Hydro-Mechanical Analysis of Cylindrical Cavity Expansion in Unsaturated Soils Under Constant Total Vertical Stress

Radial soil displacement during pile installation and pressuremeter testing is commonly interpreted using cylindrical cavity expansion theory. However, conventional plane strain solutions neglect vertical deformation and may be inadequate for unsaturated ground subjected to approximately constant overburden stress. This study develops a semi-analytical elastoplastic solution for cylindrical cavity expansion under constant total vertical stress. An unsaturated modified Cam-Clay model and a soil-water retention relationship are incorporated within a skeleton stress framework, while vertical deformation is explicitly considered in radial equilibrium. Coupled first-order governing equations are established for undrained and constant-suction drained conditions. The formulation agrees with an existing saturated drained solution in the limiting case. For the initial stress states examined, increasing overconsolidation ratio is associated with higher cavity pressure at a given expansion ratio but a smaller expansion ratio at which the cavity wall reaches the critical state. For normally consolidated soil, the corresponding ratios are 1.203 (undrained) and 1.375 (constant-suction drained). Under undrained conditions, changes in suction and saturation cause the vertical skeleton stress to evolve despite constant total vertical stress. The proposed framework provides a theoretical basis for evaluating cavity-induced soil disturbance and stress redistribution relevant to foundation construction in unsaturated ground.