Upper and lower bound solutions for pressure-controlled cylindrical and spherical cavity expansion in semi-infinite soil

Previous cavity expansion analyses are all performed in infinite soil. However, cavity expansion problem in half space (or semi-infinite soil) is also required in geotechnical engineering (tunneling and compaction grouting). New upper and lower bound solutions are derived for expanded spherical and cylindrical cavities in half space of Tresca soil based on the method of finite element limit analysis in this paper. Two types of case, namely homogenous soil and non-homogenous soil with undrained strength linearly increased with depth, are consider in the analysis. Simple empirical closed-form equations are then proposed for predicting the limit cavity expansion pressure through nonlinear regression analysis. The present solutions provide theoretical reference for the corresponding geotechnical engineering problems such as tunneling and compaction grouting.