Strength and failure characteristics of marble spheres subjected to paired point loads

Failure of irregular rock samples may provide implications in the rapid estimation of rock strength, which is imperative in rock engineering practice. In this work, analytical, experimental and numerical investigations were carried out to study the mechanical properties and failure characteristics of rock spheres under paired point loads. Analytical solutions indicted that with the increase in sample size (contact angle) and decrease in Poisson's ratio, the uneven tensile stress in theta direction decreased. Then laboratory experiments were carried out to investigate the load characteristics and failure mode of spherical marble samples with different sizes subjected to a pair of diametral point loads. The discrete element method (DEM) was adopted to study the failure process of rock spheres. The effect of the sphere diameter on the point load contact angle was examined in terms of peak load, crushed zone distribution and energy dissipation. Experimental and numerical results showed that the samples primarily fail in tension, with crushed zones formed at both loading points. With increase in the sample size, the contact angle, crushed area and total work increase. As the specimen diameter increases from 30 mm to 50 mm, the peak load on the specimen increases from 3.6 kN to 8.8 kN, and the percentage of crushed zone (ratio of crushing zone to sample radius, d/r) increased from 0.191 to 0.262. The results of the study have implications for understanding the failure of irregular rock specimens under point loading conditions and their size effects.