Energy equation and stress-dilatancy relationship for crushable granular materials incorporating particle breakage

The ROWE's stress-dilatancy relationship is widely employed to characterise the shear dilatancy behaviour of granular materials. However, particle breakage energy dissipation is excluded from the ROWE's energy balance equation. In this study, three crushable granular soils with significantly different strengths were subjected to triaxial testing, and the dissipation of energy during the tests was explored. For all three materials, the incremental particle breakage energy dissipation increases and then decreases. It was assumed that at the critical state, particle breakage ended and only frictional energy dissipation occurred. To more accurately characterise the energy dissipation process, an exponential expression of particle breakage energy dissipation is added to the ROWE's stress-dilatancy relationship. The proposed stress-dilatancy relationship is consistent with the shear dilatancy behaviour of crushable granular materials, and the modified energy equation can more precisely describe the energy dissipation process. The hypothesised stress-dilatancy relationship is applicable to three distinct types of crushable granular materials with varying strengths, including sand-gravel material, landslide dam material and calcareous sand.