Analytical Solution for Stress Field and Intensity Factor in CSTBD under Mixed Mode Conditions

Document Type : Research Paper


1 School of Mining, College of Engineering, University of Tehran, Iran

2 School of Civil, College of Engineering, University of Tehran, Iran


Considering the fact that rocks fail faster under tensile stress, rock tensile strength is of great
importance in applications such as blasting, rock fragmentation, slope stability, hydraulic fracturing,
caprock integrity, and geothermal energy extraction. There are two direct and indirect methods to
measure tensile strength. Since direct methods always encompass difficulties in test setup, indirect
methods, specifically the Brazilian test, have often been employed for tensile strength measurement.
Tensile failure is technically attributed to crack propagation in rock. Fracture mechanics has
significant potential for the determination of crack behaviour as well as propagation pattern. To apply
Brazilian tests, cracked disc geometry has been suggested by the International Society for Rock
Mechanics ISRM. Accordingly, a comprehensive study is necessary to evaluate stress field and stress
intensity factor (SIF) around the crack in the centre of the specimen. In this paper, superposition
principle is employed to solve the problem of cracked straight-through Brazilian disc (CSTBD), using
two methods of dislocation and complex stress function. Stress field and SIF in the vicinity of the
crack tip are then calculated. With the proposed method, the magnitude of critical load for crack
initiation in structures can be predicted. This method is valid for any crack of any arbitrary length and
angle. In addition, numerical modelling has been carried out for the Brazilian disc. Finally, the
analytical solution has been compared with numerical modelling results showing the same outcome
for both methods.