Perturbation solution for Bingham-plastic mudflows

An analytical solution is proposed for laminar mudflows and debris flows that can be modeled by a Bingham-plastic law. Two-dimensional, unsteady, nonuniform, Bingham flows released from a point source or a source of finite size (dam-break problem or mudslide problem) on a steep slope are considered. The method of matched asymptotic expansions was implemented to get a first-order solution. For the dam-break problem, the proposed model is found to be valid when the shock wave has advanced three reservoir lengths downstream. Also, it is found that the Bingham flow only propagates a finite distance downstream, with the shock depth asymptotically approaching the yield depth and the shock velocity asymptotically falling to zero. The hydrograph produced by a Bingham flow is seen to have a slower and lower flood peak and a longer and higher flow tail than that produced by Newtonian flow having the same dynamic viscosity. Comparison of the model predictions with laboratory observations shows reasonable agreement.