Size effect in layered rocks under Brazilian tests considering three-dimensional anisotropy: A DEM study

Slate, as a typical layered rock, exhibits significant anisotropy and size-dependent mechanical behavior. However, the coupled effects of three-dimensional schistosity orientation and initial fractures on the size effect remain insufficiently understood. This study develops a three-dimensional discrete element model integrating the flat-joint model, smooth-joint model, and discrete fracture network to investigate the size effect of slate under Brazilian tests across specimen diameters of 25 to 100 mm, schistosity angles ψ of 0° to 90° and β of 0° to 90°. Results show that the Brazilian failure strength of specimen generally decreases with the specimen diameter, while the degree of strength reduction varies with the schistosity orientation. The angle ψ primarily controls the macroscopic failure mode, whereas β governs the strength anisotropy and crack-type transformation. Increasing specimen diameter weakens the strength differences caused by different schistosity orientations and promotes progressive failure with enhanced participation of schistosity-related cracks, especially shear cracks. The coupled influences of β , ψ , and specimen diameter jointly determine the tensile behavior of slate, with size effects modulating the anisotropic response. These findings provide a basis for understanding the three-dimensional anisotropic failure mechanism of layered rocks and for selecting representative mechanical parameters in engineering stability analysis.