Kinematic response of the single floating piles in the two-layered soil subjected to vertically incident P-waves

An analytical model for the kinematic response of a single floating pile in a two-layered soil under vertically propagating P-waves is proposed by elastodynamics. A Heaviside step function is introduced to simulate the variability of the layered soil. The continuity of the pile and the fictitious soil column are considered based on Tajimi's theory. The main contribution of the present solution is that the model of the fictitious soil column for the floating pile in the homogeneous soil under vertically propagating P-waves is extended to the two-layered soil with the simulation of the depth-dependent soil mode function. The effect of the properties of the soil layer and the shaft on the vibration of the soil-pile system is investigated. For the soil with the upper softer layer, the dimensionless cutoff frequency of the two-layered soil is smaller than that of homogeneous soil and the opposite trend is for the soil with an upper stiffer layer. For the soil with upper stiff and lower soft layers, the axial pile strain decreases with the decrease of the soil modulus ratio and the effect of soil modulus ratio on the soil resistance at the lower part of the shaft is negligible.