Fractal in soil mechanics
Encyclopedia
The fractal approach to soil mechanics is a new line of thought. There are several problems in soil mechanics which can be dealt with by applying a fractal approach. One of these problems is the determination of soil-water-characteristic curve (also called (water retention curve
) and/or capillary pressure curve). Its determination 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
—father of fractal mathematics—showed the world fractals, scientists of agronomy, agricultural engineering and earth scientists have developed more fractal-based models.
It is noteworthy that almost all of these models have been used to extract hydraulic properties of soils and the potential capabilities of fractal mathematics to investigate mechanical properties of soils have been overlooked. Therefore, it is really important to use such physically based models to promote our understanding of the mechanics of the soils. That is why it can be of great help for researchers in the area of unsaturated soil mechanics. Not only determination of SWCC but also mechanical parameters can be driven from such models and of course it needs further works and researches.
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....
) and/or capillary pressure curve). Its determination 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
Benoît Mandelbrot
Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...
—father of fractal mathematics—showed the world fractals, scientists of agronomy, agricultural engineering and earth scientists have developed more fractal-based models.
It is noteworthy that almost all of these models have been used to extract hydraulic properties of soils and the potential capabilities of fractal mathematics to investigate mechanical properties of soils have been overlooked. Therefore, it is really important to use such physically based models to promote our understanding of the mechanics of the soils. That is why it can be of great help for researchers in the area of unsaturated soil mechanics. Not only determination of SWCC but also mechanical parameters can be driven from such models and of course it needs further works and researches.