### Abstract:

Recent experimental studies on unlithified sediments suggest that the compaction is in part viscous. At the basin scale and on a geological time scale, processes such as pressure solution can be approached by creep deformation, subjected to a viscous rheology. In the present work, we have studied porosity reduction and fluid pressure development resulting from the visco-elastic compaction of a sedimentary basin during its formation. Model equations include continuity equations, Darcy’s law and a visco-elastic rheology law which relates the strain rate to the effective stress and to the rate of change of this effective stress. Under the assumption that permeability is a power law function of porosity, the equations become essentially non-linear. Model results illustrate how the decrease of porosity starts at the base of the basin and spreads upward with increasing time. In a wide range of input parameter values calculations indicate a zone of almost linear increasing of pore pressure just below the basin surface, a transition zone of rapidly increasing fluid pressure with a large pressure gradient and a zone of lithostatic fluid pressure below. This is consistent with the general features of zoning of fluid pressure distribution in overpressured areas but zones with high pressure also correspond to low porosity at depth. The relative thickness of the zones depends on time, subsidence velocity and the physical parameters of sediments which can be combined in order to define a characteristic compaction length and a characteristic compaction time. In the upper zone, the decrease of porosity results in a boundary layer; within this layer, the porosity decreases from its initial value down to its minimum value. The deeper zone appears when the time of formation of the given depth basin exceeds the characteristic compaction time and the thickness of the basin is in order of compaction length. Zones of fluid overpressure may also develop due to the spatial variations of the physical properties of the sediments.