SBG model for particle breakage of rockfills based on fractal gradation equation

Accurately predicting the particle breakage rate and the corresponding gradation changes of rockfills in shearing process is beneficial to revealing their characteristics such as strength, penetration and deformation under complex stress conditions. Based on the fractal gradation equation, a model for realizing the conversion of "stress strain-breakage index-gradation distribution (SBG)" is established. The breakage index B_E is used to measure the particle breakage rate. The fractal gradation equation is deformed and integrated, and the mathematical conversion of particle breakage rate B_E and fractal dimension D is derived, that is, the conversion of "breakage index-gradation distribution". The existing triaxial shear test data are analyzed, and a mathematical model that can quantitatively express the change of particle breakage rate with shear strain and average normal stress is proposed. The model has three parameters a, b and c. The parameter b is related to the critical state of soils and can be directly determined according to the critical shear strain. Two sets of different test data are fitted, and it is found that the predicted values by the model has a high degree of agreement with the test ones, and the conversion of "stress strain-breakage index" is realized. Combining the above two conversions, the gradation changes of rockfills under different shear strains and average normal stresses are successfully predicted.