Cohesive granular materials play a major role in nature and industry. Cohesive interactions between particles have various physico-chemical origins such as capillary bonding, Van der Waals forces, and a cementing matrix. Despite extensive experimental and numerical work on these materials, their mechanical behavior under the action of external loading is still poorly understood, and the compaction behavior of cohesive granular materials is highly dependent on the loadings applied. In a previous study we established a link between the material properties, applied force and porosity of a cohesive granular sample submitted to an isotropic compaction. Here we study the influence of the adhesion force under triaxial compression on dense granular samples. We find that shear stress increases linearly with void ratio in the critical state (state of continuous deformation). We show that the cohesive strength is linearly dependent on the adhesion force between the particles. Furthermore, the shear strength and the void ratio are linearly linked in the critical state. We also identify two limiting behaviors in the evolution of the microstructure based on the coordination number and the anisotropy of the contact network: an increase of coordination number at constant anisotropy for the most cohesive cases, and an increase of anisotropy at constant coordination number for the least cohesive cases. We show that these two microstructural parameters are linked together in the fabric space as a result of steric exclusions.