The Brazilian disc under parabolically varying load: Theoretical and experimental study of the displacement field

The displacement field in an intact Brazilian disc under the influence of a parabolically varying radial pressure distribution acting along two symmetric arcs of its periphery is studied. The specific loading type closely approaches the actual load-distribution as obtained by considering the specimen and the load platen as a system of two elastic bodies in contact. The problem is solved adopting the complex potentials method and a closed form full-field solution is proposed. The results of the theoretical analysis for discs made either from Dionysos marble or PMMA are considered in juxtaposition to the respective ones obtained for uniform radial pressure as well as for concentrated point load. Critical points related to the variation of the displacement field in the immediate vicinity of the load platen-specimen interface are enlightened. The accuracy of the solution is assessed by comparing the analytic results with the experimental ones obtained from series of Brazilian-disc tests carried out using the standardized device suggested by the international society for rock mechanics. The specimens were made from PMMA and the 3D digital image correlation technique was employed for measuring the components of the displacement field developed. It is proved that the experimental results are in very good qualitative and quantitative agreement with the theoretical predictions.