A simplified analytical method to evaluate the seismic pressure on plane lock gates

•The paper is concerned with the seismic analysis of plane lock gates.•The seismic hydrodynamic pressure is computed analytically.•The method is based on the Rayleigh–Ritz method and the virtual principle.•The fluid–structure interaction is taken into account in this derivation.•The analytical solutions are used as a meshless method.•The meshless method is corroborated by comparisons with finite element simulations.

This paper presents a meshless method to perform the seismic analysis of a plane lock gate. The approach is based on the analytical derivation of the total hydrodynamic pressure, with due consideration for the gate flexibility. In particular, the flexibility of the gate and the fluid–structure interaction are taken into account in the calculation of the equivalent force that has to be applied on the gate to model the action of the water. To reach this goal, the Rayleigh–Ritz method is first used to determine the modal properties of the dry structure. This is achieved by using mode shapes extracted from the beam theory as generating functions. The results obtained in this way are validated by comparison with numerical solutions. The second step consists in performing the dynamic analysis of the gate by deriving a weak form of the equilibrium equation. Based on the Galerkin method, a matrix formulation is derived and the Newmark integration scheme is used for the evaluation of the pressure during the earthquake. Here again, non-linear finite element simulations including water modeling are carried out to corroborate the analytical developments. In addition, the lumped-mass method is also investigated and a criteria is proposed to check its applicability. Finally, some concluding remarks are given to perform more easily the seismic analysis of lock gates.