非均匀卵砾石粗糙床面的分形特征

针对传统方法刻画粗糙床面总体特征存在缺陷的问题,将分形几何理论引入非均匀卵砾石粗糙床面特征研究,以卵砾石床面激光扫描试验资料为基础,探讨了分形尺度区宽度与中值粒径d50的关系,分析了覆盖基准面对分形维数的影响,研究了床面整体与局部分形维数的特征与联系,获得了分形维数随床面颗粒组成及高程统计参数的变化规律。结果表明:分形尺度区宽度与床面颗粒中值粒径d50有关,上临界尺度可取为1.5d50;分形维数与覆盖基准面位置有关,覆盖基准面距平均床面的距离越大,分形维数越大且逐渐失真,为有效量化和区分床面粗糙特征,覆盖基准面宜取平均床面;粗糙床面分形维数具有良好的稳定性,局部分形维数变异性很小,并与整体分形维数接近;粗糙床面的分形维数与颗粒大小、级配组成及床面高程统计参数有关,中值粒径越大,颗粒组成越均匀,床面高程极差、标准差、偏度(绝对值)和峰度越大,分形维数越小。

Fractal characteristics of non-uniform gravel rough surfaces

This study presents a fractal geometry method to study the characteristics of non-uniform gravel rough bed surfaces(RBS),based on the experimental data of laser scanning of non-uniform gravel bed surfaces,the relationship between the width of the fractal scale region and the mean particle size d50 was discussed,the influence of the coverage base level on fractal dimension was analyzed,the characteristics and relationships of the global and local fractal dimension of RBS were studied,and the variation regularity of the fractal dimension with the particle size and the statistical parameters of the elevation was obtained.Results showed that the fractal scale width is related to the median size d50of the bed sand particles,the upper critical value can be taken as 1.5d50.The fractal dimension of RBS is related to the location of the coverage base level,the greater the distance from the average bed elevation,the greater the fractal dimension and gradually distortion.In order to quantify and distinguish the characteristics of RBS effectively,the average bed elevation should be taken as the coverage base level.The fractal dimension of RBS has good stability,the variability of the local fractal dimension of RBS is very small,and is close to the global fractal dimension.The fractal dimension of RBS is related to the particle size,the composition of the gradation and the statistical parameters of the bed elevation,the bigger the median particle size,the more uniform the particle composition,the higher the value of bed elevation range,standard deviation,skewness (absolute value) and kurtosis,the smaller the fractal dimension.