Undrained Cavity Expansions in Critical State Soils

Boundary value problems for hardening/softening soils, such as Cam-Clay, usually require the extensive use of finite element methods. Here analytical and semi-analytical solutions for the undrained expansion of cylindrical and spherical cavities in critical state soils are presented. The strain is finite, the initial cavity radius is arbitrary and the procedure applicable to any isotropically hardening materials. In all cases only simple quadratures are involved, and in the case of the original Cam-Clay a complete analytical solution can be found. In addition to providing models of the behaviour of displacement piles and pressuremeters these results also provide valuable benchmark solutions for verifying various numerical methods.