The critical dimensionless shear stress, τ*ci, required to entrain a given size particle, di, was computed from extensive bedload-transport measurements in three self-formed rivers that have naturally sorted gravel and cobble bed material. The value of τ*ci was determined to be significantly affected by the size distribution of the riverbed material. For bed particles between 0.3 to 4.2 times the median diameter of the subsurface bed material, d̂50, the average critical dimensionless shear stress, τ̄*ci, is equal to
τ̄*ci = 0.0834 (di/d̂50)-0.872
with a coefficient of determination of 0.980. For bed particles larger than 4.2 times d50, τ̄*ci appears to approach a constant value of approximately 0.020 in a noneroding channel. Thus, τ̄*ci varies from 0.25 to 0.020 for a given particle, depending on the ratio of di to d̂50. Previous investigations of the hydraulic conditions required to entrain coarse riverbed material have reported critical shear stress values ranging from 0.25 to 0.020 for a given particle size. This analysis indicates that virtually all of the variation is due to differences in the subsurface bed-material size distribution. This analysis shows that τ̄*ci varies almost inversely proportional to the particle diameter for a nonuniform bed material; therefore, bed particles between 0.3 to 4.2 times d̂50 are entrained at nearly the same discharge.
An investigation of the hydraulic characteristics and bed-material mobility of 24 self-formed gravel-bed rivers in Colorado determined that particles as large as the median diameter of the bed surface were entrained by discharges equal to the bankfull stage or less. Particles as large as the 90th-percentile fraction were entrained by the bankfull discharge in nine of the rivers studied. Consequently, in these rivers, a significant fraction of the riverbed was entrained rather frequently over a period of years, although the transport rate was very small.