Assuming no slippage occurred on the interface between pile and soil, an equivalent equation of displacement coordination is obtained to constitute a new method calculating settlement of single pile.

Based on the wave equation in unsaturated soil, the dynamic response of a pile under transient torsional loading was theoretically investigated.

Secondly, with using the design of pile foundation by M-method, the stiffness equation of pile under the interaction of piles and soils is derived.