In order to accurately analyze the internal force and deformation of pile under the combined horizontal dynamic load (H(t)) and torsional vibration () on the top of the pile

a simplified analytical model of loaded pile in layered foundation is established based on the Pasternak model

considering the interaction of multidirectional loads. The numerical solutions of the internal forces and displacements of the pile are derived by using the finite beam element method

and the results are compared with the existing theoretical solutions

model tests and finite element simulations. Parametric analysis shows that: (1) Compared with the calculation results of Winkler model

the horizontal displacement at the top of the pile and the maximum bending moment of the pile are reduced by 11.8% and 10.5%

respectively

after considering the shear effect of the soil. (2) Increasing the dimensionless frequency of the external load reduces the horizontal displacement and bending moment of the pile

and also reduces the coupling stiffness. (3) In the layered foundation

the surface soil has the greatest influence on the internal force and displacement of the pile

and there is a critical influence depth of the surface soil. The critical influence thickness of the surface hard soil is 3.5–6.5 times that of the surface soft soil. (4) The beam element model reduces the number of element divisions and calculation time

which can effectively improve the calculation efficiency.