The existence of surface parallel Griffith cracks in elastic homogeneous or layered semi-infinite media, results to a severe reduction of the critical buckling stress leading to surface exfoliation phenomena. A numerical procedure based on the Displacement Discontinuity Method is used to demonstrate the influence of surface parallel cracks in the critical buckling stress. This numerical method is also implemented to investigate the effect of the initial stress field on crack propagation. The combined effect of surface instabilities and crack propagation is discussed.
Experiments on rock specimens reveal that failure under conditions of uniaxial compression is usually manifested in the form of splitting and slabbing. Similar phenomena have been observed around highly stressed holes in thick-wall hollow cylinders (Santarelli 1987, Ewy and Cook 1989). The fundamental fracture mechanism is the growth of small opening-mode splitting cracks oriented parallel to the free surface, starting very close to it and progressing deeper into the rock with increased stress. This cracks line up to form macroscopic splitting fracture and also form echelon patterns that meet the free surface. These two features combine to define the extent of a spalled piece. Based on similar observations, Freudenthal (1977) viewed rock splitting and rock bursting near an opening as the result of crack initiation and propagation associated with the existence of radial tensile stresses around the excavation. The existence of such stresses was predicted first by Reiner (1949) on the basis of a non-linear elasticity theory with second order terms to account for shear induced volume expansion. Vardoulakis (1984) and Vardoulakis and Mahlhaus (1986) based their analyses of surface rock bursting phenomena on the assumption that splitting and slabbing are the results of surface instabilities (Bazant 1967). Surface buckling phenomena cause secondary tensile stresses, which for material points close to the free surface remain unbalanced in the direction normal to this surface. The opened cracks magnify the effect of the diffuse bifurcation, since under a field of uniaxial compressive stress, parallel to the Griffith cracks, tensile stress concentrations are established at the crack tips. It is then assumed that this mechanism may result in an unstable crack growth and finally in splitting of the material. Unstable crack growth and splitting correspond to some critical crack surface density (distributed material damage) which manifests itself in the mean spacing of the forming plates. The split material is finally becoming much weaker than the intact material due to the lower buckling stress of the individual plates. Keeping this model in mind, we may consider that rock bursting, as well as borehole breakouts, are the result of buckling of flaked rock surfaces, the flaking itself being triggered by surface instabilities. Analytical solutions to buckling problems in media containing cracks parallel to the surface have been considered in the past by Keer et al. (1982), who solved the buckling problem in solids containing a periodic array of coplanar cracks and by Nazarenko, who considered the axisymmetric (1985) and plane-strain problem (1986) of a single coplanar crack.
