Nonlinear acceleration wave propagation in the DKM theory

•Propagation of an acceleration wave in a saturated porous material is studied.•The porous material model is based on a Biot theory of Donskoy, Khashanah and McKee.•The theory is fully nonlinear, includes dissipation, and the analysis is exact.•Sufficient conditions to show that two distinct waves propagate are derived.•A solution for the amplitude of a wave moving into an equilibrium region is presented.