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A new multifractal-based grain size distribution model
Geoderma ( IF 6.1 ) Pub Date : 2021-06-19 , DOI: 10.1016/j.geoderma.2021.115294
Filip Stanić , Ioulia Tchiguirinskaia , Pierre-Antoine Versini , Yu-Jun Cui , Pierre Delage , Patrick Aimedieu , Ana Maria Tarquis , Michel Bornert , Daniel Schertzer

Previous works related to the application of the multifractal theory for analyzing the grain size distribution (GSD), showed the potential of this approach to deal with this complex issue. However, absence of the practical application of this kind of statistical analysis raised some doubts among the soil scientists. Compared to the experimental dry sieving method, which is based on mass representations of different grain sizes, the approach presented in this work relies on the analysis of grain densities (density indicators) scanned by means of X-ray CT (Computed Tomography). By reducing the resolution of the scanned soil image(s), the cumulative representation of solid particles equal to or larger than the actual discretization element can be determined, and described analytically by means of the universal multifractals (UM).

For validation of the new UM approach, the X-ray CT results of three different soils were used: the volcanic substrate covering Green Wave (a green roof of Champs-sur-Marne in France), and two horizons of the soil collected from the low land mountain area of Sierra de Guadarrama in Spain. Comparison between the proposed UM model and the experimental data of these three materials confirms that the GSD can be reasonably well predicted from the scanned images of soils covering wide range of grain sizes. The UM model, unlike the fractal-based models, accounts for fractal dimension that depends on grain size, and hence, based on the preliminary results presented in this work, it could be rather useful in case of multi-modal soils whose GSD curves are described with multiple fractal dimensions.



中文翻译:

一种新的基于多重分形的粒度分布模型

先前与应用多重分形理论分析粒度分布 (GSD) 相关的工作显示了这种方法处理这一复杂问题的潜力。然而,这种统计分析的实际应用的缺乏引起了土壤科学家的一些怀疑。与基于不同粒度的质量表示的实验干筛法相比,这项工作中提出的方法依赖于通过 X 射线 CT(计算机断层扫描)扫描的颗粒密度(密度指标)的分析。通过降低扫描土壤图像的分辨率,可以确定等于或大于实际离散化元素的固体颗粒的累积表示,并通过通用多重分形 (UM) 进行分析描述。

为了验证新的 UM 方法,使用了三种不同土壤的 X 射线 CT 结果:覆盖 Green Wave 的火山基质(法国马恩河畔香榭丽舍的绿色屋顶),以及从西班牙瓜达拉马山脉的低地山区。所提出的 UM 模型与这三种材料的实验数据之间的比较证实,可以从覆盖广泛粒度范围的土壤的扫描图像中合理地预测 GSD。与基于分形的模型不同,UM 模型考虑了取决于粒度的分形维数,因此,根据本工作中提供的初步结果,它在 GSD 曲线为多模态土壤的情况下可能相当有用用多个分形维数来描述。

更新日期:2021-06-19
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