Horizontal Stiffness and Damping of Single Piles

Simple expressions are developed for the equivalent horizontal spring and damping coefficients at the top of an end-bearing pile embedded in a uniform linear soil. Beam on elastic foundation (BEF) and dynamic finite element analyses are used for this purpose. It is demonstrated that, for long end-bearing piles, the top displacement response at high frequencies is independent of the pile length, and the pile behaves identically to a long floating pile in a half-space. A numerical criterion is presented to decide when a pile is long or short. All results are expressed as a function of the pile and soil Young's Moduli, E_p and E_s, and they are valid for a range of Poisson's Ratios of the soil between 0.25 and 0.49. Finally, expressions are also presented for the soil springs and dashpots required for more complicated BEF analyses of piles in multilayer soils. The results presented in the paper show good agreement with previous studies.