Fractal dimension estimate of rock crack curve in three-dimensional space
Abstract：Based on the randomness and spatial of rock crack form in three-dimensional space and the definition of Minkowski dimension, the area covering method of 6-right triangle was proposed which was validated by comparing the calculated data and theoretical data of the Koch curve. Then a space fractal curve was generated according to fractal interpolation theory with the establishment of spatial fraetal curve vector model. The fraetal dimension of the spatial fractal and its projection plane fractal curve was estimated by the area covering method. The differences of fractal di- mension of the vector component reflect roughness differences of space fractal curve in all directions, resulting in ani- sotropy of rock and ultimately affecting the mechanical properties of materials. The establishment of vector fractal di- mension provides a new way to further study relationship of the crack and rock material properties.
Keywords：rock crackspace fractal curvearea covering methodvector model
Publication Date：2012-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：6( 1522-1527 )