Reanalysis and Correction of Bed-Load Relation of Meyer-Peter and Müller Using Their Own Database

Abstract

The pioneering predictor of fluvial bed-load transport rate proposed by Meyer-Peter and Müller in 1948 is still extensively used in basic research and engineering applications. A review of the basis for its formulation reveals, however, that an unnecessary bed roughness correction was applied to cases of plane-bed morphodynamic equilibrium. Its inclusion followed a flow resistance parameterization in terms of the Nikuradse roughness height, which has been shown (well after the publication of their work) to be inappropriate for the characterization of mobile bed rough conditions in rivers. Removing the unnecessary correction and incorporating an improved correction of the boundary shear stress due to sidewall effects allow elucidation of the most parsimonious form of the bed-load relation of Meyer-Peter and Müller that is dictated by their own data set. The new predictor is presented in terms of two alternative power law forms. These amended forms show that, in the case of lower-regime plane-bed equilibrium transport of uniform bed sediment, the new estimates of volume bed-load transport rates are less than or equal to half the values that would be obtained with the original relation of Meyer-Peter and Müller in the absence of the unnecessary bed roughness correction. The meticulous database and clear analysis of the original work of Meyer-Peter and Müller greatly aided the present writers in their reanalysis, which liberally uses the hindsight offered by 58 years of subsequent research.