Abstract An experimental study is presented of the elastic anisotropy of a shale at different length scales probed by a cross-scale, big data-based, statistical nanoindentation technique. A large number (~1000) of indentation measurements with depths of up to ~8 μm were conducted under continuous stiffness measurement mode on each of three differently oriented (i.e., 0°, 45°, and 90° relative to the bedding plane) samples, yielding massive depth-dependent Young’s modulus datasets for different orientations. Segmentation at different depths of these continuous modulus-depth curves resulted in multiple sub-datasets that were statistically deconvoluted, leading to the extraction of Young’s moduli of mechanically distinct phases at each segmentation depth, which were then re-assembled against depth. Such modulus-depth curves, each pertaining to a specific phase, were further fitted by the surround effect model to determine the elastic moduli of individual minerals at the microscale and the bulk rock at the macroscale. Results show that the shale possesses multiscale elastic anisotropy: at the macroscale, the bulk rock’s horizontal Young’s modulus is 1.24 times greater than the vertical counterpart; at the microscale, the clay matrix is highly anisotropic, with anisotropy ratios of 1.36 and 1.96 at the 45° and 90° orientations referenced to the bedding plane, while the anhedral, coarse-grained minerals (i.e., quartz and feldspar) are only slightly anisotropic owing to their random orientation and equidimensional geometry, suggesting that the macroscale elastic anisotropy is mainly attributed to the highly anisotropic clay matrix that acts as a major load-bearing medium, but disturbed by isolated, randomly distributed silt and sand particles embedded as solid inclusions in the clay matrix. As such, the degree of anisotropy decreases with increasing length scale. The origin, formation, and evolution of such multiscale anisotropy are discussed in terms of the shale’s composition, depositional history, and post-depositional geological processes.

中文翻译：

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以跨尺度大数据纳米压痕为特征的页岩多尺度弹性各向异性

摘要 通过跨尺度、基于大数据的统计纳米压痕技术探测了不同长度尺度的页岩弹性各向异性的实验研究。在连续刚度测量模式下，对三个不同方向（即相对于层理平面的 0°、45° 和 90°）样品中的每一个进行了大量（~1000）次深度高达~8 μm 的压痕测量，产生不同方向的大量依赖于深度的杨氏模量数据集。这些连续模量-深度曲线在不同深度的分割导致多个子数据集被统计解卷积，导致在每个分割深度提取机械不同阶段的杨氏模量，然后根据深度重新组装。这样的模量-深度曲线，每一个都与特定的相有关，通过环绕效应模型进一步拟合，以确定微观尺度的单个矿物和宏观尺度的大块岩石的弹性模量。结果表明，页岩具有多尺度弹性各向异性：宏观尺度上，大块岩石的水平杨氏模量是垂直对应物的1.24倍；在微观尺度上，粘土基质是高度各向异性的，在以层理面为基准的 45°和 90° 方向的各向异性比分别为 1.36 和 1.96，而无面体粗粒矿物（即石英和长石）的各向异性比仅为由于它们的随机取向和等维几何形状而具有各向异性，这表明宏观弹性各向异性主要归因于作为主要承载介质的高各向异性粘土基质，但受到孤立的、随机分布的粉砂和沙粒的干扰，这些粉粒和沙粒作为固体包裹体嵌入粘土基质中。因此，各向异性程度随着长度尺度的增加而降低。这种多尺度各向异性的起源、形成和演化从页岩的组成、沉积历史和沉积后地质过程的角度进行了讨论。