot axial force
  • Time-history response of vault displacement under various conditions of non-seismic isolation
  • Time-history response of vault lateral velocity in each case of seismic isolation
  • Time-history response of lateral acceleration of nine vaults under working conditions
  • Hysteresis curve

1. Introduction

In recent years, there have been frequent earthquakes around the world. As a lifeline project for postdisaster reconstruction and disaster relief, bridges have always received extensive attention. A large number of concrete-filled steel tube arch bridges have been built, and research on related cross-bracing arrangements is also ongoing.

Dong Rui et al. [1] studied the effectiveness of new L-shaped cross-braces in the stability of long-span concrete-filled steel tube truss arch bridges. Hejiang Third Bridge was taken as the engineering background, using a combination of numerical calculation and theoretical analysis to compare and analyze its mechanical performance and stability, and use orthogonal experiment and variance analysis methods to evaluate the significance of L-shaped cross braces in the stability of long-span CFST truss arch bridges Zhang Sumei and Yundi [2] analyzed and compared the possible layout schemes of cross braces and X braces for a 360-meter-span half-through concrete-filled steel tube arch bridge, and proposed the rationality of X braces and cross braces accordingly. According to the principle of equal bracing area and similar material consumption of transverse bracing system, four bracing schemes were proposed and analyzed for ultimate bearing capacity respectively; Wan Peng et al. [3] designed the Guangzhou Xinguang Bridge with a main span of 428 meters in plan, the large-scale finite element software ANSYS was used to establish a three-dimensional finite element model of the full bridge, and the influence of the number and position of the transverse braces on the elastic stability and the ultimate bearing capacity of the plane was analyzed. Jin Bo et al. [4] used the finite element method to analyze the influence of transverse bracing on the overall stability of a cable-stayed concrete-filled steel tube arch bridge; Chen Baochun et al. [5] found arch and arch-girder composite bridges are the main ones; Liu Zhao et al. [6] derived the analytical calculation formula for the lateral elastic stability bearing capacity of arch bridges with transverse braces based on the energy principle, and verified the proposed finite element numerical solution through a numerical example. The correctness of the analytical formula and finally discussed the influence of structural parameters on the stability of bearing capacity; Wu Meirong et al. [7] stepped into the non-thrust half-through concrete-filled steel tube arch bridge in terms of rise-span ratio, width-span ratio, main arch rib stiffness, transverse bracing Changes in the dynamic characteristics of the bridge structure when the layout mode, suspender failure, and support layout are changed; Kong Dandan et al.[8] took a steel truss arch bridge in a certain city as the research object and showed that increasing the number of wind bracing structures can significantly improve the structure’s performance stability; but when the number of wind bracing is sufficient, the continue to increase the number of wind bracing structures, the stability of the structure cannot be greatly improved, and the setting of diagonal braces has a great influence on the overall stability, especially “K” and “X” diagonal braces have a significant impact on the structural stability; Li Xiayuan et al. [9] relying on a certain through-type steel tube concrete arch bridge, based on the original bridge wind bracing form, using the MIDAS Civil finite element analysis software to establish the “-” The calculation model for the through-type steel tube concrete arch bridge with “X”-shaped wind bracing, “K”-shaped wind bracing, “m”-shaped wind bracing, and “X”-shaped wind bracing, extracts the first 20-order natural frequency and The vibration mode types of the first 6 steps were compared and analyzed with the original bridge; Zheng Xiaoyan et al. [10] studied the stability of the tied arch bridge during the construction phase and the influence of temporary transverse bracing on the structural stability.

In this paper, nine non-isolated and earthquake-isolated structural models under different cross-bracing arrangements were established, and Elcentro seismic waves were selected. The internal force, displacement, velocity, absolute acceleration, relative acceleration, and separation of arch ribs of each model were compared and analyzed under uniform excitation along the bridge, transverse and vertical directions, multi-dimensional combined excitation, and multipoint excitation considering the traveling wave effect.

The layout position and layout of the transverse bracing have different effects on the through-type concrete-filled steel tube seismic arch bridge and the seismic isolation arch bridge. The article will conduct comparative analysis and research to provide the necessary references for the design and construction of similar arch bridges.

2. Principles of time history analysis

The vibration equation for dynamic time history analysis is:

1
My..+Cy.+Ky=P,

where MS, CS, KS denote the mass matrix, damping matrix and stiffness matrix of the corresponding structural non-supporting position, respectively, use Mb, Cb, Kb to denote the mass matrix, damping matrix and stiffness matrix of the corresponding structural support position, respectively, and use y¨s, y˙s, ys to denote the structural non-supporting position under earthquake action, the acceleration, velocity and absolute displacement of the support, with y¨b, y˙b, yb, respectively represent the acceleration, velocity and absolute displacement vector of the structural support position under the action of an earthquake. Fb is the reaction force of the support under the action of an earthquake. Then the vibration equation can be expressed in the following form:

2
Mss0 0Mbbys..yb..+CssCbs CsbCbbys.yb.+KssKbs KsbKbbysyb=0Fb.

3. Finite element model

Taking an actual through arch bridge as the background, nine non-seismic and seismic finite element models of different transverse bracing arrangements are established. The transverse bracing arrangement and finite element model are shown in Table 1 and Fig. 1. The seismic isolation model is equipped with lead-core rubber seismic isolation bearings, and the bearing parameters are shown in Table 2. The bridge has a main span of 127 m and a bridge deck width of 31 m. The arch rib cross-section is dumbbell-shaped. The diameter of the upper and lower arch ribs is 1.2 m, and the diameter of the cross brace is 1.3 m.

Table 1The layout of transverse bracing in various working conditions

Working condition 1
Working condition 2
Working condition 3
Working condition 4
Working condition 5
Working condition 6
Working condition 7
Working condition 8
Working condition 9
A cross brace in the shape of “-” on the vault
Three “-”-shaped cross braces on the vault and the middle and upper parts
Three “-”- shaped cross braces on the vault and the middle and lower parts
Five-way "-" cross brace
One “-”- shaped cross brace on the vault, and two “K” cross braces in the middle and upper part
One “-”- shaped cross brace on the vault, two “K” cross braces in the middle and lower part
The vault has one
“-”- shaped cross brace and four “K”-shaped cross braces
One “-”- shaped cross brace on the vault and four “X” cross braces
Five
“X”- shaped cross braces

Table 2Parameter table of lead rubber bearing

Support plane size (mm×mm)
Lead core yield (kN)
Rigidity before yielding (kN/mm)
Rigidity after yielding (kN/mm)
Horizontal equivalent stiffness (kN/mm)
1320×1320
964
25.6
3.9
6.4

Fig. 1Finite element model diagram

Finite element model diagram

a) Working condition 1

Finite element model diagram

b) Working condition 2

Finite element model diagram

c) Working condition 3

Finite element model diagram

d) Working condition 4

Finite element model diagram

e) Working condition 5

Finite element model diagram

f) Working condition 6

Finite element model diagram

g) Working condition 7

Finite element model diagram

k) Working condition 8

Finite element model diagram

l) Working condition 9

4. Analysis of dynamic characteristics

Through the finite element software analysis of the dynamic characteristics, the frequency and mode shape of the non-isolated and isolated models under nine working conditions are obtained. The first three orders are shown in Table 3, and the frequency comparison is shown in Fig. 2. It can be seen that the first-order modes of the two models under nine working conditions are all arch rib lateral inclination, and the first-order frequencies of working conditions 1, 2, 3, and 4 have little difference, while the first-order frequencies of working conditions 8 and 9 are relatively different. Large “K”-shaped cross braces and “X” cross braces can increase the fundamental frequency, and the effect of being close to the lower part of the arch rib is obvious. The “X” cross brace on the dome actually reduces the fundamental frequency. The second and third order frequencies and modes of the two models are quite different, and the influence of the cross bracing of the non-isolated model is more obvious than that of the isolated model.

Table 3The first third-order frequency and mode shape of each working condition

Working condition
Types
Frequency and mode shape
First order
Second order
Third order
Working condition 1
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.167
0.520
0.521
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.160
0.253
0.283
Working condition 2
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.167
0.517
0.647
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.160
0.252
0.284
Working condition 3
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.168
0.518
0.647
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.161
0.252
0.284
Working condition 4
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
0.168
0.515
0.645
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.161
0.252
0.284
Working condition 5
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.188
0.522
0.645
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.177
0.252
0.290
Working condition 6
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.213
0.546
0.645
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.195
0.252
0.297
Working condition 7
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.231
0.548
0.642
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.205
0.252
0.306
Working condition 8
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.332
0.619
0.640
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.233
0.251
0.363
Working condition 9
Non-isolated
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.330
0.640
0.691
isolation
Mode shape
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
The first third-order frequency and mode shape of each working condition
Frequency
0.232
0.251
0.365

5. Selection of seismic wave and apparent wave speed

The seismic fortification intensity of the area where the bridge is located is 8 degrees (0.2 g), and the site category is Type II. The El Centro seismic wave is selected, and the peak acceleration value of the seismic wave is multiplied by a coefficient of 0.339 for adjustment. The adjusted seismic wave is shown in Fig. 3, and the action time is taken as 20 s, the excitation direction is uniform excitation along the bridge direction, uniform excitation across the bridge direction, uniform excitation vertical direction, multi-dimensional combination one (long bridge direction + 0.3 horizontal bridge direction + 0.3 vertical) excitation, multi-dimensional combination two (0.3 forward bridge direction + Transverse bridge direction + 0.3 vertical direction) excitation, multi-dimensional combination three (0.3 along bridge direction + 0.3 transverse bridge direction + vertical direction) excitation and the apparent wave speed is 100 m/s, 200 m/s, 300 m/s, 400 m/s, Multi-point excitation of 500 m/s, 1000 m/s, 1500 m/s, 2000 m/s.

Fig. 2Frequency comparison

Frequency comparison

a) First order

Frequency comparison

b) Second order

Frequency comparison

c) Third order

Fig. 3El-centro seismic wave adjusted

El-centro seismic wave adjusted

6. Earthquake response analysis

6.1. Internal force of arch rib

See Table A1 for the maximum internal force and damping rate of arch ribs in different models under uniform excitation. See Table A2 for the maximum internal force and damping rate of arch ribs in different models under multi-dimensional combined excitation. Under multi-point excitation considering traveling wave effect, the maximum internal force and shock absorption rate of arch ribs in different models under various working conditions are shown in Table A3. The time-history response of partial arch foot axial force is shown in Fig. 4.

Through the comparison of Table A1 to Table A3 and Fig. 4, we can get:

(1) Under the action of seismic waves with different wave speeds in the bridge direction, transverse bridge direction, combination 1 and bridge direction, the main internal force of the seismic isolation structure arch rib in each working condition is significantly reduced;

(2) Under the action of vertical earthquake, the main internal forces of the seismic isolation structure arch ribs in various working conditions increased, the shear force FZ increased by more than twice, and the bending moment My increased by more than three times;

(3) Under the action of the second combination earthquake, the arch rib axial force of each working condition of the seismic isolation structure decreases, the shear force Fz increases, the bending moment Mz in working condition 8 and 9 increase, and the rest decrease. Under the action of the combination three earthquakes. The main internal force of the arch rib of the seismic isolation structure in the working condition increased, the shear force FZ increased more than doubled, and the bending moment My increased more than doubled;

(4) Under the effects of lateral earthquake and combination, the main internal force of the seismic isolation structure arch ribs in working conditions 8 and 9 increase significantly.

Fig. 4Time history response of arch foot axial force

Time history response of arch foot axial force

a) Working condition1 along the bridge

Time history response of arch foot axial force

b) Condition 7 along the bridge

Time history response of arch foot axial force

c) Condition 1 Cross-bridge direction

Time history response of arch foot axial force

d) Working condition 5 Combination one

6.2. Arch rib displacement

The maximum displacement of the arch rib under transverse excitation is shown in Table 4, and the time-history response of the DY time history of the vault displacement under non-seismic conditions is shown in Fig. 5.

Fig. 5DY time-history response of vault displacement under various conditions of non-seismic isolation

DY time-history response of vault displacement under various conditions of non-seismic isolation

Through the comparative analysis of Table 4 and Fig. 5, we can get:

(1) Under the action of transverse bridge seismic wave, the arch ribs of non-seismic and isolation models mainly undergo lateral displacement. The lateral displacements of working conditions 1, 2, 3, and 4 are not much different. The lateral displacements of working conditions 5, 6, and 7 are more than other, the working condition is small, and it is concluded that the “K”-shaped cross brace is better than the “-” cross brace and the “meter” cross brace in reducing the lateral displacement of the arch rib;

(2) Comparing various working conditions, it can be concluded that setting up transverse bracing on the upper part can reduce the vertical displacement of the arch rib of the non-seismic model.

Table 4Arch rib displacement (unit: cm)

Incentive direction
Displacement direction
Model
Working condition
1
2
3
4
5
6
7
8
9
Cross bridge
Along the bridge
Non-isolated
0.220588
0.217772
0.218886
0.216088
0.19172
0.215155
0.190403
0.234662
0.238253
Vertical
Horizontal
Vertical
Isolated
0.095618
0.095142
0.095793
0.095229
0.08672
0.090369
0.097304
0.14055
0.138715
Cross bridge
Non-isolated
12.178108
12.190638
12.160166
12.177714
10.963965
9.490335
8.852437
11.574302
11.437827
Vertical
Horizontal
Vertical
Isolated
13.456979
13.433771
13.436001
13.414679
12.387384
11.74146
10.855834
17.104378
16.846004
Vertical
Non-isolated
0.575183
0.569438
0.572487
0.566709
0.505177
0.567788
0.505335
0.55977
0.564412
Isolated
0.225666
0.225264
0.225162
0.224671
0.19714
0.210035
0.216076
0.3417
0.344369

6.3. Arch rib speed

The maximum speed of arch ribs under transverse excitation is shown in Table 5. The time-history response of the transverse velocity of the vault under each condition of seismic isolation is shown in Fig. 6. Through the comparative analysis of Table 5 and Fig. 6, we can get:

(1) Under the action of transverse bridge seismic waves, the lateral velocity of arch ribs in non-seismic and seismic isolation models basically increases in working conditions 1 to 8, while working condition 9 decreases slightly;

(2) Under the action of transverse bridge seismic waves, the longitudinal and vertical speeds of arch ribs in non-seismic and seismic models are relatively small in condition five;

(3) The speed of the arch ribs of the seismic isolation structure in each working condition is reduced.

Table 5Arch rib speed (unit: cm/s)

Incentive direction
Speed direction
Model
Working condition
1
2
3
4
5
6
7
8
9
Cross bridge
Along the bridge
Non-isolated
1.572553
1.573233
1.55233
1.555467
1.481314
1.592136
1.495981
1.442885
1.443201
Isolated
0.8401
0.842009
0.831214
0.836434
0.801512
0.875925
0.845275
0.88414
0.885579
Cross bridge
Non-isolated
25.172737
25.105125
25.468387
25.328813
27.179484
29.70583
31.043626
39.780206
38.68521
Isolated
19.793487
19.782502
19.837443
19.837609
18.940581
23.446982
26.028057
39.182534
38.69969
Vertical
Non-isolated
3.808268
3.734763
3.786084
3.709999
3.400459
3.806481
3.455232
3.459467
3.521407
Isolated
1.711642
1.729262
1.698642
1.715102
1.625263
1.767564
1.702519
1.688422
1.690779

Fig. 6Time-history response of vault lateral velocity in each case of seismic isolation

Time-history response of vault lateral velocity in each case of seismic isolation

6.4. Absolute acceleration of arch rib

The maximum absolute acceleration of the arch rib under transverse excitation is shown in Table 6, and the time-history response of the lateral acceleration of the nine vaults under working conditions is shown in Fig. 7. Through the comparative analysis of Table 6 and Fig. 7, it can be obtained:

(1) Under the action of the transverse bridge seismic wave, the non-isolated and isolated model arch rib lateral acceleration, the non-seismic structure working condition 5 and working condition 7 are smaller, the seismic isolation structure working condition 7 is relatively small, and the working condition 9 is relatively small. Working condition 8 is reduced, it can be inferred that the “米”-shaped cross brace at the top of the arch rib, and the “K”-shaped cross brace at the lower part will help reduce the absolute acceleration of the arch rib.

(2) The absolute acceleration of the arch rib of the seismic isolation structure in each working condition is significantly reduced.

Table 6Absolute acceleration of arch ribs (unit: cm/s2)

Incentive direction
Absolute acceleration direction
Model
Working condition
1
2
3
4
5
6
7
8
9
Cross bridge
Cross bridge
Non-isolated
302.069666
298.588074
314.635446
306.619751
291.123396
315.517481
291.100165
343.150259
338.930472
Isolated
83.273905
82.935068
82.92821
83.290524
82.154905
81.068172
79.804811
91.825414
88.816718

Fig. 7Time-history response of lateral acceleration of nine vaults under working conditions

Time-history response of lateral acceleration of nine vaults under working conditions

6.5. Relative acceleration of arch rib

The maximum relative acceleration of arch ribs under transverse excitation is shown in Table 7.

Table 7Relative acceleration of the arch ribs (unit: cm/s2)

Incentive direction
Relative acceleration direction
Model
Working condition
1
2
3
4
5
6
7
8
9
Cross bridge
Cross bridge
Non-isolated
350.799422
353.664181
349.011316
349.716454
351.965781
330.543943
325.231323
348.104201
346.062742
Isolated
157.707118
157.621842
157.721081
157.612437
156.244506
156.104435
154.734779
150.697906
151.129868

Through the comparative analysis of Table 7, we can get:

(1) Under the action of the transverse bridge seismic wave, the relative acceleration of the arch ribs of the non-seismic and isolation models is relatively small for the non-seismic structure working conditions 6 and 7, and the seismic isolation structure working conditions 1 to 7 basically show a decreasing trend;

(2) The relative acceleration of the arch rib of the seismic isolation structure in each working condition is significantly reduced.

6.6. Shear force and displacement of seismic isolation support

See Table 8 for the maximum shear force and displacement of the seismic isolation support. See Fig. 8 for the shear force comparison of some supports. See Fig. 9 for the displacement comparison of some supports.

Table 8Maximum shear force and displacement of seismic isolation support

Incentive direction
Working condition
1
2
3
4
5
6
7
8
9
Along the bridge
Shear force / kN
940.21
939.78
939.62
940.56
940.73
940.49
939.69
938.43
938.22
Displacement / cm
4.87
4.87
4.86
4.90
4.90
4.90
4.89
4.84
4.84
Cross bridge
Shear force / kN
873.87
873.54
873.76
873.44
861.16
844.86
843.41
762.70
753.41
Displacement / cm
4.34
4.33
4.34
4.33
4.23
4.09
3.95
3.40
3.35
Vertical
Shear force / kN
190.50
190.67
190.48
190.66
190.81
190.56
190.93
191.25
191.63
Displacement / cm
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.76
Combination one
Shear force / kN
934.84
937.98
937.77
936.80
934.97
936.03
937.64
938.89
938.63
Displacement/cm
4.97
4.99
5.00
5.01
4.98
4.98
4.96
4.94
4.91
Combination two
Shear force / kN
852.10
851.64
855.63
852.19
837.90
822.17
815.99
745.03
741.08
Displacement / cm
4.37
4.38
4.41
4.37
4.22
4.18
3.91
3.45
3.34
Combination three
Shear force / kN
448.11
450.55
448.51
452.70
440.66
442.84
446.90
442.42
442.31
Displacement / cm
1.88
1.84
1.84
1.81
1.88
1.85
1.85
1.86
1.86

Fig. 8Comparison of bearing shear force

Comparison of bearing shear force

a) Along the bridge and combination one

Comparison of bearing shear force

b) Cross-bridge direction and combination two

Fig. 9Comparison of bearing displacement

Comparison of bearing displacement

a) Along the bridge and combination one

Comparison of bearing displacement

b) Cross-bridge direction and combination two

See Figure 10 for the shear response time history of some supports. Hysteresis curve for some supports. See Fig. 11. From the analysis of Table 8 and Fig. 8 to Fig. 11, we can get:

(1) The maximum shear force of the seismic isolation support under the excitation of working conditions 1 to 7 is greater than that of combination 1, and the maximum shear force of the seismic isolation support under the excitation of working conditions 8 and 9 is greater than the excitation of the forward bridge;

(2) Under the action of the transverse bridge direction and combination two, the maximum shear force of the seismic isolation support of working conditions 1 to 9 shows a decreasing trend, and the linear direction is basically similar, and the transverse bridge excitation of each working condition is greater than the combination two excitation;

(3) The maximum displacement of each working condition is that the excitation of combination one is greater than the excitation along the bridge direction, and the cross-bridge direction and combination two are basically the same, and there is a decreasing trend from working condition 1 to working condition 9;

Under the vertical excitation, the shear force and displacement of all working conditions are basically the same.

Fig. 10Time history response of bearing shear force

Time history response of bearing shear force

a) Working condition 5, along the bridge direction excitation

Time history response of bearing shear force

b) Working condition 1 cross-bridge excitation

Fig. 11Hysteresis curve

Hysteresis curve

a) Condition 1 along the bridge direction excitation

Hysteresis curve

b) Working condition 9 combination one incentive

7. Conclusions

Nine non-isolated and earthquake-isolated structural models under different cross-bracing arrangements were established, and Elcentro seismic waves were selected. The internal force, displacement, velocity, absolute acceleration, relative acceleration, and separation of arch ribs of each model were compared and analyzed under uniform excitation along the bridge, transverse and vertical directions, multi-dimensional combined excitation, and multipoint excitation considering the traveling wave effect.

Through the above comparative analysis, we can get:

1) The main internal force of the arch ribs of the seismic isolation structure in each working condition decreases significantly under the action of the bridge direction, the horizontal bridge direction, the combination one, and the seismic waves with different wave speeds. Under the vertical earthquake action, the arch of the seismic isolation structure, the main internal force of the rib increases. Under the action of the second combination earthquake, the axial force of the arch rib in each working condition of the seismic isolation structure decreases, the shear force Fz increases, the bending moment Mz working conditions eight and nine increase, and the rest decrease, and the combination three under the action of an earthquake, the main internal forces of the seismic isolation structure arch ribs in various working conditions have increased;

2) Under the action of transverse bridge seismic waves, the arch ribs of non-seismic and isolation models mainly undergo lateral displacement. The “K”-shaped cross brace is better than the “-” cross brace and the “meter” shape in reducing the lateral displacement of the arch rib. Transverse bracing, setting transverse bracing on the upper part of the arch rib can reduce the vertical displacement of the arch rib of the non-seismic model;

3) Under the action of transverse seismic waves, the lateral velocity of the arch ribs of the non-seismic and isolation models basically increased, and the velocity of the arch ribs of the seismic isolation structure under various working conditions decreased;

4) The “meter”-shaped cross brace at the top of the arch rib and the “K”-shaped cross brace at the lower part help reduce the lateral acceleration of the arch rib. The absolute acceleration and relative acceleration of the arch rib of the seismic isolation structure under various working conditions are significantly reduced;

5) Under the action of the maximum shear force of the seismic isolation support in the transverse direction and the combination two, working conditions 1 to 9 show a decreasing trend, and the linear directions are basically similar. In all conditions, the excitation of combination one is greater than the excitation along the bridge direction, and the cross-bridge direction and combination two are basically the same, and there is a decreasing trend from working condition one to working condition nine.

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About this article

Received
01 April 2022
Accepted
07 July 2022
Published
28 December 2022
SUBJECTS
Seismic engineering and applications
Keywords
transverse bracing
seismic isolation
through concrete-filled steel tube arch bridge
time history analysis
Acknowledgements

This research was funded by the Fundamental Research Funds for the Central Universities (31920210078), the National Natural Science Foundation of China (51868067).

Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflict of interest

The authors declare that they have no conflict of interest.