Size effect and anisotropy on the strength of shale under compressive stress conditions

Abstract

The underground coal mines in the Appalachian region report the highest rate of roof falls in the United States. The immediate roof of these mines is mostly composed of shale. The in-situ strength of shale is necessary for designing roof support to prevent roof falls. Estimating the in-situ strength of shale requires the knowledge of both size effect and anisotropy. This research used literature review, theoretical analysis, numerical modeling, and laboratory experiment to systematically investigate the size effect and anisotropy of shale strength under compressive strength conditions. Literature review involved a comprehensive summary of previous research on the size effect and anisotropy of rock strength. This research collected experimental data on the size effect of rock strength to form a database. Most data showed that rock strength decreased with the increase in rock size and followed the decreasing trend. Similarly, the strength of transversely isotropic rocks varied with the rock orientation and matched the “U-shaped” curve. Further, cracks and bedding planes inside the rock caused size effect and anisotropy. As shale and other transversely isotropic rocks contain crack and bedding planes, the strength of these rocks should exhibit the decreasing trend and the “U-shaped” curve. Theoretical analysis involved the derivation of the size-dependent and anisotropic Mohr-Coulomb failure criterion that can describe the strength behavior of shale. The analysis assumed that cracks and bedding planes cause size effect and anisotropy. Therefore, the simplified structure of shale consisted of shale matrix, cracks, and bedding planes. Based on the Griffith theory and the single plane of weakness theory, this analysis then derived the size-dependent and anisotropic Mohr-Coulomb failure criterion. This failure criterion captured the decreasing trend and the “U-shaped” curve. Finally, the experimental database validated the failure criterion. Numerical analysis involved the development of the size-dependent and anisotropic bonded-particle model that can replicate the strength behavior of shale. The bonded-particle model of shale consisted of shale matrix, cracks, and bedding planes. The model used bonded particles, discrete fractures, and smooth joints to model these three components in the particle flow code 2D (PFC2D). The model introduced the three components and calibrated them progressively. The strength of shale model presented the decreasing trend and the “U-shaped” curve. The strength fitted well with the proposed failure criterion. Laboratory experiment contained the uniaxial, biaxial, and triaxial compression tests on shale specimens of different sizes using an in-house polyaxial compression test setup. The setup included a uniaxial