The data in Figs 2–8.

In practical engineering, pile foundation will be subject to the combined action of vertical and Rayleigh wave, and the existence of vertical dynamic load will cause the second-order effect that will lead to the increase of horizontal displacement. This paper presents a computational model for the effect of vertical load on the lateral response of monopole under Rayleigh wave. The pile cap is equivalent to a rigid block, and the constraint of pile head is regarded as a flexible constraint. By means of operator decomposition theory and variable separation method, the horizontal dynamic response of single-phase soil in uniform free field under Rayleigh wave propagation is obtained. The closed form solution of soil resistance under the combined action of Rayleigh wave and vertical load is obtained by means of operator decomposition theory and variable separation method. Based on Timoshenko beam theory, the dynamic differential equation of pile considering vertical load is established. A comparison with an existing solution is performed to verify the proposed solution. Through numerical examples, the effects of the vertical load, flexible constraints, dimensionless frequency and Poisson’s ratio on the lateral response of monopile are assessed.