A Simplified Approach for Analysis of a Pile under Combined Horizontal Dynamic and Axial Static Loads Resting on a Nonhomogeneous Pasternak Foundation

This paper presents a streamlined methodology to assess the horizontal response of an embedded pile subjected to combined horizontal dynamic and axial static loads in a nonhomogeneous Pasternak medium. The stiffness matrix equations for the pile elements are formulated using the modified finite beam element method (FBEM), enabling a comprehensive consideration of factors such as the axial second-order effect of the pile (P-Δ effect), soil shear effect, and side friction on the pile. Utilizing the FBEM, the solutions for the pile’s lateral displacements and bending moments are derived while accounting for continuous pile–soil system boundary conditions. The accuracy of the FBEM is verified against existing solutions. Subsequently, a thorough parametric analysis is performed to investigate the influences of various properties of the pile, soil, and applied load on the pile’s horizontal vibration response. This study underscores the significant role of the shear effect exerted by the surrounding soil in restraining the lateral deformations and internal forces of the pile. In stratified soils, the horizontal performance of the pile is notably impacted by the properties of the surface soil. Reducing the strength of the surface soil results in a substantial increase in the pile’s bending moments and lateral displacements. Additionally, an increase in axial load at the pile head significantly affects the bending moments and lateral displacements due to the P-Δ effect. Moreover, the study reveals that the lateral displacements and bending moments of the pile exhibit an increase with the increases of the horizontal harmonic load amplitude H0 and a decrease with the increases in the dimensionless frequency a0 of the applied load.