Elasto-plastic solution for elliptical cavity expansion in saturated soils

The cavity expansion theory has been widely used in geotechnical engineering as a mature theoretical tool. However, many practice problems are related to elliptical cavity expansion rather than cylindrical cavity expansion. The elliptical cavity on the physical plane is mapped to the unit circle on the phase plane by conformal mapping method, and the velocity boundary condition caused by the elliptical cavity expansion on the physical plane is transformed to the phase plane. The elasto-plastic solution of displacement-controlled elliptical cavity expansion is presented by the plane complex variable elasticity method. This solution is compared with the Gibson's elasto-plastic cylindrical cavity expansion solution, and the reliability of this study is verified. Then, the proposed solution is used to calculate the excess pore water pressure induced by the PVD installation using a mandrel. The theoretical prediction of the excess pore water pressure is compared with the model tests by Indraratna. The results show that this solution is consistent with the conventional cylindrical cavity expansion method when this study is degenerated to the cylindrical cavity. The proposed solution can simulate the excess pore water pressure induced by the PVD installation very well.