Undrained Spherical Expansion Analysis for Clay

The application of cavity expansion methods in geotechnical engineering has been extensively developed in the last six decades and has resulted in solutions of great interest, such as in situ soil testing and pile foundations. This paper presents a large-strain analytical solution which allows obtaining the constitutive properties of clay from the pressure-expansion curve of a spherical cavity. The theory applies to the interpretation of static cone penetration tests, which are often modelled as spherical expansion processes in an unbounded medium. Shear stress-strain curves of clay are found from experimental pressure-expansion relationships, without making assumptions regarding the constitutive properties of the material, i.e., elastic and elastic-plastic. The only assumptions made are that the expansion takes place under undrained conditions and an initial hydrostatic stress field. For illustration purposes, the theory is applied to the determination of clay properties from two idealized spherical expansion relationships which are known to yield strain-hardening and strain-softening responses. The solution is also obtained for the case when the expansion takes place in a clay medium of finite outer radius.