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Based on the seismic isolation design concept of functional separation, a seismic isolation system with bearings and braces combination for railway bridge was proposed. The sliding bearings afford the vertical loads, and the self-centering energy dissipation brace (SCED) and buckling restrained brace (BRB) control the horizontal displacement of the beam, so the functional separation was achieved under the combined action. Taking a long-span railway continuous beam-arch bridge as an example, the corresponding analysis model was established to study lateral seismic response and the girder’s displacement pattern of the continuous beam-arch bridge under the earthquake excitations. The seismic response of bridges with different seismic isolation schemes was studied. The result showed that the presence of arch rib in a continuous beam-arch bridge amplifies the transverse displacement response of the girder compared with that in a continuous beam bridge of equal mass. The seismic isolation system with sliding bearings and energy dissipation braces can control the relative displacement between the pier and beam greatly, and the SCED can reduce or even eliminate the residual displacement between pier and beam. Furthermore, under the strong ground motions, the combined use of SCED and BRB can achieve the seismic isolation to the maximum extent when the self-centering force ratio

The continuous beam-arch bridge is a special kind of bridge structure that consists of two structural systems, the beam bridge and arch bridge. It applies the girder’s axial force organically to balance the arch’s horizontal thrust. The structure’s total bending moment is represented in the form of the girder in tensile and arch compression, and the shear force is the vertical component of arch pressure [

In recent years, continuous beam-arch bridge and continuous rigid-frame bridge have attracted increasing interest in railway bridge construction because of their outstanding performance, such as large vertical stiffness, spanning capability, and excellent landscape effect [

Seismic isolation technology is an effective means to improve structures’ seismic capability and is applied widely in bridges and buildings [

Thus, it is necessary to enhance the seismic performance of the conventional isolation bearing isolation bridge under strong earthquake. Implementing passive energy dissipation devices can be an efficient approach, since an increase in damping reduces both the force and displacement demands placed on bridges [

In recent years, friction pendulum bearing has been widely used in bridges because of its superior seismic isolation effect and self-centering ability. Xu et al. [

In this paper, based on the functional separation seismic isolation design concept, a seismic isolation system comprised of bearings and braces for railway bridges was proposed. The sliding bearings afford vertical loads, and buckling restrained braces (BRB) and self-centering energy dissipation braces (SCEDs) control the horizontal displacement. This paper adopted long-span railway continuous beam-arch bridge as the research object, and its seismic response was calculated by nonlinear time-history analysis. The influence of arch rib on the continuous beam-arch bridge’s lateral seismic response and displacement pattern was taken into account. In addition, the SCED and BRB braces’ effects on bridge seismic isolation were studied.

A typical three-span continuous beam-arch bridge was selected in this study as the proto bridge. Figure

Long-span railway continuous beam-arch bridge (unit: cm): (a) elevation view of the bridge; (b) section A-A; (c) section B-B; (d) section C-C; (e) section D-D.

Three-dimensional finite element model of the continuous beam-arch bridge was developed in OpenSees (Figure

Finite element model of the prototype bridge.

where Δ_{I} is the displacement at yielding of the shear key reinforcement; Δ_{II} is the displacement at peak force, and, in the simplified model, Δ_{III} is the displacement where the shear key reinforcement fails.

_{c} and _{s} are the concrete and reinforcement contributions to the strength of the shear key, respectively. The concrete contribution, _{c}, is expressed as

where

The steel contribution to the capacity of the shear key, _{s}, can be obtained by the following equation:

where _{s,1} and _{y,1} are the total area of steel and the yield strength of the horizontal tension tie, respectively. _{s,2} and _{y,2} are the total area of steel and the yield strength of vertical shear reinforcement, respectively. _{s,s} and _{y,s} are the cross-sectional area and the yield strength of the side reinforcement, respectively. _{h} and _{h} =

The yield displacement, peak displacement, and limit displacement of the shear key can be calculated by

where _{a} is the cracked region, _{d} is the reinforcement development length, _{y} is the yield strain of the steel.

The values of relevant parameters in shear key are presented as follows:

The concrete contribution, _{c}, can be calculated as

The relevant mechanical parameters of reinforcement in the shear key are shown as follows:

The reinforcement contribution, _{S}, can be obtained as

The yield displacement, peak displacement, and limit displacement of the shear key can be calculated as

The shear force at Levels I and II can be calculated as

Pounding modeling. The impact between the superstructure and the abutment in the transverse direction was modeled by using the Hertz-damp model, which can simulate the energy dissipation in pounding well. The mechanical properties of the model are shown in Figure _{h} is the impact stiffness, the value of which is the shear key’s bending stiffness; _{m} is the maximum penetration in the impact. The effective stiffness is calculated using the following equation:

Parameter values for various analytical models for continuous beam-arch bridge.

Bridge component model | Parameters |
---|---|

Bearing | |

Abutment | _{y} = 0.003 m |

Pier | _{y} = 0.003 m |

Shear key | _{I} = 639.8 kN, _{II} = 886 kN |

Δ_{I} = 0.0036 m, Δ_{II} = 0.0115 m, Δ_{IV} = 0.0573 m | |

Pounding | |

Abutment | Δ_{G} = 0.03 m, _{1} = 28224 kN/m, _{2} = 11904 kN/m |

Pier | Δ_{G} = 0.03 m, _{1} = 179954 kN/m, _{2} = 75662 kN/m |

Analytical models of shear key.

Hertz-damp model for pounding simulation.

To ensure the accuracy of the model, the dynamic analysis models of the continuous beam-arch bridge were established in both OpenSees and MIDAS/Civil. The dynamic characteristic analysis was carried out. The first three periods obtained from OpenSees and MIDAS/Civil are listed in Table

Dynamic characteristics of the continuous beam-arch bridge.

Number | Period (s) | Description | |
---|---|---|---|

OpenSees | MIDAS/Civil | ||

1 | 2.32 | 2.30 | Lateral flexure of arch rib |

2 | 1.33 | 1.32 | Antisymmetric flexure of arch rib |

3 | 1.01 | 1.05 | Lateral flexure of girder |

Three typical modal shapes (MIDAS/Civil): (a) first vibration mode; (b) second vibration mode; (c) third vibration mode.

To study the arch ribs’ effect on the lateral seismic response of continuous beam-arch bridge and the lateral displacement patterns of the girder, seven ground motions of hard site were selected from the strong ground motion record database [

Selected ground motion recorders.

Number | Earthquake | Station | Component | Year | PGA (g) | PGV (m/s) | PGV/PGA |
---|---|---|---|---|---|---|---|

1 | Imperial Valley | 6621 Chihuahua | CHI012 | 1979 | 0.27 | 0.25 | 0.92 |

2 | Landers | 22074 Yermo Fire Station | YER270 | 1992 | 0.24 | 0.52 | 2.10 |

3 | Northridge | 90063 Glendale-Las Palmas | GLP177 | 1994 | 0.36 | 0.12 | 0.34 |

4 | Northridge | 90016 LA-N Faring Rd | FAR000 | 1994 | 0.27 | 0.16 | 0.58 |

5 | Northridge | 90091 LA-Saturn St | STN020 | 1994 | 0.47 | 0.35 | 0.73 |

6 | Imperial Valley | 6621 Chihuahua | CHI282 | 1979 | 0.25 | 0.30 | 1.18 |

7 | Chi-Chi | CHY036 | CHY036-W | 1999 | 0.29 | 0.39 | 1.32 |

Spectra of selected ground motion.

To investigate the arch ribs’ influence on the lateral seismic response of the continuous beam-arch bridge and the girder’s lateral displacement patterns, it was assumed that the girder at the abutment and pier can move freely without the constraints of the shear keys in lateral direction. Based on OpenSees seismic analysis platform, the different dynamic analysis models were established and nonlinear time-history analysis was performed. There are three different analysis models: In Model 1, a continuous beam-arch bridge model with sliding bearings was adopted. In Model 2, a continuous beam-arch bridge model with sliding bearings was adopted, the arch ribs’ mass was assigned to the girder, and only the contribution of stiffness was considered in the arch ribs. In Model 3, a continuous beam bridge model with sliding bearings was adopted and the arch ribs’ mass was assigned to the girder.

The first five periods of the three models are shown in Table

Period of three finite element models (units: s).

Number | Model 1 | Model 2 | Model 3 |
---|---|---|---|

1 | 2.32 | 1.17 | 1.19 |

2 | 1.33 | 0.73 | 0.73 |

3 | 1.05 | 0.72 | 0.72 |

4 | 0.73 | 0.51 | 0.52 |

5 | 0.72 | 0.32 | 0.32 |

Figure

The peak displacement of key position of the girder.

Displacement time-history curve of continuous beam-arch bridge (Imperial Valley): (a) displacement time-history curve of the girder and arch rib; (b) displacement time-history curve of the girder.

The above study did not consider the constraint of lateral shear keys. However, several shear keys were installed at the abutments and piers to restrain the girder’s lateral displacement in fact. To consider the shear keys’ restraint effect on the girder, three different finite models that considered the lateral shear keys were established. To study the seismic response of the bridge with shear keys, nonlinear time-history analysis was carried out. Figure

The peak displacement of key positions of the girder.

As Figures

Displacement time-history curve of the girder and arch rib.

In this paper, the lateral displacement patterns of girder and ribs were judged according to the coefficient of displacement variation proposed by Dwairi and Kowalsky [

Coefficient of displacement variation of the girder and arch ribs (unit: %).

Position | Unconstraint | The constraint by shear keys | ||||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 3 | Model 1 | Model 2 | Model 3 | |

Girder | 1.1 (2.7) | 1.6 (3.1) | 1.2 (3.4) | 4.9 (4.8) | 6.5 (8.5) | 6.5 (7.6) |

Arch ribs | 9.5 (11.3) | 1.2 (1.9) | — | 33.2 (33.8) | 4.1 (5.5) | — |

The seismic response of nonlinear elements of a continuous beam-arch bridge under the Landers earthquake motion is shown in Figure

Force-displacement responses of various nonlinear elements of continuous beam-arch bridge under Landers earthquake motions: (a) shear key of abutment; (b) bearing; (c) pounding.

A seismic isolation system that can be used in railway bridges was proposed based on the functional separation seismic isolation design concept. The system consists of bearings and braces. Two types of braces, self-centering energy dissipation braces (SCED) and buckling restrained braces (BRB), were adopted. The sliding bearings accommodate the vertical loads caused by girder, and the braces (SCED and BRB) control the horizontal displacement, so the function separation is achieved under the combined action. In addition, the SCED can control the residual displacement between the pier and girder to realize the bridge’s functional recoverability after an earthquake.

The hysteretic response of the SCED brace is common for self-centering systems and is characterized by a “flag-shaped” hysteresis. The brace’s restoring force curve is shown in Figure

Restoring force curve: (a) SCED; (b) BRB.

The mechanical parameters of the brace.

Type | _{0} (kN/m) | _{0} (kN/m) | _{y} (kN) | _{y} (mm) |
---|---|---|---|---|

BRB | 1000000 | 32900 | 2350 | 2.35 |

SCED | 1000000 | 32900 | 2350 | 2.35 |

In the bridge’s seismic isolation design, a seismic isolation device is installed to increase the period of the bridge and dissipate seismic energy, expecting to reduce the seismic response of the bridge structure. This requires the seismic isolation devices to be sufficiently resilient to avoid the large relative displacements and residual displacements between the pier and girder. Therefore, the design scheme of seismic isolation device is determined by nonlinear time-history analysis and test methods. According to the requirement of resilience of seismic isolation devices in the AASHTO Bridge Isolation Design Guidelines, when the lateral displacement of seismic isolation device increases from half of the target displacement to the target displacement, the increase in resilience should be no less than 0.025 times the superstructure’s weight. Finally, through trial calculations, the continuous beam-arch bridge was equipped with twelve braces for seismic isolation and damage control. Two braces were mounted on each abutment and four braces were mounted on each pier to meet the seismic isolation design requirements.

To study the effect of different braces on seismic isolation of continuous beam-arch bridge, the following three analysis cases were proposed: In Case 1, the bridge was not equipped with any type of braces, and constraint of shear keys was considered. BRB and SCED played the role of isolation devices in Case 2 and Case 3, respectively. In these three cases, the selected types of bearings are all the sliding bearings. The ground motion record was input along the lateral direction of the bridge to perform the time-history analysis.

Table

The relative displacement and residual displacement between pier and girder under different analysis cases (mm).

Position | Relative displacement | Residual displacement | ||||
---|---|---|---|---|---|---|

Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | |

Abutment | 120 | 19 | 38 | 29.01 | 3.74 | 0.027 |

Pier | 106 | 42 | 54 | 28.61 | 4.82 | 0.063 |

Two types of brace, BRB and SCED, are able to reduce the residual displacement significantly. As shown in Table

Figure

Hysteretic curve and displacement time-history curves of braces: (a) hysteresis curve; (b) displacement time-history curves.

Figure

The lateral displacement of the girder and arch rib of a continuous beam-arch bridge: (a) girder; (b) arch rib.

In Cases 2 and 3, it can be seen that SCED or BRB can dissipate a portion of the input seismic energy and control the relative displacement between girders and piers under earthquake excitation. However, the displacement control effect of BRB is stronger than that of SCED, and the residual displacement of SCED tends to zero after earthquake. Therefore, the seismic isolation system combining SCED and BRB was proposed. Based on the principle of equal stiffness design, five kinds of SCED and BRB combined seismic isolation design schemes were proposed, as shown in Table

Combined design scheme of SCED and BRB.

Case 4 | SCED ( | BRB | Self-centering force ratio |
---|---|---|---|

1 | 10 | 2 | 0.124 |

2 | 8 | 4 | 0.099 |

3 | 6 | 6 | 0.074 |

4 | 4 | 8 | 0.050 |

5 | 2 | 10 | 0.025 |

In order to determine the optimal combination design scheme, the non-dimensional parameter self-centering force ratio _{ys} is the yield force of SCED braces;

The relationship between self-centering force ratio and displacement, residual displacement of braces: (a) displacement; (b) residual displacement.

Figure

The relationship between seismic mitigation ratio and self-centering force ratio.

Figure

A railway continuous beam-arch bridge was regarded as the proto structure, and the influences of arch ribs on the lateral seismic response and displacement patterns were discussed. A seismic isolation system for railway bridge was proposed; a combination of bearings and braces was used in this system to achieve the functional separation. The seismic response of the continuous beam-arch bridge with different isolation schemes was studied:

Compared with the continuous beam bridge of equal mass, the lateral displacement response of the beam is amplified due to the existence of arch ribs. Compared with the continuous beam-arch bridge without the constraint of the shear keys, the transverse displacement of the girder was reduced significantly if the constraint of shear keys is taken into account. The shear keys limited the transverse displacement of the girder. The arch rib’s influence on the girder’s displacement also was reduced because of the presence of the lateral shear keys.

When the constraint of shear keys is not considered, the girder and arch rib move in the same phase. The girder and arch ribs exhibited rigid body translation or rotation along the bridge’s transverse direction. When the constraint of shear keys is considered, the girders’ displacement pattern exhibited rigid body translation or rotation along the transverse direction of the bridge. The arch ribs exhibited a great flexural deformation along the transverse direction of bridge.

Based on the seismic isolation design concept of functional separation, the seismic isolation system with sliding bearings and energy dissipation braces (SCED, BRB) was proposed, which can significantly reduce the displacement demand of fixed pier and keep the pier in elastic state. In contrast, the displacement control effect of BRB is stronger than that of SCED, and the residual displacement of SCED tends to zero after earthquake.

The combined use of SCED and BRB can give full play to the energy consumption of BRB and the self-centering characteristic of SCED to achieve the seismic isolation effect; when the self-centering force ratio

The authors declare that they have no conflicts of interest.

This work was funded by the National Natural Science Foundation of China (Grant nos. 51768042 and 51908265) and Fund for Excellent Young Scholars of LUT (Grant no. 04-061810). The authors are grateful for their support.