Fractal Model Of Unsaturated Soils Hydraulic Properties

The development of fractal geometry by Mandelbort has found application and use in describing many natural phenomena . The advent of fractal is associated with a renewed interest in chose effects resulting from nonlinear system.Fractal objects exhibit three defining attributes: similar structure over a range of length scale, intricate structure that is scale-independent and irregular structure that can not be captured entirely by classical geometrical concepts.Soil is both a fragmented material and porous medium, a fractal representation may be especially appropriate. Fractal representation of soil as fragmented materials produced by weathering processes. A distribution of particle size reflects the relative balance of weathering and pedogenetic processes. Particle-size distribution are of renders as cumulative function, either as number of particle larger than a certain diameter, or as mass smaller than a certain diameter . These cumulative distribution function have been analyzed with power-law relation and the exponents interpreted as fractal dimension.The rate of water flow and chemical movement in soil is defined by soil hydraulic properties such as water retention and hydraulic conductivity. Laboratory or field measurement of the relation between water potential and water content, and the relation between hydraulic conductivity and either water potential or water content, are time consuming and expensive. Recent application of fractal geometry in soil science have shown that soil hydraulic properties can be related to soil physical properties, such as particle-size distribution, exhibit fractal behavior and can be characterized by mass fractal dimension values. The interface between particles forming soil pores and the pores themselves is fractal as well, with a corresponding surface fractal dimension. The fractal pore volume can be characterized by the volume fractal dimension. Representing the soil pore structure by means of a theoretical fractal, such as a Menger sponge, a Sierpinski carpet and koch curve.The objective of this papers was to develop a procedure for estimating the soil water retention function based on the fractal theory and particle-size distribution data. Establish the relationship between the fractal dimension and the soil particle-size distribution and use the fractal dimension for prediction of the soil water retention function. Establish the fractal model of unsaturated water diffusivity and unsaturated hydraulic conductivity.1 .According to Chinese texture classification, we apply pipette analysis jiangjin, zhongxian, fengdu soil have shown fractal dimension is better parameter describe texture and structure.2. Using the concept of Menger sponge derived an expression relating the pore volume increment to the pore radius. Based on it derived fractal model of the soil water retention function.3. Using the concept of random walk derived fractal model of an unsaturated water diffusivity.4. Using the concept of koch curve, Menger sponge, Navier-Stokes derived fractal model of an unsaturated...