天然岩石节理双阶粗糙度分形特征研究

doi:10.13722/j.cnki.jrme.2019.0542

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摘要为细化三维岩石节理粗糙度的表征、实现一阶大起伏及二阶小凸起的定量分离及量化，首先基于经典的三角棱镜法(triangular-prism method，TPM)将临界网格尺寸及临界波矢量确定为定量分离双阶粗糙度的界限参数。然后采用功率谱密度法(power spectrum density，PSD)分别计算双阶粗糙度表征参数，即一阶大起伏及二阶小凸起的分形维度及均方根粗糙度。以大尺寸天然花岗岩节理面为例计算并研究双阶分形参数的尺寸效应。结果表明：(1) TPM方法普遍适用于分离各尺寸节理面的双阶粗糙度，而临界网格尺寸及临界波矢量值则应视节理面尺寸范围而定；(2) 100 mm×100 mm到1 000 mm×1 000 mm范围内的各尺寸节理面的一阶大起伏和二阶小凸起均具有各自的分形维度及均方根粗糙度；(3) 双阶分形维度均具有随机尺寸效应。随着节理面尺寸的增大，一阶大起伏的均方根粗糙度不断增大，二阶小凸起的均方根粗糙度则平稳变化，且一阶大起伏的均方根粗糙度显著大于二阶小凸起的均方根粗糙度。双阶粗糙度的细化表征有助于深入分析结构面剪切过程，为诸如滑移型岩爆等地质灾害的预警提供理论基础。

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	孙盛玥1
	李迎春1
	唐春安1
	李博2

关键词 ：岩石力学, 节理粗糙度, 双阶分形维度, 双阶均方根粗糙度, 尺寸效应

Abstract：To characterize the morphological properties of natural rock joints and to quantify waviness and unevenness of rock joints，the cut-off grid size and cut-off wave vector were established as the critical parameters for two-order roughness decomposition through the classic triangular-prism method(TPM)，and the fractal dimensions and root mean squares of the two-order roughness were respectively calculated through the power spectrum density method(PSD). The scale dependence of the fractal parameters of the two-order roughness was investigated for three large-scale natural granite joints. It is found that TPM is universally applicable for separating waviness and unevenness of the joint surface at various sizes，whereas the cut-off grid size and cut-off wave vector depend on the range of the joint surface size. Waviness and unevenness of the rock joint with a size varying from 100 mm×100 mm to 1 000 mm×1 000 mm own individual fractal dimension. The fractal dimensions of two-order roughness exhibit random scale effect. It is also shown that，as the joint size increases，the root mean square of the waviness increases，whereas the root mean square of the unevenness which is obviously smaller than that of the waviness varies smoothly. Accurate characterization of the two-order roughness facilitates in-depth understanding of the shear slip of geological discontinuities，by which the early warning of geological disasters such as slip bursts can be predicted.

Key words： rock mechanics joint roughness two-order fractals root mean squares scale dependence

引用本文:

孙盛玥1，李迎春1，唐春安1，李博2. 天然岩石节理双阶粗糙度分形特征研究[J]. 岩石力学与工程学报, 2019, 38(12): 2502-2511.
SUN Shengyue1，LI Yingchun1，TANG Chun?an1，LI Bo2. Dual fractal features of the surface roughness of natural rock joints. , 2019, 38(12): 2502-2511.

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http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2019.0542 或 http://www.rockmech.org/CN/Y2019/V38/I12/2502

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