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<br />governed partially by the cohesion between fine sediment particles. <br />This cohesion, defined as the yield st.ress 1 y' must be exceeded by <br />the applied fluid stress in order '1:0 initiate motion. <br /> <br />Turbulent stresses are generat.ed in flows with large rates of <br />shear. In turbulent flows, the collision of sediment, particles <br />gives rise to an additional shear stress component called the <br />dispersive stress. At very high sediment concentrations, <br />turbulence will be suppressed and the flow will approach being <br />laminar. Sediment concentration may vary dramatically and, as a <br />result, viscous and turbulent str,esses may alternately dominate <br />producing flow surges. The following equations for mudflows <br />supplement the motion equations for water flows. <br /> <br />O'Brien and Julien (1985) suggested that the total shear <br />stress in hyperconcentrated sediment: flows can be calculated from <br />the summation of four shear stress components. <br /> <br />r = Ty + Tv + Tt + Td <br /> <br />(4) <br /> <br />where the total shear stress 1 depemds on the yield stress 1y, the <br />viscous shear stress 1 v' the turbulent shear stress 1 t' and the <br />dispersive shear stress 1 d. When ~,rri tten in terms of shear rates <br />the following quadratic rheological model has been proposed: <br /> <br />1 = Ty + ~ [:;) <br /> <br />+ <br /> <br />c [:~r <br /> <br />(5) <br /> <br />where ~ represents the viscosity and c: denotes the inertial shear <br />stress coefficient given by: <br /> <br />C = pi2 + alP>.2 d,2 <br /> <br />(6) <br /> <br />This coefficient depends on the mass densi.ty of the mi.xture p, the <br />Prandtl mixing length i, the linear sediment concentration >., the <br />sediment size d, and the empirical coefficient al defined from <br />Bagnold's experiments (1954). <br /> <br />The first two terms in Eqn. 5 represent the internal <br />resistance stresses of a Bingham fluid and are referred to as the <br />Bingham shear stresses. The sum of the yield stress and viscous <br />stress defines the shear stress of a cohesive, hyperconcentrated <br />sediment fluid in a laminar flow regime. The last term represents <br />inertial stresses and is the sum of the dispersive and turbulent <br />shear stresses which vary as the square of the vertical velocity <br />gradient. A discussion of theSE! stresses and their role in <br />mudflows can be found in Julien and O'Brien (1987). <br /> <br />If only the Bingham stresses are employed in the rheological <br />model and inertial stresses are ignored, the mudflows being <br /> <br />20 <br />