Closed full-field solutions for stresses and displacements in the Brazilian disk under distributed radial load

Abstract

The Brazilian disk test, namely the diametric compression of a circular disk by radial loads that are uniformly distributed along two symmetric arcs of its periphery, is studied using the method of complex potentials introduced by Kolosov and Muskhelishvili. The rock is assumed to be linear elastic. Closed form full-field solutions are obtained for both the stress and the displacement fields, assuming either plane-stress or plane-strain conditions. The theoretical analysis highlights some critical features of the stresses and the displacements immediately adjacent to the load contact areas, revealing the limitations of the linear elastic solutions. The problem is also studied experimentally by carrying out a series of Brazilian disk tests, according to the ISRM suggestions, with specimens mainly made from Dionysos marble. In addition, a limited number of tests are carried using specimens made from porous natural building stones or from PMMA. The results of the theoretical solution are compared with those of the experiments, and the agreement is satisfactory, at least in the regions of the disk where the stresses developed during loading remain below the linearity limit of the materials.