Constitutive relations for granular materials considering particle crushing: Review and development

Particle crushing often results in more compressibility and less strength for granular assemblies.Therefore,the researches on the influences of particle crushing on the mechanical behavior of soils are important.First,experimental studies are summarized,including the descriptive methods for particle crushing and the impact of breakage on the stress-strain relationship under different loading conditions(one-dimensional and isotropic compression,triaxial shearing,torsional and simple shearing,etc.).Then,different modeling methods are summarized:compression model,three-dimensional model and discrete element method-based modeling.Finally,through experimental investigations and the authors' researches in recent years,it is noted that the modified relative breakage index can be well adopted to represent the change of grain size distribution due to particle crushing during stress-straining.This index can be determined by using plastic work which has advantages for the condition of cyclic loadings.Then by using this index to determine the position of the critical state line(CSL),the influences of particle crushing on mechanical behavior can be estimated comparing the position of CSL with the current stress state.All the proposed constitutive equations relating to the modified relative breakage index can be directly applied to developing constitutive models under both monotonic and cyclic loadings.