为探讨颗粒排列的空间趋向对床面结构的影响,人工铺制了12组鱼鳞状床面,依托激光扫描技术获得其精确数字高程,基于统计学理论与分形理论对所铺床面的粗糙特性进行分析。结果发现:鱼鳞状床面相对高程频率分布具有负偏双峰特征,主峰近似正态且较为“高大”,次峰却极为“矮小”;卵石粒径增大,各床面高程变异函数的基台值与变程均增大;床面高程方差与变异函数基台值在量化鱼鳞状床面粗糙特性方面是基本等价的;卵石粒径越大,床面高程方差越大,变异函数基台值越大,床面越粗糙,反之亦然;鱼鳞状床面二维特征方向无标度区上限随卵石粒径的增大而单调增大,其值可近似取为0.5d₅₀(d₅₀为中值粒径),然而同一床面各二维特征方向上的无标度区上限是大致相同的;就同一二维特征方向而言,随着卵石粒径的增大,床面分形维数基本减小,床面结构复杂性减弱;鱼鳞状床面粗糙特性具有明显的方向性,尤其是在与水流方向的角度成0、π/4与π/2的3个方向上,其粗糙特性明显不同。

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.