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<br />2,7 <br /> <br />characterized by surging, abrupt flow stoppage, channel aggradation and <br />degradat i on, and channel avul s i on Dn all uvi al fans. ,- Flows often abandon the <br />normal clear,water channel, creating new flow paths across the alluvial fans. <br />Due to the transient nature of these phenomena, the most practical approach is <br />to treat the flow as a continuum, combining the water and sediment components <br />and ignoring such factors and characteristics as particle fall velocity, scour <br />and aggradation, sorting and flow competence. The purpose of modeling mud flows <br />is, therefore, to determine a reasonable general range of flow properties, such <br />as velocity and depth, a flood hydrograph, and the potential area of inundatiDn <br />on the alluvial fan. <br />To derive the equation for hyperconcentrated sediment flow, the fluid shear "" <br />stress must be investigated. The internal stresses of a hyperconcentrated <br />sediment flow can be represented mathematica"lly as <br /> <br />T = 1y + 1V + 1d + 1 <br /> <br />(2.12) <br /> <br />where 1 is the total fluid shear stress, Ty is the yield stress associated <br />with cohesive soils, 1v is the viscous shear stress giiven by 7)du/dy where <br />7) is the fluid viscosity, u is the flDW velocity in the x,direction, 1d is <br />the dispersive shear stress arising frDm the collision between particles, and <br />l' is the turbulent shear stress. <br />In general form <br /> <br />1 = 1 + T} du + <br />y dy <br /> <br />'d 2 <br />C (-.!!) <br />dy <br /> <br />(2.13) <br /> <br />where C' is a coefficient of the inertial shear stresses (the dispersive plus <br />the turbulent shear stress). <br />The first two terms are referred to as the Bingham shear stress and <br />represent the internal resistance stresses of a Bingham fluid. The sum of the <br />yi e 1 d stress and vi scous stress defi n(~s the shear stress of a cohes i ve, <br />hyperconcentrated sediment fluid in laminar flow regime. The last term <br />represents the sum of the dispersive and turbulent shear stress which are a <br />function of the vertical velocity gradient squared. A more complete treatment <br />of these stresses and their role in hyperconcentrated sediment flows can be found <br />in O'Brien (1986) Dr O'Brien and Jul ien (1987). A, mud flow model that <br />incorporates only the Bingham stresses and ignores the inertial stresses assumes <br />