Fault zone usually presents a granular gouge, coming from the wear material of previous slips. Considering a mature fault gouge with mineral cementation between particles, we aim to understand the influence of these cohesive links on slip mechanisms. As cohesion is difficult to follow and to quantify with Lab or in-situ experiments, we choose to use Discrete Element Method that has already shown its ability to represent granular gouges with relevant kinematics and rheology. In this work, we consider a dry cohesive contact model in 2D (2x20mm²) involving two rough surfaces representing the rock walls separated by the granular gouge (5000 particles, grain size 27- 260 μm). A step forward compared to literature is to add cohesion on real angular and faceted grains that modifies contact between particles. Focusing on physics of contacts inside the granular gouge, we explore contact interactions and friction coefficient between the different bodies. To represent the cementation we set up a Bonded Mohr-Coulomb law, considering that inter-particular bridges and particles are made with the same material. This numerical model is displacement-driven and is implemented to study the peak of static friction (shape, slope, duration) under a confined pressure of 40 MPa. Depending on the compacity and on the cohesion level of each model, the peak strength may be sharp, short, and intense for dense and highly cohesive cases or smooth, delayed with moderate amplitude for mid-dense and moderately cohesive cases. Three main behaviors are observed: a non-cohesive regime where the added cohesion is too small to truly disturb the global slip mechanism (Couette flow), an intermediate cohesive regime with clusters of cohesive grains, changing the granular flow and acting on slip weakening mechanisms (Riedel shear band R1) and an ultra-cohesive regime where gouge behaves as a brittle material with several Riedel shear bands emergence. We also investigate the role of cohesive bonds in energy budget, focusing on fracture energy term. Three mechanisms are playing a role in fracture energy evolution: the rupture of cohesive bonds, the dilatancy of the gouge and Coulomb dissipations due to friction. These factors are linked to the initial percentage of cohesion inside the sample and help characterize the mechanisms at stake in the initiation of sliding.