基于体积估算岩石断面分维的算法研究

Algorithm of fractal dimension of rock fracture surface based on volume estimation

在计算岩石断裂粗糙表面分维时,为充分考虑利用基于激光扫描的断面高程数据,通过将各数据点连接构成类棱柱平行体或3面平行体直接覆盖粗糙断裂面,根据盒维数直接定义,提出体积覆盖算法。与传统的立方体覆盖法相比,体积覆盖法可以直接利用无须修正激光扫描点数据,避免立方体覆盖法坐标系位置差异导致的计算分维值差异,通过直接计算覆盖平行体体积估算岩石断面分维。进一步比较两类不同的平行体覆盖方法,针对同一粗糙表面,体积覆盖法计算的岩石断面分维均具有较高的精度,很好地克服了其他覆盖法中对覆盖格子形状(全部立方体或全部圆柱体)的统一要求,具有很强的适用性。

For calculating the fractal dimension of rock fracture rough surface, the prism-like or 3-side parallel bodies may be generated by connecting the data points on the fracture surface in order to take full account of laser scanning-based elevation data of the surface. A volume covering method is proposed for estimation of the fractal dimension of rough surface according to the definition of Minkowski dimension. Compared with the traditional cubic covering method, the volume covering method can be employed to directly calculate the volume of covering body and to estimate the fractal dimension without correction point of laser scanning data so as to avoid the differences caused by different coordinate systems. Furthermore, by comparing the two different types of parallel body covering methods for the same rough surface, all the volume covering methods have high accuracy in calculating the fractal dimension and have strong applicability overcoming the uniform shape requirements of the covering cells （all cubes or all cylinders）.