Theoretical analysis of flattened Brazilian splitting test for determining tensile strength of rocks

This study aims to improve the fundamental of theory of the flattened Brazilian disk test for determining the tensile strength of rocks. On the basis of the two-dimensional elasticity theory, a mechanical model is proposed with the chordally opposing distributed compressive loads. And the approximate analytical solution of stress components inside the Brazilian disk is obtained with the superposition method of stresses. The theoretical solutions are validated to be rational through comparing with the numerical results from the finite element method. By using the solutions, the effect of flattened loading angles on the value and the concentration degree of stress inside the disk is researched contrastively. The results show that the concentration degree of stress near loading point and the ratio of compressive stress to tensile stress inside the disk quickly decrease, but the tensile stress value and tensile region slightly reduce with the increasing of flattened loading angle. Further, it is found that both too large or too small loading angle is detrimental to the central tensile splitting failure of specimen in the standard Brazilian disk test, and the optimal flattened loading angles are between 20 degrees and 30 degrees. Finally, according to the Griffith strength failure criterion, the formula for tensile strength of rocks is theoretically derived. And the theoretical tensile strength values obtained in this paper are in good agreement with the existing experimental ones.