A Semi-Analytical Solution for Interpretation of Hydro-Mechanical Responses of Cylindrical Cavity Expansion in Unsaturated Structural Loess

The cavity expansion solution for loess is absent because the existing elastoplastic models fail to model the sophisticated behaviors of unsaturated loess as a classic axisymmetric boundary-value problem. This paper develops a novel solution for cavity expansion in unsaturated structural loess, taking the coupled hydro-mechanical and structural evolution into consideration. To properly model the behavior of the loess, the Barcelona Basic Model for unsaturated clay is modified by incorporating structural parameters of loess and a volumetric strain-dependent soil–water characteristic curve. The structural parameters are evolved with the degree of saturation and the plastic strain. Leveraging the hydro-mechanical coupling elastoplastic constitutive matrix of the modified constitutive model, the governing differential equations for cylindrical cavity expansion are derived by introducing an auxiliary variable to the stress equilibrium equation and the geometric equation which preserves the intrinsic radial symmetry during spatial coordinate mapping. By considering the constant water content condition, the problem considered is expressed as seven first-order differential equations with suction, three stress components, specific volume, and two structural parameters as unknowns. The governing equations are solved as an initial value problem by the Runge–Kutta scheme. After verifying the solution with well-established solutions and the numerical results from ABAQUS, parametric studies are conducted to investigate the effects of structure degradation and saturation on the expansion response. The results show that the proposed solution can capture the hydraulic yielding behavior well during cavity expansion and the effects of structure on the expansion responses. The proposed solution provides a more reasonable theoretical basis for modelling the static cone penetration test, pile installation effects and pressuremeter tests in loess.