This paper presents a newly observed phenomenon of upscaling of rocks’ properties using big data nanoindentation and analytics involving Gaussian mixture modeling (GMM), leading to characterizing the cross-scale mechanical properties of four shales and one sandstone. A large number (i.e., ~ 500) of statistical indentation measurements to depths of 6–8 μm were performed on each rock, resulting in continuous depth-dependent hardness and Young’s modulus data from unknown phases, which were then segmented at various depths to extract an array of discretized subdatasets. Two-dimensional GMM of each subdataset yields the number, fraction, and properties of mechanically distinct phases, and re-assembly of these results leads to clearly discernible property-depth curves. Such improved data analytics consisting of data segmentation, GMM deconvolution, and re-assembly enables the transformation of a massive number of chaotic curves from unknown phases into a few discernible lines corresponding to identified phases, from which the mechanical properties of individual phases are accurately determined at relatively small depths. With increasing depth, initially unique mechanical properties of individual phases undergo multistage merging at the intermediate mesoscale and progressively homogenize into a unified value at large depths or macroscale (e.g., > ~ 5 μm), which is regarded as the bulk rock’s properties. More importantly, such depth-dependent transition and progressive merging and homogenization actually manifest the micromechanics of nanoindentation on a heterogeneous composite, including the indentation surround effect and rock’s microstructure (e.g., sizes and spacings of different solid particles and their properties). Compared to different micromechanical upscaling models, this newly developed big data indentation technique and pertinent data analytics enable more accurate, multi-parameter, and cross-scale characterization of highly heterogeneous materials and explicitly uncover the multi-staged, progressively-homogenized, depth-dependent upscaling of elasticity from individual constituents at the nanoscale to merged virtual interface phases at the mesoscale and to bulk material at the macroscale.

中文翻译：

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大数据纳米压痕和分析揭示了岩石特性的多阶段、渐进均匀化、深度相关的升级

本文使用大数据纳米压痕和涉及高斯混合模型 (GMM) 的分析，提出了一种新观察到的岩石特性升级现象，从而表征了四页岩和一个砂岩的跨尺度力学特性。对每块岩石进行了大量（即约 500 次）深度为 6-8 μm 的统计压痕测量，从而产生来自未知相的连续深度相关硬度和杨氏模量数据，然后在不同深度分割以提取一组离散化的子数据集。每个子数据集的二维 GMM 产生机械上不同相的数量、分数和特性，这些结果的重新组装导致清晰可辨的特性深度曲线。这种改进的数据分析包括数据分割、GMM 反卷积、和重新组装能够将大量混沌曲线从未知相转换为与已识别相相对应的少数可辨别线，从中可以在相对较小的深度准确确定各个相的机械性能。随着深度的增加，各个相的最初独特的力​​学特性在中间中尺度经历多阶段合并，并在大深度或宏观尺度（例如，> ~ 5 μm）逐渐均匀化为统一值，这被视为大块岩石的特性。更重要的是，这种依赖于深度的转变和渐进的合并和均质化实际上体现了异质复合材料上纳米压痕的微观力学，包括压痕环绕效应和岩石的微观结构（例如，不同固体颗粒的尺寸和间距及其特性）。与不同的微机械放大模型相比，这种新开发的大数据压痕技术和相关的数据分析能够对高度异质材料进行更准确、多参数和跨尺度的表征，并明确揭示多阶段、渐进同质化、深度依赖将弹性从纳米尺度的单个成分放大到中尺度的合并虚拟界面相和宏观尺度的块状材料。