3D failure envelope of a single pile in sand

Pile foundations are widely used in geotechnical and offshore engineering. When subjected to a combination of horizontal, vertical forces and bending moments, a 3D failure envelope is necessary in order to evaluate the safety of the pile-soil system. We present a study on the failure envelope of a single elastic pile in sand. In order to find it in the three-dimensional space (i.e. horizontal force H, bending moment M and vertical force V), the radial displacement method and swipe tests are numerically performed. An analytical equation providing good agreement with the 3D numerical results is finally proposed.