Drained analyses of cylindrical cavity expansion in sand incorporating a bounding-surface model with state-dependent dilatancy

Abstract

• Governing differential equations of the cylindrical cavity expansion problem are solved as an initial value problem . • Rigorous definitions of the invariant stresses permit the examination of the effect of k 0 value. • Model parameters that are of paramount importance for the cylindrical cavity expansion analyses are presented. This paper presents a semi-analytical drained solution for cylindrical cavity expansion in sand. By introducing an auxiliary variable, defined as the ratio of the original position to the current position of a material particle, the governing differential equations of the cylindrical cavity expansion problem can be transformed into a group of first-order ordinary differential equations. These equations are solved as an initial value problem by incorporating a bounding-surface model with state-dependent dilatancy. This approach does not require the division of the material around the cavity into an elastic zone and a plastic zone. The state-dependent dilatancy model employed in this study allows the investigation of the effects of the initial relative density and mean normal stress of the sand, whereas the rigorous definitions of the invariant stresses permit the examination of the effect of the initial ratio of the horizontal stress to the vertical stress. Moreover, the model parameters that are of paramount importance for the cylindrical cavity expansion analyses are determined via comprehensive parametric studies.