The stress–strain behavior of coarse-grained materials is significantly influenced by the initial grain size distribution (GSD). However, limited research on constitutive models for coarse-grained materials considers this influence. In this study, we introduced an initial GSD index, ϑ, measuring the distance between the initial GSD and the ultimate GSD, which associates the initial GSD with the ultimate GSD. We explored the influence of ϑ on the critical state friction angle φ_cs and the location of the critical state line (CSL) on the e- (p_cs’/p_a)^0.7 plane for coarse-grained materials. The results show that a decrease in ϑ leads to a downward movement and counterclockwise rotation of the CSL and an increase in φ_cs. The effect of initial GSD was incorporated into the state parameter, bounding stress ratio, dilatancy stress ratio and plastic modulus. Then, a state-dependent bounding surface model for coarse-grained materials has been proposed, highlighting the effect of initial GSD. The high accuracy of this model is evidenced by a good agreement between the modelling results and the experimental counterparts under drained and undrained conditions. This finding demonstrates the importance of initial GSD on granular materials, the effect of which can be well simulated by our proposed model.