  In the mathematical modelling of sediment compaction and porous media flow,
the rheological behaviour of sediments is typically modelled in terms of a
nonlinear relationship between effective pressure $p_e$ and porosity $\phi$,
that is $p_e=p_e(\phi)$. The compaction law is essentially a poroelastic one.
However, viscous compaction due to pressure solution becomes important at
larger depths and causes this relationship to become more akin to a viscous
rheology. A generalised viscoelastic compaction model of Maxwell type is
formulated, and different styles of nonlinear behaviour are asymptotically
analysed and compared in this paper.
