Seismic responses of bridges with rocking column‐foundation: A dimensionless regression analysis

Abstract

Summary Rocking column‐foundation system is a new design concept for bridges that can reduce overall seismic damage, minimize construction and repair time, and achieve lower cost in general. However, such system involves complex dynamic responses due to impacts and highly nonlinear rocking behavior. This study presents a dimensionless regression analysis to estimate the rocking and shaking responses of the flexible column‐foundation system under near‐fault ground motions. First, the transient drift and rocking responses of the system are solved numerically using previously established analytical models. Subsequently, the peak column drifts and uplift angles are derived as functions of ground motion characteristics and the geometric and dynamic parameters of column‐foundation system in regressed dimensionless forms. The proposed response models are further examined by validating against the numerical simulations for several as‐built bridge cases. It is shown that the proposed model not only physically quantifies the influences of prominent parameters, but also consistently reflects the complex dynamics of the system. The seismic demands of rocking column‐foundation system can be realistically predicted directly from structural and ground motion characteristics. This can significantly benefit the design of bridges incorporating this new design concept.

Seismic fragilities of single‐column highway bridges with rocking column‐footing

“…Such an idealization has also been utilized in previous studies for the investigation of flexible rocking oscillators. 9,28,30,32,41 The proposed model consists of a point mass on an axially rigid yet translational flexible column that is connected to the rigid footing at the bottom. The system variables are the column translational drift, u and the rigid body rotation of the footing, θ.…”

“…The nonlinear equations of motion (EOMs) of the analytical system at the rocking phase can be derived following Lagrange's equation of energy equilibrium 9 :…”

“…7,8 To take advantage of the rocking concept and avoid the complexity associated with supporting soils, this study investigates an alternative rocking isolation strategy that features a detached rocking interface between the bottom of footing and the rigid support underneath (Figure 1), a system whose seismic response has been studied using dimensional analysis previously. 9 The promise of the proposed system can be analogous to unanchored rigid structures such as water tanks, tombstones, and ancient temples, which have demonstrated exceptional seismic performance during past earthquakes. 10 However, unlike rigid structures, the relatively tall and slender rocking bridges require the consideration of inherent column flexibility.…”

“…The coexistence of column oscillation and footing rocking complicates the dynamics of the rocking system. 9 Considerable past studies have investigated the rocking dynamics of free-standing rigid blocks, rigid-rocking frames, and coupled structures. [11][12][13][14][15][16][17][18] Developed from Housner's inverted pendulum model, 11 the dynamic responses of rigid rocking systems when subjected to pulse-type motions were investigated in depth.…”

“…[24][25][26][27] Another area of research work on rocking structures has focused on the dynamic performance of flexible rocking oscillators. 9,25,[28][29][30][31][32][33] Relative studies have investigated the following: (1) the rocking impact mechanism and transition between rocking phase and full contact vibration phase, 31,32 (2) the dynamic interplay of column vibration and foundation rocking, 9 and (3) the ground motion intensity measures (IMs) that cause significant rocking amplitudes. 9,30 However, seismic responses of flexible rocking oscillators are more complex because of the extra column vibrational mode.…”