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Ashida & Michiue (1972) hiding function

The Ashida & Michiue (1972) hiding function1 allows modification of the critical Shields parameter in sediment mixtures:

\[ \frac{\theta_{c}}{\theta_{c,0}} = \begin{cases} 0.85 \dfrac{d_{50}}{d_{i}}, & \dfrac{d_{i}}{d_{50}} < 0.4 \\[2ex] \left( \dfrac{\ln(19)}{\ln\left( 19 \dfrac{d_{i}}{d_{50}} \right)} \right)^{2}, & \dfrac{d_{i}}{d_{50}} \geq 0.4 \end{cases} \]

Equation: Ashida & Michiue hiding function for the critical Shields parameter of a sediment fraction.

Ashida & Michiue is an improvement over the Egiazaroff (1965) hiding function2, the latter having a singularity when \(d_{50}/d_{i} = 19\).

Ashida & Michiue accounts both for hiding and lubrication by reducing the critical Shields parameter when \(d_{i} > d_{50}\) (exposure) and increasing the critical Shields parameter when \(d_{i} < d_{50}\) (hiding).

Ashida & Michiue can be activated when simulating more than one fraction, but only some formulas react to this activation, namely formulas that use the critical Shields parameter.

In the MIKE HYDRO GUI this is named Egiazaroff.

  1. Ashida, K., & Michiue, M. (1972). Study on hydraulic resistance and bed-load transport rate in alluvial streams. In Proceedings of the Japan Society of Civil Engineers (Vol. 1972, No. 206, pp. 59-69). Japan Society of Civil Engineers. ↩

  2. Egiazaroff, I. V. (1965). Calculation of nonuniform sediment concentrations. Journal of the Hydraulics Division, 91(4), 225-247. ↩