Theoretical Analysis and Experimental Identification of Contact Pressure in Brazilian Disc

Abstract

The contact pressure in the Brazilian disc test is investigated by theoretical analysis and experiment. A new theoretical approach is presented to obtain a semi-analytical solution of the contact pressure, limiting investigation to relatively soft to moderate rocks with moduli of elasticity much less than that of the jaw. The customary assumption of infinite half plane for the disc and the jaw is abandoned. The series solutions of stress and displacement fields in disc are given by complex potential functions, in which coefficients are approximately determined by variational technique based on Hellinger–Reissner’s variational principle. The contact angle is calculated by an iterative process. Such variational solutions have good convergence, and they satisfy the mixed-mode boundary conditions of the problem with satisfactory accuracy. The computational result indicates that the contact pressure is a semi-ellipse curve in distribution feature. The effects of elastic modulus and Poisson ratio on contact angle are tiny for a given magnitude of compressive displacement. In addition, the numerical result of FEM analysis for an elastic contact problem examines the validity of the variational solutions, and also it confirms that the jaw can be regarded as a rigid body if the elastic modulus of the disc is one order of magnitude less than that of the jaw. Moreover, the applicability of the proposed theoretical approach is illustrated as the variational solutions have very good agreement with the data measured from the implemented experiment. In addition, based on the idea of material parameter identification by inverse method, the elastic modulus of the natural sandstone sample is indirectly determined using both the experimental data and the variational solutions.