Quantification of soil structure based on Minkowski functions
نویسندگان
چکیده
Soil structure is developed across a wide range of scales including pores of different origin and herewith different size and shape. At larger scales soil structure is expressed in a heterogeneous distribution of local bulk densities. X-ray tomography is a suitable tool to measure and visualize this hierarchical structure at various scales and resolutions. However, because of the wide range of scales and the typical anisotropy of the structural units (e.g. root holes, earthworm burrows, cracks, anisotropic soil aggregates) it is not possible to represent all this complexity within a relatively small volume which would allow to simulate flow and transport directly at the pore scale based on Stokes's equation. This is in contrast to more simple granular media as unconsolidated sand or sandstone where such simulations have been successfully used to predict fluid dynamics. An alternative approach applicable to soil is based on a statistical characterization of the structural properties and the generation of simplified models having corresponding statistical properties. Minkowski functionals of binary structures (e.g. pores and solid) can be measured very efficiently and a rather comprehensive description can be obtained when these measures are considered as a function of pore size which we then denote as Minkowski functions. At the larger scale the structure of bulk densities (i.e. grey images) can be quantified by another type of Minkowski functions given by Minkowski functionals as a function of the grey threshold. We demonstrate this approach for both, a pore scale application using 3D binary images of pores and solid and a continuum scale application using the 3D distribution of bulk densities for larger samples at lower resolution. At the pore scale, Minkowski functions are used to generate an equivalent pore network model which is then used to predict hydraulic properties based on a simplified flux law. The results are compared to real experiments. At the larger scale Minkowski functions of the grey images are used as input to generate a number of realizations having equivalent properties. The numerical simulations of flow and transport within these realizations are analyzed in terms of variance and agreement to those obtained from the original structure. These exercises allow to estimate to what extend Minkowski functions comprise information on flow and transport in porous media, and herewith, in how far they can be used to predict flow and transport It is shown that Minkowski functions can successfully applied to the pore scale where the size distribution of pores within the pore network is explicitly included. In contrast, at the continuum (grey) scale additional information is required to include the spatial correlation which is critical for flow and transport but not included in the Minkowski functions since Minkowski functionals are local measures without sensitivity to long range correlations.
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ورودعنوان ژورنال:
- Computers & Geosciences
دوره 36 شماره
صفحات -
تاریخ انتشار 2010