| Abstract: | Although the Shields relation was developed for rivers, it has been applied to sediment transport by overland flow. According to the Shields relation, where the critical boundary Reynolds number Re*c exceeds 40, the critical Shields number F*c is independent of both Re*c and the ratio of the critical flow depth to particle diameter dc/D. Analyses of data collected from runoff plots in southern Arizona reveal that F*c is positively correlated with both Re*c and dc/D. Thus the Shields relation does not apply to overland flow on debris-covered desert hillslopes. Multiple regression analysis is employed to develop alternative threshold relations in which critical boundary shear stress τc is related to D and dc/D (R2 = 0.782) and to D and Sc (critical gradient) (R2 = 0.625). The computed R2 values derive in large part from the spurious correlations of dc/D and Sc with τc. Nevertheless, the relations may be utilized to predict τc. In this regard, the latter relation is likely to prove more useful than the former because Sc is generally known, whereas dc is not. An investigation of the functional relation between τc and D reveals that τc varies approximately with D2 for overland flow on the desert hillslopes under study, whereas the Shields relation predicts a linear relation (i.e. a D exponent of 1). This result is consistent with Cheng's data which show that F*c varies with (dc/D)?1 where 0.4 < dc/D < 2 and may be explained in terms of increased energy dissipation both in separation zones downslope of particles and in distortion of the water surface as dc/D decreases. Consequently, larger values of τc, and hence F*c, are required to initiate the transport of particles of a given size D as dc decreases. |
