基于分形理论的粗粒料级配缩尺方法研究

按规范要求的剔除法、等量替代法、相似级配法、混合法等4种缩尺方法，对某粗粒料原型级配进行缩尺，得到15条试验模拟级配，相应的最大颗粒粒径分别为60、40、20 mm。对原型级配和缩尺后模拟级配，进行了最大干密度试验，引入粒径分形维数，研究粒径分形维数与级配缩尺方法、最大干密度的变化规律。分析认为，粒径分形维数是一个能综合反映级配的量化评价指标，可准确反映不同缩尺方法后的试验模拟级配；级配缩尺方法本身对最大干密度有较大的影响，相似级配法的最大干密度值与原型级配的最接近，等量替代法的差异性最大；粒径分形维数与最大干密度具有较好的线性归一化，利用归一化规律，可准确推求原型级配的最大干密度值，有较好的工程应用价值。

Grading scale method for coarse-grained soils based on fractal theory

Four grade-scaling methods including scalping method, equivalent substitution method, similar grading method and hybrid method are adopted to model the site gradation of soil materials according to the code. 15 test gradations of coarse-grained materials from an engineering site have been simulated by using these grading scale methods, and the corresponding maximum particle diameters are 60 mm, 40 mm, 20 mm. The maximum dry density tests have also been conducted on the samples with test gradations and prototype gradation. The relationships among fractal dimension, grading scale methods and maximum dry density have been discussed by introducing the fractal dimension of particle diameters. It is found that the fractal dimension is a comprehensive evaluation index which can accurately reflects the test gradations by different grading scale methods. In addition, the grading scale methods significantly influence the maximum dry density, and the maximum dry density value of samples by the similar gradation methods is closest to that of prototype gradation, and the biggest disparity exists between equivalent substitution gradation method and prototype gradation. There exists a better linear normalization relationship between the fractal dimensions and the maximum dry density. Based on the normalization law, the maximum dry density of sample with prototype gradation could be calculated accurately.