Recent observations suggest that the presence of frictionally weak minerals in a majority frictionally strong matrix may explain the reduced strength and instability in faults. Experimental results on synthetic fault gouges using a mixture of a frictionally strong phase and a frictionally weak phase indicate that the fault can be weakened by even a small amount of frictionally weak minerals. These frictionally weak minerals weaken the fault by either acting as weak spots/clusters or as a through-going weak layer in the bulk gouge. A two-dimensional Distinct Element Method (DEM) numerical model using the Particle Flow Code 2D (PFC 2D) is developed to investigate the effect of frictionally weak minerals on the bulk shear strength of fault gouge. Mechanical response of particles is modeled using a linear-elastic contact model and Coulomb's friction law. Numerical direct shear experiments were performed on homogeneous mixtures of weak and strong mineral particles and also on heterogeneous mixtures consisting of a frictionally weak layer sandwiched in frictionally strong minerals. The weight percentage (wt%) of the frictionally weak mineral in the homogeneous mixtures and the relative thickness of the frictionally weak mineral layer in the heterogeneous mixtures are adjusted schematically to obtain the weakening regime of the bulk shear strength. A transition from high to low residual coefficient of friction is observed. Specifically, for homogenous mixtures a sharp drop of bulk shear strength is observed with 25% of frictionally weak mineral presented in the mixture, and a dominant influence occurs at 50%; for heterogeneous mixtures, noticeable weakening is shown at a relative weak layer thickness of 0.05, and a dominant influence quickly follows at a relative thickness of 0.10. The observed weakening regime matches well with previous lab results using talc/quartz mixtures.