Semi-analytical elastic-viscoplastic solution for dynamic spherical cavity expansion in undrained clay considering rate and dynamic effects

The phenomenon of dynamic cavity expansion is ubiquitous in engineering applications such as vibratory pile driving, dynamically installed anchors, and dynamic penetration tests. Dynamic resistance encompasses contributions from elastoplasticity, viscosity (or rate effect), and dynamic effects due to the inertia induced by accelerating surrounding soil. Existing solutions for cavity expansion in clay predominantly focuses on resistance from elastoplasticity, with a few paid to additionally consider either rate or dynamic effect. To date, there is still a lack of solution that can simulate dynamic penetration resistance into clay considering all the three effects. This study presents a semi-analytical model that integrates elastoplasticity, viscosity (or rate effect) and dynamic effects. This integration is achieved by incorporating an elastic-viscoplastic constitutive model (strain rate-dependent) into the general framework of spherical cavity expansion theory, coupled with the dynamic stress equilibrium equation to simulate dynamic effects. The proposed semi-analytical solution for dynamic spherical cavity expansion is validated by comparing its degenerate form with published quasi-static and dynamic solutions for the modified Cam-Clay (MCC) model. A comprehensive numerical parametric study is conducted to quantify and analyze the contributions of rate and dynamic effects. The results reveal three distinct velocity ranges: low, medium, and high-velocity. In the low-velocity range ((V_c/a < 1), the strain rate effect rapidly intensifies, while the dynamic effect remains negligible. In the medium-velocity range (1 < V_c/a < 25), the limit cavity pressure primarily comprises elastic–plastic deformation and strain rate effects, with the dynamic effect starts to play a role. In the high-velocity range (V_c/a > 25), the dynamic effect’s contribution becomes much more dominating, potentially exceeding 20 % at an expansion rate of 100. Regarding spatial distribution, the dynamic effect influences broader ranges of the surrounding soil than the strain rate effect.