Pushover and shaking table tests on a rocking-governed column-footing model on dry dense sand

Development of a pseudostatic method for seismic performance evaluation of rocking bridge foundations

“…𝐴 D_pier = 𝐴 D_elastic pier + 𝐴 D_plastic pier (7) where A D_elastic pier is the dissipation energy of the pier in the elastic state and A D_plastic pier is the hysteretic energy due to plastic hinging of the pier. (a) A D_elastic pier According to the dynamic model proposed by Chiou et al, 19 the damping ratio ξ e for the elastic system is set at the lowest predominant frequency (the reference frequency) ω ref of the undamped system under a given base motion.…”

“…η r is defined as the ratio of the viscous-elastic energy of the partial-contact footing to that of the full-contact footing. With the BWF model in linear elastic soil, the moment-rotation relationship of the footing can be expressed as follows 7,13 :…”

“…(4) For determining the dissipation energy of the pier, according to Figure 18 based on Equation (25). Because no plastic sliding response is observed, A D_plastic sliding = 0 kN-m. (7) The sum of the dissipation energy is 103.44 kN-m. Because the maximum elastic strain energy A E is 93 kN-m (the area below the secant through the origin and performance point of the pushover curve), the system damping ratio is 8.9%, as per Equation ( 4). (8) The system damping ratio in Step 7 differs from the initial setting.…”

“…This design allows the foundations to rock during earthquakes, which creates an isolation effect and reduces the seismic demand on structures due to the limited moment capacity of the foundation. [1][2][3][4][5][6][7][8][9] However, foundation rocking increases the displacements of structures and foundations; excessive foundation rotation and settlement may influence the functionality and safety of structures. 7,10,11 Therefore, the performance of the structure under rocking must be evaluated in a rocking-foundation design, including the rotation and settlement response of the foundation and the displacement and acceleration response of the structure.…”

“…The rotational spring model applies a rotational spring at the column base to simulate the effect of foundation flexibility; furthermore, the property of the rotational spring can be a nonlinear curve that considers soil as nonlinear and the footing uplift. 7,[12][13][14] The macro spring model is an advanced NOVELTY • We propose a pseudostatic method to evaluate the seismic response of bridge piers with footings.…”