Abstract: The viscous characteristics of fault granular interlayers have a significant impact on the dynamic mechanical behavior of faults. The problem of determining the viscosity of fault granular interlayers at different slip velocities has not yet been solved. This article conducts theoretical research on this issue. Firstly, the Maxwell relaxation model was used to study the evolution of force chains for slow shearing of granular gouge, and the dependence of force chain length on shear strain rate, effective extension speed of shear bands, and strength of granular medium was derived. Further the relaxation time of the shear band, the expression of the viscosity coefficient of the granular medium, the conditions for the transformation of solid-liquid mechanical behavior of the granular medium were established. The comparison with existing experimental data has verified the validity of this model. For high-speed slip shear, the motion of granular medium exhibits turbulent characteristics. Statistical physics was used to describe the interaction between granular particles, and it is obtained that the viscosity coefficient is inversely proportional to the shear rate at high slip rate. The research results have fundamental significance for understanding the viscous and other physico-mechanical properties of granular gouge in faults.