Cylindrical cavity expansion analysis of dilatant sand considering granule breakage

Most cavity expansion problems in sand have not considered the effects of dilatancy, granule breakage and overconsolidation ratio, and all the current researches have simplified the solution process, which can not accurately reflect the mechanical response of the soil around the cavity. The critical state model considering the breakage and dilatancy characteristics of sand was adopted to convert the drained cylindrical cavity expansion problem described by the traditional Euler into the one by Lagrangian description; combined with relevant flow rule and based on the definition of generalized average principal stress and deviatoric stress, four first-order ordinary differential equations were obtained without any simplification. Finally, the semi-analytical exact solution of the cylindrical cavity expansion problem in sand was calculated by using Matlab programming. The impact of soil overconsolidation ratio (OCR) on the cavity expansion results were analyzed by a calculation example. The results indicate that the granule breakage has a greater influence on the dilatancy behavior of sand compared with OCR and the combined effect of the two causes the soil to show different dilatancy characteristics during cavity expansion; in addition, normally consolidated and lightly/moderately overconsolidated soil has been characterized by strain hardening during cavity expansion, while the heavily overconsolidated soil has experienced a complicated stage of strain hardening-strain softening-strain hardening.