The shear behaviors of granular mixtures are studied using the discrete element method. These granular materials contain real gravel-shaped coarse particles and spherical fine particles. Dense samples have been created by the isotropic compression method. The samples are then sheared under drained triaxial compression to a large strain to determine the peak and residual shear strengths. The emphasis of this study is placed on assessing the evolutions of contributions of the coarse-coarse (CC) contacts, coarse-fine (CF) contacts and fine-fine (FF) contacts to the peak and critical deviator stresses. The results are used to classify the structure of granular mixtures. Specifically, the granular mixtures are fine-dominated or coarse-dominated materials when the coarse particle content is <30%-40% or >65%-70%, respectively. A comparison with previous findings suggests that the spherical binary mixtures will become coarse-dominated materials at a relatively larger coarse particle content (i.e., 75%-80%) than this study (i.e., 65%-70%), which is attributed to the particle shape effect of coarse particles. A microscopic analysis of CC, CF and FF contacts at the peak and critical states, including normal contact forces and proportions of strong and weak contacts of each contact type to total contacts, reveals why the contributions of CC, CF and FF contacts to the peak and residual shear strengths are varied. Finally, a detailed analysis of the anisotropies indicates that the increases of peak and residual shear strengths are primarily related to the gradual increases in geometrical anisotropy a(c) and tangential contact force anisotropy a(t) to compensate for the continuous decrease in normal contact force anisotropy a(n). Furthermore, it is interesting to note that the branch vector frame provides a better linear relationship between the stress ratio and the geometric anisotropy of the strong and nonsliding subnetwork than the contact frame for the coarse-dominated materials. (C) 2019 Elsevier B.V. All rights reserved.