This study examines the horizontal transient response of pipe piles in saturated soil, assuming a two-stage equivalent linear relationship between the bending moment and the rotation at the pile head. The potential function is introduced, and the three-dimensional wave equation for saturated soils is decoupled using operator decomposition and the method of separation of variables. By applying the appropriate initial and boundary conditions, the horizontal lateral forces on the pile from both the surrounding soil and the soil within the pile shaft are calculated. The pipe pile is modeled as a Timoshenko beam. Continuity conditions at the pile–-soil interface are applied, and a time-domain solution for horizontal transient vibrations is derived. This solution accounts for various pile top constraint conditions and is obtained through the inverse Laplace transform. Validation against existing results demonstrates the accuracy of the proposed model. Finally, a parametric study investigates the effects of factors such as impact load, permeability, pile diameter, and pile head constraints on pile displacement.
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