Abstract: A mathematical model describing the gradation for coarse-grained soils under arbitrary stress state is proposed in this paper. The model is to express the grain size distribution of soil by a gradation equation firstly, on the one hand, the relationships between the two breakage indicators BW and Bg and gradation parameter b and m were derived. On the other hand, the empirical relationships between the two breakage indicators BW and Bg and stress or strain were suggested based on laboratory test data. Therefore, the relationship between the gradation, breakage indicators and stress or strain of soils were mathematically established. Meanwhile, the methods for the determination of parameters of the proposed model are discussed. Then, a series of consolidated drainage (CD) tests was conducted under confining pressures of 0.2, 0.5, 1.0, 1.5 and 2.0 MPa, respectively. The experimental data at confining pressure of 0.2, 0.5, 1.0 and 1.5 MPa are used to obtain the model parameters, which are substituted into the model to predict the particle breaking indicators and gradation distribution when the confining pressure is 2.0 MPa. The results show that the predictive value agrees well with the experimental data and proves the applicability of the model.

Key words: coarse-grained soil, particle breakage, gradation equation, breakage indicator, model