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

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