Nonlinear dynamic analysis of the deep-water bridge piers under combined earthquakes and wave actions

When the Stokes fifth-order wave is utilized to study the wave force of large-diameter bridge piers, the iterative method is usually utilized to solve the transcendental equations and then solve the wave parameter wavelength, coefficient and wave number. The solving process is particularly complicated, and the ratio of water depth and wavelength is generally assumed to be 0.1–0.15, which is suitable for shallow water depths and has not been investigated for deep water depths. In this study, the wave force and action point of the large-diameter rectangular section bridge pier under Stokes fifth-order wave action are derived, and the range of Stokes wave number is derived when the deep water level is constant. Combined with the functional analysis of transcendental equations, a program for calculating the Stokes fifth-order wave parameters is derived, and the approximate solution of the coefficient and wavelength of the Stokes wave is accurately and quickly solved. The dynamic nonlinear analysis of super deep-water large-diameter bridge pier under combined multi-dimensional earthquake and nonlinear wave action is investigated. It is found that nonlinear waves can significantly increase the dynamic response of deep-water bridge pier structure, but under combined wave and earthquake loadings on the deep-water bridge pier structure, and earthquakes play a dominant role. The influence of resonant waves and common linear waves on the dynamic response of large-diameter bridge piers in deep water depth is quite different. Resonant waves have a significant influence on the displacement response and stress response of deep-water bridge piers. When under two-dimensional earthquake and resonant wave independent loadings, the influence on the dynamic response of deep-water bridge pier structures is insignificant. When under combined earthquakes and waves loadings on the deep-water bridge pier structure, earthquakes play a significant role. • The Stokes wave transcendental equation is transformed into a functional algorithm to obtain the parameters. • The differences effects of resonant waves and common linear waves combined earthquakes actions on the dynamic response of deep-water bridge pier are evaluated, respectively. • The influence of nonlinear wave action on the dynamic response of deep-water bridge pier is investigated. • The dynamic response of deep-water pier under combined multi-dimensional earthquakes and nonlinear wave loadings is studied.