Scale effects and strength anisotropy in coal

We explore microstructure-related effects of loading direction and specimen size on the anisotropy of uniaxial compressive strength in coal. We measure uniaxial compressive strength on coal samples of four different diameters (25 to 75 mm) and with varied dip of the bedding plane with respect to loading direction (0° 15° 30° 45° 60° and 90°) including characterizing the variation of microstructures in the specimens by X-ray imaging. The uniaxial compressive strength for each specimen size exhibits a unique U-shape curve against the angle of anisotropy (Jaeger, 1971). The degree of the strength anisotropy decreases with increasing specimen size, principally due to the enhanced microstructural volume of a larger specimen. The contribution of microstructures on uniaxial compressive strength differs for different orientations of loading relative to anisotropy. The rate of decline of the average uniaxial compressive strength with increasing specimen size is greatest when loading is parallel to bedding (anisotropic angle of 0°) and is the most moderate at 45°. An empirical equation relating specimen diameter with uniaxial compressive strength is proposed and verified against the experimental data. Based on this equation, the UCS of coal samples with different orientations relative to the anisotropy are predicted for the limiting sizes of zero and ∞. The anisotropy of the scale effect is also explored. Meanwhile, it is verified that a cosine relation between anisotropy angle and uniaxial compressive strength is applicable to coal specimens of different sizes. This demonstrates that the strength anisotropy in coal will remain constant when the specimen diameter is larger than a critical threshold. Based on these two observations/equations, a universal equation relying on the minimum strength angle, friction angle and Weibull coefficients is proposed and verified against experimental data to describe the relationship among anisotropy angle, specimen size, and uniaxial compressive strength in coal.