Smoothly waning, symmetrically expanding, cavity-pressure loads in earth materials

An approximate solution for the pressure loading required to expand a spherical cavity in rock and soil targets is derived. A dual characterization of fracture and flow material model is used. Frictional resistance to flow is also included. Non-linear volumetric strain hardening is modeled with bi-linear curves and unloading is assumed to be non-dilative. Applications of this solution form to the prediction of pressure loading on slender, convex-nosed earth penetrators and on spherically-nosed water entry vehicles are discussed