Impact dynamics of mud flows against rigid walls

Mud flows represent one of the major causes of natural hazards in mountain regions. Similarly to debris flows, they consist of a hyper-concentrated mixture of water and sediments flowing down a slope and may cause serious damages to people and structures. The present paper investigates the force produced by a dam-break wave of mud impacting against a rigid wall. A power-law shear-thinning model is used to describe the rheology of the hyper-concentrated mixture. A one-dimensional shallow water model is adopted and a second-order Finite Volume scheme is employed to numerically solve the governing equations. The results indicate that depending on the fluid rheological parameters and on the bottom slope, there exists a minimum value of the wall distance above which the peak force does not exceed the asymptotic value of the hydrostatic final condition. For two different values of the channel slope, the dimensionless value of this lower bound is individuated for several values of the power-law exponent and of a dimensionless Basal Drag coefficient. An estimation of the maximum peak force for wall distance smaller than the minimum value is also provided.