Fractal dimension estimate of rock crack curve in three dimensional space

Xue Dongjie●Zhou Hongwei●Yi Haiyang

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 δ  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 fractal curve vector model.The fractal dimension of the spatial fractal and its projection plane fractal curve was estimated by the area covering method.The differences of fractal dimension of the vector component reflect roughness differences of space fractal curve in all directions，resulting in anisotropy of rock and ultimately affecting the mechanical properties of materials.The establishment of vector fractal dimension provides a new way to further study relationship of the crack and rock material properties.

三维空间岩石裂纹分形曲线的分维估算

薛东杰，周宏伟，易海洋

摘 要 

基于三维空间中岩石裂纹扩展形态的随机性与空间性，根据盒维数直接定义，提出δ-直角三角面积覆盖法，并通过Koch曲线验证。同时根据分形插值理论构造空间分形曲线，建立空间分形曲线的矢量模型。利用面积覆盖法分别对生成的空间分形曲线与其投影平面分形曲线计算分维。矢量分维值分量的不同反映空间分形曲线在各个方向上粗糙度的差异，从而造成各向异性，最终影响材料的力学特性，矢量分维的建立为进一步研究裂纹对岩石材料特性的影响提供了一个新方法。

引用格式：

Xue DJ, Zhou HW, Yi HY. Fractal dimension estimate of rock crack curve in three-dimensional space[J]. Journal of China Coal Society, 2012, 37(9): 1522–1527. 薛东杰, 周宏伟, 易海洋. 三维空间岩石裂纹分形曲线的分维估算[J]. 煤炭学报, 2012, 37(9): 1522–1527.

EI：20124615671599   DOI：10.13225/j.cnki.jccs.2012.09.002

文章连接地址：

http://www.mtxb.com.cn/CN/Y2012/V37/I09/1522