ABSTRACT: An analytical, quasi-static, solution of the problem of bursting of confined and unconfined thick- walled rock cylinders, published earlier by the senior author, is compared in this paper with the solution of the same problem based on the linear elastic fracture mechanics (LEFM) approach. The proposed LEFM solution uses Finite Element Method (FEM) and covers cylinders containing a finite number of radial cracks ranging between 2 and 500 and analytical solution for infinite number of internal radial cracks. When the number of cracks exceeds about 100, the LEFM solution shows that the results differ very little from the previously proposed quasi-static solution, which assumed an infinite number of internal radial cracks in the cylinder. An analytical expression is found for the stress intensity factor for mode I K?, the strain energy release rate G and the strain energy U, using the infinite approximation for the stress and strain. For a number of cracks over 100 the analytical approximation for the Ki, G and U gives an excellent results. The results for the bursting pressure are found to agree favorably with those obtained in three independent experimental investigations.
INTRODUCTION The problem of quasi-static expansion of cylindrical cavities in rock has received a considerable attention in rock mechanics, because its solution is needed in connection with several practical problems, such as the design of pressure conduits, rock-socketed caissons and anchors, and the evaluation of borehole dilatometer tests in rock.
A solution of this problem, published by the senior author a number of years ago (Ladanyi, 1967), contained a number of most important aspects of the behavior of an elastic-brittle-plastic rock-like solid. Several years later (Ladanyi, 1976) this solution was used to generate the complete pressure-expansion curve of a cylindrical cavity in a laterally infinite rock medium, with the purpose of evaluating borehole dilatometer test results in rock.
This paper has a similar but slightly different task. Instead of considering a cylindrical cavity in an infinite medium it deals with the case of a thick cylinder, expanding under the action of an increasing internal pressure, which is always higher than the confining pressure applied to its exterior wall. A special attention is paid to the problem of radial tensile fracture initiation and propagation to the general brittle fracture of the cylinder.
Several years ago, the senior author (Ladanyi, 1992) has developed a statical solution of this problem. In the present paper, this former solution is compared with numerical and analytical solutions based on the Linear Elastic Fracture Mechanics (LEFM) theory.