  We study the crushing strength of brittle materials whose internal structure
(e.g., mineral particles or graining) presents a layered arrangement
reminiscent of sedimentary and metamorphic rocks. Taking a discrete-element
approach, we probe the failure strength of circular-shaped samples intended to
reproduce specific mineral configurations. To do so, assemblies of cells,
products of a modified Voronoi tessellation, are joined in mechanically-stable
layerings using a bonding law. The cells' shape distribution allows us to set a
level of inherent anisotropy to the material. Using a diametral point loading,
and systematically changing the loading orientation with respect to the cells'
configuration, we characterize the failure strength of increasingly anisotropic
structures. This approach ends up reproducing experimental observations and
lets us quantify the statistical variability of strength, the consumption of
the fragmentation energy, and the induced anisotropies linked to the cell's
geometry and force transmission in the samples. Based on a fine description of
geometrical and mechanical properties at the onset of failure, we develop a
micromechanical breakdown of the crushing strength variability using an
analytical decomposition of the stress tensor and the geometrical and force
anisotropies. We can conclude that the origins of failure strength in
anisotropic layered media rely on compensations of geometrical and mechanical
anisotropies, as well as an increasing average radial force between minerals
indistinctive of tensile or compressive components.
