  We present the microscopic equation of growing interface with quenched noise
for the Tang and Leschhorn model [L. H. Tang and H. Leschhorn, Phys. Rev. A
{\bf 45}, R8309 (1992)]. The evolution equation for the height, the mean
height, and the roughness are reached in a simple way. An equation for the
interface activity density (or free sites density) as function of time is
obtained. The microscopic equation allows us to express these equations into
two contributions: the diffusion and the substratum contributions. All these
equations shows the strong interplay between the diffusion and the substratum
contribution in the dynamics.
