In this paper, we seek the scaling laws of sediment transport under a turbulent flow by applying the phenomenological theory of turbulence. The results show that at the threshold of sediment motion, the densimetric Froude number follows a (1+σ)/4 scaling law with the relative roughness number (ratio of particle size to flow depth), where σ is the spectral exponent. For the bedload transport, the bedload transport intensity follows a 3/2 and (1+σ)/4 scaling laws with the transport stage function and the relative roughness, respectively. For the scour in a contracted stream, the dimensionless scour depth follows a 4/(3-σ), - 4/(3-σ) and -(1+σ)/(3-σ) scaling laws with the densimetric Froude number, the channel contraction ratio and the relative roughness, respectively. © The Authors, published by EDP Sciences, 2018.