Abstract: In the aim of exploring the effect of particle arrangement trend on bed surface structure,twelve groups of imbricate bed surfaces were paved manually and their precise digital elevations were obtained by using 3D laser scanning.The roughness characteristics of the imbricate bed surfaces were analysed on the basis of statistical theory and fractal theory.Results unveil that the distribution of relative elevation frequency of imbricate bed surface is negatively skewed and bimodal.The main peaks follow approximate normal distribution and are tall and large,while the minor peaks are short and small.With the increasing of particle size,the sill and the spatial correlation length of the elevation variogram increase.The elevation variance and the sill of the variogram are basically equivalent in quantifying the roughness characteristics of the imbricate bed surfaces.The larger the particle size is,the greater the elevation variance is,the larger the sill of the variogram is,and the rougher the bed surface is,and vice versa.For imbricate bed surfaces,the scale-free upper limit in a two-dimensional specific direction monotonously increases with the increasing of particle size,and its value can be approximately taken as 0.5d₅₀(half of the median particle size).However,for any imbricate bed surface,the scale-free upper limits in different two-dimensional specific directions are roughly the same.In any two-dimensional specific direction,with the expansion of particle size,the fractal dimension decreases,and the bed surface complexity reduces.The roughness characteristics of the imbricate bed surfaces are obviously directional;especially in three directions (0,π/4 and π/2(rad) relative to the flow direction),the roughness characteristics are fairly different.

Key words: imbricate bed surface, roughness characteristics, statistical parameters, variogram, fractal dimension