Critical Shields Values in Coarse-Bedded Steep Streams

Critical Shields values for poorly mobile, semi-alluvial mountain streams are not provided by the original Shields diagram and are still debated. This empirical study uses gravel bedload samples collected with unbiasing samplers at 22 stream sites and establishes a relation between instantaneous discharge and the largest sampled bedload particle size for each site. Using relations between flow depth and discharge, critical Shields values for particle sizes corresponding to the bed surface D₅₀, D₁₆, D₈₄, and D_50s sizes at each site can be backcomputed from the established critical flow or flow competence relations. Critical Shields values for all bed material particle size percentiles increase with stream gradient S_x and are stratifiable by relative flow depth d/D₅₀ and relative roughness (D₈₄/d) which improves prediction. Critical Shields values for the bed D₁₆ sizes (τ*_c16) are approximately three times larger than those for the D₅₀ size (τ*_c50), while those for the D₈₄ size (τ*_c84) are approximately half of τ*_c50. It remains unclear to what extent physical processes or numerical artifacts contribute to determining critical Shields values. Specific critical Shields values are needed to predict the average largest particle size mobile at bankfull flow (D_Bmax,bf). So far, no Shields values are available for this common task, especially not in poorly mobile semi-alluvial streams. Critical bankfull Shields values (τ*_cbf) backcomputed from the largest particles transported at bankfull flow approach τ*_c16 at steep gradient streams and τ*_c84 at low gradients and therefore increase very steeply with S_x. The relation τ*_cbf = f(S_x) is stratified by bed mobility D₅₀/D_Bmax,bf and predictable if bed mobility can be categorized in the field. Non-critical Shields values (τ*_bf50) computed from bankfull flow depth and the bed surface D₅₀ size differ from τ*_c50 and from critical bankfull Shields values τ*_cbf. Only in bankfull mobile streams where D₅₀/D_Bmax,bf = 1 can τ*_cbf, τ*_c50, and τ*_bf50 be used interchangeably. In highly mobile streams, substituting τ*_cbf by τ*_bf50 overpredicts the D_Bmax,bf size by up to fivefold and underpredicts D_Bmax,bf by the same amount in poorly mobile streams. A value of 0.03 is appropriate for τ*_cbf only on highly mobile beds with S_x ≈ 0.01, but overpredicts D_Bmax,bf by 30-fold on poorly mobile beds with S_x ≈ 0.1. Differences in field and computational methods also affect critical Shields values.