T-Stress in a Centrally Cracked Brazilian Disk Under Nonuniform Pressure Load

In an engineering structure, the rock is often subjected to nonuniform load; in addition, there is a small distribution angle under a concentrated force in actual experimental study, and the load distribution also should be nonuniform. Based on this case, a class of nonuniform loads were proposed in the trigonometric function form. Then the maximum loading pressure appeared in the middle of the distribution angle and gradually became small to both sides until 0. By means of the centrally cracked Brazilian disk (CCBD) T-stress formula under a radial concentrated load, the analytical T-stress solution under this kind of nonuniform load was acquired via the integral in the range of the distribution angle, meanwhile the finite element simulation was conducted to obtain the numerical solution. There is a very good consistency between the numerical results and the analytical results, which verifies the accuracy of each other. Compared with those under the uniform load, the dimensionless T-stress values under this nonuniform load are closer to the values under the concentrated load when the other condition is the same, and the discrepancy between the stresses under the nonuniform load and the concentrated load is very small. The further calculated results show that it is accurate and reasonable to use the T-stress formula for the CCBD subjected to the concentrated forces in actual testing.