Seismic response analysis of the precast double-deck rocking frame bridge pier system
Introduction
The collapse of the Cypress Viaduct during the 1989 Loma Prieta earthquake, which caused severe casualties and economical losses, has directed the attention of researchers to seismic performance of the frame bridge piers of double-deck viaduct [[1], [2], [3], [4]]. Currently, conventional ductility based seismic design is usually utilized in earthquake resistance design of double-deck viaduct frame bridge piers, in which the columns are designed as ductile members and the cap beams and beam-column joints are designed as capacity protection members [5,6]. However, the forenamed practice presents significant drawbacks, which can be summarized as follows: (1) there are up to eight potential plastic hinge areas in the frame bridge pier, (2) the overall stability problem may occur before the frame bridge pier approaches ductile capacity and (3) the columns are allowed to present inelastic response, which will inevitably cause considerable damages and permanent drifts and leading to time-consuming or even impossible post-earthquake repairs [7].
In this context, structural rocking has been taken as an alternative earthquake resistant design practice that overcomes the above disadvantages. The response of rocking systems display minimal damage [8] and remarkable self-centering capacity [9]. In addition, structural rocking can be implemented by prefabricated assembly technology, which can effectively reduce the construction time and thus the corresponding costs compared with conventional cast-in-place construction method.
The rocking response of free-standing rigid blocks was first studied by Housner [10], who developed the inverted pendulum model and uncovered a size-frequency scale effect. Following Housner's classical model, considerable studies have been conducted to further address the dynamics of the free standing rigid blocks [[11], [12], [13]]. Recently, several studies were conducted and extended to various forms of rocking systems, such as rocking frames [14,15], rocking bridge piers [16], rocking foundations [17,18] and three-dimensional rocking structures [19].
Compared with rigid rocking blocks, relatively few studies have investigated flexible rocking structures and even fewer consider coupled conventional structures with rocking systems. Acikgoz and DeJong [20] investigated the interaction of elasticity and rocking in flexible structures and concluded that structural flexibility changes the response of rocking structures, but it has little influence on the dynamic stability. Zhang [17]conducted studies on rocking responses of flexible column-foundation system and developed demand models by using dimensionless regression analysis. Seismic response of a yielding structure coupled with a rocking wall was examined in depth by Aghagholizadeh and Makris [21,22], who showed that participation of the rocking wall reduce peak and permanent drifts of the flexible structure. Bachmann and Vassiliou [23] carried out the study on rocking podium structures consisting of a superstructure anchored on top of a rigid slab supported by free-standing columns. An analytical model of the rocking podium structures, assuming the superstructure to be a SDOF elastic oscillator, was developed and verified by experiments. Parameters affecting the stability of the systems under earthquake excitations were investigated using the forenamed analytical model.
In the light of the previous remarks, this study develops a novel precast double-deck rocking frame bridge pier system (DDRF) coupling the ductile yielding structure and rocking structure to improve seismic performance of double-deck frame bridge piers. In this novel system, as shown in Fig. 1, the upper columns are allowed to rock between the precast cap beams to form the rocking story and the lower columns are connected to precast cap beam and footings by grouted splice sleeve to form emulative cast-in-place story. The nonlinear equations of motion that describes the two-dimensional seismic response of the proposed ductile-rocking structure are derived and presented in this paper. The effects of the design parameters on seismic demands, as well as on associated overturning potential of the system under Ricker pulse excitations are investigated using the analytical model. The interaction of structural ductility and rigid rocking has also been studied.
Section snippets
Equations of motion
The motion pattern of the DDRF system under horizontal seismic excitationsis schematically depicted in Fig. 2. From shaking table tests of single-story double-column rocking bridge structure [24,25], it can be seen that by setting suitable anti-shear and anti-torsion device, the dynamic behavior of the rocking column can be approximately simplified to in plane rigid body motion. Therefore, it is assumed that the upper rocking column and the cap beam are rigid without deformation. Further,
The example bridge
This section investigates seismic performance of the novel DDRF system with conventional bridge pier size to verify the feasibility of the proposed novel system. The example monolithic bridge pier is shown in Fig. 7. Prestressed concrete composite box girders with a span of 30 m are used as the upper and lower level girders of the double-deck bridge. The upper columns of the frame bridge pier are 8.5 m tall with a cross section of 1.6 m × 1.8 m. The weight of the two upper columns is 213.8 ton
Pulse-type ground motions
To assess the seismic stability of the DDRF system, the pulse-type ground motions are considered in this study due to the fact that rocking structures are more sensitive to long-period coherent ground motions [40]. Various closed-form expressions have been proposed in the literature that can adequately capture the impulsive character of near-field ground motions both qualitatively and quantitatively [40,41]. The Rick wavelet [42,43], which can accurately represent the dynamic features of
Conclusions
Based on ductile yielding and structural rocking, a novel precast double-deck rocking frame bridge pier system is proposed in the present paper. The upper columns of the system are allowed to rock between the precast cap beams to form the rocking story and the lower columns are connected to precast cap beam and footings by grouted splice sleeve to form emulative cast-in-place story. A dynamic model that describes the two-dimensional seismic response of the ductile-rocking structure is derived
Author statement
Bao-Fu Wang: Conceptualization, Methodology, Software, Visualization, Writing-Original draft, Writing- Reviewing and Editing.
Qiang Han: Conceptualization, Methodology, Writing-Original draft, Writing- Reviewing and Editing.
Zhen-Lei Jia: Writing-Original draft, Software.
Xiu-Li Du: Conceptualization, Writing- Reviewing and Editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research is jointly funded by the National Key of Research and Development of China (2018YFC1504306), National Natural Science Foundation of China (NSFC) (Grants No. 51878016, 51838010), Beijing Municipal Education Commission (IDHT20190504, KZ202010005001), Natural Science Foundation of Hebei Province (E2019508162) and Langfang Science and Technology Research and Development Program (2019013080,2018013022). These supports are gratefully acknowledged. The results and conclusions presented
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