Brazilian test: stress field and tensile strength of anisotropic rocks using an analytical solution

Abstract

Abstract Tensile strength of rock is among the most important parameters influencing rock deformability, rock crushing and blasting results. To calculate the tensile strength from the indirect tensile (Brazilian) test, one must know the principal tensile stress, in particular at the rock disc center, where a crack initiates. This stress can be assessed by an analytical solution. A study of this solution for anisotropic (transversely isotropic) rock is presented. The solution is given explicitly. The key expansion coefficients are obtained from a complex-valued 2×2 matrix equation. The convergence of the solution is greatly improved by a new procedure. It is shown that the dimensionless stress field depends only on two intrinsic parameters, E′/E and b. The stress at the center of the disc is given in charts as a function of these parameters (and the angle θb between the direction of applied force and the plane of transverse isotropy). Furthermore, a new, reasonably accurate, approximate formula for the principal tension at the disc center, (0,0), is derived from the analytical solution: σ pt (0,0)≅ P πRL ( E/E′ 4 ) cos (2θ b ) − cos (4θ b ) 4 (b−1) , where b= EE′ 2 1 G′ − 2ν′ E′ . The elastic parameters of rock in two perpendicular directions were measured in the laboratory. The result of the stress analysis was applied in calculating the indirect tensile strength of gneiss, which has a well-defined foliation plane (transversely isotropic). When the results were compared with the tensile strength of rock obtained by using a conventional formula that assumes isotropic material, there was a significant difference. Moreover, good agreement was observed for the tensile strength calculated from the stress charts and the proposed formula, when compared with other published stress charts.