We report the results of an analytical investigation into the deformation behaviour of rate‐dependent granular material as a refinement of previous studies on seepage phenomena during shear. The rheology has two components—a compliant part of the constitutive law associated with grain contacts as deformation takes place (dilatancy), and a rate‐dependent viscous force transmitted by the melt phase. This formulation allows intermediate, time‐dependent behaviour to be assessed for the dilatant porous medium. A key result is that during shear, the magnitude of the excess pore pressure first decreases then increases back to its initial value. Two characteristic timescales are identified that control the rate‐dependent dilatancy of the mixture, τ1, the time constant that rules the increase of the magnitude of the excess pore pressure, and τ0 that controls its decline. We consider the dilatant effect to be an internal constraint in deforming magmas in the lithosphere and other porous (partially molten) regions in the solid earth. When such regions are exposed to external loading, secular pressure changes should drive fluid flow independent of local buoyancy forces, for the duration of the governing rate‐dependent timescales. The accumulated heave of the process is also estimated.