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The mechanical properties of shales, a type of heterogeneous and multiphase composite, are of multiscale characteristics in nature. A large number of indentation measurements were performed under the continuous stiffness measurement (CSM) mode on the Longmaxi shale, followed by data segmentation, Gaussian mixture modeling (GMM) deconvolution of segmented datasets, and results re-integration. Accompanying compositional analyses by X-ray powder diffraction and surface imaging were also conducted to assist data interpretation. Results showed that the studied shale consisted of a fine-grained, relatively homogeneous clay matrix with randomly embedded, coarse-grained solid inclusions of up to ~ 100 μm in size. The CSM mode enabled the analysis of phase angle lag, which is an effective indicator for surface roughness. The Young's moduli of both microscopic constituent phases (e.g., clay matrix, carbonates, quartz, pyrite) and macroscopic bulk shale were precisely determined and, through the probability analysis of the indent locations, the characteristic lengths of the shale's constituent phases were estimated. The clay matrix and carbonates have relatively large characteristic lengths than quartz and pyrite. The data analytics proposed in this study may provide a feasible framework to assess the multiscale mechanical properties as well as the characteristic lengths of the shale's constituent phases via a single type of measurement technique on the same piece of sample. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]