Analytical solutions of soil plug behaviors in open-ended pile driven by impact load

The displacement behavior of soil inside open-ended piles during driving is associated with soil plugging performance. This study analyzed the ultimate equilibrium of the pile-soil during pile installation and then established the ultimate balance equation. A pile-soil contact dynamic resistance factor (DRF) was incorporated by the kinematic method to develop the equation under dynamic loading. The inertial force and DRF were both integrated into the displacement analytical model, and the ultimate equilibrium differential equations of the soil inside the open-ended pile subjected to hammering loads were developed to derive the analytical solution of plug displacement under drained and undrained conditions respectively. For the same average acceleration and pile diameter, the higher the magnitude of the shaft friction factor (β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}) was, the more significant the compression of the soil inside the pile was. Smaller pile diameter resulted in more dramatic compaction of the soil within the pile, although this effect was weak. Furthermore, the internal soil was exponentially compressed with the increase in acceleration. The results were compared with numerical results. The analytical solutions could predict the soil displacement of open-ended piles during driving and provide useful insights into the actual situation of soil plug.