There are few theoretical studies on lateral bearing capacity of flexible single pile under vertical-horizontal loading path in sand foundation and the influence of pre-applied vertical load on p-y curve is rarely considered. In view of this

the ultimate soil resistance of hyperbolic p-y curve was modified accounting for compacting effect of the sandy soil around the pile under the vertical force applied in advance. Cosine function was used to characterize the distribution of radial earth pressure on the passive side. The relationship between the maximum radial earth pressure on the passive side and the total soil resistance was proposed

and the analytical expression of the shaft resisting moment on the passive side was derived. Taking an included angle  between the direction of friction resistance and the vertical direction into account

the variation of pile axial force induced by friction resistance was corrected and its computational formula was obtained. The differential equation of pile deflection was established considering the modified p-y curve

the variation of axial force caused by pile dead weight and friction resistance

the P-Δ effect and the shaft resisting moment. The numerical solution was obtained by MATLAB program. The correctness of the proposed method was verified by comparing the calculated results with the existing simulations and measurements. On this basis

the influence of vertical force applied in advance on lateral bearing capacity of single pile was discussed. The results show that the computational formula of the variation of pile axial force deduced in this paper can more accurately describe the influence of friction resistance on pile axial force and can be used for large deformation conditions. The vertical force applied in advance can enhance the lateral bearing capacity of flexible single pile. The enhancement gradually decreases with the increase of the vertical force applied in advance.