  We consider the propagation of nonlinear plane waves in porous media within
the framework of the Biot-Coussy biphasic mixture theory. The tortuosity effect
is included in the model, and both constituents are assumed incompressible
(Yeoh-type elastic skeleton, and saturating fluid). In this case, the linear
dispersive waves governed by Biot's theory are either of compression or
shear-wave type, and nonlinear waves can be classified in a similar way. In the
special case of a neo-Hookean skeleton, we derive the explicit expressions for
the characteristic wave speeds, leading to the hyperbolicity condition. The
sound speeds for a Yeoh skeleton are estimated using a perturbation approach.
Then we arrive at the evolution equation for the amplitude of acceleration
waves. In general, it is governed by a Bernoulli equation. With the present
constitutive assumptions, we find that longitudinal jump amplitudes follow a
nonlinear evolution, while transverse jump amplitudes evolve in an almost
linearly degenerate fashion.
