Fractal approximation of the stress-strain curve of frozen soil

A method to approach the stress-strain curve of frozen soil is presented based on the fact that the stressstrain curve of frozen soil has fractal property. First, a linear hyperbolic iterated function system (LHJB) in which the perpendicular contraction factors are regarded as parameters is established using fractal geometry theories. Secondly, a method to calculate the best point which makes the attractor of the LHIFS an optimal approximation of the stress-strain curve of frozen soil is presented. Then, a method for calculating the fractal dimension of the stress-strain curve of frozen soil is obtained. Finally, a simple example is provided. The method presented in this paper provides a new method for simulating the stress-strain curve and calculating its fractal dimension of geomaterials that have the fractal feature by using computer