We develop a staggered finite element procedure for the coupling of a free viscous flow with a deformable porous medium, in which interface phenomena related to the skin effect can be incorporated. The basis of the developed simulation procedure is the coupled Stokes-Biot model, which is supplemented with interface conditions to mimic interface-related phenomena. Specifically, the fluid entry resistance parameter is used to relate the fluid flux through the interface to the pressure jump across the interface. The attainable jump in pressure over the interface provides an effective way of modeling sharp pressure gradients associated with the possibly reduced permeability of the interface on account of pore clogging. In addition to the fluid entry resistance parameter, the developed simulation strategy also includes the possibility of modeling fluid slip over the porous medium. Sensitivity studies are presented for both the fluid entry resistance parameter and the slip coefficient, and representative two- and three-dimensional test cases are presented to demonstrate the applicability of the developed simulation technique.