A Fractal Interpolation Model for Classification of Expansive Soil

The classification of the grade of shrink and expansion for the expansive soils is very important work for constructions in expansive soil area. Accurate evaluation of the estate of expansive soil may provide scientific data and basis for the prevention of engineering design and construction. This paper brings forward the classification method for expansive soil based on fractal interpolation theory. Firstly, five indexes, including the liquid limit, the overall rate of expansion and contraction, plastic index, moisture content, free expansion rate, are selected as the factors for synthetic evaluation of expansive soil. In addition, because of few standard samples, forty standard samples are produced by the way of stochastic interpolation on basis of classification standard. Secondly, through calculating the fractal dimension of single index of expansive soil, confirming the fractal dimension exponent evaluation of the index of single expansive soil with the maximum likelihood classification principle. Thirdly, adopting weighted summation value this method calculates the level of the colligate estimation of multi-index of expansive soil and establishes the fractal interpolation evaluation model according to the relationship between the value of comprehensive evaluation of the samples and the experience level. Finally, several samples are classified based on the model. The classification results are consistent with other methods and show that the model we made is simple, easy to solve the problem, and can get accurate solutions, and then could be used widely in classification of expansive soil. Moreover, particular score of each sample could be computed by the model; so it has more precise classification and is a rather better new method. It is possible to make use of fractal interpolation model to evaluate the levels of expansive soil. And it can provide reference for finding parameters in engineering design and calculation.