Broad bandwidth study of the topography of natural rock surfaces
Broad bandwidth study of the topography of natural rock surfaces
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DOI：
10.1029/jb090ib14p12575
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发表时间：
1985-12
影响因子：
--
通讯作者：
Stephen R. Brown;C. Scholz
中科院分区：
文献类型：
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作者：
Stephen R. Brown;C. Scholz
岩石中不连续面的力学和水力行为，如节理和断层，在很大程度上取决于接触面的地形和它们之间的关联程度。要了解地球上感兴趣的尺度上的这种行为，需要了解地形或粗糙度如何随表面大小变化。使用两台表面剖面仪，每台都对特定尺度的地形特征敏感，我们研究了从波长小于20微米到近1米的各种天然岩石表面的地形。所研究的表面包括结晶岩和沉积岩中的新鲜自然节理(I型裂缝)，由冰川作用形成的摩擦磨损表面，以及顺层平面表面。这些表面之间有着惊人的相似性。在研究的整个频段内，每个表面都有一个“红噪声”功率谱，功率平均下降2到3个数量级，空间频率每十年增加一次。这意味着均方根高度随着表面尺寸的增大而显著增加，在波长高达1米时几乎不会趋于平稳。这些观测结果可以用地形的分形模型来解释。在该模型中，表面粗糙度的尺度用分维D来描述。这些天然岩石表面的形貌不能用单一的分维来描述，因为这个参数随着所考虑的频段而显著变化。在标度参数中观察到的这种不均匀性意味着，将粗糙度外推到其他感兴趣的波段时应谨慎进行。从我们的数据中研究了两种极端情况下均方根高度随剖面长度的增加，为岩石中自然不连续面的力学和水力性质的预期变化提供了一个想法。这表明，除了地形的比例外，接触表面之间的关联程度也是量化的重要因素。
The mechanical and hydraulic behavior of discontinuities in rock, such as joints and faults, depends strongly on the topography of the contacting surfaces and the degree of correlation between them. Understanding this behavior over the scales of interest in the earth requires knowledge of how topography or roughness varies with surface size. Using two surface profilers, each sensitive to a particular scale of topographic features, we have studied the topography of various natural rock surfaces from wavelengths less than 20 microns to nearly 1 meter. The surfaces studied included fresh natural joints (mode I cracks) in both crystalline and sedimentary rocks, a frictional wear surface formed by glaciation, and a bedding plane surface. There is remarkable similarity among these surfaces. Each surface has a “red noise” power spectrum over the entire frequency band studied, with the power falling off on average between 2 and 3 orders of magnitude per decade increase in spatial frequency. This implies a strong increase in rms height with surface size, which has little tendency to level off for wavelengths up to 1 meter. These observations can be interpreted using a fractal model of topography. In this model the scaling of the surface roughness is described by the fractal dimension D. The topography of these natural rock surfaces cannot be described by a single fractal dimension, for this parameter was found to vary significantly with the frequency band considered. This observed inhomogeneity in the scaling parameter implies that extrapolation of roughness to other bands of interest should be done with care. Study of the increase in rms height with profile length for two extreme cases from our data provides an idea of the expected variation in mechanical and hydraulic properties for natural discontinuities in rock. This indicates that in addition to the scaling of topography, the degree of correlation between the contacting surfaces is important to quantify.