PERTURBATION SOLUTION FOR BINGHAM-PLASTIC MUDFLOWS

An analytical solution is proposed for laminar mudflows and debris flo ws that can be modeled by a Bingham-plastic law. Two-dimensional, unst eady, nonuniform, Bingham flows released from a point source or a sour ce of finite size (dam-break problem or mudslide problem) on a steep s lope are considered. The method of matched asymptotic expansions was i mplemented to get a first-order solution. For the dam-break problem, t he proposed model is found to be valid when the shock wave has advance d three reservoir lengths downstream. Also, it is found that the Bingh am flow only propagates a finite distance downstream, with the shock d epth 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 hi gher flow tail than that produced by Newtonian flow having the same dy namic viscosity. Comparison of the model predictions with laboratory o bservations shows reasonable agreement.