A fractal is an irregular geometric object with an infinite nesting of structure at all scales. It is mainly applicable in soil chromatography and soil micromorphology (Anderson, 1997). Internal structure, pore size distribution and pore geometry can be identified by using fractal dimension at nano scale. As soil is heterogeneous the pore spaces are made up of macropores, micropores and mesopores. When soil is studied in nanoscale it the macropore are composed of micro and meso pore and further they are composed of organo-mineral complex.
The fractal approach to soil mechanics is a new line of thought. It was first raised in "Fractal Character Of Grain-Size Distribution Of Expansion Soils" by Yongfu Xu and Songyu Liu, published in 1999, by Fractals. There are several problems in
soil mechanics
Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids (usually air and wat ...
which can be dealt by applying a fractal approach. One of these problems is the determination of soil-water-characteristic curve (also called (
water retention curve
Water retention curve is the relationship between the water content, θ, and the soil water potential, ψ. This curve is characteristic for different types of soil, and is also called the soil moisture characteristic.
It is used to predict the ...
) and/or
capillary pressure curve). It is a time-consuming process considering usual laboratory experiments. Many scientists have been involved in making mathematical models of soil-water-characteristic curve (SWCC) in which constants are related to the fractal dimension of pore size distribution or particle size distribution of the soil. After the great mathematician
Benoît Mandelbrot
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...
—father of
fractal mathematics
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...
—showed the world fractals, Scientists of
Agronomy
Agronomy is the science and technology of producing and using plants by agriculture for food, fuel, fiber, chemicals, recreation, or land conservation. Agronomy has come to include research of plant genetics, plant physiology, meteorology, and ...
,
Agricultural engineering
Agricultural engineering, also known as agricultural and biosystems engineering, is the field of study and application of engineering science and designs principles for agriculture purposes, combining the various disciplines of mechanical, civil, ...
and Earth Scientists have developed more fractal-based models.
All of these models have been used to extract
hydraulic
Hydraulics (from Greek: Υδραυλική) is a technology and applied science using engineering, chemistry, and other sciences involving the mechanical properties and use of liquids. At a very basic level, hydraulics is the liquid counter ...
properties of soils and the potential capabilities of fractal mathematics to investigate mechanical properties of soils. Therefore, it is really important to use such physically based models to promote our understanding of the mechanics of the soils. It can be of great help for researchers in the area of unsaturated soil mechanics. Mechanical parameters can also be driven from such models and of course it needs further works and researches.
Fractal calculus
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...
is a framework that includes functions with fractal support.
Soil mechanics
Fractals
Anderson, A.N., McBratney, A.B. and Crawford, J.W., 1997. Applications of fractals to soil studies. In ''Advances in Agronomy'' (Vol. 63, pp. 1-76). Academic Press.
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