A unified model for analyzing free vibration and buckling of end-bearing piles

Offshore structures are often founded on long, slender piles that extend for a substantial distance above the ground surface. This paper presents a novel unified model to analyze the free vibration and buckling of partially embedded end-bearing piles subjected to axial compressive load. Consideration is given to the tapered piles of variable cross-sectional shape with constant volume. The governing differential equation of the motions is derived, and solved by using the Runge-Kutta method in combination with the Regula-Flasi method. The accuracy of the proposed model is confirmed by comparing the obtained calculations with existing closed-form and numerical solutions. Numerical results for the natural frequency, buckling load and corresponding modal displacements are provided, which are analyzed to highlight the effects of the parameters related to the cross-sectional shape, taper ratio and embedment of the pile, soil stiffness and compressive force as well as the end constraint. The geometry and material parameters that statically and dynamically yield the strongest piles with fixed volume are identified. The analytical model is beneficial for the optimum design of the soil-pile system in engineering applications.