The cyclic response in saturated sand is gaining increasing interest owing to the soil-structure interaction in seismic regions. The evolution of the pore water pressure in liquefiable soil can significantly reduce soil strength and impact the structural dynamic response. This paper proposes a semi-analytical solution for a cylindrical cavity subjected to cyclic loading in saturated sands, incorporating an anisotropic, non-associated SANISAND model. The problem is formulated as a set of first-order partial differential equations (PDEs) by combining geometric equations, equilibrium equations, stress-strain relationships and boundary conditions. Due to the non-self-similar nature of this problem, these PDEs are solved by the hybrid Eulerian-Lagrangian approach to determine the cyclic response of the cavity. Then finite-element simulations with a user-defined subroutine are performed to validate the proposed solution. Finally, parametric studies are presented with the focus on soil parameters and cyclic loading history. It is found that the cyclic responses of the cavity in saturated sands are sensitive to the initial void ratio, and the at-rest coefficient of earth pressure primarily affects the monotonic response but marginally affects the cyclic response. Cylindrical cavities are more likely to liquefy when the sands are compacted in a loose state and under lower displacement amplitudes. The proposed solution has potential use for future research on the cyclic response of the soil-structure interaction in geotechnical engineering.

This paper proposes a powerful hybrid Eulerian-Lagrangian (HEL) approach for the analysis of cavity expansion problems. The new approach is applied to analysing the non-self-similar expansion process of a hollow cylinder of critical state soils, considering arbitrary saturation states of soils and both drained and undrained conditions. A closed-form solution for the stresses and displacements in the elastic zone is presented, taking the state-dependent soil moduli and outer boundary effect of the soil cylinder into account. Adopting large strain theory in the plastic zone, the non-self-similar cavity expansion process is formulated into a set of partial differential equations in terms of both Eulerian and Lagrangian descriptions, which is solved by a newly proposed algorithm. The HEL approach is compared with the conventional Eulerian and Lagrangian approaches for the cavity expansion analyses. It is found that the new approach can reduce to the Eulerian approach when the self-similar assumption is satisfied and to the Lagrangian approach when stress-total strain relationships are obtained analytically. Finally, the expansion process is proven to be non-self-similar by showing the stress and deformation paths, and the finite thickness of soil cylinders may greatly influence the cavity expansion behaviour, especially with a small thickness ratio. The HEL approach can provide useful tools for validating advanced numerical techniques for both saturated and unsaturated soils and interpreting pressuremeter tests in small-size calibration chambers.