An analysis of cylindrical cavity expansion in sand based on a unified state parameter model

The current studies of the cylindrical cavity expansion in sand still lack a deeper analysis for the results obtained in sands with different initial states. In addition, most of previous studies have not considered the influence of the shape of yield surface of sand, which made their results difficult to be popularized in different types of sand. In order to obtain a general solution to expansion of cylindrical cavity in sand under the drained condition, a unified state parameter model - clay and sand model (CASM) with Rowe’s stress–dilatancy relation is used to describe the characteristics of elastic-plastic deformation of sand. By employing that large strain occurs in sand and introducing an auxiliary variable, several partial differential equations to calculate the effective stress and specific volume of sand in the elastoplastic zone are derived on the basis of the Lagrangian description.Under the elastic-plastic boundary conditions and the elastic solution of cylindrical cavity expansion, a semi-analytical solution for drained cylindrical cavity expansion in sand is obtained by solving the governing equations numerically. The results show that the solution of cylindrical cavity expansion established in this paper can be used in many types of sand by changing the values of stress-state parameter n and spacing ratio r^* to select an appropriate shape of yield surface of sand, and the greater the values of n, r^* are, the greater the initial yield deviatoric stress of loose sand and the subsequent expansion pressure, but these situations will reverse in medium dense and dense sand. The ultimate expansion pressure increases with the decreasing initial state parameter of the sand, and together with the volume variation rule of sand changes from always contraction into dilatation first and then contraction, the radius of the elastic-plastic zone decreases first and then increases, and the hardening response of sand changes from always hardening into softening first and then hardening. The ultimate expansion pressure increases with the increasing coefficient of earth pressure at rest of sand, but the volume change law of sand has little change. This study provides a reliable theoretical support for the analysis of related geotechnical engineering problem.