The application of a modified Voronoi logic to brittle fracture modelling at the laboratory and field scale

• Develop a novel UDEC ‘Trigon’ logic to explicitly simulate brittle fracture in both 2 and 3 dimensions.
• Proposed a ‘damage parameter’ to quantitatively evaluate simulated rock damage.
• The ‘Trigon’ logic can capture various fracture patterns under different loading conditions.

A modified distinct element Voronoi method, which we refer to as “Trigon” logic, is proposed for use in both two and three-dimensional modelling. A rock material is represented by an assembly of triangular (in 2D) or tetrahedral (in 3D) blocks bonded through their contacts. To evaluate the ability of the proposed Trigon logic in simulating brittle fracture, a series of unconfined and confined compression and Brazilian tests is performed illustrating the sample failure mechanisms under two and three dimensional conditions. Typical failure fracture patterns (damage) experienced by brittle rock are explicitly simulated including axial tensile failure under unconfined compression, shear failure under confined compression, and tensile crack extension during indirect tension (Brazilian) testing. A ‘damage parameter’ D and a ‘damage intensity’ D21 measure are proposed to allow the evaluation of the simulated rock damage in a more quantitative manner. At the mine opening scale, the process of roof shear failure is successfully captured using the Trigon logic. In comparison with the conventional Voronoi model, the proposed Trigon model is less mesh-sensitive and predicts both a more realistic friction angle and failure pattern under varied loading conditions.