A cross-validated discharge–grain-size model for maximum bed scour in a mobile-bed open channel
Keywords:
bed scour, mobile-bed channel, discharge, grain size, cross-validationAbstract
This study develops a compact empirical model for maximum bed scour in an unobstructed mobile-bed open channel. Experiments were conducted in a 9 m flume using a 3×3 matrix that combined discharges of 0.0026, 0.0034, and 0.0045 m³ s⁻¹ with nominal grain sizes of 2.36, 1.18, and 0.85 mm. Final bed change was measured at 20 sections and seven transverse points for each condition, providing 1,260 spatial observations. Maximum scour increased from 0.8 to 4.5 cm, while the proportion of scoured observation points rose from 19.3% to 100%. The additive relation dₛ(cm)=1.272+0.883Q*−1.037d* explained 93.5% of the fitted variance and retained R²=0.843 under leave-one-condition-out cross-validation, with RMSE=0.394 cm. A particle-densimetric-Froude formulation produced a very strong fit on the normalized response scale but only a marginal reduction in cross-validated error after back-transformation. Discharge and grain size therefore acted as comparably strong controls in opposite directions within the tested range. The proposed relation is intended for interpolation within this experimental domain rather than as a universal design equation.
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