A mechanistic insight into the shaft resistance of vertically vibrating piles

A mechanism for the dynamic shaft resistance of vertically vibrating single end-bearing and infinitely long piles is proposed through the use of elastodynamics. The generalized expression for the shaft resistance is obtained by means of Hamilton's principle. The shaft resistance is divided analytically into three parts, namely, the Winkler spring, the membrane and the participating mass of the surrounding soil. In light of the contributions of these three components of shaft resistance, a physical model is presented for the nature of single piles subjected to dynamic loading. The three components are obtained as explicit forms. The first is linear to the pile settlement. The second is related to the derivative of the second order of the pile settlement. The third involves the participating mass of the surrounding soil. The effect of the properties of the soil-pile system on the dynamic responses of the characteristic coefficients of the shaft resistance is investigated. The results indicate that the Winkler spring contributes the most to the shaft resistance. The contributions of the membrane and the participating mass of the surrounding soil are negligible for cases of high incident frequency.