Analytic solutions for diametral point load strength tests

This paper investigates the tensile stress distribution within a solid circular cylinder of diameter D and length 2L subjected to double diametral indenters or diametral point load strength test (PLST). The contact problem between the indenters and the cylinder is solved analytically, and exact solution for stress distribution is obtained through the use of displacement functions and double Fourier expansion in theta- and z-coordinates. Numerical results show that the tensile stress at the center of the cylinders, in general, decreases with Poisson's ratio nu and increases with 2L/D for 2L/D < 1, but remains roughly constant for 2L/D > 1. This prediction agrees exactly with the shape effect observed experimentally for the PLST for marbles, granite, and tuff found in Hong Kong and with previous published results for other rocks. The magnitude of tensile stress at the center is about three times the prediction obtained by using Wijk's formula, but seems more comparable with experimental results. The size effect of the point load strength index observed experimentally is also predicted by our theory.