Fractal Simulation of the Stress-strain Curve of Frozen Soil

The stress-strain relationship of frozen soil is important to indicate the strength of frozen soils in use. According to traditional mechanics, the stress-strain relationship in geomaterials is a smooth curve. However, some studies have shown that the real stress-strain curves of geomaterials, such as concrete, rock and frozen soil, are step-like and that they have fractal characteristics. Therefore, the traditional mathematical and mechanical methods used to describe the stress-strain curves of frozen soil are not accurate. Mandelbrot's fractal geometry theory is a new mathematical branch whose primary object is to describe natural structures that are irregular, rough or fragmented. It can also describe the degree of variation of a curve, a surface or a volume by using a fractal dimension. Therefore, fractal geometry theory can be used to analyze the stress-strain curve of frozen soil more accurately and in greater detail.