Shockwave model and Lagrangian series solution of quiescent sedimentation

Based on the mixture theory, a mathematical model for the sedimentation of soils in the steady water is established, depending on the volume fraction of the soils. The results show that the progress of the sedimentation of the soils is similar to the propagation of the shock wave, and thus the "blow up" of the solution can be treated as the beginning of the sedimentation. Under certain initial conditions, the analytical solution is obtained by Lagrangian series method. Finally, the rationality and the validity of the solution achieved are shown by a case study.