Seismic residual displacement of gravity quay walls under coupled motion between rotation and sliding by simple method

Predicting the residual displacements induced by earthquake loading is a key to the seismic design of quay walls,and the motion of quay walls is influenced to some extent by the excess pore water pressure in the backfill acting on the back of quay walls.Considering the effect of excess pore water pressure in the backfill acting on the back of quay walls,the Mononobe-Okabe equivalent static method of calculating the dynamic active earth pressure and the dynamic water pressure in backfill soil is modified by the index of extent of liquefaction.Considering both the horizontal and vertical earthquake waves,the rotation block method of Steedman is applied.The sliding and rotation threshold acceleration coefficients are confirmed by the equilibrium of forces and moments respectively.Two situations of coupled motion with sliding starting first and rotation starting first are analyzed,the sliding and rotation threshold acceleration coefficient are modified because of the effect of coupled motion,and the calculation method of residual displacement of gravity quay walls is developed primarily.An example is shown by the present method under a sine wave of ground motion,and some laws are discussed simply between the extent of liquefaction and the seismic residual displacement.