Abstract: This paper investigates the permeability of solids containing a crack network with finite connectivity through micromechanical method. The main factors of permeability include crack density, connectivity, crack opening and permeability of porous matrix. Firstly, for solids with unconnected cracks, the interaction direct derivative (IDD) method is employed to obtain the crack-altered permeability considering crack density \rho and crack opening b. Then, for networks containing randomly oriented cracks with intersection, the amplification of permeability by crack connectivity is quantified for local crack clusters. This amplification effect is modeled by arranging parallel cracks on transport direction. By introducing the definition of hypothetically parallel crack density \rho^\rm h, the hypothetically parallel cracks are embedded in a host matrix whose permeability are those of the effective medium. In this way the IDD model is extended to evaluate the permeability of part-connected networks before total percolation occurs, considering the permeability of porous matrix K_\rm m, crack density \rho , opening aperture b and parallel crack density \rho^\rm h. Finally, the representative volume element is built for cracked solids with cracks having random spatial locations and the permeability is solved by finite element method. Through this numerical tool, the validity and accuracy of IDD solutions for non-connected and part-connected crack networks are confirmed by several case analysis. The results show that: (1) For non-connected networks, crack opening is found to have little impact on the effective permeability due to the continuous matrix and its low permeability; (2) For part-connected networks, when crack density \rho <1.1 (uncorrelated networks, the fractal dimension is 2.0), 1.2 (correlated networks, the fractal dimension is 1.75), the IDD extended model show a good agreement with numerical results and loses its accuracy due to the clustering effect at more higher \rho level.