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.