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COSTA AND JARRETT-DEBRIS FLOWS where K strength in dn/cm' (690 dn/cm' ~ I lbf/in'), T thickness of deposit, y unit weight of debris, and a: slope angle. Typical values of strength for debris flows range from 0.1 x 1()4 to 5 X 10' dn/cm' (1.4-72 lbf/in'), Newtonian fluids, such as water, have no strength and the stress. relationship is: du T ~ I" dy where T = shear stress, J.t = dynamic viscosity, u velocity, and y ~ depth. Equation 2 can be used to model mechanical per. formance of the fluid. Fluids with large sediment concentrations begin to have strength when an applied force is required to cause deformation, Debris flows and other fluids, such as freshly mixed concrete that have strength and do not deform until that strength is exceeded, are non.Newtonian or Bingham fluids. The stress. strain relation for a Bingham or plastic fluid is: T ~ K + I" du dy (3) '. where K critical shear stress (strength), I" dynamic viscosity, u velocity, and y depth, Johnson (1970) has shown that many debris flows probably flow in a laminar fashion. In a Bingham fluid, the transition from laminar to turbulent flow is a function of not only the Reynolds number, but also the Bingham number (Hampton, 1972): B ~ Kd. I"U where (4) B Bingham number, K critical shear stress (strength), d linear dimension, I" dynamic viscosity, and u velocity. l'~ ~. 311 (2) OCCURRENCE OF DEBRIS FLOWS Debris flows result when material is eroded from basins by a combination of running water and mass- wasting processes, Progressively smaller and steep. er basins tend to transport an increasingly larger percentage of eroded material by mass-wasting pro. cesses such as debris flows. This is because: (I) thunderstorms drop proportionally larger volumes of water on smaller basins, and (2) smaller basins have steep side slopes resulting in instability of sur- ficial deposits. Sufficiently intense precipitation sat. urates permeable surficial deposits. This increases pore-water pressure and results in slope failures. Because of sparse rainfall data in most mountain areas, the intensity or duration of precipitation re- quired to mobilize side.slope materials is unknown. However, Campbell (1975) determined that a 6.4 mm (0.25 in) per hour rainfall intensity in areas where the total seasonal antecedent rainfall has reached 254 mm (10 in) are the threshold condi- tions for the initiation of soil slips and debris flows in the Santa Monica Mountains in southern California. In five ofthe seven small mountain basins studied in Colorado (Figure 2), debris-source areas were slope failures in poorly sorted colluvium on sparse. ly vegetated or unvegetated side slopes above tim. ber line. The elevation, drainage area, date and type of event, and slope.area discharge are provided for the seven sites investigated (Table I). Despite the lack of precipitation data, mobilization of material on unvegetated slopes steeper than 30 degrees prob. ably is not restricted to periods of intense precipi- tation. When precipitation data are sparse, one indirect indicator of the rainfall intensity is the extent of rill erosion resulting from overland flow of excess rain- fall on non. vegetated land surfaces such as exposed soils and road cuts. Although rainfall information is lacking, our observations of small mountain ba- sins following rainstorms indicate that only mod. erate rainfall intensities are required to produce overland flow and create rills on exposed surfaces, At the sites investigated with recent dates of rain. produced flows-East River tributary (A very Peak tributary referred to by Mears, 1979) near Crested Butte, Colo., South Halfmoon Creek tributary near Leadville, Colo., and South Fork Dutch Creek trib. utary near Redstone, Colo.-rill erosion was mini~ mal or absent following rainstorms which produced debris flows. Thus it appears debris flows can occur during most rainfalls, provided sufficient amounts