In case of inappropriateness of ground conditions, it should be improved in order to attain the strength required for structure. One method to serve this purpose, is grouting in rock mass. Various experimental and numerical studies have been conducted regarding grouting progress in a single joint or disciplined joint set analytically, physically, and numerically but studies carried out in the field of physical and particularly in Discrete Fracture Network (DFN) models are scarce. The initial version of GrouIUT 2D which utilizes pressure drop method to compute fluid flow in DFNs. It is attempted to remedy the scarcity and resolve the issues of the prototype GrouIUT 2D using modeling fracture networks at laboratory scale and modeling it numerically. The simulation was performed using Lattice Boltzman (LB) method which has an ability for rapid calculations and parallel processing, and led to the second version of the software which is capable of generating DFNs and also operational agents such as the viscosity and density of grout. The criterion adopted in this research is the distributable area of grout which the code can show according to an algorithm for determining the area around the grouting well during calculation. The number of physical modeling was optimized with Taguchi experimental design and three different fracture networks, non-identical fractal dimensions, and varying pressure and time conditions and three fluids with the viscosities of hydraulic and gear oils, cement grout with the water-to-cement ratio of 1:2, and joint aperture in dry and saturated conditions were examined. Following the designed experiments, the influence of each agent on the distributable area was determined and numerical simulations were conducted accordingly. The results showed the effects of different factors on grout spreading. The results of physical and numerical modeling show that the saturated media and front pressure head has a negative impact on grout spreading progress in DFN. The investigation of time and pressure revealed that these two components are of optimum values and excessive increase in them do not affect grout distribution characteristics. The influence of viscosity is significant and its increase results in a decrease in the distributable area. Using physical simulations and LB, the numerical model and were verified. Since the validity of was confirmed, a large scale fracture network was simulated and the results substantiated the presence of optimized time and pressure in grouting.