The propagation of a high intensity sound wave is determined mainly by the nonlinear and dissipative effects. If the initially sinusoidal wave is intensive, the steepness of the wave fronts increases, resulting in the occurrence of a discontinuity in each period of the wave. On the other hand, the influence of dissipative processes tends to smooth the wave profile, diminishing the gradients of velocity and temperature. Consequently, during the propagation of the intense wave its profile is forming as a result of the balance of nonlinear and dissipative effects. Many aspects of the high intensity sound wave evolution were described in the set of papers of D. T. Blackstock. The standard nonlinear medium with viscosity and thermal conductivity was considered. However, later, M. J. Buckingham has developed the theory of sound propagation in saturated marine sediments which includes a new dissipation term representing internal losses arising from interparticle contacts. The balance of nonlinearity and dissipation in such a medium has specific features that are considered in the present paper.