This contribution presents an integrated and automated methodology for the computational analysis of permeability alterations in natural rocks under varying stress states, taking explicitly into account the complexity of the rock microstructure. The capacity of the methodology is highlighted on a subset of the microCT scans of a Vosges sandstone. After the generation of a high quality conformal mesh of the subset, isotropic compression at the scale of the microstructure is applied through FEM simulations. The adoption of non linear elastoplastic constitutive laws allows considering the local stress redistributions within the specimen. The mechanical loading of the subset highlights pore closures by local plastification. Permeability is evaluated at different confining pressures using the Lattice-Boltzmann method. Such a procedure allows analysing the impact of the pore space morphology (i.e. total porosity, pore size distribution, connectivity of the pore space, etc.) as well as the mechanical properties (i.e. stiffness and shear strength) on the evolution of the permeability under loading.