Virtually every rock mass contains various kinds of weak zones such as faults, joints, cleavages, layers of soft sediments, altered pockets, weak grains or grain boundaries. The deformation and failure of weak zones cause stress concentration in the intact rocks and often result in the failure of whole rock mass. Thus, the mechanical behavior of weak zones or planes of weakness controls total failure process of rock mass.
The Griffith theory for fracture (Griffith,1924) is widely accepted as the most reasonable model describing fracture propagation in rocks under tensile or low compressive stress conditions. The pre-existing cracks which are considered in the Griffith theory are dry clean elliptical pores which do not contain any foreign materials. As the parting along planes of weakness easily occurs under tensile stress, clean Griffith cracks can provide virtually adequate model for fracture initiation from planes of weakness in rocks under tensile or atomospheric stress conditions. Under overall compressive stresses, however, the presence of lubricants or obstacles within the pre-existing cracks has significant effect on fracture propagation.
A relatively small plane of 'weakness in large rock mass can be mechanically analyzed as a penny-shaped inclusion. Penny-shaped inclusions("Griffith inclusions")have some analogy in mechanical behavior with penny-shaped clean" cracks(Griffith cracks in the three dimensions). However, the Griffith inclusions are more effective sources for fractures under high compressive stress' than Griffith cracks in a narrow sense (Koide,1972).
The maximum stress concentration is induced at about the tip of the Griffith inclusion. Koide(1968) has obtained the exact stress distribution around a penny-shaped inclusion within an infinite homogeneous elastic host material by the Boussinesq's three function method. Although this assumption for analysis is very simple, this solution provides an adequate estimation for stress concentration around foreign inclusions within relatively large host material. The stress concentration factor of mode I for a penny-shaped inclusion is obtained as:
(Equation in full paper)
where "s" is the aspect ratio of the penny-shaped inclusion. The aspect ratio is very small for a sharp thin inclusion. "G" and "v"are rigidity and Poisson's ratio of host rocks, respectively."G" 'and "K "'are rigidity and bulk modulus of the inclusion, respectively. When only normal stress(compressive stress is positive) infinitely far in the host rocks acts perpendicularly to the equatorial plane of penny-shaped inclusion, then, the stress concentration of mode I only occurs at the inclusion tip even under the existence of internal pressure "p" and dilatancy of inclusion "v'" as follows:
The rigidity of inclusion "G'" is zero in the above equations for fluid-filled cracks or fluid inclusions. For a penny-shaped fluid inclusion, the stressconcentration factor "b" of mode II is very high but the stress concentration factor "a" of mode I is relatively low due to the incompressibility of the undrained fluid inclusion. Therefore, the generalized Griffith criterion for undrained fluid inclusion is expected to be a very flat parabola on the Mohr's diagram. On the other hand, the generalized Griffith criterion for drained fluid inclusion is similar to the Griffith crack case.