The aim of this paper is to present an overall model for the study of resin infusion based processes, in particular, the impregnation of a liquid resin through dry deformable fibrous reinforcements. This model can be appliedto a wide range of activities in many fields of engineering. Here, our approach based on a monolithic formulation in a level-set framework allows to strongly couple a Stokes-Darcy flow in low permeability media undergoing finite strains. The Stokes-Darcy coupled problem is solved using a mixed velocity-pressure formulation stabilized by a multi-scale method. A key feature of our approach is the fluid-solid interaction leading to couple a fluid/porous flow to a non-linear solid mechanics formulation. The interaction phenomenon due to the resin flow in the orthotropic highly compressible preform is based on both Terzaghi's law and on explicit relation expressing permeability as function of porosity in finite strains mechanical framework. Finally, simulations of industrial design parts are performed to illustrate the abilities of our approach and the relevance of this fluid/porous-solid mechanics coupled problem for composite material process simulations.