Numerous studies have demonstrated that the strength and deformation characteristics of coarse-grained materials are significantly influenced by the initial particle size distribution (GSD). However, research on constitutive models for coarse-grained materials that consider this influence is still limited. In this study, we introduced an initial GSD index, 9, which reflects the ease of particle breakage and links the initial GSD to the ultimate GSD. We systematically investigated and elucidated the mechanism by which ,9 affects the peak shear strength (qp), peak strain (eap), and the position of the critical state line (CSL) on the e-p plane. The results regarding the effect of S on qp and eap indicate that as ,9 increases, qp decreases, whereas eap increases. Based on these findings and the hump-shaped quadratic curve model proposed by Shen Zhujiang, we established a tangent Young's modulus that considers the effects of initial GSD and confining pressure. The study on the effect of ,9 on the CSL position reveals that a decrease in S leads to a downward shift and a counterclockwise rotation of the CSL. Subsequently, within the framework of critical state soil mechanics (CSSM), we proposed a state-dependent tangent Poisson's ratio that considers the effects of initial GSD and confining pressure. For a specific type of coarse-grained material, the model only requires a set of model parameters, and the model's high accuracy is evidenced by the good agreement between the modeling results and the experimental data.