Using rodogram function to characterize hurst coefficient in rock profiles

Abstract Roughness is a fundamental feature to define rock deformability and resistance. A detailed characterization of discontinuity surface geometry is essential for understanding some of the rock’s mechanical behaviors. Fractal geometry has been used by several authors to correlate parameters such as the Hurst coefficient for JRC (Joint Roughness coefficient) to better describe a surface geometry. Surface profiles might be characterized by a fractal dimension that represents the small scale of the geometric recurrence. In this paper, we propose to modify the methodology used to identify the Hurst coefficient incorporating the rodogram function in the JRC analysis. The proposed function is less influenced by drifting effects, and seems to be more precise than the commonly used variogram function. Robust mathematical models of spatial continuity can be a better alternative to characterize the roughness of rock discontinuities.

摘要：粗糙度是定义岩体变形特性与抗破坏性能的核心特征。对节理面几何形态开展精细表征，是理解岩体部分力学行为的关键前提。已有多位学者借助分形几何（Fractal geometry），将节理粗糙度系数（Joint Roughness Coefficient, JRC）对应的赫斯特系数（Hurst coefficient）等参数进行关联，以更精准地刻画节理面的几何形态。表面轮廓可通过分形维数进行表征，该参数能够反映几何重现性的微观尺度特征。本文提出改进现有赫斯特系数的识别方法，在JRC分析中引入杆函数（rodogram function）。相较于常用的变异函数（variogram function），所提出的杆函数受漂移效应的影响更小，且具备更高的精度。可靠的空间连续性数学模型，可作为表征岩体节理面粗糙度的更优方案。