Multiscale elastic anisotropy of a shale characterized by cross-scale big data nanoindentation

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.